Mercury Isotope Fractionation by Environmental Transport and ... · mercury isotope fractionation by three environmental transport and transformation processes – mercury diffusion

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Mercury Isotope Fractionation by Environmental

Transport and Transformation Processes

By

Paul Gijsbert Koster van Groos

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

in

Engineering – Civil and Environmental Engineering

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor James R. Hunt, Chair

Professor David L. Sedlak

Professor Donald J. DePaolo

Dr. Bradley K. Esser

Spring 2011



Copyright © 2011

by


1

Abstract



by


Doctor of Philosophy in

Engineering – Civil and Environmental Engineering

University of California, Berkeley

Professor James R. Hunt, Chair

Mercury is a toxic metal with well known health risks, but uncertainties regarding

its environmental fate remain. Analytical tools capable of distinguishing small variations in

mercury isotope composition have recently become available and there is considerable

interest in applying these to help improve understanding of mercury’s complex

biogeochemical cycle, and to identify specific sources to remediate. In this dissertation,

mercury isotope fractionation by three environmental transport and transformation

processes – mercury diffusion through a polymer, thermal decomposition of HgS(s), and

mercury diffusion through air – are investigated. Clear understanding of processes that

affect mercury isotopes, such as these, is needed to ensure field scale isotopic data are

interpreted correctly.

A new analytical method for measuring mercury isotopes with high precision was

developed to pursue the work described here. In this method, both mercury and thallium

(for instrumental mass bias corrections) are introduced to a multi-collector inductively

coupled plasma mass spectrometer (MC-ICP-MS) as a liquid aerosol. The addition of

cysteine to liquid samples effectively controlled mercury memory effects. A purge and trap

sample preparation technique, using KMnO4 or HOCl as mercury oxidants, was used in this

work to prepare mercury in a common matrix. The long-term reproducibility of the method

was approximately 0.3 ‰ for δ202Hg, which is similar to other contemporary methods.

Mercury diffusion through a polymer was found to have a very large isotope effect.

This effect was determined by measuring Hg0 that permeated PVC tubing and matching this

with models of the rate and isotopic composition of this gas. The isotope fractionation

factor for this process, α202 = 1.00288±0.00040, is the largest factor yet determined for

mercury near ambient conditions. This fractionation factor represents the relative diffusion

coefficients of 198Hg and 202Hg in the polymer.

There have been recent observations of mercury isotope variations at mercury

mines that were speculated to have resulted from heating of mercury ores. In experiments

2

described here, thermal decomposition of HgS(s) did not result in bulk isotope fractionation

of the remaining HgS(s). This was evaluated by heating HgS(s) particles in an argon gas flow

for different periods of time and measuring the mass and isotopic composition of

remaining HgS(s). A model of congruent evaporation from a solid explained this lack of bulk

isotope fractionation well. This model indicates that, while changes in the isotopic

composition of a thin surface layer are possible, isotopic changes of the bulk material are

very small.

Mercury diffusion in air was found to have a large isotope effect that can be

predicted by kinetic gas theory using only the molecular masses of mercury isotopes and

air. This effect was determined by observing mercury remaining in a well mixed reservoir

that was depleted by diffusion through a set of hypodermic needles. The ratio of 198Hg to 202Hg diffusion coefficients in air was determined to be 1.00125±0.00011. Kinetic theory

predicts this ratio to be 1.00126. The fractionation factor of this fundamental and common

environmental process is similar to the larger isotope fractionation factors documented

previously.

The determination of mercury isotopic variations with new analytical tools offers a

promising approach for examining mercury in the environment. Interpretations of field

measurements will need to be guided by mechanistic understanding developed under

controlled conditions. The work described in this dissertation enables better

understanding of mercury isotope fractionation by environmental transport and

transformation processes that lead to isotopic variations throughout the environment.

These isotopic differences suggest not only a means of interpreting environmental

transport and transformation processes but also determining the dominant sources of

mercury where there have been multiple releases.

i

To my family

ii

Table of Contents

List of Figures ......................................................................................................................................................... v

List of Tables ........................................................................................................................................................... x

Acknowledgements ............................................................................................................................................. xi

Chapter 1 Introduction .................................................................................................................................. 1

1.1 Problem Description ................................................................................................................................ 1

1.2 Background ................................................................................................................................................. 1

1.2.1 Mercury Isotopes ........................................................................................................................ 1

1.2.2 Mercury Isotope Fractionation Processes......................................................................... 3

1.3 Previous Mercury Isotope Research .................................................................................................. 4

1.3.1 Field Studies .................................................................................................................................. 5

1.3.2 Experimental Studies ................................................................................................................ 5

1.4 Present Work .............................................................................................................................................. 7

Chapter 2 High Precision Mercury Isotope Measurements ............................................................ 9

2.1 Introduction ................................................................................................................................................ 9

2.2 Multi-collector ICP-MS Measurements ............................................................................................. 9

2.2.1 Sample Introduction ............................................................................................................... 10

2.2.2 Signal Integrity .......................................................................................................................... 14

2.2.3 Mass Bias Effect ........................................................................................................................ 17

2.2.4 Measuring Delta Values ......................................................................................................... 17

2.2.5 Measurements of Standards ................................................................................................ 19

2.3 Sample Preparation............................................................................................................................... 22

2.3.1 Potassium Permanganate Trapping ................................................................................. 22

2.3.2 Hypochlorous Acid Trapping .............................................................................................. 24

2.4 Summary ................................................................................................................................................... 26

Chapter 3 Elemental Mercury Diffusion in a PVC Polymer .......................................................... 27

iii

3.1 Introduction ............................................................................................................................................. 27

3.2 Preliminary Observations ................................................................................................................... 28

3.3 Experimental Methods ......................................................................................................................... 29

3.3.1 Setup and Procedure .............................................................................................................. 29

3.3.2 Analytical Methods .................................................................................................................. 31

3.3.3 Numerical Modeling................................................................................................................ 32

3.4 Results ........................................................................................................................................................ 33

3.4.1 Mercury Permeation ............................................................................................................... 33

3.4.2 Isotope Values ........................................................................................................................... 35

3.4.3 Calculation of Isotope Effects .............................................................................................. 36

3.4.4 Numerical Modeling................................................................................................................ 40

3.5 Discussion ................................................................................................................................................. 47

3.5.1 Permeation Isotope Effects .................................................................................................. 47

3.5.2 Temperature Effects ............................................................................................................... 49

3.6 Summary ................................................................................................................................................... 50

Chapter 4 Thermal Decomposition of Mercury Sulfide ................................................................. 52

4.1 Introduction ............................................................................................................................................. 52




4.3 Results ........................................................................................................................................................ 56

4.3.1 Thermal Decomposition ........................................................................................................ 56

4.3.2 Isotope Values ........................................................................................................................... 57

4.4 Discussion ................................................................................................................................................. 60

4.4.1 Thermal Decomposition ........................................................................................................ 60

4.4.2 Isotope Effects ........................................................................................................................... 61

iv

4.5 Summary ................................................................................................................................................... 65

Chapter 5 Elemental Mercury Diffusion Through Air .................................................................... 67

5.1 Introduction ............................................................................................................................................. 67




5.3 Results ........................................................................................................................................................ 70

5.3.1 Mercury Diffusion .................................................................................................................... 70

5.3.2 Calculation of Measured Diffusion Coefficients ........................................................... 71

5.3.3 Isotope Values ........................................................................................................................... 74

5.3.4 Calculation of Measured Isotope Effects ......................................................................... 75

5.4 Discussion ................................................................................................................................................. 80

5.4.1 Diffusion Coefficient ............................................................................................................... 80

5.4.2 Diffusive Isotope Effect .......................................................................................................... 80

5.5 Summary ................................................................................................................................................... 83

Chapter 6 Conclusion .................................................................................................................................. 85

6.1 Summary ................................................................................................................................................... 85

6.2 Recommendations ................................................................................................................................. 86

References ............................................................................................................................................................ 89

Appendix A Visual Basic Code ................................................................................................................. 99

Appendix B Additional Data ................................................................................................................... 106

v

List of Figures

Figure 1.1 The abundances of mercury isotopes for NIMS-1 (or NIST 3133). (Meija et al.

2010) .......................................................................................................................................................................... 2

Figure 1.2 Illustration of Rayleigh fractionation model system. R indicates isotope ratios

and α is the fractionation factor. ..................................................................................................................... 4

Figure 1.3 Experimentally observed fractionation factors, α202. An asterisk indicates that

MIF was reported for the process. α202 for equilibrium effects are given as the ratio of the

first term to second term. For all other effects, α202 is a defined in the text. Sources are

indicated by letter: a), Estrade et al. (2009), b) Wiederhold et al. (2010), c) W. Zheng et al.

(2007), d) Yang & Sturgeon (2009), e) Bergquist & Blum (2007), f) W. Zheng & H.

Hintelmann (2009), g) Kritee et al. (2008), h) Kritee et al. (2009), and i) Rodríguez-

González et al. (2009) .......................................................................................................................................... 7

Figure 2.1 Simplified schematic of IsoProbe MC-ICP-MS ................................................................... 10

Figure 2.2 Mercury signals for different sample introduction systems. Cysteine effectively

reduces the memory effect. ............................................................................................................................ 12

Figure 2.3 Mercury signals using the IsoProbe and different solution chemistries. The range

from smallest to largest measured value is indicated by the whiskers and the box indicates

the range from the 25th to 75th percentile. ............................................................................................... 13

Figure 2.4 Thallium signals using the IsoProbe and different solution chemistries. The

range from smallest to largest measured value is indicated by the whiskers and the box

indicates the range from the 25th to 75th percentile. ............................................................................ 14

Figure 2.5 Tailing effect in LLNL IsoProbe at analyzer vacuum of 7.9x10-8 mbar .................... 16

Figure 2.6 Relative signals of mass 197 to mass 198 during the analytical runs. The range

from smallest to largest measured value is indicated by the whiskers and the box indicates

the range from the 25th to 75th percentile. ............................................................................................... 16

Figure 2.7 Log plot of measured 202Hg/198Hg vs measured 205Tl/203Tl for two standards

illustrating the mass bias correction approach ...................................................................................... 18

Figure 2.8 Measured δ202Hg values for the UM-Almaden mercury standard. ............................ 19

Figure 2.9 Measured δ202Hg values for the In-House LLNL mercury standard. The asterisk

indicates an outlier discussed further in the text .................................................................................. 21

Figure 2.10 Measured δ202Hg values for the UC-Berkeley mercury standard. .......................... 21

Figure 2.11 Illustration of the purge and trap system used for sample preparation. ............. 23

vi

Figure 2.12 Recoveries of mercury standards using the trapping solutions indicated. The

outlier, indicated by asterisk, among HOCl trapping had lower concentrations as indicated

in the text. ............................................................................................................................................................. 24

Figure 2.13 Difference in δ202Hg resulting from sample preparation techniques. The outlier,

indicated by asterisk, among HOCl trapping had lower concentrations as indicated in the

text. .......................................................................................................................................................................... 25

Figure 3.1 Observed mercury fractionation in stored centrifuge tubes. The concentrations

indicated are the initial concentrations of mercury stored in the tubes. ..................................... 29

Figure 3.2 The setup for diffusion in PVC experiments ...................................................................... 31

Figure 3.3 The cumulative mass of mercury trapped after permeating through tube walls.

The data are for the three experiments (80 °C, 68 °C, and 23 °C). .................................................. 34

Figure 3.4 The estimated fraction of mercury remaining in the system (tubing and

reservoir). ............................................................................................................................................................. 34

Figure 3.5 Linearized time series indicating first order loss in all three experiments (80 °C,

68 °C, and 23 °C). ................................................................................................................................................ 35

Figure 3.6 Isotope composition of mercury trapped after permeating tubing .......................... 38

Figure 3.7 δ202Hg of individual samples at different temperatures plotted by fraction

remaining in tubing and reservoir. All three different temperatures appear to behave

similarly. ................................................................................................................................................................ 38

Figure 3.8 Multi-isotope plot indicating that fractionation is mass dependent as anticipated.

All data from the experiments (80 °C, 68 °C, and 23 °C) are plotted. ............................................ 39

Figure 3.9 Linearized plot of δ202Hg for all experiments (80 °C, 68 °C, and 23 °C) indicating

Rayleigh isotope fractionation ...................................................................................................................... 39

Figure 3.10 Analytical and model determination of the relationship between Kpoly and Dpoly

for 23 °C permeation of tubing ..................................................................................................................... 42

Figure 3.11 Modeled Hg0 mass rate permeating tubing compared to experimental data for

different Kpoly at 23 °C ...................................................................................................................................... 43

Figure 3.12 Modeled Hg0 mass rate permeating tubing compared to experimental data for

different Kpoly at 23 °C ...................................................................................................................................... 44

Figure 3.13 Model runs for isotope effects for 23 °C permeation comparing model run with

α202=1.00288 and different Kpoly .................................................................................................................. 45


α202=1.00288 and different Kpoly .................................................................................................................. 45

vii

Figure 3.15 The sensitivity of isotope effects to equilibrium isotope fractionation between

polymer and air at 23 °C. αpart is the Rpoly/Rair. Evaluated with Kpoly=50, αdiff=1.00288. ........ 46

Figure 3.16 Isotope composition of permeating mercury illustrating the uncertainty in αdiff

at 23 °C Evaluated with Kpoly=50, αpart=1. ................................................................................................. 47

Figure 3.17 Comparison of β between this experiment and Agrinier et al. (2008). The minor

gas isotopologues for the measurements were C-18O-O, 36Ar, 18O-O, 19N-N, D-H. ..................... 49

Figure 3.18 Temperature-dependence of mercury diffusion through PVC tubing with the

range of Dpoly estimates as given in Table 3.3. ........................................................................................ 50

Figure 4.1 Schematic of quartz decomposition tube used for thermal decomposition .......... 54

Figure 4.2 Temperature inside quartz tube measured by thermocouple .................................... 55

Figure 4.3 Hg remaining after thermal decomposition and representative temperature in

the decomposition tube ................................................................................................................................... 57

Figure 4.4 δ202Hg measurements at different levels of mercury remaining for thermal

decomposition experiments. ......................................................................................................................... 58

Figure 4.5 Multi-isotope plot indicating that behavior is as expected for all isotopes. .......... 59

Figure 4.6 Linearized isotope fractionation of δ202Hg shows very limited effects for thermal

decomposition experiments. ......................................................................................................................... 59

Figure 4.7 Partial pressures of Hg and S in equilibrium with phases given. The time

necessary to remove 10 µg of Hg assuming vapor equilibrium with HgS at the given

temperature and experimental flow rates is also given. Based on (Ferro, Piacente, and

Scardala 1989; Weast 1999; Peng 2001) .................................................................................................. 61

Figure 4.8 Evolution of δ values in the solid mineral. Time 0 is the initial condition. Time 2

is later than time 1. The surface moves inward at a velocity of Uevap, and the surface layer

thickness is defined by the diffusion coefficient and the evaporation velocity, 2Ds/Uevap. ... 63

Figure 4.9 δBULK202Hg evolution of a hypothetical particle with Rinitial=5µm, Uevap = 8.6*10-6

cm/s,and Ds=10-11 cm2/s ................................................................................................................................. 64

Figure 5.1 The diffusion reactor used for determining mercury diffusion coefficients and

fractionation factors ......................................................................................................................................... 70

Figure 5.2 Mercury mass remaining in reactors with time for air diffusion experiments. ... 71

Figure 5.3 Illustration of the expected steady-state Hg0concentration profile in the needles

................................................................................................................................................................................... 72

Figure 5.4 Linearized time series ................................................................................................................ 73

Figure 5.5 Change in isotope composition with time. The asterisk identifies an outlier. ...... 75

viii

Figure 5.6 δ202Hg of mercury remaining in the reservoir. The asterisk identifies an outlier.

................................................................................................................................................................................... 77

Figure 5.7 Multi-Isotope Plot indicating that fractionation is mass dependent as anticipated.

The asterisks identify outliers. ..................................................................................................................... 78

Figure 5.8 Linearized isotope fractionation of δ202Hg. The asterisk identifies an outlier. .... 79

Figure 5.9 isotope effects associated with Henry's partitioning. Data from Benson & Krause

(1980), Beyerle et al. (2000), and Klots & Benson (1963) ................................................................ 81

Figure 5.10 Comparison of experimental results and kinetic theory for Hg0 diffusion in air.

................................................................................................................................................................................... 82

Figure 5.11 Isotope composition of Hg0(l) recovered and Hg0

(g) lost to atmosphere relative

to the composition of the initial Hg0(g) if diffusion controlled condensation. ............................. 83

Figure 6.1 Experimental results for all three processes examined. Lines represent

mechanistic models using the determined isotope fractionation factors. ................................... 86

Figure A.1 Comparison of analytical solution for plane sheet and numerical model for large,

thin hollow cylinder. Dpoly = 0.004 cm2/min, thickness = 1 cm, radius = 500 cm, initial mass

= 1 µg. .................................................................................................................................................................... 105

Figure A.2 Comparison of analytical solution for plane sheet and numerical model for large,

thin hollow cylinder. thickness = 1 cm, radius = 500 cm.................................................................. 105

Figure B.1 δ201Hg in individual samples at different temperatures plotted by fraction

remaining in polymer tubing and reservoir. ......................................................................................... 106





Figure B.4 Linearized isotope fractionation of δ201Hg variations during experiments of

mercury permeation of polymer tubing. ................................................................................................ 108





Figure B.7 Model mass rate permeating tubing compared to experimental data for different

Kpoly at 68C .......................................................................................................................................................... 109

ix

Figure B.8 Model mass rate permeating tubing compared to experimental data for different

Kpoly at 80C .......................................................................................................................................................... 110

Figure B.9 Model runs for isotope effects for 68 °C permeation comparing model run with

α202=1.00288 and different Kpoly ................................................................................................................ 110


α202=1.00288 and different Kpoly ................................................................................................................ 111

Figure B.11 δ201Hg observed in reservior during experiments of mercury diffusion in air.

................................................................................................................................................................................. 111


................................................................................................................................................................................. 112


................................................................................................................................................................................. 112


mercury diffusion in air. ................................................................................................................................ 113





x

List of Tables

Table 2.1 Literature δ202Hg values for UM-Almaden standard. Errors are 2SD ........................ 20

Table 3.1 Evaluated rates of mercury loss from reservior and tubing at different

temperatures ....................................................................................................................................................... 35

Table 3.2 Observed Isotope fractionation factors in the polymer permeation experiments 40

Table 3.3 Results of diffusion experiments and calculated diffusion Coefficients ................... 47

Table 4.1 Rayleigh fractionation factors for thermal decomposition experiments ................. 60

Table 5.1 Results of air diffusion experiments and calculated diffusion coefficients ............. 74

Table 5.2 Observed Isotope fractionation factors in the air diffusion experiments ................ 79

Table 5.3 Hg0 diffusion coefficients through air .................................................................................... 80

xi

Acknowledgements

My success in graduate school is owed to many wonderful role models and

colleagues found in Berkeley and at Lawrence Livermore National Laboratory.

This work would have been impossible without the steady guiding hand of my

advisor, James Hunt. His confidence and support were invaluable as I worked to develop

suitable analytical methods and experiments for examining mercury isotopes. His calm

demeanor often helped relieve stress when progress seemed difficult.

Brad Esser and Ross Williams at Livermore were not only instrumental to this work

by facilitating the use of the IsoProbe ICP-MS, but were also wonderful resources that I

often turned to with problems that arose. They always found time in their busy schedules

to meet with me and I am very grateful. I am further indebted to Brad Esser for providing

valuable feedback that helped improve this dissertation greatly.

I am thankful for the excellent faculty and staff within the Department of Civil and

Environmental Engineering as well as across campus. I thank David Sedlak, Mark Stacey,

Kara Nelson, and Rob Harley for serving on various committees during my time at Cal. I

would further like to thank David Sedlak for reviewing this dissertation. His feedback

helped clarify several topics. Shelley Okimoto and Dee Korbel both aided my time at

Berkeley greatly by smoothly addressing whatever administrative needs existed.

The isotope courses on campus taught by Donald DePaolo, Todd Dawson, and Ron

Amundson provided a wonderful foundation for this work. These afforded me an

opportunity to explore the field of isotope geochemistry, and taught me many of the basic

principles used in this work. I greatly appreciate the time Donald DePaolo took to read and

contribute to this dissertation.

I am extremely grateful to the U.S. EPA STAR fellowship and the Jane Lewis

fellowship programs for financial assistance during my time in graduate school.

My time at Berkeley was made much more enjoyable by the many wonderful

students and post-docs I have met. I cannot think of a better lab-mate than Patrick Ulrich,

who always was ready to give a hand with whatever experiments I was attempting and his

suggestions saved me many headaches. I am grateful to all the students and post-docs in

O’Brien Hall, and particularly the Environmental Fluid Mechanics group, for keeping things

fun.

I thank my family for their never ending support and encouragement. Finally, I am

grateful for the unwavering support of Janet Casperson. She, most of all, helped make my

time in graduate school successful.

1

Chapter 1 Introduction

1.1 Problem Description

Mercury is highly toxic. At low concentrations, its distribution in the environment

greatly impacts human and ecological well-being. As evidence of the significant concern

mercury pollution causes, consider that more than 65% of lake area and 80% of river

distance with fish advisories in the United States are due, at least in part, to elevated

mercury concentrations (USEPA 2009). Interest in identifying and removing sources of

mercury continues to grow as public awareness of potential mercury exposure increases.

The most relevant forms of mercury in the environment are elemental Hg0, Hg(II),

and methylmercury, CH3Hg+. Hg0 in the atmosphere can oxidize to Hg(II), which readily

deposits over land and water. If mercury is methylated, it may bioaccumulate in animal

tissues. Humans are primarily exposed to mercury through fish that have accumulated

methylmercury.

To effectively address mercury pollution, it is essential to accurately assess its

complex biogeochemical cycle. Great resources are being invested to do so. The recent

discovery of small mercury isotope variations in the environment introduces a new

powerful tool to help evaluate components of the mercury cycle. This includes the potential

of differentiating and quantifying anthropogenic and natural sources. The work described

in this dissertation focuses on improving knowledge of mercury isotope effects such that

observed variations in mercury isotope composition can be interpreted better, leading to

more accurate understanding of mercury fate at many scales, from local to global.

1.2 Background

1.2.1 Mercury Isotopes

Mercury belongs to a set of “non-traditional” stable isotope systems that have been

investigated intensively only during the past decade. This recent activity is due to advances

in mass spectrometry instrumentation, primarily the development of multi-collector

inductively coupled plasma mass spectrometers (MC-ICP-MS). In the case of mercury, these

new instruments have enabled accurate observations of small environmental variations in

mercury isotope composition for the first time.

There are seven stable isotopes of mercury: 196Hg, 198Hg, 199Hg, 200Hg, 201Hg, 202Hg,

and 204Hg. Two radioactive isotopes, 197Hg and 203Hg with respective half lives of 2.7 and 47

days, complement these seven, and are used with some frequency as tracers in

experiments. The abundances of mercury stable isotopes are listed and illustrated in Figure

1.1 (Meija et al. 2010). These abundances are best estimates for a mercury standard, NIST

3133 SRM, which was certified for isotope composition as NIMS-1. The uncertainty of the

abundances is on the order of 10-3 (for 198Hg).

2

Figure 1.1 The abundances of mercury isotopes for NIMS-1 (or NIST 3133). (Meija et al. 2010)

The uncertainties in mercury abundances given in Figure 1.1 are greater than many

observed variations in mercury isotope composition. As such, it is useful to describe

variations relative to a standard measured at the same time. This is done with standard

delta(δ) notation and is reported on a per mil (‰) basis:

��‰� � 1000 ��

� � 1 !!!!!!" 1.1

where the 198Hg isotope is used to set ratios because it is the lightest isotope with

reasonable abundance. This is consistent with nomenclature used historically in other

isotope systems, where ratios of heavy to light isotopes are typically used (J.D. Blum &

Bergquist 2007). With this convention, larger δ values correspond to isotope compositions

relatively enriched in the heavier isotope. This dissertation uses the δ notation above with

NIST 3133 as the common reference standard, as suggested by Blum and Bergquist (2007).

Most relative changes in stable isotope composition, or fractionations, observed to

date are mass dependent fractionations (MDF). With this type of fractionation, variations in

0

10

20

30

Ab

un

da

nce

(%

)

Stable Hg Isotopes (%)

(Meija et al. 2010)

196Hg = 0.155 ± 0.004198Hg = 10.038 ± 0.010199Hg = 16.938 ± 0.009200Hg = 23.138 ± 0.006201Hg = 13.170 ± 0.012202Hg = 29.743 ± 0.009204Hg = 6.818 ± 0.006

3

isotope composition vary by relative difference in isotope mass, Δm/m, where m indicates

the isotope mass. For mercury δ values, this can be approximated as:

11 �� # 12 �%&&�� # 13 �%&�� # 14 �%&%�� # 16 �%&*�� 1.2

where δ204Hg should yield the largest and most accurate representation of MDF. However,

because it is difficult to accurately measure 204Hg due to an interference with 204Pb, δ202Hg

is customarily reported to describe variations in the MDF of mercury isotopes.

Uncertainties for δ202Hg measurements in the literature currently range from 0.1 to 0.3 ‰.

Measurements in this work have an uncertainty of approximately 0.3 ‰.

There is considerable excitement in the isotope community due to observed

deviations from MDF, as in equation 1.2, for mercury. This deviation has been termed both

mass independent fractionation, MIF (used here), and non-mass dependent fractionation,

NMF (Bergquist & J.D. Blum 2007; Estrade et al. 2009). In either case, a capital Δ value,

reported on a per mil basis (‰), has been defined to describe this deviation (J.D. Blum &

Bergquist 2007):

∆�� ‰� # �� 0.25 �%&%�� 1.3

∆%&&�� ‰� # �%&&�� 0.50 �%&%�� 1.4

∆%&�� ‰� # �%&�� 0.75 �%&%�� 1.5

Processes that produce MIF appear to change Δ199Hg and Δ201Hg and not Δ200Hg. MIF

appears indicative of more specific processes than MDF, and there is hope it will help

characterize specific aspects of the mercury cycle (Bergquist & J.D. Blum 2007). Because it

provides an additional dimension of isotopic information, MIF will also be helpful for

source identification. As MIF was not observed in this work, it will not receive much further

discussion.

1.2.2 Mercury Isotope Fractionation Processes

All observed variations in stable mercury isotope composition result from isotope

fractionation processes. This is in sharp contrast to variations among lead isotopes, where

three of the four stable isotopes are daughter products of radioactive decay. Knowledge of

fractionation processes is essential for understanding the information isotopes may

provide. Isotope fractionation processes separate isotopes into two or more fractions with

different isotope compositions. Slight property differences among isotopes introduce

isotope effects that lead to this fractionation. Usually, isotope effects result directly from

differences in isotope mass, leading to MDF, but other differences, such as in nuclear

volume or nuclear spin, can lead to MIF. Isotope effects may occur at equilibrium or not, in

which case they are most often termed kinetic isotope effects.

One model of isotope fractionation frequently encountered is the Rayleigh

fractionation model. In this model system, two fractions exist, as illustrated in Figure 1.2.

4

One fraction serves as a reservoir and the other as an outflow, which flows from the system

with no back flow. If isotope ratios of the outflow are inversely proportional to the

composition of the reservoir by a constant fractionation factor α, one finds:

0�1�02 � 1��34� 1.6

where R is the isotope ratio of the reservoir, the subscript i indicates the initial condition,

and F is the mass fraction of the initial reservoir remaining. The definition of the

fractionation factor, α, here is such that fractionation factors greater than unity correspond

to outflows with smaller isotope ratios than the reservoir. In this text, a subscript is used to

identify the specific fractionation factor for a given mercury isotope ratio. For example, α202

indicates the fractionation factor for the 202Hg/198Hg ratio. Natural and engineered systems

that closely match the Rayleigh model are common, especially with kinetic fractionation

where back reactions are often inhibited. The catalyzed transformation of organic

compounds can match this model, for example. Most of the mercury isotope effects

examined experimentally, as described in section 1.3.2, and throughout this dissertation

were quantified using the Rayleigh model.

Figure 1.2 Illustration of Rayleigh fractionation model system. R indicates isotope ratios and α is

the fractionation factor.

1.3 Previous Mercury Isotope Research

Mercury isotope research has been approached in two complementary ways:

through field work and through laboratory experiments. The pace of developments on both

fronts is increasing and a review of literature is quickly outdated. Brief or more exhaustive

reviews of contemporary research are available (Yin et al. 2010; Bergquist & J.D. Blum

2009). I will mention some results briefly to place the current work in context.

Routflow=R/αR

Reservoir Outflow

5

1.3.1 Field Studies

Many mercury isotope field studies to date have been exploratory. Variations in

excess of 6 ‰ in δ202Hg and 6 ‰ in Δ201Hg have been observed (Bergquist & J.D. Blum

2009). These relatively large variations are encouraging because they greatly exceed

current measurement uncertainties and should enable the discrimination of informative

patterns, be they for source identification or transformation processes. Some noteworthy

cases where observations of 1 ‰ or greater in δ202Hg and Δ201Hg were observed are coal

(Biswas et al. 2008), fish (Bergquist & J.D. Blum 2007), and arctic snow (Sherman et al.

2010).

Mercury ores and areas of mining have been a significant focus of mercury isotope

work to date. Foucher and Holger Hintelmann (2009) investigated sediments originating

from the Idrija mercury mine in Slovenia and observed mercury with the same isotopic

composition extending from the mine into the Gulf of Trieste. This mercury isotope

composition was distinct from background values in the Adriatic Sea, supporting the

application of mercury isotopes as a tracer for this mine.

San Francisco Bay (SF Bay), which is heavily impacted by historic mercury and gold

mining has also been the subject of mercury isotope research. Gehrke et al. (2011) reported

systematic variation of δ202Hg values in sediments along the length of SF Bay, with values

ranging from -0.3 ‰ in the south to -1.0 ‰ in the north. This trend, along with some MIF,

was mirrored in mercury isotope variations of fish caught at similar locations (Gretchen E

Gehrke et al. 2011). Smith et al. (2008) measured isotope compositions of mercury ores in

California and found δ202Hg variations of approximately 5 ‰ with no MIF. These observed

differences among ores provide one potential explanation for variations in SF Bay. Gehrke

et al. (2011) offered an alternative explanation. They suggested that incomplete processing

of Hg ores at mines may have led to the isotope fractionation observed in SF Bay. The

largest mercury mine that operated in North America, the New Almaden mine, was located

upstream of the southern end of SF Bay. The general supposition is that processing at

mines led to Hg0(l) products with more negative δ202Hg values and processed mine tailings,

often termed calcines, with more positive δ202Hg values. Evidence of more positive δ202Hg

values in calcines was reported by both Stetson et al. (2009) and Gehrke et al. (2011). A

simple interpretation of these calcines may be difficult, however, as Stetson observed co-

located mercury-bearing minerals that also exhibited larger δ202Hg values. Uncertainties

regarding the potential role of isotope fractionating processes at mercury mines provided

much of the inspiration for the work in this dissertation.

1.3.2 Experimental Studies

Interpretation of observed variations in mercury isotope composition requires

knowledge of mercury isotope fractionation processes. While understanding of these

processes can be informed by knowledge developed in other isotope systems, significant

uncertainties exist and experimental studies of mercury isotope effects are necessary. To

date, most studies examining mercury isotope effects have been phenomenological.

6

It is perhaps interesting to note that one of the earliest observations of intentional

isotope fractionation for all elements was with mercury (Brönsted & Hevesy 1920). In their

experiments, Brönsted and Hevesy (1920) distilled liquid mercury under vacuum and

observed significant differences in mercury density between condensates and the initial

reservoir. Similar experiments under vacuum were recently performed by Estrade et al.

(2009), who found a large fractionation factor, α202, of 1.0067±0.0011, indicating large

kinetic isotope effects associated with the evaporation of Hg0(l) into vacuum. This is a large

mercury isotope effect, but smaller than the theoretical maximum, given the inverse square

root of mercury isotope masses. That is, in this case:

5%&% � 1.0067 6 0.0011 7 89%&%9��:� %; � 1.010 1.7

where m indicates the mass of the isotope indicated by the subscript. This inverse square

root relationship is revisited in Chapter 5.

In contrast to the vacuum experiments described above, most experiments

examining mercury isotope effects have been performed near ambient pressures and

better represent effects expected in natural systems. Figure 1.3 shows many, if not all, of

the experimentally determined mercury isotope effects to date. It is interesting to observe

significant equilibrium isotope effects for mercury, despite its large mass (Estrade et al.

2009; Wiederhold et al. 2010). These equilibrium effects have been attributed to

differences in the nuclear volume of mercury, as this effect is predicted to be significant for

very heavy isotopes (Schauble 2007).

Most of the isotope effects studied are kinetic effects. The isotope effect of Hg0

volatilization from water likely indicates a diffusive isotope effect of Hg0(aq), as this controls

Hg0 volatilization under most conditions (Kuss et al. 2009). Many experiments use gas

sparging to separate the two fractions for subsequent measurement and do not explicitly

address mercury isotope fractionation potentially caused by this process.

Several experiments exhibited MIF after exposure to ultraviolet (UV) light. The

mechanisms leading to this effect are still unclear, but they appear to involve interactions

between nuclear spin and radical pair intermediates (Bergquist & J.D. Blum 2009).

Observed MIF is indicated in Figure 1.3 by an asterisk. Photochemical processes leading to

MIF have drawn significant attention as potential explanations for observed MIF in the

environment. Photodemethylation, in particular, has been shown to lead to methylmercury

with large MIF, which can then bioaccumulate in fish.

With the exception of the vacuum distillation experiment described earlier, α202 of

experiments ranged from 1.0004 to 1.0026. The fractionation factors determined in this

dissertation work are also indicated on Figure 1.3 and are described further below.

7

Figure 1.3 Experimentally observed fractionation factors, α202. An asterisk indicates that MIF was

reported for the process. α202 for equilibrium effects are given as the ratio of the first term to

second term. For all other effects, α202 is a defined in the text. Sources are indicated by letter: a),

Estrade et al. (2009), b) Wiederhold et al. (2010), c) W. Zheng et al. (2007), d) Yang & Sturgeon

(2009), e) Bergquist & Blum (2007), f) W. Zheng & H. Hintelmann (2009), g) Kritee et al. (2008),

h) Kritee et al. (2009), and i) Rodríguez-González et al. (2009)

1.4 Present Work

Variations among mercury isotope compositions observed in the environment were

noted above, along with experimentally determined fractionation factors. It is important to

have a comprehensive understanding of mercury isotope effects to interpret

environmental observations. Furthermore, knowledge of isotope effects can help future

experiments and field work by guiding expectations. The present work expands knowledge

of mercury isotope effects by experimentally determining new fractionation factors, and in

one case, matching this factor with fundamental mechanistic theory. These new

fractionation factors are more mechanistic in nature than many described previously.

Mechanistic factors are particularly useful because they can be applied in more cases.

Chapter 2 describes the development of a new analytical method, using liquid

sample introduction, for measuring mercury isotopes with sufficient precision for the work

1 1.002 1.004 1.006 1.008

THIS WORK - Hg0(g) diffusion in air

THIS WORK - Thermal decompostion of …

THIS WORK - Hg0 diffusion of PVC polymer

Fermentive methylation - i

Fermentive methylation - i

UV demethylation and sparge - e

UV demethylation and sparge - e

Microbial demethylation and sparging - h

Bacteria reduction and sparging - g

NaBEt4 ethylation and sparging - d

Dark abiotic reduction and sparging - e

Dark abiotic reduction and sparging - e

UV reduction and sparging - f

UV reduction and sparging - f

UV reduction and sparging - e

UV reduction and sparging - d

Chemical reduction and sparging - d

Chemical reduction and sparging - d

Hg0 volatilization from water - c

Hg0 volatilization from water - c

Vacuum evaporation - a

Hg(OH)2/Hg(thiol) - b

HgCl2/Hg(thiol) - b

Hg0(l)/Hg0(g) - a

Fractionation factor, α202

Equilibrium

effects

Kinetic

effects

**

***

*

**

*

8

that follows. Mercury isotope effects associated with Hg0 diffusion through a polyvinyl

chloride (PVC) polymer is described in Chapter 3. As shown in Figure 1.3, this is the largest

mercury isotope effect yet observed at ambient pressures. This suggests that large mercury

isotope fractionation may be associated with systems where polymer or polymer-like

materials are present, such as with mercury permeation of cell walls and membranes, plant

cuticles, or even geomembrane liners used at landfills.

The potential of mercury isotope fractionation resulting from processing at mercury

mines inspired the experiments described in Chapter 4 and Chapter 5. The thermal

decomposition of HgS(s), or cinnabar, was an essential component of mercury production.

This process is described in Chapter 4, and resulted in negligible isotope fractionation. As

such, this process is unlikely to be the cause of larger δ202Hg values for calcines as observed

by Stetson et al. (2009) and Gehrke et al. (2011). Chapter 5 describes a significant isotope

effect due to Hg0(g) diffusion through air. This likely led to isotope differences between

Hg0(l), produced through condensation, and ore materials at mercury mines. The observed

isotope effect of Hg0(g) diffusion through air matched kinetic gas theory well. The final

chapter summarizes the findings of this dissertation and suggests future research

questions these findings prompt.

9

Chapter 2 High Precision Mercury Isotope Measurements

2.1 Introduction

This chapter describes the analytical methods used to measure relative isotope

ratios of mercury with high precision. After a brief description of multi-collector

inductively coupled plasma mass spectrometers (MC-ICP-MS) presently needed to make

these precise isotope measurements, I detail the sample introduction method used, factors

affecting the accuracy and precision of measurements, and corrections made to counter

instrumental mass bias. The long-term reproducibility of standards measured using this

approach is evaluated and compared to contemporary methods. The development and

performance of the two sample preparation methods used in this work are also described.

2.2 Multi-collector ICP-MS Measurements

All methods used today to observe small differences in the isotope composition of

mercury rely on MC-ICP-MS instruments. Previous to the development of these

instruments, larger differences were observed with techniques such as density

measurements or neutron activation analysis (Kumar et al. 2001). Most investigations,

however, utilized mass spectrometers. A. O. Nier (1937) made early measurements of

mercury isotopes using electron impact gas source mass spectrometry, which remained the

predominant method of examining mercury isotopes until recently. The recent advent of

ICP-MS instruments allowed for more efficient ionization of mercury and better

measurements. Single-collector ICP-MS instruments are capable of very accurate and

precise mercury concentration measurements through isotope dilution methods (Mann et

al. 2003; Christopher et al. 2001). Contemporary single-collector ICP-MS instruments,

however, do not provide enough precision to measure variations in mercury isotopes.

Natural variations in the isotope composition of mercury are too small to investigate with

these tools, and require the high precision made available by collecting multiple isotopes

simultaneously with more expensive MC-ICP-MS instruments (Ridley & Stetson 2006).

All mass spectrometers operate using the same general design: 1) ions are

generated at an ion source, 2) an ion beam is accelerated, shaped, and separated by their

charge to mass ratio electromagnetically, and 3) ions are collected and counted. Figure 2.1

is a simplified schematic illustrating the IsoProbe (GV Instruments) MC-ICP-MS instrument,

located at Lawrence Livermore National Laboratory (LLNL), used for this work. Like all

ICP-MS instruments, it uses an argon inductively coupled plasma (ICP) torch to produce

ions. Because the ICP is very energy rich and operates at very high temperatures, it

effectively ionizes most atoms, including mercury. However, as a result of the high first

ionization potential of mercury, 10.43 eV, its ionization is usually incomplete resulting in

smaller signals relative to other elements such as thallium.

10

Figure 2.1 Simplified schematic of IsoProbe MC-ICP-MS

Ions produced in the plasma are near atmospheric pressures and enter the high

vacuum mass spectrometer through an interface consisting of a set of cones designed to

sample ions in the plasma torch, while maintaining a vacuum. The plasma produces ions

with a relatively wide range of energies and this must be reduced to effectively separate

the ions by mass. This is accomplished with an energy filter. The IsoProbe instrument used

in this work is unique in using a hexapole collision cell for this energy filter.

In contrast to many ICP-MS instruments that use a quadrupole filter to separate ions

by mass, MC-ICP-MS instruments use a magnetic sector to separate the ions to be collected

by multiple collectors. Because ions of interest are collected simultaneously with multi-

collector instruments, instrumental fluctuations affect all isotopes similarly, allowing much

greater precision. In this work, all nine Faraday collectors of the IsoProbe were used to

measure signals corresponding to singly charged atomic ions with masses 195, 197, 198,

199, 200, 201, 202, 203, and 205 simultaneously.

2.2.1 Sample Introduction

The introduction of samples to the plasma occurs in the form of a gas mixture, often

with fine aerosols containing the analyte(s) of interest. The analyte is usually sourced from

liquid samples, and aerosols are easily generated with a nebulizer and, most often, a spray

chamber. The spray chamber selects for the smallest aerosols, enhancing atomization and

subsequent ionization within the plasma. Because it is desirable to maximize the delivery

of analyte atoms rather than those of water, systems have been developed to dry aerosols.

Plasma Ion

Source

Ion acceleration and

separation

Ion collection and

counting

11

One such system, an Aridus desolvating nebulizer (Cetac, Omaha, NE, USA) was used in this

mercury work. By contrast, most contemporary mercury isotope measurements have used

gaseous elemental mercury, Hg0(g), generated in-line for introduction to the plasma

(Stetson et al. 2009; Lauretta et al. 2001; D. Foucher & H. Hintelmann 2006; Estrade et al.

2009). However, because most of these cases used a thallium aerosol to correct for

instrumental biases, liquid introduction systems were still necessary, leading to complex

hybrid sample introduction systems.

One difficulty encountered in handing mercury using liquid introduction systems is

its ability to sorb to many system components. This causes what has been termed a

mercury “memory effect.” The memory effect is of concern, because it can affect the

integrity of sample signals by reducing their overall contribution to measured signals. Thiol

containing compounds, such as cysteine, have been used to effectively address this memory

effect (Harrington et al. 2004; Y. Li et al. 2006; Malinovsky et al. 2008). Figure 2.2 shows

mercury signals measured using the IsoProbe instrument at LLNL during sample

introduction, and subsequent washout, using an Aridus desolvating system, with and

without cysteine, and a cyclonic spray chamber. It is evident in Figure 2.2 that the Aridus

desolvating system with cysteine performed best, with little evidence of a memory effect.

The mercury signal decreased to less than 1% of the sample signal in less than three

minutes using a solution of approximately 200 mg/L cysteine. Because this concentration

of cysteine appeared effective, it was added to most standards, samples, and washout

solutions throughout this work. Some later analytical runs were performed using washout

solutions without cysteine to help minimize the buildup of materials on instrumental

cones, but this was found to adversely affect the accuracy of blank solutions.

12

Figure 2.2 Mercury signals for different sample introduction systems. Cysteine effectively reduces

the memory effect.

The precision of isotope measurements is a function of the number of ions counted.

Large counts lead to more precise measurements. One challenge faced in maximizing ion

counts is the solution chemistry of aerosols introduced to the plasma. Figure 2.3 and Figure

2.4 show box and whisker plots of the LLNL IsoProbe signals for mercury and thallium over

the analytical runs performed. Indicated on the figures are periods where potassium (K),

manganese (Mn), and sodium (Na) were present in solutions as part of the sample

preparation process. While the mechanism of signal suppression is unknown (be it reduced

ionization in the plasma, or poor transmission through the cones and the remainder of the

instrument), it is clear that more complex matrices reduce the overall signal. This

decreased the precision of measurements from more complex samples. Later sample

preparation procedures minimized these affects as much as possible by lowering the level

of salts in the samples. Not all the variability in signal response can be attributed to the

solution chemistry and may be a factor of cone cleanliness.

High ion counts can be achieved by increasing either the concentration of solutions

or analysis time. It is difficult to increase the aerosol production rate without drastically

altering other factors. Some efforts during sample preparation were aimed at increasing

mercury concentrations. The concentrations of mercury and thallium used in this work

ranged from 10 to 100 µg/L and 10 to 15 µg/L, respectively. Sample uptake rates were 50

to 90 µL/min and individual measurements were integrated for 5 minutes. Each measured

sample reflects the measurement of 3 to 50 ng of mercury and 3 to 8 ng of thallium. As a

0.01

0.1

1

10

100

1000

0 200 400 600 800

Me

rcu

ry S

ign

al

(mV

/pp

b)

Time (seconds)

Aridus with 200 ppm cysteine

Aridus Desolvating Nebulizer

Cyclonic Spray Chamber

Measurement Period Washout Period

13

result of more efficient ionization in the plasma, and their relative abundances, thallium

isotope measurements yield larger signals and more precise isotope measurements than

mercury. The least common thallium isotope, 203Tl, and the most common mercury isotope, 202Hg, both have abundances of approximately 30%.

Figure 2.3 Mercury signals using the IsoProbe and different solution chemistries. The range from

smallest to largest measured value is indicated by the whiskers and the box indicates the range

from the 25th to 75th percentile.

1

10

100

1000

Me

rcu

ry S

ign

al

(mV

/pp

b)

Mercury

Cysteine Cysteine, K, and Mn Cysteine and Na

14

Figure 2.4 Thallium signals using the IsoProbe and different solution chemistries. The range from



2.2.2 Signal Integrity

It is important for calculating isotope ratios that signals truly represent only

isotopes of interest. Factors that adversely affect these signals can be viewed as affecting

the integrity of the intended signal. To optimize the accuracy and precision of isotope

measurements, it is important to evaluate the integrity of each isotope signal and to

mitigate, as much as possible, factors affecting this integrity. The three primary corrections

applied to maximize signal integrity were: 1) on-peak zero, 2) isobaric interference, and 3)

tailing corrections.

While adding cysteine to the liquid sample introduction system reduced the

memory effect greatly, it was still important to control for background mercury

concentrations and other interferences. This was primarily achieved through on-peak zero

corrections. This correction was performed by observing background signals at all masses

produced from blank solutions bracketing samples or standards. The observed on-peak

zero signals were subtracted from sample or standard signals. Many factors are relatively

constant among blanks, samples, and standards and this correction largely addresses these.

Most mercury isotope measurements are reported relative to the 198Hg isotope (e.g., 202Hg/198Hg). This is advantageous because it allows for a large relative mass difference

with relatively abundant isotopes. However, of the isotopes typically examined for mercury

1

10

100

1000

Th

all

ium

Sig

na

l (m

V/p

pb

)

Thallium

Cysteine Cysteine, K, and Mn Cysteine and Na

15

(198Hg, 199Hg, 200Hg, 201Hg, and 202Hg), 198Hg is the least abundant, comprising 9.97% of the

mercury, and ensuring the integrity of its signal poses the greatest challenge. Of the

mercury isotopes considered, it is the only one with a possible atomic isobaric interference,

from 198Pt. During our analyses, this was addressed by measuring the 195Pt signal and

subtracting any expected 198Pt signal, assuming Pt isotopes are at their natural abundances.

Platinum signals were typically quite small and accounted for less than 10-4 of the signal at

mass 198. As such, errors after correction associated with the presence of platinum were

expected to be negligible.

Another factor affecting signal integrity is the tailing effect. The tailing effect

describes the signal produced by stray ions that are measured at collectors other than

intended. One common manner for characterizing this effect is the abundance sensitivity of

the instrument. The abundance sensitivity is a relative measure of the signal measured 1

mass unit removed from the primary mass. For example, an abundance sensitivity of 10

ppm would indicate a measured signal of 50 µV one mass unit removed from a primary

signal of 5 V. This tailing effect is greatest at masses nearest that of the stray ion and

appears to be a function of the pressure within the spectrometer. This pressure, and

associated tailing effects, tends to be greater in IsoProbe instruments than in similar MC-

ICP-MS instruments. Thirlwall (2001) reported an abundance sensitivity of approximately

25 ppm at mass 237 from a 238U signal using an IsoProbe instrument operating with a

vacuum of approximately 2.5x10-8 mbar. Because the LLNL IsoProbe was operated at a

higher pressure, >7x10-8 mbar, it expected that the tailing effect is greater. I was fortunate

to examine the tailing behavior of Au+ in the LLNL IsoProbe instrument while rhodium

hexapole rods were installed. Figure 2.5 shows the tailing effect in the LLNL IsoProbe at a

pressure of 7.9x10-8 mbar, when 197Au was introduced to the system. At these conditions,

the abundance sensitivity at 198 mass is estimated to be approximately 40 ppm as a result

of tailing. The additional signal of 76 ppm, observed at mass 198, was presumed to result

from gold hydride, AuH+, ions. Corrections for both the tailing effect and hydride formation

are performed by calculating their contribution to signals at adjacent masses and

subtracting.

The analysis of the LLNL IsoProbe tailing effect, and potential gold hydride

formation, was fortunate, because the instrument was reconfigured to enhance other uses

soon after. This change involved the replacement of the rhodium hexapole rods with gold

rods. During all subsequent runs, these gold hexapole rods inevitably released gold ions.

Figure 2.6 shows the ratio of 197 to 198 mass signals as measured over the runs. This

figure shows that once the hexapole rods were replaced, the Au+ ion signal increased

dramatically. Corrections for tailing of these ions, as well as AuH+ ions formed, were

applied in all cases. In cases where the 197/198 ratio was particularly large, the variability

in Au signal was potentially large enough to affect 198Hg signal integrity. However, upon

investigating signal intensities after blank and tailing corrections, the cumulative error in 198Hg signal in these worst cases is less than 0.25‰. The cumulative error for the other Hg

and Tl isotopes was significantly less.

16

Figure 2.5 Tailing effect in LLNL IsoProbe at analyzer vacuum of 7.9x10-8 mbar

Figure 2.6 Relative signals of mass 197 to mass 198 during the analytical runs. The range from



1

10

100

1000

10000

194 195 196 197 198 199 200

Sig

na

l re

lati

ve

to

ma

ss 1

97

sig

na

l (p

pm

)

Ion Mass

Model Fit:

y=40*|X-197|-1.5

AuH+=76 ppm

1E-05

0.0001

0.001

0.01

0.1

1

10

100

Ra

tio

of

me

asu

red

19

7/1

98

sig

na

l

Rhodium

hexapole rods

Gold hexapole rods

17

2.2.3 Mass Bias Effect

One drawback of ICP-MS instruments is that measured isotope values are altered by

the instrument itself. This change is termed the instrumental mass bias and is often

attributed to space-charge effects that occur in the ion beam (Taylor 2001). Due to the

positive charge of the ion beam, ions are deflected slightly away. Light ions are deflected

more than heavy ions, resulting in a measured signal enriched in heavy ions. This effect can

be as large as several percent. In the mercury system, several approaches to correct for this

effect have been used, including simple standard/sample bracketing (Stetson et al. 2009)

and mercury double spike addition (Mead & T. M. Johnson 2010), but most commonly

spiking with thallium (H. Hintelmann & Lu 2003; Smith et al. 2005; Evans et al. 2001). This

later method uses observed variations in the 205Tl/203Tl ratio to correct instrumental

variations in mercury isotope ratios and this is the approach used in this work. Most

researchers to date have applied an exponential fractionation law to correct for

instrumental mass bias. This, however, assumes identical mass bias for mercury and

thallium, which has not been adequately proven (Meija et al. 2010).

This work approaches instrumental mass bias correction through an empirical

approach first outlined by Marechal et al. (1999) and described for the mercury system by

Meija et al. (2010). The empirical approach was determined to be the most appropriate for

avoiding biases. Additionally, an empirical approach may compensate for unaccounted

factors. The empirical approach is to observe the log-linear behavior of mercury and

thallium isotope ratios following the general equation:

ln � �� > ? @ � ln � AB%&CAB%&� � 2.1

Where a and b are least squares estimates determined for each analytical run. Figure 2.7

illustrates this approach using the NIST 3133 standard. Without correction, the measured 202Hg/198Hg ratios for NIST 3133 shown in the figure vary by approximately 3‰. With

corrections, however, individual deviations from the estimated linear behavior are on the

order of 0.1‰. During analytical sessions, deviations from linear behavior for NIST 3133

were used to estimate in-run uncertainty.

The instrumental mass bias is a function of the ion composition generated in the

plasma and traveling through the mass spectrometer. It is important that standards and

samples are matched by concentration and solution matrix. In this work, solution matrices

were matched as much as possible, and concentrations were matched within 10%.

2.2.4 Measuring Delta Values

There is currently no mercury standard sufficiently well characterized to allow

variations in mercury isotope compositions to be reported with absolute ratios. Instead,

researchers describe isotope ratios relative to a commonly available standard. As

suggested by Blum and Bergquist (2007), this work uses the NIST 3133 SRM as the

18

reference standard and relative isotope ratios are reported as delta (δ)-values. Formally,

δ-values used in this work are for ratios relative to 198Hg and defined as follows:

��‰� � 1000 ��

� � 1 !!!!!!" 2.2

Practically, when (xxxHg/198Hg)sample ≈ (xxxHg/198Hg)NIST3133, as is the case with samples near

natural abundances, delta values can be estimated as follows:

��‰� # 1000 � Dln � �� ln � �� E 2.3

The errors introduced with this simplification are significantly smaller than errors

associated with measurements. δ values in this work were estimated using equation 2.3,

where the value for NIST 3133 at the same 205Tl/203Tl value is estimated with the linear

behavior described in 2.2.3. This is illustrated in Figure 2.7 for a secondary atomic

absorption standard, termed the in-house LLNL standard.

Figure 2.7 Log plot of measured 202Hg/198Hg vs measured 205Tl/203Tl for two standards illustrating

the mass bias correction approach

1.103

1.104

1.105

1.106

1.107

0.877 0.878 0.879 0.88

ln(m

ea

sure

d 2

02H

g/1

98H

g)

ln(measured 205Tl/203Tl)

NIST 3133 Standard

In-House LLNL Std

Estimated δ202Hg ≈-0.9‰

19

2.2.5 Measurements of Standards

It is important to repeatedly measure standards other than the reference standard

(NIST 3133) to assess the long-term reproducibility of measurements and to allow

inter-laboratory comparisons. Figure 2.8 shows repeated measurements of a mercury

standard produced from the Almaden Mine in Spain, UM-Almaden, kindly provided by

Professor Joel Blum of the University of Michigan. The errors shown for individual sample

points are the greater of: i) two times the estimated in-run standard deviation (2SD) based

on NIST 3133 as described in section 2.2.3, or ii) two times the estimated standard error

(2SE) of sample replicates during the analytical run. The UM-Almaden standard has been

shared among several laboratories and Table 2.1 shows reported values and errors found

in the literature. The long-term δ202Hg value for the UM-Almaden reported here,

-0.69±0.27‰, is not significantly different than other reported values.

Figure 2.8 Measured δ202Hg values for the UM-Almaden mercury standard.

Figure 2.9 and Figure 2.10 show the long-term reproducibility of two additional

in-house mercury standards available during this work, an atomic absorption standard at

LLNL and one at UC-Berkeley. The reproducibility of these standards is similar to that of

UM-Almaden. There is an interesting outlier among the LLNL standard measurements,

indicated with an asterisk. This was an older standard kept in a plastic centrifuge tube that

had lost approximately 30% of its mercury mass. This loss of mercury was accompanied by

significant isotope fractionation on the order of 1‰ in δ202Hg. This fractionation will be

revisited in Chapter 3, where fractionation due to Hg0(g) permeation of polymers is

discussed.

-2

-1

0

1

δ2

02H

g (

‰)

UM-Almaden

Cysteine, K, and Mn Cysteine and Na

Average = -0.69 ± 0.27‰

20

Table 2.1 Literature δ202Hg values for UM-Almaden standard. Errors are 2SD

Reference δ202Hg (‰) (2SD)

This work -0.69±0.27

(J.D. Blum & Bergquist 2007)* -0.54±0.08

(J.D. Blum & Bergquist 2007)* -0.58±0.15

(Epov et al. 2008)* -0.61±0.12

(Epov et al. 2008)* -0.51±0.17

(Stetson et al. 2009)* -0.61±0.24

(Stetson et al. 2009)* -0.58±0.09

(W. Zheng & H. Hintelmann 2010) -0.57±0.07

(Sonke et al. 2010) -0.48±0.16

(Wiederhold et al. 2010) -0.48±0.11

(Mead & T. M. Johnson 2010) -0.58±0.08

* Multiple δ202Hg values for the UM-Almaden standard are reported in these

publications reflecting different methodologies such as sample matrix,

introduction method, and concentration

21

Figure 2.9 Measured δ202Hg values for the In-House LLNL mercury standard. The asterisk

indicates an outlier discussed further in the text

Figure 2.10 Measured δ202Hg values for the UC-Berkeley mercury standard.

-2

-1

0

1

δ2

02H

g (

‰)

LLNL

Cysteine, K, and Mn Cysteine and NaCysteine

Average = -0.96 ± 0.14‰

*

-2

-1

0

1

δ2

02H

g (

‰)

UC-Berkeley

Cysteine, K,

and Mn Cysteine and Na

Average = -0.55 ± 0.26‰

22

2.3 Sample Preparation

Reproducible and precise mercury isotope measurements require sample

preparation. The primary goals of this sample preparation are to remove potential

interferences and to ensure consistent and correctable instrument mass bias by supplying

analytes at constant concentrations and in a common matrix. When necessary, it is also

desirable to be able to increase analyte concentrations for isotope analysis. Here, we

describe the sample preparation methods used in this work. The aim of these sample

preparation methods was to find a simple and useful approach, but efforts to optimize each

was limited by time constraints.

The general approach adopted for sample preparation in this work is similar to

purge and trap approaches used to measure total mercury concentrations. It involves the

production of Hg0 using a strong reductant, such as SnCl2, stripping this mercury as a gas

with N2(g), and trapping the gaseous mercury. The Hg0(g) was transmitted to traps using

PTFE tubing after either permeation of PVC tubing as described in Chapter 3, or generation

using a 150 mL bubbler system, as in Chapter 4 and Chapter 5. To ensure that mercury was

not trapped in condensed water in transmission tubing, gas streams generated using the

150 mL bubbler were dried using soda lime traps that had previously been purged of Hg0(g).

Instead of gold traps used for concentration measurements, strong oxidizing

solutions were used with the goal of quantitatively trapping mercury as Hg(II). Near

quantitative trapping is desired because this ensures negligible isotope fractionation

during processing. A purge and trap system, such as described here, allows for increasing

the concentration of samples by purging large volumes and trapping in smaller volumes.

Cold traps using N2(l) or a CO2(s)-acetone slurry to trap Hg0(g) were evaluated but

determined to be impractical (Fitzgerald et al. 1974).

The sample trapping technique eventually adopted is illustrated in Figure 2.11,

along with the Hg0 vapor generation system used in the experiments described in Chapter

4 and Chapter 5. A 12 mL glass distillation receiver was loaded with a solution containing

either KMnO4 or HOCl as an oxidant and N2 gas containing Hg0(g) was bubbled through the

solution using a Pasteur pipette. Fritted glassware was evaluated as a bubble source, but

mercury losses were observed, presumably due to sorption of Hg(II) to the high surface

area of the glass frit. Following is a discussion of the two different trapping chemistries

used for sample preparation in this work.

2.3.1 Potassium Permanganate Trapping

Trapping Hg0(g) using an acidic solution of potassium permanganate (KMnO4) is

common and has been used previously for mercury isotope work (W. Zheng et al. 2007).

Zheng et al. (2007) found that solutions with KMnO4 concentrations as low as 5 mg/L were

effective at trapping Hg0(g) nearly quantitatively, and without isotope fractionation.

Following this work, I evaluated the possibility of introducing KMnO4 solutions to the mass

spectrometer. Isotope signals were suppressed using KMnO4, as described in section 2.2.1,

but isotope measurements with this solution showed promise.

23

Figure 2.11 Illustration of the purge and trap system used for sample preparation.

Sample preparations used 2.5 to 10 mL of acidic KMnO4 solutions (100 mg/L in 0.8

M HNO3). Gas flow rates were approximately 200 mL/min. After trapping, samples were

pre-reduced with 5 to 20 μL of a NH2OH-HCl solution (300 kg/m3 NH2OH-HCl in high purity

water). Concentrations were then determined using cold vapor atomic fluorescence

spectroscopy, and cysteine was added from a stock solution for a final concentration of 200

mg/L. Additionally, thallium was added to a final concentration of 15 µg/L. Solutions were

diluted to match all concentrations for analytical runs using the LLNL IsoProbe.

KMnO4 trapping was used primarily during experiments trapping Hg0(g) that had

permeated PVC tubing, as described in Chapter 3. Total recoveries during those

experiments were in excess of 90%. Recoveries and isotope fractionation of mercury were

evaluated using mercury standards and is illustrated in Figure 2.12 and Figure 2.13.

Consistent with the work of Zheng et al. (2007), KMnO4 trapping displayed little isotope

fractionation during sample preparation.

N2(g)

Hg0(g)

N2(g)

Strong reductant

Hg2+(aq) Hg0

(aq)

Strong oxidant

Hg0(aq) Hg2+

(aq)

Soda Lime

Trap

24

Figure 2.12 Recoveries of mercury standards using the trapping solutions indicated. The outlier,

indicated by asterisk, among HOCl trapping had lower concentrations as indicated in the text.

2.3.2 Hypochlorous Acid Trapping

The development of the HOCl sample preparation technique resulted from issues of

Mn contamination that inhibited some other uses of the mass spectrometer. KMnO4 sample

preparations introduced larger quantities of Mn to the instrument and efforts aimed at

measuring strontium isotope ratios suffered. Specifically, 86Sr measurements appeared to

suffer interferences from MnNOH+ molecular ions formed in the mass spectrometer. As a

result, KMnO4 use was halted and another sample preparation method was developed. Due

to discussions in the literature regarding mercury oxidation, K2S208 (Xu et al. 2008) and

HOCl (Lin & Pehkonen 1998; L.L. Zhao & G.T. Rochelle 1999) were evaluated. After some

early successes, HOCl was pursued as an alternative trapping solution suitable for the

purposes of this work.

The best performing HOCl trapping solution contained 2.0x10-3 M of HOCl, prepared

from a NaOCl stock solution (Fisher Scientific) and lowered to a pH of 5 using HNO3 acid.

This solution was seeded with Hg(II) at a concentration of approximately 1.0 µg/L to help

catalyze the absorption of Hg0 as suggested by Morita et al. (1983) and Zhao and Rochelle

(1998). Hg2+(aq) reacts rapidly with Hg0

(aq) to form Hg2+2

(aq), which is subsequently oxidized

to form two Hg2+(aq) ions (Morita et al. 1983). The low concentration of mercury used for

seeding was negligible relative to trapped concentrations.

0

20

40

60

80

100

120

Sta

nd

ard

re

cov

ere

d (

%)

Trapping Recoveries

KMnO4 Trap HOCl Trap

Average = 98 ± 10%

*

25

Figure 2.13 Difference in δ202Hg resulting from sample preparation techniques. The outlier,

indicated by asterisk, among HOCl trapping had lower concentrations as indicated in the text.

Sample preparations typically used 0.2 mL of the above HOCl solution placed in a

well rinsed distillation receiver. N2 gas containing Hg0(g) to be trapped was bubbled

through this solution using a Pasteur pipette at a flow rate of approximately 50 mL/min for

25 minutes. After this period the gas flow was halted and 0.8 mL of 0.12 M HCl or 0.8 M

HNO3 was added and the solution was transferred to a sample tube. The distillation

receiver and Pasteur pipette were twice rinsed for five minutes with 2.0 mL of 0.12 M HCl

or 0.8 M HNO3 to recover Hg(II) sorbed to the glass and the rinsate was transferred to

sample tubes as well. Concentrations were determined using cold vapor atomic

fluorescence spectroscopy and cysteine was added from a stock solution for a final

concentration of 200 mg/L. Thallium was then added to a final concentration of 15 µg/L.

Solutions were diluted to match all concentrations for analytical runs using the LLNL

IsoProbe.

The performance of trapping with HOCl was evaluated repeatedly using mercury

standards and is shown in Figure 2.12 and Figure 2.13. Sample preparations using HOCl

changed throughout the period of this work, but most followed the procedure outlined

above. Recoveries with this sample preparation technique were nearly quantitative, and

isotope fractionation appeared negligible.

The outlier in Figure 2.12 and Figure 2.13, indicated by an asterisk, showed

incomplete recovery and associated isotope fractionation. This was the result of lower

HOCl concentrations (approximately 5 x 10-4 M), a higher pH (approximately 6.5), and a

-1

0

1

2

δ2

02H

gtr

ap

pe

d-δ

20

2H

gd

ire

ct(‰

)

Trapping Offset

KMnO4 Trap HOCl Trap

Average = 0.00 ± 0.25‰

*

26

smaller trapping volume (0.1 mL). While isotope fractionation was evident during this

analytical run, it was consistent from sample to sample, such that the data were used after

corrections, as described in Chapter 5.

2.4 Summary

In this chapter, I have described the analytical methods used here to measure the

relative isotope ratios of mercury with high precision. This method used a liquid sample

introduction approach with cysteine added to solutions to control for memory effects. This

is a simpler sample introduction method than the hybrid cold-vapor generation (for Hg)

and liquid sample (for Tl) introduction method utilized by most previous researchers, and

could lead to broader adoption of mercury isotope measurements. Several corrections

were made to ensure the integrity of mercury signals, including on-peak zero and tailing

corrections. Instrumental bias was addressed with the introduction of thallium and an

empirical correction approach. Reproducibility of standards was approximately 0.3‰ for

δ202Hg and relative measurements are similar to contemporary methods. Two sample

preparation methods, using KMnO4 and HOCl, were developed, and used to obtain the

isotope results described in this text.

27

Chapter 3 Elemental Mercury Diffusion in a PVC Polymer

3.1 Introduction

The permeation of polymers may serve as illustrative analogs for permeation

processes in environmental systems, such as permeation of cell membranes (Nagle et al.

2007; Missner & Pohl 2009; Lieb & Stein 1969). As such, determining the magnitude of

isotope effects associated with permeation processes is important, but mostly unexplored

for gases. For many lighter gases, the permeation of polymers has been shown to produce

significant isotope fractionation (Agrinier et al. 2008). This chapter describes experiments

performed to verify that Hg0 permeation of polymers leads to similarly large isotope

fractionation.

Most experiments examining isotope fractionation resulting from gaseous

permeation of polymers have been performed using pure H2 and D2 (deuterium) gases and

observing both permeation (indicative of partitioning and diffusion) and time lag

(indicative of diffusion) for each individually and observing differences (Toi et al. 1980;

Mercea 1983; Ziegel & Eirich 1974). Gas chromatography has also been used to measure

hydrogen gas isotopes in permeation experiments (Sakaguchi et al. 1989). The precision of

these early measurements left much to be desired.

A more recent paper found large isotope effects for a wider range of gases: H2, N2,

O2, Ar, and CO2 (Agrinier et al. 2008). Agrinier et al. (2008) used these gases at their natural

abundances and utilized dual inlet isotope ratio mass spectrometry to determine isotopes

permeating polydimethysiloxane (PDMS) and polytetrafluoroethylene (PTFE) membranes.

These experiments were all performed under conditions where partitioning into the

polymer, described by Kpoly here, and diffusion through the polymer, described by Dpoly

here, are important factors. In this prior work, small overall fractions of the gases were

partitioned into the polymer at any time, such that quasi-steady state conditions were

quickly reached with the flux of gas through the polymer described by a product of Kpoly and

Dpoly:

F�G�H � I�G�HJ�G�H �K� � K%�B 3.1

where Jpoly is the permeation flux through the polymer, C1 and C2 are gas concentrations on

either side of the membrane, and l is the thickness of the membrane. Independently, both

the partitioning term and diffusive term may exhibit isotope effects.

The direct application of the steady state relationship in equation 3.1 to the

experiments described in this chapter, however, was difficult due to the large fraction of

mercury that partitioned into the polymer. As will be explored in section 3.4.4, the

consequence of this is that the present results describe diffusion effects more so than

partitioning effects.

28

In the following sections, I describe the experimental methods and procedures used

here to explore mercury diffusion through a polymer, as well as the results. Overall, the

process of mercury diffusion through polymer tubing exhibited a large isotope effect that

was reproducible. While diffusion rates of the polymer were sensitive to changes in

temperature, isotope effects were observed to be independent of temperature.

3.2 Preliminary Observations

During the development of the analytical method described in Chapter 2, slight

mercury isotope fractionation of diluted mercury standards stored in plastic centrifuge

tubes was observed. A quick preliminary experiment was performed to explore this

further. Centrifuge tubes initially containing 1 mg/L and 10 mg/L of Hg(II) were stored for

select periods of time and their isotope compositions were later measured. Figure 3.1

shows the progression of mercury isotope composition during the experiment. Due to

analytical limitations at the time of this preliminary experiment, mercury concentration

measurements were poorly constrained and concentrations were not matched with

standards for isotope measurements. As such, the results led only to a qualitative

assessment of overall behavior. With that caveat, a very large degree of mercury isotope

fractionation was clearly apparent in stored tubes, associated with mercury losses from the

centrifuge tubes. The exact mechanisms of mercury loss are unknown, but permeation of

Hg0 through the tube walls is a likely candidate. First, small quantities of reductants or

photoreduction in these tubes can be responsible for the generation of minute quantities of

Hg0. Further, changes of mercury concentrations in plastic containers have been shown to

occur due to the permeation of container walls by Hg0 (Bothner & Robertson 1975). The

large degree of isotope fractionation observed here motivated the detailed investigation

described in this chapter.

29

Figure 3.1 Observed mercury fractionation in stored centrifuge tubes. The concentrations

indicated are the initial concentrations of mercury stored in the tubes.

3.3 Experimental Methods

3.3.1 Setup and Procedure

The permeation of elemental mercury through a polymer, and associated isotope

fractionation, was examined using a system as illustrated in Figure 3.2. Aspects of this

design are similar to some approaches for evaluating gasoline permeation of respirator

hoses (National Institute for Occupational Safety and Health (NIOSH) 2005). The aim of the

experiment here was to deplete a reservoir containing elemental mercury via the

permeation through polymer tubing of known dimensions. Isotope effects measured during

the depletion reflect diffusive isotope effects within the polymer.

Two and a half meters of one eighth inch diameter (one sixteenth inch inner

diameter) R-3603 Tygon tubing (St. Gobain) were coiled inside a 180 mL PFA jar (Savillex).

This tubing is primarily composed of a PVC polymer and significant quantities of

plasticizers. The bulk of the tubing was held together with a cable tie and the two ends

were passed through ports contained in the lid of the jar. Mercury free N2 gas was passed

through the tubing at a rate of 200 mL/min to keep Hg0(g) concentrations inside the tubing

negligibly low, and transport mercury that permeated the tubing walls to an acidic KMnO4

trap (100 mg/L in 0.8 M HNO3). The negligible concentrations inside the tubing create a

concentration gradient within the tube walls in the radial dimension. The KMnO4 trapping

-2

-1

0

1

2

3

4

5

6

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

1 mg/L Hg

1 mg/L Hg

10 mg/L Hg

30

solution was held in a glass 12 mL distillation receiver and the gas was bubbled through it

using a Pasteur pipette as described in section 2.3.1.

The 180 mL PFA jar was filled with a PTFE stir bar and 37 mL of high purity

deionized water (Millipore) and closed. The jar was then placed in a water bath at a fixed

temperature for sufficient time to achieve thermal equilibrium. During this equilibration

period, N2 gas flowing through the tubing was trapped in KMnO4. These trap solutions

contained less than 3 ng of mercury, a negligible level relative to quantities to be trapped

later. The temperature of the water bath remained relatively constant, varying by less than

two degrees throughout experiments.

Two mL of a fresh 1 mg/L Hg stock solution (prepared with the UC-Berkeley Hg

standard) and 500 µL of a NaBH4 reductant solution (1% in high purity water) were added

to the PFA jar, which was then immediately sealed to start the experiment. The solution

was vigorously mixed with the stir bar and the temperature of the water bath was

observed with a laboratory thermometer. Within the reactor, the excess of NaBH4 reacted

very rapidly with all the Hg(II) in solution to produce approximately 2000 ng of Hg0 that

quickly partitioned among the gas, liquid, and polymer phases. At this point, Hg0 began to

diffuse through the tubing walls to be swept by N2 gas to the KMnO4 trapping solution.

After different periods of time, the KMnO4 trap was replaced with a clean distillation

receiver containing fresh KMnO4 trapping solution. The KMnO4 solution containing trapped

Hg was transferred to a sample tube for subsequent concentration and isotope analysis.

31

Figure 3.2 The setup for diffusion in PVC experiments

3.3.2 Analytical Methods

The mass of mercury trapped in the KMnO4 solutions was measured by cold vapor

atomic fluorescence spectroscopy. KMnO4 oxidized sample solutions were diluted and

pre-reduced with 5 μL of a NH2OH-HCl solution (300 kg/m3 NH2OH-HCl in high purity

water) prior to analysis. Hg2+ in known solution volumes was reduced to Hg0 by NaBH4,

transferred to gold traps using a bubbler, and analyzed by dual-stage gold amalgamation

(Gill & Fitzgerald 1987). The relative error of calibration standards was observed to be less

than 14%, calculated as two times the standard deviation of errors. Sample errors were

estimated as either the error of replicates, or the error of calibration standards, whichever

was greater.

The isotope composition of mercury remaining in reactors was measured by

MC-ICP-MS as described in Chapter 2. Trapped samples were in a common KMnO4 matrix

and were diluted to a common mercury concentration between 23 and 33 µg/L. Cysteine

(to 200 mg/L) and thallium (to 10 µg/L) were added to control for the memory effect and

N2(g)Hg0

(g)

trap

Water bath

Hg0(g)

NaBH 4(aq)Hg0(aq)

Reactor

R-3603

PVC

tubing

Stir bar

32

instrumental mass bias as described in Chapter 2. Errors in δ values are taken as the

greatest of: i) the long-term reproducibility of the UM-Almaden standard as described in

section 2.2.5, ii) two times the estimated in-run standard deviation (2SD) based on NIST

3133 as described in section 2.2.3, or iii) two times the estimated standard error (2SE) of

sample replicates during the analytical run.

3.3.3 Numerical Modeling

A numerical model was developed using Visual Basic in Microsoft Excel to help

evaluate the temporal behavior of the permeation process and isotope effects. The diffusion

equation for radial transport of mercury through the tubing walls is:

LKLM � 1N LLN 8NI LKLN: for a<r<b 3.2

where C is the concentration of mercury in the tube, t is the time variable, r is the spatial

variable, a and b are the inner and outer radii of the tubing, and D is the diffusion

coefficient, which is assumed to be constant. The tubing is initially essentially free of Hg0

before the experiments and this is reflected in the initial condition:

K�N, 0� � 0 for all a<r<b 3.3

Because the N2 sweep gas is assumed to keep Hg0 concentrations negligibly low on the

inside of the tubing, a Dirichlet boundary condition holds at r=a:

K�>, M� � 0 for t>0 3.4

The second boundary condition couples tubing mercury concentrations at the outer surface

of the tubing with concentrations of reservoir air and water, assuming equilibrium

throughout:

K�@, M� � J�G�HK� for t>0 3.5

where Ca is the Hg0(g) concentration of the air inside the reactor and Kpoly is a linear

partition constant (by volume) that is assumed to hold at all times. This second boundary

condition, coupling the tubing with a reservoir of limited volume and mercury mass, makes

analytical solutions problematic and necessitates the numerical model.

The numerical approach to this problem was to use a simple finite difference model

with a forward difference scheme in time and central difference scheme in space:

KPQR∆Q � KPQ ? I∆N SKP3∆PQ 8 1∆N ? 12N: � 2KPQ∆N ? KPR∆PQ 8 1∆N � 12N:T ∆M 3.6

The discretization in space used 50 or more cylinders of equal wall thickness, Δr. The time

step used was calculated to meet the Courant-Friedrich-Lewy (CFL) condition for stability.

Specifically, in this work, Δt was chosen to be smaller than (Δr)2/(4Dpoly), where Dpoly was

the diffusion coefficient for the model run. The coupling of the reservoir and tubing, as

33

indicated by the boundary condition in equation 3.5, was achieved by assuming

equilibrium amongst the outer layer of tubing and the reservoir water and air, and

reducing masses lost in Δt accordingly. The Visual Basic code used is found in Appendix A.

Results from the numerical model matched analytical solutions with simplified conditions.

3.4 Results

3.4.1 Mercury Permeation

The cumulative mass of mercury that permeated the polymer tubing walls is

presented in Figure 3.3. Total recovery was very good with more than 90% recovered. The

data show that higher temperatures lead to faster permeation of the tubing, as expected.

Using estimates for the cumulative mass trapped, one can calculate the fraction of mercury

remaining to be trapped. This represents the fraction of mercury remaining in the system

(i.e., tubing and reservoir) and is plotted vs. time in Figure 3.4. A log plot of the fraction of

mercury remaining in the system is given in Figure 3.5. The linear relationship for all three

experiments (at different temperatures) suggests a first order relationship between the

rate of loss and the estimated mass of mercury remaining in the system:

UVUM � �WV 3.7

where M is the mass remaining in the system, and k is an observed first order rate.

Error-weighted linear regressions of the data, as shown in Figure 3.5, were performed

using Isoplot 3.70 (K. R. Ludwig 2008), based upon an algorithm described by York (1968).

The slopes of these regressions were used to estimate first order rates as presented in

Table 3.1. These rates are revisited in section 3.4.4 to help evaluate diffusion coefficients

within the polymer. There was an observed time delay before the period of linear first

order loss. This time lag is explored further in section 3.4.4 using the numerical model.

34

Figure 3.3 The cumulative mass of mercury trapped after permeating through tube walls. The data

are for the three experiments (80 °C, 68 °C, and 23 °C).

Figure 3.4 The estimated fraction of mercury remaining in the system (tubing and reservoir).

0

500

1000

1500

2000

2500

0 500 1000 1500 2000

Ma

ss o

f H

g T

rap

pe

d (

ng

)

Time (minutes)

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 500 1000 1500 2000

Fra

ctio

n o

f H

g R

em

ain

ing

Time (minutes)

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

35

Figure 3.5 Linearized time series indicating first order loss in all three experiments (80 °C, 68 °C,

and 23 °C).

Table 3.1 Evaluated rates of mercury loss from reservior and tubing at different temperatures

Experiment Rate (min-1)

1 (80 °C) 0.0160±0.0006

2 (68 °C) 0.0130±0.0003

3 (23 °C) 0.0025±0.0001

3.4.2 Isotope Values

The isotope composition of mercury trapped in individual KMnO4 solutions is

presented in Figure 3.6. Isotope measurements were limited to a subset of all trapped

samples due to low mercury concentrations and limited instrument capacity. Samples

selected for isotope measurements were representative of the permeation process.

Samples reflect the average isotope composition of mercury permeating the tubing walls

during the time interval over which they were collected. As such, the average time of this

collection interval was used as the abscissa. As Figure 3.6 shows, there was a systematic

increase in δ202Hg values with time. This indicates that lighter isotopes permeated the

tubing walls quicker than heavier isotopes. A very broad range of isotope compositions,

with δ202Hg values varying from -9.5±0.3‰ to 7.4±0.3‰, was measured during these

experiments.

-8

-7

-6

-5

-4

-3

-2

-1

0

1

0 500 1000 1500 2000

ln(F

raci

ton

of

Hg

Re

ma

inin

g)

Time (minutes)

Experiment 1

(80 C)

Experiment 2

(68 C)

Experiment 3

(23 C)

36

Isotope processes are often evaluated in fractional terms to normalize fractionation

effects by the size of the system. Figure 3.7 is a plot of the mercury isotope composition of

trapped samples vs. the estimated fraction of mercury remaining in the system. Despite the

large differences in permeation rates, this figure shows remarkable similarity in isotope

behavior over the different temperatures.

Figure 3.8 is a multi-isotope plot that shows the relationship between measured

isotope ratios. The lines in this figure illustrate expectations for mass dependent behavior

based on the initial isotopic composition. The samples measured show mass dependent

behavior, with no indication of mass independent behavior during the permeation of the

tubing walls. Individual plots similar to Figure 3.7 for other isotope pairs (δ201Hg, δ200Hg ,

and δ199Hg) are provided in Appendix B as Figure B.1, Figure B.2, and Figure B.3.

3.4.3 Calculation of Isotope Effects

Isotope effects during this experiment were calculated using the measured delta

values. One solution to Equation 3.7 is:

V�M� V2; � 1 � XY�QZ3Q� 3.8

where the subscript i describes the initial state of the system, F is the fraction of Hg0

initially present remaining, k is the first order rate constant, and t0 is a lag time to account

for the time lag prior to first order loss. Based on equation 3.8, the normalized rate of Hg

loss from the tubing and reservoir system is then:

� 1V2UV�M�UM � � V[V2 � WXY�QZ3Q� 3.9

where V[ is the rate of Hg loss. This is equal to the rate at which mercury is trapped in

KMnO4 solutions once the period of first order loss is reached.

If each mercury isotope permeates the tubing walls independently, the ratio of these

rates reflects isotopic changes:

V[ ��M�V[ ��M� V��,2V�,2 � W�XY\�QZ3Q�W��XY]^_�QZ3Q� 3.10

where the subscripts x and 198 indicate different mercury isotopes. After replacing Mx/M198

with the ratio Rx and rearranging, one finds:

0��M�0�,2 � W�W�� XY�QZ3Q�`�3Y]^_ Y\; a

3.11

Another set of substitutions yields:

37

0��1�0�,2 � 15� 1��34\� 3.12

where F is the fraction of initial mercury remaining in the system, as shown in equation 3.8,

and αx is an isotope fractionation factor defined by the first order rates in this system:

5� � W��W� 3.13

Equation 3.12 is the Rayleigh equation for a constant fractionation factor. Given the

relationship between δxHg and isotope ratios, Rx, equation 3.12 can be linearized to give:

ln 81 ? ��1000 : � �1 � 5�� ln 1 ? ln �1 ? �2��1000 � � ln �5�� 3.14

such that a plot of ln(1+δxHg/1000) vs ln F will have a slope equal to (1-αx). The remaining

terms are all constants and are reflected in the intercept. Figure 3.9 shows a log-log plot as

indicated by equation 3.14 for δ202Hg. Individual plots similar to Figure 3.9 for other

isotope pairs (δ201Hg, δ200Hg, and δ199Hg) are provided in Appendix B as Figure B.4, Figure

B.5, and Figure B.6. Error-weighted linear regressions of the data were performed using

Isoplot 3.70 (K. R. Ludwig 2008). The data at large fractions remaining, F, were not used in

the linear regressions as this occurred before the first order loss. The linearity of the data

indicates that a Rayleigh model describes the data well, as anticipated. All three

experiments show very similar isotope fractionation, despite large differences in rates.

Table 3.2 summarizes the experimental fractionation factors as derived from the results.

Because no trend in temperature was apparent, the fractionation factors were averaged.

The weighted average α202 of the experiments, calculated using Isoplot 3.70 (K. R. Ludwig

2008), was determined to be 1.00288±0.00040.

38

Figure 3.6 Isotope composition of mercury trapped after permeating tubing

Figure 3.7 δ202Hg of individual samples at different temperatures plotted by fraction remaining in

tubing and reservoir. All three different temperatures appear to behave similarly.

-10

-8

-6

-4

-2

0

2

4

6

8

0 500 1000 1500 2000

δ2

02H

g T

rap

pe

d (

‰)

Time (minutes)

Experiment 1

(80 C)

Experiment 2

(68 C)

Experiment 3

(23 C)

-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

39

Figure 3.8 Multi-isotope plot indicating that fractionation is mass dependent as anticipated. All

data from the experiments (80 °C, 68 °C, and 23 °C) are plotted.

Figure 3.9 Linearized plot of δ202Hg for all experiments (80 °C, 68 °C, and 23 °C) indicating

Rayleigh isotope fractionation

-8

-6

-4

-2

0

2

4

6

-10 -5 0 5

δxH

g (

‰)

δ202Hg (‰)

δ199Hg

δ200Hg

δ201Hg

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

-4 -3 -2 -1 0

ln(1

+δ

20

2H

g/1

00

0)

ln (Fraction Remaining)

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

40

Table 3.2 Observed Isotope fractionation factors in the polymer permeation experiments

Experiment α199 α200 α201 α202

1 (80 °C) 1.00069±0.00011 1.00141±0.00010 1.00211±0.00025 1.00282±0.00024

2 (68 °C) 1.00082±0.00012 1.00165±0.00014 1.00235±0.00021 1.00316±0.00032

3 (23 °C) 1.00069±0.00008 1.00144±0.00011 1.00211±0.00016 1.00282±0.00020

Weighted

Average 1.00072±0.00016 1.00147±0.00029 1.00218±0.00033 1.00288±0.00040

3.4.4 Numerical Modeling

The complex permeation behavior in the tubing prior to first order loss, as

evidenced by the time lag and extreme negative δxHg values at large fractions remaining,

was evaluated using the numerical model described in section 3.3.3. This analysis provided

insight into the relationship between the first order rate constant k, determined earlier, the

diffusion coefficient Dpoly, and the partition coefficient Kpoly.

One difficulty faced while evaluating the permeation behavior in these experiments

was the unknown partitioning behavior of Hg0 with the polymer used, described by Kpoly.

The diffusion equation for the system described in section 3.3.3 leads to two asymptotic

solutions that can be explored analytically for the period of first order loss. This will be

used to evaluate the performance of the computational model. One asymptotic solution

results from a low Kpoly, such that negligible mercury is partitioned to the tubing, and the

other is with a large Kpoly such that most mercury in the system is partitioned to the tubing.

In the case of low Kpoly, the dimensions of the reservoir and tubing are relevant.

Under these conditions, a steady-state profile develops within the tubing such that the flux

through the tubing is first order:

UVUM � � 2bcln`@ >; a `d� ? de� a I�G�HJ�G�H,f��V 3.15

where L is the length of the tubing inside the reservoir, a and b are the inner and outer radii

of the tubing, Va and Vw are the volumes of air and water inside the reservoir respectively,

H is a unitless Henry’s constant defined as the ratio of air to water concentrations, Dpoly is

the diffusion coefficient in the polymer and Kpoly,small is a small partition constant relating

tubing concentrations to air concentrations. Equation 3.15 holds in cases where Kpoly,small is

sufficiently small such that low quantities of mercury are partitioned to the tubing. The

range of Kpoly,small can be estimated for the parameters of the system:

J�G�H,f�� 7 0.01 `d� ? de� abc�@% � >%� 3.16

41

where the terms are as defined above. Henry’s constant, H, was estimated using the

empirical equation provided by Sanemasa (1975):

log J � �1078A ? 6.250 3.17

where K is a Henry coefficient, expressed as the partial pressure of mercury vapor (atm)

divided by the mole fraction of the dissolved mercury, and T is the temperature, in kelvin.

Conversion of this K value to the unitless H used in this text, is accomplished as:

� � J0A � Ke 3.18

where R is the universal gas constant and T is the temperature, in Kelvin, and Cw is the

molar concentration of water in liquid water. It should be noted that equation 3.15 above is

analogous to equation 3.1 presented earlier.

Using equation 3.15, one can determine the relationship between Dpoly and Kpoly,small for an

observed first order decay rate, k:

I�G�H � ln`@ >; a `d� ? de� a2bcJ�G�H,f�� W 3.19

This relationship is indicated in Figure 3.10 by the line with constant negative slope for the

measured first order rate loss at 23 °C.

At high Kpoly, the great majority of the mercury is associated with the tubing rather

than air or water in the reservoir. A range of Kpoly,large, where this statement holds, can be

estimated for the parameters of the system:

J�G�H,��Pj� k 50 `d� ? de� abc�@% � >%� 3.20

Under this condition, the flux of mercury across the reservoir air/tubing interface is quite

small such that it is appropriate to assign the interface a no-flux Neumann boundary

condition:

UK�@, M�UN � 0 for t>0 3.21

Using this boundary condition, for the period of first order loss:

UVUM � �I�G�H5%V 3.22

where α is an inverse length term determined from the roots of:

42

l�>5m� � F&�>5m�n��@5m� � F��@5m�n&�>5m� � 0 3.23

where Jn and Yn are Bessel functions of the first and second kind, respectively, and a and b

are the inner and outer radii of the tubing. Note that equation 3.22 is no longer a function of

Kpoly,large. For the one eighth inch diameter tubing used, and at large t, we are interested in

the first root of this function, α=17.14 cm-1. In cases of Kpoly,large, then:

I�G�H � W�17.14 o93��% 3.24

This relationship is indicated in Figure 3.10 by the horizontal line for the measured first

order rate loss at 23 °C. It is expected that Dpoly is insensitive to Kpoly,large, and reservoir

dimensions.

The numerical model was used to determine the relationship between Dpoly and Kpoly

for the period of first order rate loss. The modeled relationship is plotted in Figure 3.10 for

the experiment at 23 °C. Results from numerical modeling match the asymptotic solutions

at low and high Kpoly well. It is apparent that Dpoly becomes less sensitive to Kpoly as it

increases. The close match with the asymptotes suggests that the model effectively

reproduces the permeation behavior.

Figure 3.10 Analytical and model determination of the relationship between Kpoly and Dpoly for 23

°C permeation of tubing

1.E-07

1.E-06

1.E-05

1 10 100 1,000 10,000

Dp

oly

(cm

2/s

)

Kpoly

Analytical - Low Kpoly

Analytical - High Kpoly

Numerical Model

43

Figure 3.11 and Figure 3.12 show the calculated rate of Hg0 mass loss using the

numerical model and includes experimental data at 23 °C for comparison. Figure 3.12

shows a subset of Figure 3.11 focused on the permeation behavior, and time lag, prior to

the first order loss for different values of Kpoly. The experimental data are consistent with

models using large Kpoly values, which indicate high partitioning of mercury in the polymer.

Similar figures for temperatures of 68 °C and 80 °C are included as Figure B.7 and Figure

B.8 in Appendix B.

Figure 3.11 Modeled Hg0 mass rate permeating tubing compared to experimental data for different

Kpoly at 23 °C

0

1

2

3

4

5

0 500 1000 1500 2000

Ma

ss R

ate

(n

g/m

in)

Time (minutes)

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 50

Kpoly = 500

44

Figure 3.12 Modeled Hg0 mass rate permeating tubing compared to experimental data for different

Kpoly at 23 °C

Figure 3.13 and Figure 3.14 show experimental data and modeled mercury isotope

compositions permeating the tubing wall for different values of Kpoly, assuming that relative

diffusion rates of mercury isotopes are equal to the average observed isotope fractionation

factor, as given in Table 3.2:

I�G�H,��I�G�H,� � 5� 3.25

A large Kpoly suggests the system is not very sensitive to differences in partitioning such

that this assumption is appropriate. This will be further explored in the next paragraph.

Figure 3.14 shows a subset of the data focused on permeation prior to the range where

Rayleigh fractionation occurs. Numerical models with large Kpoly, again, match the

experimental data well. Similar figures for temperatures of 68 °C and 80 °C are included as

Figure B.9 and Figure B.10 in Appendix B.

0

1

2

3

4

5

0 100 200 300 400 500

Ma

ss R

ate

(n

g/m

in)

Time (minutes)

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 50

Kpoly = 500

45


α202=1.00288 and different Kpoly



-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 50

Kpoly = 500

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

0.70.750.80.850.90.951

δ2

02H

g (

‰)

Fraction Remaining

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 50

Kpoly = 500

46

Equilibrium isotope fractionation between air and polymer, defined here as

αpart=Rpoly/Rair, is expected to be very close to unity, but sensitivity to this value can be

tested using the numerical model. Figure 3.15 shows model runs with a Kpoly value of 50,

which is near the lower end of values that match experiments, and αpart values of 0.999,

1.000, and 1.001. This reflects the largest reasonable influence of equilibrium isotope

effects because lower Kpoly values exhibit the largest equilibrium isotope effects in this

system. The range of αpart used is representative of the largest equilibrium isotope effects

observed in the literature for mercury at ambient temperatures. αpart should approach

unity as temperatures increase. Figure 3.15 shows that, for the experimental parameters,

different values of αpart do not greatly alter δ202Hg values. As a point of comparison, Figure

3.16 shows modeled δ202Hg values for the system reflecting the uncertainties in α202. The

potential influence of αpart under these conditions is of the same magnitude as the

uncertainty in α202.

Figure 3.15 The sensitivity of isotope effects to equilibrium isotope fractionation between

polymer and air at 23 °C. αpart is the Rpoly/Rair. Evaluated with Kpoly=50, αdiff=1.00288.

The numerical modeling described here leads to the conclusion that Kpoly in the

experimental system is large, such that most of the mercury is found partitioned to the

tubing. Lower bound values for Kpoly consistent with observed data were estimated for the

three experimental temperatures using the numerical model, and are indicated in Table

3.3. As a result of the large Kpoly values, the observed behavior mostly reflects diffusion

within the polymer. The ranges of diffusion coefficients of Hg0 in the tubing material at the

three different temperatures are found in Table 3.3. These ranges cover the possible Kpoly

values determined using the data and model. Under these conditions, the average ratios

-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experimental Data

αpart=0.999

αpart=1.000

αpart=1.001

47

among diffusion coefficients are equal to the fractionation factors listed in Table 3.2 as

expressed in equation 3.25. That is, in R-3603 Tygon tubing, D198/D199, D198/D200, D198/D201,

and D198/D202 are estimated to be 1.00072±0.00016, 1.00147±0.00029, 1.00218±0.00033,

and 1.00288±0.00040, respectively.

Figure 3.16 Isotope composition of permeating mercury illustrating the uncertainty in αdiff at 23

°C Evaluated with Kpoly=50, αpart=1.

Table 3.3 Results of diffusion experiments and calculated diffusion Coefficients

Experiment Rate

(min-1)

Kpoly range Dpoly range

(cm2/s) x 107

1 (80 °C) 0.0160±0.0006 >20 8.8 – 18

2 (68 °C) 0.0130±0.0003 >20 7.2 – 14

3 (23 °C) 0.0025±0.0001 >50 1.3 – 2.2

3.5 Discussion

3.5.1 Permeation Isotope Effects

The experimentally determined isotope effects for the polymer system here, αx, are

provided in Table 3.2. As described in section 3.4.4, these effects primarily reflect

differences in the relative diffusion rates among the mercury isotopes.

-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experimental Data

αdiff=1.00328

αdiff=1.00288

αdiff=1.00248

48

One manner that has been used to examine differences in diffusive isotope behavior

is with an empirical factor, β, defined by the relationship:

I�IH � 89H9�:p

3.26

where D and m are the diffusion coefficient and mass, respectively, of isotopes x and y

(Richter et al. 2009). Richter et al. (2009) reviewed the literature of isotope self-diffusion in

metals and metalloids and determined that β primarily ranged from 0.1 to 0.4. The ceiling

value for β is assumed to be 0.5 as this would indicate square root mass dependence.

The empirical factor β can be used to compare the permeation isotope effect for

mercury observed here with values for other gases in polymers found in the literature.

Figure 3.17 compares the β for mercury with the isotope effects determined for a variety of

gases by Agrinier et al. (2008). The β for mercury diffusion in the PVC tubing used in this

experiment is similar to values for other gases in PTFE and PDMS. Examining the results of

Agrinier et al., (2008), the similarity among different gases for the same polymer matrix

suggests that β incorporates behavior inherent to that polymer. One potential explanation

for differences in β among gases and polymers that must be noted is that equilibrium

isotope effects for partitioning were unknown and not explicitly accounted by Agrinier et

al. (2008). To use the relationship given in equation 3.26 for the experiments of Agrinier et

al. (2008), I assumed that all observed isotope effects were described by variations in

diffusion coefficients, rather than a combination of diffusive and equilibrium partitioning

isotope effects. The behavior illustrated in Figure 3.17 suggests that the permeation of

gases, including mercury, through many polymeric materials leads to large isotope effects.

It is likely that the isotope fractionation observed in stored centrifuge tubes resulted from

such permeation.

49

Figure 3.17 Comparison of β between this experiment and Agrinier et al. (2008). The minor gas

isotopologues for the measurements were C-18O-O, 36Ar, 18O-O, 19N-N, D-H.

3.5.2 Temperature Effects

Diffusion in polymers has been shown to have an Arrhenius relationship:

I � I&X3qr s�; 3.27

where D is the diffusion coefficient in the polymer, D0 is the pre-exponential factor, and ED

is the activation energy of the diffusion process (Crank & Park 1968). This can be linearized

to give:

ln�I� � ln�I&� � tu0A 3.28

such that D0 and ED can be determined from the intercept and slope of a plot of values

plotted as ln(D) and 1/T, respectively. Figure 3.18 shows this relationship for the range of

Dpoly determined in section 3.4.4 for Kpoly values consistent with the data. For the

experiments here, D0 is estimated to be 0.06 cm2/s and ED is estimated to be 30 kJ/mol. Due

to the relatively large range of Dpoly estimates, there is significant uncertainty in both

values, but particularly for the estimate of D0, which relies on extrapolation. I am unaware

of any such values for the diffusion or permeation of mercury through polymers in the

literature, but these values fall within the range of values for the diffusion of simple gases

in polymers (Crank & Park 1968).

0.0

0.1

0.2

Hg CO2 Ar O2 N2 H2

βv

alu

e

PVC

PTFE

PDMS

50

As stated earlier, there was no apparent trend in mercury isotope effects related to

temperature. This indicates that differences in activation energy, ED, as described above,

between isotopes are very small. One potential reason for this is that changes in

temperature may greatly change the permeation behavior for all permeating substances by

changing the dynamic structure of the polymer matrix. This could lead to large, but equal,

changes of ED for the individual isotopes. Such common behavior for a given polymeric

matrix could also indicate why variations in isotope effects among different gases can be

smaller than between different polymers, as illustrated in Figure 3.17.

Figure 3.18 Temperature-dependence of mercury diffusion through PVC tubing with the range of

Dpoly estimates as given in Table 3.3.

3.6 Summary

In this chapter, I have described experiments examining the diffusion of Hg0 through

a PVC polymer. A numerical model was used to help constrain estimates of partitioning

with the polymer and diffusion coefficients. Mercury permeation of PVC polymer tubing

and the isotope effect of diffusion through PVC were found to be large. An empirical

comparison to other gases permeating polymers suggested that this large isotope effect is

common. As such, large mercury isotope variations may be expected in engineered and

environmental systems associated with permeation of polymeric materials. The mercury

isotope fractionation observed in stored centrifuge tubes likely resulted from such

permeation processes.

-16

-15

-14

-13

0.0028 0.003 0.0032 0.0034

ln (

D)

(cm

2/s

)

T-1 (K-1)

y = -3770.8x - 2.842

R2 = 0.8809

51

Many processes of interest for mercury are potentially controlled by permeation

processes, and isotopic tools for evaluating these will be helpful. Three such processes

immediately come to mind. First, methylation of mercury has been suggested to be

controlled by the passive uptake, or permeation, of neutral species, such as HgS(aq) and

Hg(HS)2(aq), through cell membranes (Drott et al. 2007). Isotope measurements could

provide additional evidence of this process. Mercury methylation by fermentative bacteria

with a large isotope fractionation factor provides preliminary support for this concept

(Rodríguez-González et al. 2009). Second, there is uncertainty regarding uptake

mechanisms of atmospheric mercury by plant leaves (Stamenkovic & Gustin 2009). One

potential mechanism is passive uptake of Hg0 through the plant cuticle, which can be

viewed as a polymer. Such a mechanism may lead to large isotope fractionation, such that

leaves and litterfall might bear an interesting isotope signal. Last, mercury emissions to the

atmosphere from materials placed in landfills is of interest (Lindberg & Price 1999).

Permeation of geomembrane liners may control the rate of these emissions and lead to

identifiable mercury isotope compositions. Further exploration of mercury isotope

fractionation due to polymer permeation could provide insight into these processes.

52

Chapter 4 Thermal Decomposition of Mercury Sulfide

4.1 Introduction

The thermal decomposition of cinnabar, HgS(s), was an essential component of

mercury production. Cinnabar ores were heated in furnaces and retorts to break Hg-S

bonds and release Hg0(g), which was later recovered through condensation, as mercury

product. As noted earlier, the solid waste materials from this process, often termed

calcines, are reported to exhibit altered Hg isotope compositions (Stetson et al. 2009; G.E.

Gehrke et al. 2011). Here, I describe experiments performed to examine whether the

thermal decomposition of HgS(s) leads to bulk isotope fractionation.

Bonds containing heavier isotopes are often more stable and difficult to break than

those containing lighter isotopes. This often leads to observable kinetic isotope effects as

rates of reactions differ. For example, the following reaction results in a kinetic isotope

effect if kx≠ky.

�� v� Y\w ��j� ? 12 v%�j��

�� vH Yxyz ��j� ? 12 v%�j�H

4.1

where the Hg-S bond is being broken for different isotopes of Hg indicated by x and y, and

kx and ky are the respective reaction rates. The ratio of these reactions can be used to define

a kinetic fractionation factor, αkin:

5Y2m � W� WH{

4.2

Transition state theory can be used to estimate the magnitude of these isotope effects

(Anbar 2004). At high temperatures, or when the structures of the reactant and activated

complex are similar, αkin can be estimated as:

5Y2m # |}H }�; ~� %; 4.3

where μ is the reduced mass along the decomposition coordinate (Melander 1960;

Smithers & Krouse 1968). That is:

1}� � 19�j,� ? 19� 4.4

where m represents the masses of individual atoms of the bond being broken, or the

masses of separating fragments (Melander 1960). In the case of the evaporation of Hg from

53

HgS(s) due to its thermal decomposition, one of these masses will be the mass of the

particular Hg isotope.

There is good experimental evidence of significant kinetic isotope effects associated

with breaking of bonds in liquid and gas phases (Smithers & Krouse 1968; Krouse & Thode

1962; Frank & Sackett 1969). These observed effects appear consistent with transition

state theory. Observations of this kinetic isotope effect in solid phases are much more

debatable. For example, Davis et al. (1990) found very little fractionation, <1‰ amu-1,

during the breakdown and evaporation of synthetic forsterite (Mg2SiO4) as a solid despite

nearly 80% reduction in mass. This is different from the much larger isotope fractionation,

>15‰ amu-1, observed from molten forsterite (Davis et al. 1990). However, isotope

fractionation was observed during the breakdown of solid SiO2 in vacuo, suggesting that the

molten state is not necessary for observable isotope fractionation (Young et al. 1998).

Observations of isotope fractionation resulting from the thermal decomposition of

sulfur containing compounds are limited and have focused on sulfur isotope composition.

Kajiwara et al. (1981) reported a kinetic isotope effect with a fractionation factor of greater

than 1.011 for sulfur released from pyrite (FeS2(s)) while under vacuum. While not

presenting kinetic fractionation factors, Tsemekhman et al. (2001) also observed

significant sulfur isotope fractionation during the thermal decomposition of pyrite in an

argon gas stream. A kinetic isotope effect for sulfur was also reported during the roasting of

copper-nickel sulfide ores in air during these same studies (Tsemekhman et al. 2001).

I performed experiments to evaluate the overall effects of the thermal

decomposition of HgS(s) and to assess whether equations 4.2 to 4.4 could be used to

evaluate this effect. Because equation 4.3 describes the dissociation of individual bonds

rather than bulk behavior, there was significant uncertainty whether thermal

decomposition of solids would lead to isotope fractionation. In the following sections, I

describe the experimental methods, procedures, and results. Briefly, the thermal

decomposition of HgS(s) did not lead to observable Hg isotope fractionation.



The isotope effects of thermal decomposition of HgS(s) were evaluated with a quartz

decomposition tube as illustrated in Figure 4.1. One end of the tube was constricted and

filled with quartz wool to prevent solid materials from escaping. The tube was then filled

with silica gel, SiO2(s) (Fisher Scientific), a mixture of HgS(s) (Alfa Aesar) and silica gel, and

more silica gel. This order was chosen to ensure relatively consistent heating and maximal

recovery of HgS(s) following the decomposition process. The mass of tubes was measured

with an error of better than 0.5 mg after each addition of materials to account for the mass

of solid added. The mixture of HgS(s) and silica gel was prepared by solid dilution of

synthetic mercury sulfide. Using a microscope, the large majority of HgS(s) particles were

observed to have diameters smaller than 1 µm, while several had diameters of 10 µm or

54

larger. The prepared mixture was found to have a concentration of 200 ± 26 mg/g

characterized through multiple digestions described below. The total amount of Hg added

to the tubes ranged from 7 to 16 μg.

Figure 4.1 Schematic of quartz decomposition tube used for thermal decomposition

The decomposition tube was heated by a coil of nickel-chrome wire under a voltage

regulated by a variable transformer. This heating system was characterized separately

using quartz tubes filled with silica gel and a K-type thermocouple. Figure 4.2 shows that

the temperature in quartz tubes increased to a final temperature of approximately 350 °C

during the first three minutes. It is important to note that this is only a representative

temperature at a single location within the tubes and regions within the tube are heated at

different rates due to variations in the distance from the heating coil and other factors. The

tubes were cooled by a blowing fan.

NiChrome

wire

Argon

gas

HgS+SiO2

SiO2

Quartz

wool

55

Figure 4.2 Temperature inside quartz tube measured by thermocouple

Mercury-free Argon was passed thru the decomposition tube at a rate of 100

mL/min during the decomposition process to remove any Hg0(g) formed. After passing

through the decomposition tube, this gas stream was bubbled through 10 mL of a KMnO4

solution (1.0 kg/m3 KMnO4 in 0.8 M HNO3) to trap liberated Hg0(g).

After heating the decomposition tubes for different periods of time, and allowing

them to cool, their contents were deposited in 20 mL glass vials. Acid digestions of these

solid materials were performed for 24 to 48 hours through the addition of 3 mL of 12 M

HCl and 1 mL of 16 M HNO3. After initial dilution with high-purity water, these samples

were transferred to 125 mL bottles and diluted with additional water to a total volume of

40 mL. Digestions of the unheated HgS(s) and silica gel mixture were also performed to

characterize its concentration. Additionally, digestions of NIST SRM 2709, performed

simultaneously to assess the overall performance of this method, indicated complete

recoveries.


The mass of mercury trapped in the KMnO4 solutions and in digests was measured

by cold vapor atomic fluorescence spectroscopy. KMnO4 oxidized sample solutions were

diluted and pre-reduced with 5 μL of a NH2OH-HCl solution (300 kg/m3 NH2OH-HCl in high

purity water) prior to analysis. Hg2+ in known solution volumes was reduced to Hg0 by

SnCl2, transferred to gold traps using a bubbler, and analyzed by dual-stage gold

0

50

100

150

200

250

300

350

400

0 1 2 3 4

Tem

pe

ratu

re (

C)

Time after action (minutes)

Voltage on, fan off

Voltage off, fan on

56

amalgamation (Gill & Fitzgerald 1987). The relative error of calibration standards was

observed to be less than 7%, calculated as two times the standard deviation of errors.

Sample errors were estimated as either the error of replicates, or the error of calibration

standards, whichever was greater.


MC-ICP-MS as described in Chapter 2. Samples were prepared by reducing known masses

of Hg2+ with SnCl2 in a 150 mL bubbler, purging with N2(g) at 50 mL/min, and trapping in

HOCl as described in section 2.3. Standard and sample recoveries during sample

preparation were monitored. Errors in δ values are taken as the greatest of: i) the

long-term reproducibility of the UM-Almaden standard as described in section 2.2.5, ii) two

times the estimated in-run standard deviation (2SD) based on NIST 3133 as described in

section 2.2.3, or iii) two times the estimated standard error (2SE) of sample replicates

during the analytical run.

4.3 Results

4.3.1 Thermal Decomposition

The fraction of mercury remaining after thermal decomposition is shown in Figure

4.3. The reported value is the average of the fraction remaining based on mercury

recovered in the digest (a floor value), and based on mercury recovered in the KMnO4 traps

(a ceiling value). There is significant uncertainty regarding the exact fraction remaining due

to poor total recoveries during the decomposition process. Despite the large uncertainties

associated with assessing the thermal decomposition, it is clear that this reaction proceeds

rapidly when the representative temperature of the thermal decomposition tube reaches

250 °C. When this temperature is reached, a characteristic time for the decomposition, τd,

appears to be approximately one minute.

57

Figure 4.3 Hg remaining after thermal decomposition and representative temperature in the

decomposition tube


The isotope composition of digested samples prepared after the completion of

experiments is presented in Figure 4.4. Despite some errors in δ202Hg value on the order of

0.4‰ resulting from low Hg concentrations and poor mass spectrometer performance,

there is no evidence of isotope fractionation during the experiment. The average δ202Hg

value of all samples was -0.73±0.13 ‰, as indicated by the heavy dashed line on Figure 4.4.

This is no different than the average δ202Hg value of the initial mixture added to

decomposition, which was -0.75±0.19 ‰.

One sample of Hg0(g) liberated during decomposition, and trapped in KMnO4

solution, was also analyzed for its isotope composition. The isotope composition of this

sample is indicated by a triangle in Figure 4.4. This sample had a δ202Hg value of -0.72±0.27

‰, which is the same as the value for all the solids. This provides further evidence of the

lack of overall isotope fractionation during the experiment.

0

50

100

150

200

250

300

350

400

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8

Tem

pe

ratu

re (

C)

Fra

ctio

n R

em

ain

ing

Time (minutes)

Experiment A

Fraction Remaining

Experiment B

Fraction Remaining

Temperature

58

Figure 4.4 δ202Hg measurements at different levels of mercury remaining for thermal

decomposition experiments.



relative to the NIST 3133 mercury standard. No deviations from mass dependent behavior

were observed.

While the application of a Rayleigh fractionation model to this experimental data is

not necessarily appropriate (J. Wang et al. 1999), it may be useful to do so for purposes of

comparison to other results. A Rayleigh fractionation factor, α202, can be determined by

plotting ln(1+δ202Hg/1000) vs. ln F. The slope should correspond to (1-α202). Figure 4.5

shows such a plot and error-weighted linear regressions for the data performed using

IsoPlot 3.70 (K. R. Ludwig 2008). Table 4.1 shows the calculated Rayleigh fractionation

factors, αx, for different isotope pairs in this experiment. None of these fractionation factors

are significantly different from 1.0000.

-2

-1

0

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experiment A

Experiment B

Experiment B - Trap

Initial Mixture

59

Figure 4.5 Multi-isotope plot indicating that behavior is as expected for all isotopes.

Figure 4.6 Linearized isotope fractionation of δ202Hg shows very limited effects for thermal

decomposition experiments.

-1

0

-2 -1 0

δxH

g (

‰)

δ202Hg (‰)

δ199Hg

δ200Hg

δ201Hg

-0.002

-0.001

0.000

-4 -3 -2 -1 0

ln(1

+δ

20

2H

g/1

00

0)


Experiment A

Experiment B

Experiment B - Trap

Initial Mixture

60

Table 4.1 Rayleigh fractionation factors for thermal decomposition experiments


A 1.00000±0.00006 1.00001±0.00007 1.00002±0.00009 1.00002±0.00014

B 0.99999±0.00008 0.99999±0.00006 0.99999±0.00008 0.99998±0.00010

Weighted

Average 1.00000±0.00004 1.00000±0.00006 1.00000±0.00004 0.99999±0.00008

4.4 Discussion

4.4.1 Thermal Decomposition

The thermal decomposition of HgS(s) in these experiments occurred at temperatures

ranging from 250 to 350 °C, with a maximum near 300 °C. This is very similar to the

behavior of “synthetic cinnabar” mixtures prepared similarly, as reported by Biester and

Nehrke (1997) and others (Biester et al. 1999; Biester et al. 2000; Biester & Scholz 1997;

Palmieri et al. 2006; Sladek et al. 2002; Windmöller et al. 1996).

The decomposition observed here is also consistent with what is known about the

phase equilibria of the Hg-S system. Figure 4.7 shows the equilibrium partial pressures for

Hg0(g) and S2(g) over Hg(l), S(l), and Hg-S(s) as found in Lide (2004), Peng (2001), and Ferro

(1989), respectively:

log ��j,& � 7.122 � 3190A �kPa� 4.5

ln ��,& � 208.6 � 18810A � 29.03 ln�A� ? 0.0183A �kPa� 4.6

log 2 � ��,�j,& 2m �j� � 8.96 � 5902A �kPa� 4.7

where T is the temperature in kelvin. The factor of two in equation 4.7 accounts for both

Hg0(g) and S2(g) contributing equally to the total partial pressure described by the empirical

relationship provided. It should be noted that the partial pressures of Hg0(g) and S2(g) over

pure liquids are always greater than over HgS(s), such that pure liquid phases should not

develop during the thermal decomposition of HgS(s). Given equilibrium partial pressures of

Hg0(g) with HgS(s), Figure 4.7 also indicates the time needed to transport 10 µg of Hg, a

representative mass in my thermal decomposition tubes, at the experimental flow rate

(100 mL/min). This transport time decreases dramatically as the partial pressure increases

over the temperature range of the experiments.

The results suggest that the experimental setup operated in a similar manner to

other experiments in the literature and that HgS(s) is the dominant Hg species present in

the prepared mixture.

61

Figure 4.7 Partial pressures of Hg and S in equilibrium with phases given. The time necessary to

remove 10 µg of Hg assuming vapor equilibrium with HgS at the given temperature and

experimental flow rates is also given. Based on (Ferro, Piacente, and Scardala 1989; Weast 1999;

Peng 2001)

4.4.2 Isotope Effects

As described in section 4.3.2, I did not observe any significant isotope fractionation

associated with the thermal decomposition of HgS(s). As such, it is inappropriate to model

isotope fractionation of this process with a Rayleigh model and fractionation factor as

expressed in equations 4.2 to 4.4.

One explanation for this result may lie with the experimental design. The quartz

decomposition tube was heated externally by a surrounding nickel-chrome wire, which

may have lead to inconsistent heating within the tube. We can estimate the time needed for

temperature equilibration, τtherm, using the dimensions of the tube, and estimates for the

thermal diffusivity of dry silica gel, αtherm:

�Q��P� # cQ��P�%5Q��P� 4.8

where Ltherm is the length over which temperature must equilibrate. The inner radius of the

decomposition tube is 0.2 cm, and αtherm≈2*10-3 cm2/s (Gurgel & Kluppel 1996). Using

these values, τtherm=20 seconds. Because this time is comparable to the time of the

experiment, it is conceivable that locations within the tube may have experienced lower

0

50

100

150

200

250

300

350

400

450

500

-5

-4

-3

-2

-1

0

1

2

3

200 250 300 350 400

Se

con

ds

to d

ep

lete

10

µg

Hg

at

eq

uil

ibra

ted

10

0 m

L/m

in

Log

P0

(kP

a)

Temperature(C)

Hg(l)

S(l)

Hg-S(s)

Time to depletion

62

temperatures and experienced less thermal decomposition. Additionally, the tube was

heated from the outside inward. This would lead to a process where outer regions

evaporate sooner than interior regions. Both processes could result in bulk isotope values

skewed towards particles that experienced less or no thermal decomposition.

The experiments of Davis (1990) and Wang (1999), and additional analysis of

Richter (2004), suggest a compelling alternative explanation for the experimental results

presented here. These authors examined the free evaporation from solids and their

analyses indicate that significant kinetic isotope effects during evaporation (as described in

equation 4.1) can, perhaps counter-intuitively, result in negligible observable bulk isotope

effects. This was suggested to result from a lack of homogeneity in the solid. Richter

(2004)and Wang (1999) provide detailed explanations for this process, and below, I will

describe the reasoning for the case of HgS(s).

The thermal decomposition of HgS(s) is believed to be a case of congruent

evaporation. This means that the evaporating gases have the same elemental composition

as the mineral itself. This is important because it means that the rate of mercury

evaporation from the surface is the same rate at which mercury is delivered to the surface

from interior regions.

If the decomposition rates for the individual isotopes at the solid/gas interface differ

by the fractionation factor αkin, as described in equation 4.2, the evolution of the δ value of

the remaining solid will be as illustrated in Figure 4.8. The δ value at the mineral surface,

δsurf, is related to the δ value of evaporating gases, δevap, in relation to the fractionation

factor, αkin:

�f�P� � �� ? 1000 � �5Y2m � 1� 4.9

As the thermal decomposition of HgS(s) starts, the initial gas produced is enriched in lighter

isotopes as a result of their faster decomposition rates. This is reflected in a δ value lower

than the mineral as indicated at time 0 in Figure 4.8. Progressive loss of lighter isotopes

eventually leads to the condition indicated at time 1 in Figure 4.8. A surface layer of

thickness L is proposed to develop at steady state, such that the advective evaporative front

is balanced with diffusive mixing inward. L can be estimated as:

c # 2I�l�� 4.10

where Ds is the solid diffusion coefficient within the mineral, and Uevap, is the surface

velocity. At this stage, mercury lost from the surface layer is replaced with mercury of

identical isotopic composition (δinterior) as the surface layer moves inward. Under these

steady state conditions, the surface layer maintains its isotope composition as thermal

decomposition continues. The average δ value of the surface layer, δlayer, can be estimated

as:

63

��H�P # �f�P�2 4.11

Figure 4.8 Evolution of δ values in the solid mineral. Time 0 is the initial condition. Time 2 is later

than time 1. The surface moves inward at a velocity of Uevap, and the surface layer thickness is

defined by the diffusion coefficient and the evaporation velocity, 2Ds/Uevap.

The average δ value of the solid phase, δbulk, as would be measured upon acid digestion of

samples, can be found by taking a volume average of its δ values. Once steady state of the

surface layer has developed, δbulk for spherical particles is:

δ V

alu

e

Radius

δinterior

δevap

Particle

interior

Free

GasTime 0

δsurf

Surface δ

Va

lue

Radius

δsurf

Particle

interior

Free

GasTime 1

Radius

δinterior δevap

Surface

Layer

δ V

alu

e

Radius

δinterior δevap

δsurf

Particle

interior

Surface

Layer

Free

GasTime 2

64

��Y # 3000�5Y2m � 1�Ifl��0 ? �2mQ�P2GP 4.12

where R is the radius of the spherical particle and δinterior is the δ value of the unaffected

interior of the particle.

With the reasoning above, it is possible to constrain the maximum isotope

fractionation one might anticipate for HgS(s) resulting from thermal decomposition, and

compare this with experimental observations. From equation 4.12, it is clear that the

maximum δbulk results from large αkin and Ds. The largest reasonable value for αkin can be

found by using a large value for ms in equation 4.4, indicating mercury breaking a bond

with a very massive fragment. In this case, αkin =1.01 for 202Hg and 198Hg. There seems to be

little information regarding mercury diffusion rates in sulfides, but information regarding

other metal sulfides is available (Mrowec & Przybylski 1985). For these purposes, I assume

that diffusion of Fe in Fe1-yS(s) around the temperatures of interest, Ds≈10-11 cm2/s, is

representative of the maximum diffusion rate for mercury. I estimate Uevap and R given my

observations of the HgS(s) material used. As noted in section 4.2.1, larger particles were

observed to have radius on the order of 5 µm. Given the characteristic time for thermal

decomposition, τd=60s, observed in experiments, Uevap can be estimated:

l�� # 02�� # 5 � 103*o960 � � 8.3 � 103� o9 �⁄ 4.13

Figure 4.9 δBULK202Hg evolution of a hypothetical particle with R initial=5µm, Uevap = 8.6*10-6

cm/s,and Ds=10-11 cm2/s

0.0

0.2

0.4

0.6

0.8

1.0

0.00.20.40.60.81.0

δb

ulk

20

2H

g-δ

inte

rio

r20

2H

g (

‰)

Fraction Remaining

65

Figure 4.9 shows (δbulk202Hg -δinterior

202Hg) vs. mass fraction remaining for a

hypothetical 10 µm diameter particle, with the relevant parameters, αkin, Ds, and Uevap as

described above. It is informative that with these conservative parameters, more than 90%

of the mass can evaporate and change δbulk202Hg by less than 0.2‰. This is consistent with

the experimental results. Through inspection of equation 4.12, it is clear that reductions in

αkin and Ds, or a particle with greater initial radius will reduce isotope fractionation further.

The above analysis indicates that the development of a steady state surface layer,

enriched in heavy isotopes, can act to inhibit bulk isotopic fractionation in cases of

congruent evaporation. This analysis suggests that HgS particles with the largest

dimensions, which likely dominate bulk measurements, likely exhibit the least isotope

fractionation. Because many environmentally relevant HgS(s) minerals are larger than those

used in the experiments described here, the process of HgS(s) thermal decomposition and

congruent evaporation is unlikely to have led to observable isotope fractionation.

These conclusions are consistent with some early work focused on the isotopic

composition of chondrites that also used MC-ICP-MS instrumentation (Lauretta et al.

2001). Based on thermal release profiles, these meteorites were found to contain mercury

primarily as HgS(s). While the meteorites experienced conditions that encouraged the free

evaporation of mercury, no evidence of isotope fractionation was found with a precision of

0.2 to 0.5‰. Lauretta et al. (2001) also evaluated the thermal release of mercury from

ground samples of the meteorites using a single-collector ICP-MS instrument and did not

observe any isotope fractionation during the process with a precision of 5 to 30‰. These

data are consistent with the results presented here regarding isotope fractionation

resulting from thermal decomposition.

4.5 Summary

In this chapter, I describe experimental efforts aimed at characterizing bulk isotope

fractionation that results from the rapid thermal decomposition of HgS(s). No isotope

fractionation was observed during this thermal decomposition. As such, it is inappropriate

to apply equations 4.2 to 4.4 to estimate the degree of bulk isotope fractionation using a

Rayleigh model. The explanation of an inhomogeneous solid undergoing congruent

evaporation was found to be an attractive explanation for these results. It should be noted

that this model suggests that the bulk isotope composition of particles could vary by

particle size, with smaller particles exhibiting more fractionation than larger ones.

The lack of isotope fractionation observed in experiments here is not incompatible

with field observations of isotope fractionation among calcine waste materials. These

waste materials may have undergone some form of incongruent evaporation similar to that

of sulfur during the thermal decomposition of pyrite (Kajiwara et al. 1981; Tsemekhman et

al. 2001). In cases of incongruent evaporation, diffusive isotope effects are important and

these can be significant for mercury as shown in Chapter 3. Equilibrium isotope effects may

also explain some of these field observations. Equilibrium isotope effects, primarily

resulting from differences in nuclear volume, have been estimated to be on the order of 1

66

‰ for 202Hg/198Hg between Hg0 and other mercury species at 300 °C and higher (Schauble

2007). Finally, the occurrence of other mercury minerals with large δ202Hg values, as

observed by Stetson et al. (2009), may explain observed differences. Many of these other

minerals require higher temperatures for thermal decomposition such that they may

represent a large proportion of mercury sampled in calcine materials.

67

Chapter 5 Elemental Mercury Diffusion Through Air

5.1 Introduction

The condensation of elemental mercury, Hg0, to form liquid mercury products was

an essential process during mercury production. The goal at historic mercury mines was to

capture Hg0(g) quickly and economically rather than completely. Aside from impacting

workers’ health, this incomplete recovery may have resulted in isotope fractionation. The

low vapor pressure of Hg0 at cooler condensing surfaces and its high affinity for particulate

phases often present in the gases (e.g. condenser soot), suggest that equilibrium between

gas and liquid phases was not always achieved. As such, diffusion often limited Hg0 mass

transfer from the gas phase. Because mercury isotopes have slight differences in their

diffusion rates, the mercury production process likely led to mercury products and

emissions with altered isotope compositions. This chapter describes an experimental

investigation used to verify predictions describing the isotope effects of Hg0(g) diffusion

through air.

Predictions of relative diffusion rates can be made using the kinetic theory of gases.

When the mean free path of molecules is in the Knudsen regime, Graham’s law of diffusion

is believed to hold:

I�IH � ��H � �9H9� 5.1

where D is the molecular diffusivity, v is the velocity, and m is the mass of isotopologues

indicated by their subscript. At higher pressures, molecular collisions increase, and the gas

through which the diffusion occurs needs to be accounted for, such that:

I�IH � ��H � �9H�9j ? 9��9��9j ? 9H� � �� ? �j�� ? �j�%

5.2

where mg refers to the average isotopologue mass of the background gas, such as air, and Γ

is the collision diameter of the molecules (Horita et al. 2008; Cappa et al. 2003). The

collision diameters of isotopologues are usually assumed to be equal such that the second

term has negligible effect.

The effectiveness of predicting relative diffusion rates and related isotope effects

with kinetic theory is debated. Its importance in evaluating isotope effects during water

evaporation has prompted many experimental investigations. Some support the

appropriateness of kinetic theory (Cappa et al. 2003), while others suggest that theory does

not effectively describe isotope behavior and must incorporate other factors, such as

collision diameters (Merlivat 1978; Barkan & Luz 2007). It has been observed that the ratio

of diffusivities for water isotopologues used most frequently is based on the empirical

work of Merlivat (1978) in contrast to kinetic theory (Horita et al. 2008).

68

Relative diffusion rates have also been investigated for gases other than water.

Severinghaus et al. (1996) demonstrated nitrogen and oxygen isotope fractionation

resulting from diffusion that behaves in good agreement with theory. Diffusion of

hydrocarbons through porous columns also exhibited isotope behavior consistent with

theory. However, in contrast to experiments supporting kinetic theory, diffusion of N2O

resulted in isotope fractionation inconsistent with kinetic theory (Well & Flessa 2008).

I experimentally determined diffusion coefficients and isotope effects for Hg0(g)

through air and compared it with kinetic theory. In the following sections, I describe the

experimental methods and procedures used as well as the results. In short, mercury

diffusion coefficients match literature values, and its isotope behavior agrees with kinetic

theory as expressed by equation 5.2.



Mercury diffusion coefficients and isotope effects were determined using a reactor

as illustrated in Figure 5.1. This is similar to an experiment described in Well (2008). A

reservoir containing elemental mercury gas, Hg0(g) was depleted via diffusion through a set

of hypodermic needles of well known dimensions.

A small PTFE coated stir bar, 20 mL of high purity deionized water (Millipore) and

75 μL of SnCl2 stock solution (200 kg/m3 in 1.2M HCl) were added to clean 70 mL serum

bottles. In later experiments, 200 μL of concentrated HCl was added to prevent the

formation of precipitates. After the addition of 150 μL of 10 mg/L mercury (NIST 3133)

solution, the serum bottles were immediately sealed with PTFE septa and capped.

Within the serum bottles, an excess of Sn(II) reacted quantitatively with mercury to

produce approximately 1500 ng of Hg0 within the reactors. This quantity of mercury was

selected to avoid the formation of a separate Hg0(l) phase. The reactors were stirred for two

hours to ensure equilibrium between gas and aqueous phases:

��& � ��j�& 5.3

Five hypodermic needles with inner diameters of 0.1194 cm and either 2.54 cm or 3.81 cm

lengths were inserted through the PTFE caps to connect the bottles with the laboratory

atmosphere. The needles unambiguously define important dimensions of diffusion. Hg0(g)

concentrations within the bottles were several orders of magnitude greater than the

laboratory atmosphere. Ambient temperatures were monitored using a laboratory

thermometer.

After different periods of time, during which Hg0 diffused from the reactors to the

laboratory atmosphere, 800 μL of a KMnO4 solution (20 kg/m3 KMnO4 in 0.8 M HNO3) was

added through one of the diffusion needles. The needles were immediately removed to

reseal the reactors. The addition of KMnO4 was to oxidize both Hg0 and any remaining

69

Sn(II). These actions effectively ended diffusive losses and trapped mercury for both mass

and isotope analysis. The KMnO4 was allowed to react for several hours before analysis.


The mass of mercury remaining in reactors was measured by cold vapor atomic

fluorescence spectroscopy. KMnO4 oxidized sample solutions were pre-reduced with 30 μL

of a NH2OH-HCl solution (300 kg/m3 NH2OH-HCl in high purity water) prior to analysis.

Hg2+ in known volumes of these solutions was reduced to Hg0 by SnCl2, transferred to gold

traps using a bubbler, and analyzed by dual-stage gold amalgamation (Gill & Fitzgerald

1987). The relative error of calibration standards was observed to be less than 5%,

calculated as two times the standard deviation of errors. Sample errors were estimated as

either the error of replicates, or the error of calibration standards, whichever was greater.


MC-ICP-MS as described in Chapter 2. Samples were prepared by reducing known masses

of Hg2+ with SnCl2 in a 150 mL bubbler, purging with N2(g) at 50 mL/min, and trapping in

HOCl as described in section 2.3. Standard and sample recoveries during sample

preparation were monitored. Errors in δ values are taken as the greatest of: i) the

long-term reproducibility of the UM-Almaden standard as described in section 2.2.5, ii) two

times the estimated in-run standard deviation (2SD) based on NIST 3133 as described in

section 2.2.3, or iii) two times the estimated standard error (2SE) of sample replicates

during the analytical run.

70

Figure 5.1 The diffusion reactor used for determining mercury diffusion coefficients and

fractionation factors

5.3 Results

5.3.1 Mercury Diffusion

The mass of mercury that remained in reactor bottles at the completion of

experiments is presented in Figure 5.2. Mercury was lost through the needles in a

reproducible manner and recoveries were good. As expected, the loss of mercury through

longer needles was slower due to the smaller gradient. The loss of mercury appears to be

exponential, and this will be explored in the following section. The characteristic time for

mercury loss in these experiments, τr, was observed to be on the order of one thousand

minutes.

Hg0(g)

SnCl2(aq)Hg0(aq)

Diffusion

Needles

Reactor

Stir bar

71

Figure 5.2 Mercury mass remaining in reactors with time for air diffusion experiments.

5.3.2 Calculation of Measured Diffusion Coefficients

Diffusion coefficients were calculated using the time series data of mercury

remaining in the reservoirs and some simplifying assumptions. First, equilibrium

partitioning between aqueous and gas phases within the reactors was assumed, as

expressed in equation 5.3. With this assumption, the concentration of Hg0(g) in the reactors,

Ca (expressed as mass per volume), relates to the total Hg mass in the reactor, M, as:

K� � V`d� ? d��a 5.4

where Va is the volume of air in the reactor, Vl is the volume of liquid in the reactor, and H is

a unitless Henry’s constant defined as the ratio of air to water concentrations. Second,

because concentrations of Hg0(g) in the laboratory atmosphere were several orders of

magnitude less than in the reactors, they were assumed to be negligible. Third, the gradient

of Hg0(g) concentrations within needles was assumed to be constant, as illustrated in Figure

5.3 .

0

500

1000

1500

2000

0 500 1000 1500 2000

Ma

ss o

f H

g R

em

ain

ing

(n

g)

Time (minutes)

Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

72

Figure 5.3 Illustration of the expected steady-state Hg0concentration profile in the needles

This is reasonable after noting that the characteristic time for mercury diffusion across the

needle, τn, estimated to be a on the order of one minute, is considerably shorter than the

characteristic time for mercury loss from the reactors, τr. τr was observed from

experimental data and τn was estimated as

�m # cm%2I� 5.5

where Ln is the needle length and Da is an estimated diffusion coefficient through air.

Incorporating Fick’s Law with a mass balance across the reactor and expression 5.4,

the rate of mercury change in the reactors is:

UVUM � � ��mI�`d� ? d��a cm V 5.6

where n is the number of needles and An is the cross-sectional area of each needle.

The solution to equation 5.6 indicates that the mass of mercury remaining in

reactors decays exponentially:

V�M� V2; � 1 � X3YQ 5.7

Hg0(g)

Diffusion

Needles

C=Ca

C=0

0

Concentration

73

where Mi is the initial Hg0 mass in the reactor at time t=0, F is the fraction of Hg0 initially

present remaining, and k is a first order rate constant defined as:

W � ��mI�`d� ? d��a cm 5.8

Equation 5.7 indicates that the time series can be linearized as:

ln�1� � �WM 5.9

such that a plot of ln(F) vs. t will have a slope equal to –k. Figure 5.4 shows a logarithmic

plot of the fraction of mercury remaining with time as indicated by equation 5.9.

Figure 5.4 Linearized time series

Error-weighted linear regressions were performed using Isoplot 3.70 (K. R. Ludwig 2008),

based upon an algorithm described by York (1968). The good agreement of data and linear

fits indicate that loss of mercury matches first order exponential decay as expected. The

shallower slope associated with the longer needles indicates slower loss from the reactors.

Table 5.1 summarizes the rate constants, k, as determined by the linear regressions, and

their uncertainties.

-3

-2

-1

0

1

0 500 1000 1500 2000

ln(F

raci

ton

of

Hg

Re

ma

inin

g)

Time (minutes)

Experiment 1

(2.54 cm needles)Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

74

Table 5.1 Results of air diffusion experiments and calculated diffusion coefficients

Experiment Needle Length

(cm)

Rate at 23 °C

(min-1) x 103

Estimated D at 23 °C

(cm2/s)

1 (2.54 cm) 2.54 1.49±0.07 0.132±0.007

2 (2.54 cm) 2.54 1.45±0.04 0.129±0.004

3 (3.81 cm) 3.81 1.02±0.05 0.137±0.006

Weighted Average 0.131±0.010

The temperature during the all the experiments was observed to be 23 °C. Henry’s

constant, H, was estimated to be 0.303, using the empirical equation provided by Sanemasa

(1975):

log J � �1078A ? 6.250 5.10

where K is a Henry coefficient, expressed as the partial pressure of mercury vapor (atm)

divided by the mole fraction of the dissolved mercury, and T is the temperature, in kelvin.

Conversion of this K value to the unitless H used in this text is accomplished as:

� � J0A � 55.4 9�B c; 5.11

where R is the universal gas constant and T is the temperature, in kelvin. Using the

relationship expressed in equation 5.8, and estimated values of H, estimates of diffusion

coefficients are listed in Table 5.1. The weighted average diffusion coefficient of the

experiments, calculated using Isoplot 3.70 (K. R. Ludwig 2008), was determined to be

0.131±0.010 cm2/s.


The isotope composition of samples prepared after the completion of experiments is

presented in Figure 5.5. As indicated by progressively larger δ202Hg values, reactors

preferentially lost lighter isotopes through diffusion, as expected.

The measured δ202Hg values for experiment 1 differ from the other two experiments

despite starting with mercury with the same isotopic composition. This was the result of

poor recoveries during sample preparation. The incomplete recoveries resulted from the

use of lower HOCl oxidant concentrations during preparation of these samples. Lower HOCl

concentrations were used in an attempt to decrease the introduction of salts to the

MC-ICP-MS instrument. Preparations using NIST 3133 Hg standards, performed

concurrently, also exhibited isotope fractionation, and are indicated in Figure 5.5 as hollow

points. Despite the observed fractionation during preparation, recoveries and fractionation

75

were consistent from sample to sample. Recoveries were approximately 60% and

fractionation was approximately 1.07±0.24‰ in δ202Hg. Because variability among

recovered standards was less than the uncertainty of mercury isotope measurements,

corrections for this fractionation were made. This was appropriate as it was assumed that

all samples and standards were exposed to the same degree of isotope fractionation during

sample preparation.

All further data presented for the experiments was corrected for fractionation that

occurred during sample preparation. It should also be noted that fractionation during

sample preparation for experiments 2 and 3 was negligible due to the almost 100%

recoveries.

Figure 5.5 Change in isotope composition with time. The asterisk identifies an outlier.

5.3.4 Calculation of Measured Isotope Effects

Isotope effects during the experiment were calculated using measured δxHg values.

Equation 5.7 can be used to examine individual mercury isotopes:

V��M�V��M� � V�,2X3Y\QV��,2X3Y]^_Q 5.12

where subscripts x and 198 indicate different isotopes remaining in the reactor. After

replacing Mx/M198 with the ratio, Rx and rearranging, we get:

-1

0

1

2

3

4

5

6

0 500 1000 1500 2000

δ2

02H

g R

em

ain

ing

(‰

)

Time (minutes)

Experiment 1

(2.54 cm needles)

Experiment 1

Recovered Standards

Experiment 2

(2.54 cm needles)

Experiment 2,3

Recovered Standards

Experiment 3

(3.81 cm needles)

*

76

0��M�0�,2 � X3Y\Q�`�3Y]^_ Y\; a

5.13

Another set of substitutions yields:

0��1�0�,2 � 1��34\� 5.14

where F is the fraction of initial mercury remaining in the reactor, as shown in equation 5.7,

and αx is an isotope fractionation factor defined by the isotope reaction rates in this system.

5� � W��W� 5.15

Equation 5.14 is the Rayleigh equation for a constant fractionation factor. As this equation

shows, examining isotope ratios with respect to the fraction of mass remaining effectively

normalizes for many different factors in the system, including time. Figure 5.6 shows

δ202Hg of mercury in the reservoirs vs. the fraction remaining. All three experiments show

very good agreement with each other. An outlier in the data was identified, and it is

indicated by an asterisk on the plots. The presence of the outlier is evident by looking at all

isotope pairs, and exhibits mass independent fractionation. The outlier may have resulted

from incomplete oxidation with KMnO4 (oxidation time was shortened towards the end of

the experiment), or perhaps an unexplained source of laboratory contamination, that led to

an interference. Calculations and linear regressions that follow do not incorporate this

outlier data point.

77

Figure 5.6 δ202Hg of mercury remaining in the reservoir. The asterisk identifies an outlier.



based on the initial isotopic composition. With the exception of the outlier described above,

data appear to follow this mass dependent behavior. Individual plots similar to Figure 5.6

for other isotope pairs (δ201Hg, δ200Hg, and δ199Hg) are provided in Appendix B as Figure

B.11, Figure B.12, and Figure B.13 respectively.

-1

0

1

2

3

4

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles) *

78

Figure 5.7 Multi-Isotope Plot indicating that fractionation is mass dependent as anticipated. The

asterisks identify outliers.

Given the relationship between δxHg values and isotope ratios, Rx, equation 5.14 can

be linearized to give:

ln 81 ? ��1000 : � �1 � 5�� ln 1 ? ln �1 ? �2��1000 � 5.16

such that a plot of ln(1+δxHg/1000) vs. ln F will have a slope equal to (1-αx). Figure 5.8 show

a log-log plot as indicated by equation 5.16. Again, error-weighted linear regressions were

performed using Isoplot 3.70 (K. R. Ludwig 2008).

-1

0

1

2

3

-1 0 1 2 3 4

δxH

g (

‰)

δ202Hg (‰)

δ199Hg

δ200Hg

δ201Hg

*

*

79

Figure 5.8 Linearized isotope fractionation of δ202Hg. The asterisk identifies an outlier.

The linearity of the data indicates that a Rayleigh relationship describes the data well, as

anticipated. All three experiments show very similar isotope fractionation, indicated by the

similarity of the slopes. Using the measured δ values, and a linear regression, fractionation

factors, αx for the different isotopes in this system were calculated. Table 5.2 summarizes

the experimental fractionation factors αx derived from the results. The weighted average

α202 of the experiments, calculated using Isoplot 3.70 (K. R. Ludwig 2008), was determined

to be 1.00128±0.00011.

Table 5.2 Observed Isotope fractionation factors in the air diffusion experiments


1 (2.54 cm) 1.00034±0.00008 1.00063±0.00011 1.00095±0.00014 1.00125±0.00019

2 (2.54 cm) 1.00035±0.00010 1.00064±0.00010 1.00094±0.00014 1.00126±0.00016

3 (3.81 cm) 1.00040±0.00017 1.00070±0.00018 1.00105±0.00023 1.00137±0.00027

Weighted

Average 1.00035±0.00006 1.00064±0.00007 1.00096±0.00009 1.00128±0.00011

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

0.006

-3 -2 -1 0

ln(1

+δ

20

2H

g/1

00

0)


Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

*

80

5.4 Discussion

5.4.1 Diffusion Coefficient

The diffusion coefficients determined for mercury diffusion through air for the

experiments are listed in Table 5.1. Table 5.3 compares the value determined in these

experiments with literature values for Hg0 diffusion in both air and N2, and includes the

temperatures they were determined at. The experimental value for Hg diffusion through air

determined here matches those in the literature well. This indicates that diffusion was the

limiting process for mercury loss from the reactors, and that equilibrium between gas and

water of Hg0 occurred. This increases confidence that measured isotope effects reflect a

diffusion effect.

Table 5.3 Hg0 diffusion coefficients through air

Gas Composition Reference Temperature (°C) Diffusion Coefficient

(cm2/s)

Hg-Air This experiment 23 0.131±0.010

Hg-Air (Lugg 1968) 25 0.1423±0.0003

Hg-Air (Massman 1999) 23 0.138±0.008*

Hg-N2 (Spier 1940) 19-25 0.138±0.019

Hg-N2 (Nakayama 1968) 28 0.13±0.01

Hg-N2 (Gardner et al. 1991) 156-317 0.273-0.482

Hg-N2 (Gardner et al. 1991) 23 0.144*

Hg-N2 (Massman 1999) 23 0.140±0.007*

* The diffusion coefficients are estimated at temperature given the relationships provided

5.4.2 Diffusive Isotope Effect

The experimentally determined isotope effects for the system, αx, are provided in

Table 5.2. We can use the determined values, and estimates for the relative effects of

Henry’s constant, Hy/Hx, among the isotopes, to estimate Dy/Dx. We can examine the

relationship between αx, D, and H by combining equations 5.8 and 5.15:

5� � W��W� � 8I��I� : 8�� : 8 ��d� ? d��d� ? d�: 5.17

where the terms are defined as before with the subscripts x and 198 indicating different

isotopes. The effect of Henry’s constant and the air and liquid volumes can be simplified if

we assume that H198/Hx≈1. With this assumption, it can be shown that:

81

5� # W��W� # 8I��I� : 8�� : ��R�� 5.18

where H≈Hx≈H198. Examining equation 5.18, it is clear that an estimate of H198/Hx is

essential to estimating D198/Dx with the experimental data.

There does not appear to be much data in the literature regarding the equilibrium

partitioning of gases between air and aqueous phases, as would be indicated by Henry’s

constants (Beyerle et al. 2000). Such data appears to be limited to He, Ne, N2, O2, and Ar

(Benson & Krause 1980; Beyerle et al. 2000; Klots & Benson 1963). Figure 5.9 shows the

equilibrium isotope effect of Ne, N2, O2, and Ar found in the literature vs. a scaling factor

Δm/m2, which has been suggested to be an effective scaling term for traditional

mass-dependent behavior at equilibrium (Schauble 2007). In this case, Δm is the difference

in masses of the isotopologues, and m is the average mass of the isotopologues.

Figure 5.9 isotope effects associated with Henry's partitioning. Data from Benson & Krause

(1980), Beyerle et al. (2000), and Klots & Benson (1963)

Because data scale well in this relationship, it was used to estimate Hy/Hx for Hg0. Using this

relationship, H198/H202≈1.000045, which is quite small as expected. With the determined αx

from the experiments and estimates for H198/Hx, we can estimate relative diffusion rates.

Figure 5.10 shows D198/D199, D198/D200, D198/D201, and D198/D202 and compares the values to

kinetic theory. These are 1.00034±0.00006, 1.00063±0.00007, 1.00094±0.00009, and

1.00125±0.00011, respectively

1.000

1.001

1.002

1.003

0 0.001 0.002 0.003 0.004 0.005 0.006

Hy/H

x

Δm/m2

20Ne/22Ne

36Ar/40Ar

32O2/34O229N2/28N2

20Ne/22Ne

36Ar/40Ar

32O2/34O229N2/28N2

y=0.452x+1

R2 = 0.9741

82

Figure 5.10 Comparison of experimental results and kinetic theory for Hg0 diffusion in air.

The experimental determinations of the relative diffusion rates here and kinetic

theory match well. As mentioned earlier, the effectiveness of using kinetic theory for

examining isotope effects is debated, but in the case of Hg0(g), here, it performs well. It is not

clear why experiments examining H2O and N2O do not match theory (Merlivat 1978; Well &

Flessa 2008; Barkan & Luz 2007). Equilibrium effects for these lighter isotopologues are

greater than for mercury and it has been suggested that these effects have not been

properly accounted for (Cappa et al. 2003).

The experiments performed here suggest that kinetic theory describes diffusive

isotope effects well for Hg0(g) in air. If kinetic theory holds, diffusive isotope effects should

be independent of temperature and valid at higher temperatures such as during mercury

production. Figure 5.11 shows the consequences of these effects for mercury production if

condensation of Hg0 is diffusion limited. In this analysis, the δ202Hg value of the Hg0(l)

produced cannot be less than 1.3 ‰ smaller than the δ202Hg value of the initial Hg0(g).

Depending on the extent of condensation from the Hg0(g) stream, emission of Hg0

(g) to the

atmosphere can exhibit large δ202Hg values. This Hg0(g) could be distributed globally if it not

oxidized near the source.

1.0000

1.0002

1.0004

1.0006

1.0008

1.0010

1.0012

D198/D199 D198/D200 D198/D201 D198/D202

Re

lati

ve

Dif

fusi

on

Co

eff

icie

nt Experimentally

Determined

Kinetic Theory

83

Figure 5.11 Isotope composition of Hg0(l) recovered and Hg0

(g) lost to atmosphere relative to the

composition of the initial Hg0(g) if diffusion controlled condensation.

5.5 Summary

In this chapter, I have described experiments examining isotope effects attributed to

diffusion of Hg0 through air. Diffusion coefficients similar to literature values were

measured and experimental isotope effects of Hg0 diffusion through air matched kinetic

theory well. These results suggest that Hg isotope ratios can be used to investigate many

mercury processes in environmental and engineered systems where diffusion is limiting.

The potential of mercury isotope fractionation during mercury production resulting

from diffusion processes is described above. Under these conditions Hg0(l) products will

have δ202Hg values slightly smaller than the initial gas composition and gas lost to the

atmosphere should have δ202Hg values significantly greater. Contemporary gold mining

processes used by artisanal miners often rely on mercury amalgamation and recover

mercury by similar condensation processes. Knowledge of relative diffusion rates and

isotope measurements could be helpful in examining these artisanal mining sources.

The behavior shown in Figure 5.11 of large δ202Hg values in the gas lost to the

atmosphere could be of significant interest to the coal power community. Today, coal

power is the largest contributor of anthropogenic mercury to the global environment. Due

to current and future regulations, there is currently great interest in sorbents for mercury

removal from combustion flue gases power plants. Some of the limitations in performance

of these sorbents can be attributed to diffusive mass transfer (Pavlish 2003; Yan et al.

-2.0

0.0

2.0

4.0

6.0

0.00.20.40.60.81.0

δ2

02H

g-δ

20

2H

gi(‰

)

Fraction lost to atmosphere

84

2009; Zhuang et al. 2004). This diffusion limited isotope signal could be helpful in

evaluating the performance of sorbents. Also, because diffusion limitations during sorption

may lead to isotope fractionation of Hg0(g) lost to the atmosphere as indicated in Figure

5.11, use of sorbents could lead to a source of large δ202Hg to the environment that can be

traced.

Lastly, mercury transport though soil gases is of interest (D. W. Johnson et al. 2003;

Walvoord et al. 2008). For example, there appears to be some controversy regarding the

role of diffusion in controlling evasion of Hg0(g) from soils(D. W. Johnson et al. 2003).

Measurement of mercury isotopes could help answer this question because diffusive

control should lead to isotope fractionation as described in this chapter.

85

Chapter 6 Conclusion

6.1 Summary

Mercury is a persistent, global pollutant with known human health and ecosystem

impacts. Understanding of mercury isotope fractionation is necessary for quantifying how

transport and transformation processes alter the distribution of mercury isotopes

throughout the environment. This includes the identification and tracking of large mercury

sources with isotopes. Previous mercury isotope research focused on observing isotopic

variations in the field to demonstrate quantifiable differences in various environmental

compartments. There have been complementary efforts at measuring isotope fractionation

factors under laboratory conditions, most frequently to reproduce environmental

processes to guide interpretation of field data. This prior work of others included the

unexpected discovery of large mass independent variations among mercury isotopes,

which will be very helpful in providing greater understanding of mercury processes. The

research described in this dissertation characterizes isotope effects of specific transport

and transformation processes relevant in the environment to help provide mechanistic

explanations of environmental and laboratory data.

The research necessitated the development of an analytical method for measuring

mercury isotopes with high precision and good reproducibility. The method described here

is different from most contemporary methods as it introduces mercury to the MC-ICP-MS

instrument as a liquid aerosol rather than as a gas. The performance of this new method

was comparable to other methods, and its application is perhaps simpler. It uses a single

liquid sample introduction system for both mercury and thallium, as opposed to a liquid

sample introduction system for thallium along with a cold vapor generation system for

mercury. The addition of cysteine to liquid samples was effective at controlling the memory

effect of mercury in the MC-ICP-MS system and enabled this new approach. Thallium is

needed in both cases to correct for instrument mass bias. The long-term reproducibility of

δ202Hg measurements with this analytical method was approximately 0.3 ‰.

Three different processes hypothesized to affect mercury isotope composition were

examined in this work. Figure 6.1 shows the isotope fractionation observed for all three

processes along with mechanistic models used to help determine specific isotope

fractionation factors for each. The models matched data well.

The process that resulted in the largest isotope fractionation was permeation

through a PVC polymer. A model accounting for mercury partitioning into the polymer and

diffusion with an isotope fractionation factor of α202 = 1.00288±0.00040 matched the

experimental data well. This fractionation factor was independent of temperature and is

the largest yet reported for mercury near ambient conditions. It is similar to isotope effects

of other gases permeating polymers.

The potential for mercury isotope fractionation during mercury metal production

inspired the investigation of the later two processes studied: the thermal decomposition of

HgS(s) and the diffusion of Hg0(g) through air. Thermal decomposition of synthetic cinnabar,

86

HgS(s), did not result in bulk isotope fractionation. This lack of bulk fractionation was

consistent with a model of an inhomogeneous solid undergoing congruent evaporation.

Congruent evaporation should lead to a thin surface layer on HgS(s) particles with larger

δ202Hg values, but does not greatly alter the bulk isotope composition of these particles.

The diffusion of Hg0(g) through air was examined by depleting a reservoir through

diffusion alone. The diffusion coefficient of Hg0(g) at room temperature was determined to

be 0.131±0.010 cm2/s and the ratio of 198Hg(g) to 202Hg(g) diffusion coefficients through air

was determined to be 1.00125±0.00011. These values match literature and kinetic theory

well and suggests this theory can be applied in many different circumstances.

Figure 6.1 Experimental results for all three processes examined. Lines represent mechanistic

models using the determined isotope fractionation factors.

6.2 Recommendations

The work presented here will enable better interpretation of field data. For example,

the thermal decomposition of HgS(s) examined here was fundamental to mercury

production and has previously been suggested to lead to mercury isotope fractionation at

mercury mines (Stetson et al. 2009; G.E. Gehrke et al. 2011). Those prior works

documented larger δ202Hg values among calcine waste piles than among unprocessed ores,

-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

PVC Diffusion

Thermal Decomp

AirDiffusion

87

and suggested that isotope effects associated with thermal decomposition were the cause.

The lack of isotope fractionation during thermal decomposition of HgS(s) observed here

suggests that this interpretation should be reconsidered. Two alternative explanations for

differences in bulk isotope composition between ore and calcine waste are equilibrium

isotope effects exhibited during the decomposition process, or comingled mercury

minerals with larger δ202Hg values that decompose at higher temperatures, such as HgO(s).

The later explanation is supported by data in Stetson et al. (2009), who observed HgO(s)

with large δ202Hg values at mercury mines. This suggests that further isotopic examination

of a variety of mercury minerals located within mercury ore deposits is appropriate, as

these may constitute a large proportion of mercury in calcine waste piles. These mercury

minerals are of additional interest because they can be more soluble and bioavailable than

HgS(s).

The processes examined here can help guide future research by suggesting sources

and transformations that can be traced by their isotopic composition. At mercury mines,

condensation processes used to produce Hg0(l) were probably limited by diffusion. Based

on the isotope effect of diffusion through air, this likely resulted in Hg0(l) with slightly

smaller δ202Hg values than the ore, but greater δ202Hg values in gas emissions. Whether an

atmospheric record of such large δ202Hg signals is apparent deserves further investigation,

but may be difficult due to the potential global distribution of Hg0(g). For the largest

contemporary anthropogenic mercury sources, coal power plants, the isotope effect of

diffusion in gases could be interesting. Strong mercury sorbents are being considered to

help control global mercury emissions and these sorbents will likely introduce some

diffusion limited isotope fractionation. The use of such sorbents, then, could not only result

in fewer mercury emissions, but also result in isotopically fractionated releases that could

prove a powerful tool in tracking these mercury sources.

The observation here of very large mercury isotope effects resulting from diffusion

through a polymer is noteworthy as similar processes could result in large isotopic

variations in the environment. The important process of mercury methylation, which leads

to most mercury exposures, has been suggested to be limited by permeation of cell

membranes by neutral mercury compounds such as HgS(aq) and Hg(HS)2(aq). The results

here suggest this process has a large isotope effect, such that methylmercury could exhibit

lower δ202Hg values. This could be useful for tracking mercury methylation processes in

experiments and the environment.

Some of the ideas for further research listed above can be pursued in the short term,

with modern methods, and on small scales. Others, such as the evaluation of large scale

isotope effects resulting from sorbent use in power plants are further off. Much of this

research will require further improvements in methods for measuring mercury isotopes.

While expensive MC-ICP-MS instruments, such as that used in this research, are currently

the only tool that reliably measures mercury isotopes with high precision, developments in

other isotope systems suggest this may change. One such development is cavity ring-down

spectroscopy (CRDS). This method has proven effective at measuring carbon and water

isotopes, providing similar performance, with greater throughput, and at significant lower

cost than traditional isotope ratio mass spectrometers (IRMS) (Koehler & Wassenaar 2011;

88

Brand et al. 2009; Lis et al. 2008). CRDS operates by observing the photo absorption

properties at frequencies specific to isotopic components. This simple methodology should

be applicable to other gases, such as mercury. Early investigations of CRDS systems for the

measurement of low mercury concentrations indicate that different absorption

wavelengths of mercury isotopes may be resolvable (C. Wang 2007; Anderson et al. 2007).

Future development of cheaper and more accessible mercury isotope measurements will

enable much broader use of mercury isotope information.

There is universal concern regarding mercury in the environment. It is very toxic

and affects human and ecological health even at low environmental concentrations. Current

levels of mercury actively cycling in the environment are a factor of three greater than

prior to human activity, and despite large research investments, there are major

uncertainties regarding stocks and flows in mercury’s complex biogeochemical cycle (Selin

2009). The recent discovery of variations in the isotopic composition of mercury will help

address some uncertainties in its cycle, as isotope studies have helped in other isotopic

systems, such as with lead. Whereas a decade ago the first reliable measurements of small

mercury isotopic variations were made by Lauretta et al. (2001), today it is clear that

significant variations exist that will be useful in better characterizing mercury’s

environmental fate. The work presented in this dissertation describes the isotope effects of

three transport and transformation processes, two of which are quite significant. These

two processes, the diffusion of mercury through air, and the diffusion of mercury in

polymers could lead to large isotope variations and should be examined further in the lab

and in the field. The combination of determining isotopic variation in environmental

samples and mechanistic studies under controlled conditions will permit greater abilities

to identify mercury sources and environmental transformations.

89

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99

Appendix A Visual Basic Code

Dim TRV 'Total Reservoir volume (cm^3)

Dim LV ' liquid volume in reservoir (cm^3)

Dim TOR ' tube outer radius (cm)

Dim TIR ' tube inner radius (cm)

Dim TL ' tube length (cm)

Dim TPC ' tube partitioning coeffiecient (ctube/cair)

Dim H ' henry's constant (cwater/cair)

Dim TDC ' tube diffusion coefficient (cm^2/min)

Dim THgMa, THgMb ' total mercury mass

Dim rsteps ' total number of radial spatial steps

Dim tottime ' total time to run for in minutes

Dim calcdepth ' depth of delt to iterate to

Dim errorallowance ' error allowance in calculation

Dim TDCalpha

Dim TPCalpha

Dim THgMalpha

Dim measureddata 'input of measureddata

Dim DelR ' size of rstep (cm)

Dim Vwall 'volume of inner tube wall layer

Dim Parta, partb 'Partitioning concentration on tubewall/totalmass

Dim Pi ' Pi

Dim RArray ' Array of radius lengths

Dim SAArray ' Array of surface areas for diffusion flux at large end

Dim ConcMatrixA, ConcMatrixB ' matrix to store concentration data for calculations

Dim OutputMatrixA, OutputMatrixB ' matrix to store concentrations by minute

Dim Delt ' initial large time step

Dim timstep

Dim fluxa, fluxb

Sub RunDiffusion()

LoadInputInfo

ConcMatrixA = CalculateConcMatrix(ConcMatrixA, TDC, Delt, DelR, Parta, RArray, SAArray, rsteps,

calcdepth, THgMa)

ConcMatrixA = updateconcmatrix(ConcMatrixA, rsteps)

placeholder = 2

counter1 = 0

Counter2 = 0

Do While OutputMatrixA(placeholder, 0) > ConcMatrixA(1, 0) And OutputMatrixA(placeholder, 0) < tottime

counter1 = counter1 + 1

Cells(2, 1) = counter1

100

timestep = OutputMatrixA(placeholder, 0) - ConcMatrixA(1, 0)

If timestep < Delt Then

ConcMatrixA = CalculateConcMatrix(ConcMatrixA, TDC, timestep, DelR, Parta, RArray, SAArray, rsteps,

calcdepth, THgMa)

Else

ConcMatrixA = CalculateConcMatrix(ConcMatrixA, TDC, Delt, DelR, Parta, RArray, SAArray, rsteps,

calcdepth, THgMa)

End If

ConcMatrixA = updateconcmatrix(ConcMatrixA, rsteps)

If OutputMatrixA(placeholder, 0) = ConcMatrixA(1, 0) Then

For j = 1 To rsteps

OutputMatrixA(placeholder, j) = ConcMatrixA(1, j)

Next

placeholder = placeholder + 1

Cells(1, 1) = placeholder

counter1 = 0

End If

Loop

ConcMatrixB = CalculateConcMatrix(ConcMatrixB, TDC * TDCalpha, Delt, DelR, partb, RArray, SAArray,

rsteps, calcdepth, THgMb)

ConcMatrixB = updateconcmatrix(ConcMatrixB, rsteps)

placeholder = 2

counter1 = 0

Counter2 = 0

Do While OutputMatrixB(placeholder, 0) > ConcMatrixB(1, 0) And OutputMatrixB(placeholder, 0) < tottime

counter1 = counter1 + 1

Cells(2, 1) = counter1

timestep = OutputMatrixB(placeholder, 0) - ConcMatrixB(1, 0)

If timestep < Delt Then

ConcMatrixB = CalculateConcMatrix(ConcMatrixB, TDC * TDCalpha, timestep, DelR, partb, RArray,

SAArray, rsteps, calcdepth, THgMb)

Else

ConcMatrixB = CalculateConcMatrix(ConcMatrixB, TDC * TDCalpha, Delt, DelR, partb, RArray, SAArray,

rsteps, calcdepth, THgMb)

End If

ConcMatrixB = updateconcmatrix(ConcMatrixB, rsteps)

If OutputMatrixB(placeholder, 0) = ConcMatrixB(1, 0) Then

For j = 1 To rsteps

OutputMatrixB(placeholder, j) = ConcMatrixB(1, j)

Next

placeholder = placeholder + 1

Cells(1, 1) = placeholder

counter1 = 0

End If

Loop

For i = 1 To tottime + 1

fluxa(i) = OutputMatrixA(i, rsteps - 1) / DelR * SAArray(rsteps - 1) * TDC

101

fluxb(i) = OutputMatrixB(i, rsteps - 1) / DelR * SAArray(rsteps - 1) * TDC * TDCalpha

Next

outputdata

End Sub

Sub LoadInputInfo()

Pi = 3.14159

inputsize = 0

Do While Cells(26 + inputsize, 3) <> ""

inputsize = inputsize + 1

Loop

measureddata = readindata(inputsize)

TRV = Cells(8, 5) 'Total Reservoir volume (cm^3)

LV = Cells(9, 5) ' liquid volume in reservoir (cm^3)

TOR = Cells(10, 5) ' tube outer radius (cm)

TIR = Cells(11, 5) ' tube inner radius (cm)

TL = Cells(12, 5) ' tube length (cm)

TPC = Cells(13, 5) ' tube partitioning coeffiecient (ctube/cair)

H = Cells(14, 5) ' henry's constant (cwater/cair)

TDC = Cells(15, 5) ' tube diffusion coefficient (cm^2/min)

THgMa = Cells(16, 5) ' total mercury mass

rsteps = Cells(19, 5) ' total number of radial spatial steps

tottime = Cells(20, 5) ' total time

calcdepth = Cells(21, 5) ' depth of delt to iterate to

errorallowance = Cells(22, 5) ' allowance for errors in calcs

TPCalpha = Cells(13, 6)

TDCalpha = Cells(15, 6)

THgMalpha = Cells(16, 6)

THgMb = THgMa * THgMalpha

TubingVolume = Pi * TOR * TOR * TL

airvolume = TRV - TubingVolume - LV

DelR = (TOR - TIR) / rsteps

ReDim RArray(rsteps)

ReDim SAArray(rsteps)

ReDim ConcMatrixA(2, rsteps), ConcMatrixB(2, rsteps)

ReDim OutputMatrixA(tottime + 1, rsteps), OutputMatrixB(tottime + 1, rsteps)

ReDim fluxa(tottime + 1), fluxb(tottime + 1)

For j = 1 To rsteps

RArray(j) = TOR - (2 * j - 1) / 2 * DelR ' Array of radius lengths

SAArray(j) = 2 * Pi * (RArray(j) - DelR) * TL ' Array of surface areas for diffusion flux at large end

102

Next

Vwall = 2 * Pi * RArray(1) * TL * DelR

Parta = 1 / (airvolume / TPC + LV * H / TPC + Vwall) ' conc on wall/total mass

partb = 1 / (airvolume / (TPC * TPCalpha) + LV * H / (TPC * TPCalpha) + Vwall) ' conc on wall/total mass

For j = 0 To rsteps

For k = 0 To 2

ConcMatrixA(k, j) = 0

ConcMatrixB(k, j) = 0

Next

For k = 0 To tottime + 1

OutputMatrixA(k, j) = 0

OutputMatrixB(k, j) = 0

Next

Next

For k = 1 To tottime + 1

OutputMatrixA(k, 0) = k - 1

OutputMatrixB(k, 0) = k - 1

Next

ConcMatrixA(1, 1) = THgMa * Parta

ConcMatrixB(1, 1) = THgMb * partb

OutputMatrixA(1, 1) = ConcMatrixA(1, 1)

OutputMatrixB(1, 1) = ConcMatrixB(1, 1)

Delt = 1

i = 1

Do While Delt > (DelR ^ 2) / (4 * TDC)

Delt = Delt / 2

Loop

End Sub

Function readindata(inputsize1)

ReDim temp(inputsize1, 7) As Single

For i = 1 To inputsize1

For k = 1 To 7

temp(i, k) = Cells(25 + i, 2 + k)

Next

Next

readindata = temp

End Function

103

Function CalculateConcMatrix(concmatrix1, tdc1, delt1, delr1, part1, rarray1, saarray1, rsteps1, calcdepth1,

thgm1)

ReDim tempdeltc(calcdepth1 + 1, rsteps1)

ReDim tempconc(calcdepth1, rsteps1)

ReDim concupdate(2, rsteps1)

tempdeltc(1, 1) = -tdc1 * (concmatrix1(1, 1) - concmatrix1(1, 2)) / delr1 * saarray1(1) * part1

tempconc(1, 1) = concmatrix1(1, 1) + 0.5 * tempdeltc(1, 1) * (delt1)

For j = 2 To rsteps1 - 1

If concmatrix1(1, j - 1) = 0 And concmatrix1(1, j) = 0 And concmatrix1(1, j + 1) = 0 Then

tempdeltc(1, j) = 0

Else

tempdeltc(1, j) = tdc1 / delr1 * ((concmatrix1(1, j - 1) * ((1 / delr1) + (1 / (2 * rarray1(j))))) - 2 *

concmatrix1(1, j) * (1 / delr1) + concmatrix1(1, j + 1) * ((1 / delr1) - (1 / (2 * rarray1(j)))))

End If

tempconc(1, j) = concmatrix1(1, j) + 0.5 * tempdeltc(1, j) * (delt1)

Next

i = 1

errortempdeltc = 1

Do While errortempdeltc > errorallowance And i < calcdepth1

tempdeltc(i + 1, 1) = -tdc1 * (tempconc(i, 1) - tempconc(i, 2)) / delr1 * saarray1(1) * part1

tempconc(i + 1, 1) = concmatrix1(1, 1) + 0.5 * tempdeltc(i + 1, 1) * (delt1 / (i + 1))


If tempconc(i, j - 1) = 0 And tempconc(i, j) = 0 And tempconc(i, j + 1) = 0 Then

tempdeltc(i + 1, j) = 0

Else

tempdeltc(i + 1, j) = tdc1 / delr1 * ((tempconc(i, j - 1) * ((1 / delr1) + (1 / (2 * rarray1(j))))) - 2 *

tempconc(i, j) * (1 / delr1) + tempconc(i, j + 1) * ((1 / delr1) - (1 / (2 * rarray1(j)))))

End If

tempconc(i + 1, j) = concmatrix1(1, j) + 0.5 * tempdeltc(i + 1, j) * (delt1 / (i + 1))

Next

errortempdeltc = (((tempdeltc(i + 1, 1) - tempdeltc(i, 1)) / thgm1) ^ 2) ^ (0.5)


If tempdeltc(i, j) = 0 Then

newerror = 0

Else

newerror = (((tempdeltc(i + 1, j) - tempdeltc(i, j)) / thgm1) ^ 2) ^ (0.5)

End If

If newerror > errortempdeltc Then

errortempdeltc = newerror

Else

errortempdeltc = errortempdeltc

End If

Next

i = i + 1

Loop

concmatrix1(2, 0) = concmatrix1(1, 0) + (delt1 / i)

concmatrix1(2, 1) = concmatrix1(1, 1) + tempdeltc(i, 1) * (delt1 / (i))


104

concmatrix1(2, j) = concmatrix1(1, j) + tempdeltc(i, j) * delt1 / i

Next

CalculateConcMatrix = concmatrix1

' For j = 2 To rsteps1 - 1

' concupdate(

End Function

Function updateconcmatrix(concmatrix1, rsteps1)

ReDim temp(2, rsteps1)

For i = 0 To rsteps1

temp(1, i) = concmatrix1(2, i)

Next

updateconcmatrix = temp

End Function

Sub outputdata()

For i = 1 To tottime

Cells(50 + i, 10) = OutputMatrixA(i, 0)

Cells(50 + i, 11) = fluxa(i)

Cells(50 + i, 12) = fluxb(i)

Next

End Sub

105

Figure A.1 Comparison of analytical solution for plane sheet and numerical model for large, thin

hollow cylinder. Dpoly = 0.004 cm2/min, thickness = 1 cm, radius = 500 cm, initial mass = 1 µg.

Figure A.2 Comparison of analytical solution for plane sheet and numerical model for large, thin

hollow cylinder. thickness = 1 cm, radius = 500 cm.

106

Appendix B Additional Data

Figure B.1 δ201Hg in individual samples at different temperatures plotted by fraction remaining in

polymer tubing and reservoir.

-8

-6

-4

-2

0

2

4

6

8

00.20.40.60.81

δ2

01H

g (

‰)

Fraction Remaining

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

107





-6

-4

-2

0

2

4

6

00.20.40.60.81

δ2

00H

g (

‰)

Fraction Remaining

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

-4

-3

-2

-1

0

1

2

3

4

00.20.40.60.81

δ1

99H

g (

‰)

Fraction Remaining

Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

108

Figure B.4 Linearized isotope fractionation of δ201Hg variations during experiments of mercury

permeation of polymer tubing.



-0.010

-0.008

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

0.008

-4 -3 -2 -1 0

ln(1

+δ

20

1H

g/1

00

0)


Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

-0.006

-0.004

-0.002

0.000

0.002

0.004

0.006

-4 -3 -2 -1 0

ln(1

+δ

20

0H

g/1

00

0)


Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

109



Figure B.7 Model mass rate permeating tubing compared to experimental data for different Kpoly at

68C

-0.003

-0.002

-0.001

0.000

0.001

0.002

0.003

-4 -3 -2 -1 0

ln(1

+δ

19

9H

g/1

00

0)


Experiment 1

(80 C)Experiment 2

(68 C)Experiment 3

(23 C)

0

5

10

15

20

25

30

0 100 200 300 400 500

Ma

ss R

ate

(n

g/m

in)

Time (minutes)

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 20

Kpoly = 500

110

Figure B.8 Model mass rate permeating tubing compared to experimental data for different Kpoly at

80C



0

5

10

15

20

25

30

35

0 100 200 300 400

Ma

ss R

ate

(n

g/m

in)

Time (minutes)

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 20

Kpoly = 500

-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 20

Kpoly = 500

111




-10

-8

-6

-4

-2

0

2

4

6

8

10

00.20.40.60.81

δ2

02H

g (

‰)

Fraction Remaining

Experimental Data

Kpoly = 1

Kpoly = 5

Kpoly = 20

Kpoly = 500

-1

0

1

2

3

00.20.40.60.81

δ2

01H

g (

‰)

Fraction Remaining

Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles) *

112



-0.5

0.0

0.5

1.0

1.5

2.0

00.20.40.60.81

δ2

00H

g (

‰)

Fraction Remaining

Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles) *

-0.5

0.0

0.5

1.0

1.5

00.20.40.60.81

δ1

99H

g (

‰)

Fraction Remaining

Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

*

113


diffusion in air.


diffusion in air.

-0.001

0.000

0.001

0.002

0.003

0.004

0.005

-3 -2 -1 0

ln(1

+δ

20

1H

g/1

00

0)


Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

*

-0.001

0.000

0.001

0.002

0.003

-3 -2 -1 0

ln(1

+δ

20

0H

g/1

00

0)


Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

*

114


diffusion in air.

-0.001

0.000

0.001

0.002

-3 -2 -1 0

ln(1

+δ

19

9H

g/1

00

0)


Experiment 1

(2.54 cm needles)

Experiment 2

(2.54 cm needles)

Experiment 3

(3.81 cm needles)

*

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Mercury Isotope Fractionation by Environmental Transport and ... · mercury isotope fractionation by three environmental transport and transformation processes – mercury diffusion