Supplementary material

Validation and modelling of a novel diffusive sampler

for determining concentrations of volatile organic

compounds in air

Pascual Pérez Ballesta1*, Emanuela Grandesso1, Robert A. Field2 Ana Cabrerizo1

1 European Commission, Joint Research Centre, Institute for Environment and Sustainability, Air and Climate

Unit, I-21027 Ispra (VA), Italy.

2 Department of Atmospheric Science, University of Wyoming, Laramie, Wyoming, 82071, USA.

* (European Commission, Joint Research Centre, Institute for Environment and Sustainability, Air and

Climate Unit, Via E. Fermi, 2749, TP 123, I-21027 Ispra (VA), Italy. E-mail: pascual.ballesta@jrc.ec.europa.eu;

Tel.: +39 0332 78 5322

Table of content

Table of content..................................................................................................................................................1

List of Figures.......................................................................................................................................................2

List of Tables ...................................2

S-A.- Dynamic atmosphere generation system....................................................................................................4

S-B.- Analysis of the POD sampler.......................................................................................................................6

S-B.1.- Calibration of the analytical system.....................................................................................................6

S-B.2.- Breakthrough volumes for Carbopack X..............................................................................12

S- C.- Desorption Efficiency................................................................................................................................14

S-D.-Uncertainty of the experimental sampling rates.......................................................................................19

S.E.- Sampling rate and wind velocity................................................................................................................21

S-F.-Uncertainty of the estimated sampling rates.............................................................................................23

S-G.- Additional Figures.....................................................................................................................................30

S-H.- Additional Tables......................................................................................................................................34

List of Figures

Figure S-1.-Wind velocity profile in the wind tunnel...........................................................................................5Figure S- 2.- POD sampler adsorbent cartridge inside of PE glass tubes for analysis...........................................6Figure S- 3.- Experimental set-up for tube loading..............................................................................................7Figure S- 4.- Description of the analytical system for VOC analysis.....................................................................8Figure S- 5.- Chromatogram from a primary reference gas mixture..................................................................10Figure S- 6.- Chromatogram from a POD sampler exposed to ambient air for 24 hours...................................10Figure S- 7.- Chromatogram from a POD blank sample.....................................................................................11Figure S- 8.- Breakthrough volume for C3-C4 hydrocarbons in Carbopack X.....................................................13Figure S- 9.- Correlated desorption isotherm for different compounds according to Eq.S-3 and S-4................16Figure S- 10. - Desorption efficiency and mass of the desorbed analyte in the active standard tube (Standard DE) and the POD adsorbent cartridge (POD-DE)................................................................................................17Figure S- 11.- Sampling rate versus wind velocity for different compounds......................................................22Figure S- 12.- Uncertainty contributions to the sampling rate at reference temperature (20 °C).....................27Figure S- 13.- Uncertainty contributions to the sampling rate at different temperatures.................................28Figure S- 14.- Relative uncertainties for the input variables of the model (Diffusivity, porosity and temperature).....................................................................................................................................................29Figure S- 15.-Sampling rates determined for different diffusion body porosities..............................................30Figure S- 16.- Correlations SR0,avs Da. and SR0,a vs ka..........................................................................................31Figure S- 17.- Experimental versus estimated sampling rates for all the compounds and the whole set tests at different temperatures......................................................................................................................................32Figure S- 18.- Individual compound correlations for concentrations determined by canisters and POD samplers in field conditions...............................................................................................................................33

List of Tables

Table S- 1.- Analytical conditions for desorption and analysis.............................................................................9Table S- 2.- Blank level, method detection and quantification limit of different VOCs for 1 week storage of the adsorbent cartridge inside of a closed POD sampler.........................................................................................12Table S- 3.- Desorption efficiency for different compounds..............................................................................18

Table S- 4.- Wind velocity test series.................................................................................................................21Table S- 5.- Correlation coefficients for Eq.S-9..................................................................................................21Table S- 6.- Diffusion coefficient and Bubble points for the considered compounds and porosities.................25Table S- 7.- Correlation coefficients for Eq. (8)..................................................................................................25Table S- 8.- Correlation coefficients for Eq. (10)................................................................................................26Table S- 9.- Sampling rate and temperature tests.............................................................................................34

S-A.- Dynamic atmosphere generation system

This system can simulate a wide range of diurnal temperature ranges. A fan inside of the chamber allows

wind velocities to be controlled up to 4 m/s inside of a wind tunnel (Figure S-1) where samplers are

placed. A zero air Generator, with a tank reservoir of 150 L, provides, through a purification system

(MCZ, GmbH), a dilution flow of up to 50 l/min controlled by a series of mass flow controllers (Brooks

smart DDE series). Other mass flow controllers allow additional flow from lines with gravimetric

standard cylinders or permeation ovens. The humidifier unit consists of gas-liquid surface contactor,

with liquid and temperature control, located inside of the climatic chamber to avoid condensation

effects.

The static dilution chamber is attached to the dynamic generation system with a ten meter deactivated

capillary column of 0.5 µm internal diameter. This is used to prepare known concentrations of organic

pollutant mixtures in the gas phase. The static dilution system is a 110 L borosilicate glass chamber

equipped with a motor-driven fan for mixing of the supplied air. The pressure (Druck, DPI-260) and

temperature (Azonix, model A1011-A0-RS-RT41) in the chamber are continuously measured. A turbo-

molecular vacuum pump (Alcatel, Drytel-100) is used to evacuate the air from the static dilution

chamber. Injections of liquid VOC mixtures are performed manually with a calibrated 1 L syringeμ

(Hamilton series 7000).

The static dilution VOC mixtures are prepared by using 99.9% high purity solvent analytical standards

(FLUKA, Supelco). These VOC mixtures, at ppm levels and 1.6 bar, flow from the static dilution chamber

at a rate of circa 1 ml/min for a week through the capillary column into the mixing chamber enabling

dilution to ppb levels. Concentrations inside of the exposure chamber are measured by an automatic GC

analyzer connected on-line (Thermal Desorber Unity from Markes International Ltd. and GC Agilent

7890A).

1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 60.06

0.6

6

Position

Win

d ve

locit

y, m

/s

wind direction

Figure S-1.-Wind velocity profile in the wind tunnel

S-B.- Analysis of the POD sampler

The dimensions of the adsorbent cartridge are compatible with a tube of 4 mm internal diameter, thus

allowing easy adaptation of the cartridge to the main desorption systems on the market, e.g. Perkin

Elmer (PE) thermal desorption system, GERSTEL Thermal Desorption System (TDS) or Thermal

Desorption Unit (TDU), MARKES thermal desorption (Figure S- 2).

Figure S- 2.- POD sampler adsorbent cartridge inside of PE glass tubes for analysis

The current analytical conditions correspond to those obtained in a Perkin Elmer thermal desorption

system (TURBOMATRIX) coupled with an Agilent gas chromatograph GC 6890 with a Dean Switch

system and two FID detectors. With this equipment it is possible to cover an analytical range of VOCs

from C2 to C12.

S-B.1.- Calibration of the analytical system

A series of PE glass tubes with 35 mg of Carbopack X are activated and conditioned by thermal

treatment before preparation of the corresponding calibration curves. Tubes are loaded by means of a

mass flow controller with known volumes of a primary reference gas mixture traceable to primary

international standards (i.e., NPL or VSL primary reference gas mixture). The line from the gas cylinder

to the loading tube is kept at 80 °C to prevent losses of the heaviest VOCs by adsorption in the line.

The experimental setup is described in Figure S- 3.

Figure S- 3.- Experimental set-up for tube loading

Typical calibration amounts for individual compounds range from 0 to 2 mg, with loaded volumes from

100 ml to 20 litres, depending on the standard concentration levels. Breakthrough volumes are checked

with a backup tube in series during loading. Lines are heated at 80 °C to avoid adsorption of the heaviest

compounds and the flow is regulated by a mass flow controller. The thermal desorption conditions

correspond to those determined in a Perkin Elmer thermal desorption system (Turbomatrix) operating

DESORPTION STEP

ANALYSIS STEP

TUBE/SAMPLE

TUBE/SAMPLE

COLD TRAP

COLD TRAP

INLET SPLIT

DESORPTION FLOW

OUTLET SPLIT

P1

P2

FID-2

FID-1

HP-Plot Al2O3 - 40 m, 0.32 mm, 8µm

DB-1- 50 m, 0.32 mm, 1.2µm

Restrictor- 0.45 m, 0.1 mm

VALVE ON (0.1’)VALVE OFF (11.7’)

22.5 psi

25 psi

25 ml/min

8 ml/min

under a two-step desorption process and coupled to a double column gas chromatograph system. The

system is shown in Figure S- 4.

Figure S- 4.- Description of the analytical system for VOC analysis

Table S- 1 gives the thermal desorption conditions for the analysis of the adsorbent cartridges

containing Carbopack X. The same conditions are applied to the corresponding active tubes prepared

with the same adsorbent amount.

Table S- 1.- Analytical conditions for desorption and analysis

Turbomatrix TD parameters

Column pressure, psi 25Outlet flow, ml/min 10Desorption flow, ml/min 25Inlet flow, ml/min 0.0 (splitless)Desorption time for the sample tube, min

10

Desorption trap hold time, min 10Cold trap adsorbent VOC mixture cold trap low flowTemperature valve, ºC 225Temperature transfer line, ºC 250Temperature desorption tube, ºC 350Temperature cold trap, ºC -30 to 350GC Analytical conditionsOven initial temperature, ºC 40Initial time, min 5Temperature ramp, ºC/min 6Final temperature, ºC 200Final time, min 15Run time, min 46.67Column 1 HP-Plot Al2O3 M, 40 m, 0.320 µm id,

8µm t.f.Column 2 BP1- 50 m, 0.32 µm i.d., 1.2 µm t.f.Secondary pressure, psi 22.5Restrictor 0.45 m, 0.1µm i.d. FID: H2 flow, ml/min 40FID: Air flow, ml/min 450FID: Makeup flow, N2, ml/min 40

Figure S- 5, Figure S- 6 and Figure S- 7 show the chromatograms from a reference standard, a POD

sampler exposed to ambient air for 24 hours and a field blank, respectively. In these chromatograms

benzene’s peak corresponds to approximately 113, 48 and 1.2 ng, respectively. Table S- 2 shows blank

levels, method detection and quantification limits of different VOCs for 1 week storage of the POD

adsorbent cartridge inside a POD sampler.

Tra ns-2 -b ute ne1-Bu te ne

C is-2 -Bute neN -Pe nta ne

1,3 -b u ta d ie ne

Ac e thyle neN -Buta ne

Iso -Bu ta ne

Tra ns-2 -Pe n te neC is-2 -Pe n te ne

Iso p re ne

2-m e thyl-p e nta ne

He xa ne

Be nze ne

C yc lo -he xa ne

2-m e thyl-he p ta ne

He p ta ne

To lue ne

O c ta ne

Ethyl-b e nze ne

M ,p -xyle ne

O -xyle ne

1,3 ,5 trim e thyl-b e nze ne

1,2 ,4 trim e thyl-b e nze ne

1,2 ,3 trim e thyl-b e nze ne

Figure S- 5.- Chromatogram from a primary reference gas mixture

Isoprene

N-Bu tane

Iso-B utane

Hexane

Benzene

C yclo-hexaneH eptane

Toluene

Ethyl-benzene

M ,p-xylene

O -xylene

Figure S- 6.- Chromatogram from a POD sampler exposed to ambient air for 24 hours

Benzene

Toluene

IsopreneC is-2-Pentene

Acethylene

1-Butene

N-Butane

Figure S- 7.- Chromatogram from a POD blank sample

Table S- 2.- Blank level, method detection and quantification limit of different VOCs for 1 week storage of the adsorbent cartridge

inside of a closed POD sampler

Blank level

Blank’s standard deviation

MDL,24 h sampling

MQL,24 h sampling

pg pg ng/m3 ng/m3

Propene 1843 305 20.2 67.22-Me-Propane 132 33 8.6 28.71-Butene 1926 196 45.0 149.9n-Butane 130 17 4.0 13.21,3-Butadiene 127 32 3.3 11.0Trans-2-Butene 52 11 2.6 8.5Cis-2-Butene 123 123 28.1 93.72-Me-Butane 44 7 1.8 5.91-Pentene 635 91 23.8 79.2n-Pentane 47 6 1.5 4.9Trans-2-Pentene 38 14 3.7 12.4isoprene 134 31 7.8 26.0n-Hexane 80 14 4.1 13.6Benzene 934 325 77.4 258.12,2,4-TriMe-Pentane 92 130 40.5 134.9n-Heptane 76 8 2.4 8.1Toluene 2466 1068 283.3 944.4n-Octane 1784 52 18.7 62.3Ethyl-benzene 148 149 45.3 150.9m,p-Xylene 389 290 91.8 305.9o-Xylene 232 187 58.9 196.51,3,5-TriMe-benzene 481 31 10.8 35.9

S-B.2.- Breakthrough volumes for Carbopack X

No breakthrough (BT) volumes were observed for C5 to C9 hydrocarbons when loaded in Carbopack X

in amounts similar to the one contained in the POD adsorbent cartridge. This was not the case for the ≤

C4 hydrocarbons. Figure S-8 shows the BTs identified for C3-C4 compounds for 0.5 and 5 L of a 4 ppb

concentration level of hydrocarbons on 35 mg of Carbopack X.

Figure S- 8.- Breakthrough volume for C3-C4 hydrocarbons in Carbopack X

No losses of adsorbate were observed for ≥C5 hydrocarbons when tubes were loaded with a maximum

of 2-9 µg/40 mg of Carbopack X. Such an upper limits covered the operative analytical calibration range

of the POD samples.

S- C.- Desorption Efficiency

Desorption efficiencies and desorbed concentration of analyte can be correlated by the isotherm that

relates the equilibrium concentrations between adsorbent and the extraction medium at a particular

temperature.

For VOCs and Carbopack X, Freundlich or Dubinin-Raduskevich isothermal could be applied.

Freundlich isotherm

Cads=r ∙Cads

1n

(S- 1)

Relationship between desorption efficiency, DE, and desorbed concentration of analyte

ln ( DE1−DE )=α+β ∙ ln (Cdes )

(S- 2)

Dubinin-Raduskevich isotherm

ln (Cads )=A+B ∙ ln2(Cdes

C s)

(S- 3)

Relationship between desorption efficiency, DE, and desorbed concentration of analyte1

1 P. Pérez Ballesta, E. González Ferradas, A. Miñana Aznar. Desorption Isotherms of Volatile Organic Compounds Adsorbed on Active Charcoal. Am. Ind. Hyg. Assoc. J., 56, 171-177. 1995

ln ( DE1−DE )=α+β ∙ ln (Cdes )+γ ∙ ln2 (C des )

(S- 4)

where Cads, Cdes are the concentrations of analyte in the adsorbent and in the desorption medium,

respectively. Parameters r, n, A, B, Cs are characterizing the corresponding isotherms. While Alfa, beta

and gamma correspond to the correlation coefficients for the respective equations.

By assuming that a particular isotherm controls the equilibrium concentrations in the standard tube and

in the POD adsorbent cartridge, it is possible to estimate the desorption efficiency by means of the tests

described in this paper. Results of these correlations are shown in Figure S- 9 and Figure S- 10 . Table S-

3 shows desorption efficiencies estimated for other VOCs.

Figure S- 9.- Correlated desorption isotherm for different compounds according to Eq.S-3 and S-4

Figure S- 10. - Desorption efficiency and mass of the desorbed analyte in the active standard tube (Standard DE) and the POD

adsorbent cartridge (POD-DE)

Table S- 3.- Desorption efficiency for different compounds

Compound Range DE, %n-Butane 4- 40 ng > 97% 3 - 8 ng >80 %n-Pentane 5 - 50 ng >98 % 3-12 ng >80 %n-Hexane 6-60 ng >97 % 3- 12 ng > 87 %Heptane 7 - 70 ng >93 % 4- 8 ng > 50 %n-Octane 8-80 ng > 90 % 5 - 9 ng > 76 %2-Methylbutane (i-pentane) 5- 50 ng >97 % 3 - 10 ng >90 %2-methyl-Pentane 3 - 60 ng >99 %2,2,4-Trimethyl-pentane 4 - 80 ng >92 %cis-2-Butene 4-40 ng >96 % 3- 8 ng >80 %trans-2-Butene 4- 40 ng >98 % 2 - 8 ng > 88 %trans-2-Pentene 5-50 ng > 98 % 3-12 ng >87 %1-Pentene 5 - 50 ng >96 % 3 - 12 ng >30 %Isoprene 5 - 50 ng >91 % 3 -12 ng >61 %1,-butadiene 4-40 ng >95 % 2-8 ng >88%

S-D.-Uncertainty of the experimental sampling rates

In each laboratory test, sampling rates, SRi,a, and standard deviations were calculated for each diffusion

body (porosity) and compound. Averaged sampling rates from different tests were characterized by the

standard deviation of the sampling rates determined in each individual test. The relative standard

deviation of the average sampling rate was called inter-coefficient of variation, inter-CVa (%):

SRav ,a=∑i=1

n

[ SRi , a ]n

(S- 5)

inter−CV a (% )=stdev (SR1 , a , SR2 , a ,…,SRn ,a )

SRav ,a∙100

(S- 6)

Therefore, the uncertainty associated with the sampling rate of a compound and porosity for a set of

tests carried out at different concentrations, uSRc,a, is calculated by the following expression:

uSR c, a=√∑i=1

i=n

[σ SRci , a ]2

n + [ stdev (SRc1 , a , SRc2 ,a ,…,SRci , a)]2

(S- 7)

where SRc i ,a and σ SRc i, a are the sampling rate and standard deviation of the sampling rate for the test

carried out at concentration ci and n is the number of tests carried out at different concentrations.

Similarly, the uncertainty associated with the average sampling rate calculated for a range of

temperatures, uSRTi,a, is calculated as follows:

uSRT ,a=√∑i=1

i=n

[σSRT i, a ]2

n +[ stdev (SRT1 , a, SRT2 , a

,…, SRT i , a)]2

(S-8)

where SRT i , a and σ SRT i , a are the sampling rate and sampling rate standard deviation of the test carried

out at temperature Ti and n is the number of tests carried out at different temperatures.

S.E.- Sampling rate and wind velocity

Sampling rates and wind velocity are correlated according to the following equation model2:

SRWV=SRo ∙WV 0.5

a ∙SRo+WV 0.5

(S-9)

Table S- 4 shows the results of three wind velocity tests and Table S- 5 the corresponding correlation

coefficients of the (S-9 for these data. Graphic representation of these results is shown in Figure S- 11.

Table S- 4.- Wind velocity test series

Temp.Exposure

timeRelative humidity

Wind velocity

SR (20 °C) Stdev SR (20 °C) Stdev SR (20 °C) Stdev SR (20 °C) Stdev SR (20 °C) Stdev SR (20 °C) Stdev

°C h % m/s cm3/min cm3/min cm3/min cm3/min cm3/min cm3/min 0.36 9.19 0.24 9.19 0.24 8.38 0.22 7.37 0.17 6.98 0.14 7.04 0.160.37 8.91 0.17 8.91 0.17 8.14 0.13 7.12 0.12 6.77 0.11 6.84 0.110.47 8.99 0.20 8.99 0.20 8.18 0.15 7.17 0.10 6.85 0.04 6.89 0.080.65 8.92 0.25 8.92 0.25 8.12 0.22 7.08 0.18 6.75 0.16 6.83 0.170.88 8.73 0.24 8.73 0.24 7.93 0.23 6.95 0.23 6.64 0.18 6.69 0.201.15 8.84 0.23 8.84 0.23 8.07 0.30 7.04 0.15 6.70 0.20 6.81 0.220.13 8.86 0.56 8.86 0.56 7.98 0.46 7.04 0.42 6.67 0.40 6.77 0.470.15 8.81 0.48 8.81 0.48 7.92 0.44 7.06 0.46 6.68 0.43 6.75 0.380.22 9.23 0.24 9.23 0.24 8.13 0.06 7.23 0.04 6.95 0.08 7.02 0.040.32 8.96 0.26 8.96 0.26 8.22 0.23 7.19 0.37 6.84 0.26 6.89 0.260.40 8.81 0.15 8.81 0.15 7.98 0.08 6.99 0.14 6.62 0.18 6.65 0.220.46 8.99 0.20 8.99 0.20 8.18 0.15 7.17 0.10 6.85 0.04 6.89 0.080.89 8.73 0.24 8.73 0.24 7.93 0.23 6.95 0.23 6.64 0.18 6.69 0.200.95 8.61 1.12 8.61 1.12 7.30 0.42 6.36 0.45 6.23 0.60 6.16 0.461.29 7.91 0.66 7.91 0.66 7.04 0.58 6.00 0.35 5.60 0.04 5.72 0.101.89 8.59 1.17 8.59 1.17 7.40 0.71 6.48 0.72 6.37 0.86 6.30 0.762.71 7.98 0.69 7.98 0.69 7.10 0.61 6.12 0.63 5.88 0.57 5.92 0.553.74 8.41 0.24 8.41 0.24 7.35 0.43 6.43 0.37 6.28 0.11 6.26 0.26

2420

CompoundConc. µg/m3

m,p-xylene o-xylene

53.4

o-xylene 56.4

benzene toluene ethyl-benzene

benzene 85.8

toluene 328.0

ethyl-benzene 62.4

m,p-xylene

50

Table S- 5.- Correlation coefficients for (S-9

Compound Correlation parameters Lo. Conf Limit Up. Conf Limit

benzene

SRo 8.28 7.97 8.59

a -0.004503 -0.007322 -0.001683

toluene

SRo 7.27 6.95 7.60

a -0.007119 -0.010877 -0.003360

ethyl-benzene

SRo 6.33 6.01 6.65

a -0.008774 -0.013675 -0.003872

m,p-xylene

SRo 6.11 5.79 6.42

a -0.008070 -0.013293 -0.002848

o-xylene

SRo 6.12 5.80 6.43

a -0.008659 -0.013773 -0.003546

2 P. Pérez Ballesta, E. González Ferradás, A. Miñana Aznar. Effects of the Diffusion Membrane on Passive Sampling. Environ. Sci. Technol., 27 (10), 2031-2034. 1993.

Level of: 95.0% ( alpha=0.050)

Figure S- 11.- Sampling rate versus wind velocity for different compounds

_____ Correlation curve eq. S-9 ____ Expanded uncertainty of the correlation

S-F.-Uncertainty of the estimated sampling rates

The uncertainty associated with the estimation of the sampling rate on the basis of the diffusivity and

porosity of the diffusion body can be calculated according to a general expression for uncertainty

estimation3:

u f2=∑

i ( ∂ f∂ xi )2

∙ ux i

2 +2∙∑i=1

N−1

∑j=i+1

N

( ∂ f∂ x i )2

∙( ∂ f∂ x j )

2

∙covar (x i ∙ x j¿¿¿)¿¿¿

(S-10)

in which uxi2 represents the variance of the input quantities, xi,,covar (xi ∙ x j) the estimated covariance

associated with xi, xj and N the total number of inputs considered in the function model, f, and if applied

to Eq. (8) the following result is given:

uSRTref ,a

=√Da2 ∙[1−Bbp

C0 ]2

∙ua2+b2∙ [1−Bbp

C0 ]2

∙ ub2+[a0∙ Da−b0 ]2∙ Bbp

2

co4 ∙ uc0

2 +ao2 ∙[1− Bbp

C0 ]2

uDa

2 +¿+[a0 ∙ Da−b0 ]2

co2 uBbp

2 −2 ∙D a∙ b ∙[1−BbpC0 ]

2

∙ covar (a ,b)

(S- 11)

where u2a, u2

b, u2c0, u2

Da, u2Bbp are the corresponding variances of the correlation parameters and the input

variables of diffusivity and bubble point, while covar(a,b) are the covariance between the correlation

coefficient from Eq. (8).

3 JCGM, 2008. “Evaluation of Measurement Data — Guide to the Expression of Uncertainty in Measurement.” International Organization for Standardization Geneva ISBN 50: 134

In a similar way, Eq. (10) provides the following expression for the uncertainty of an estimated sampling

rate on the basis of temperature, bubble point of the diffusion body and a reference sampling rate for a

defined temperature:

uSR T,a=√

uα2 +T2 ∙ uβ

2+T4 ∙ uγ2 +Bbp∙ uδ

2 + Bbp2 ∙ uε2+SRT ref,a ∙ uξ

2+SRT ref ,a2 ∙uθ

2+ T∙SRTref ,a ∙ uϑ2 +T ∙Bbp ∙uμ

2+Bbp∙ SRT ref,a ∙ uπ2 +

++T∙Bbp∙SRT ref,a ∙ uρ

2+ (β+2∙γ∙T+ϑ ∙ SRTref ,a+μ∙Bbp+ρ∙Bbp∙SR Tref ,a )2 ∙ uT2 +

++ (δ+2∙ε∙Bbp+μ∙T+π∙SR Tref ,a +ρ∙T∙SR Tref ,a )2 ∙ uBbp

2 + (ξ+2∙θ∙SRTref ,a +ϑ ∙T+π∙Bbp+ρ∙T∙Bbp )2 ∙ uSR Tref ,a

2 +

+ 2∙∑i=1

13

∑j=i+1

14

(∂ SRT,a

∂ z i )2

∙(∂ SRT,a

∂ z j )2

∙covar ( z i ,∙ z j)

(S- 12)

where z1 to zN corresponds to the correlation coefficients of eq. (10) [α, ,…, ]β ρ

Figure S- 12 and Figure S- 13 show the budget contribution of uncertainties according to (S- 11 and (S-

12, respectively.

Figure S- 14 shows the adopted uncertainties of the input variables for the diffusion model. A constant

standard deviation of 0.57 mbar and 0.3 °C was considered as uncertainty for all porosities and

temperature during the tests. The input uncertainty for the diffusivities of the different compounds was

derived from the bias between the refereed value and the obtained from the optimization of the

correlation parameters in Eqs. (4) and (5).

Table S- 6 shows the values of bubble points and diffusivities considered for each porosity and

compound, respectively. The correlation coefficients for Eqs. (8) and (10) are shown in Table S- 7 and

Table S- 8, respectively.

Table S- 6.- Diffusion coefficient and Bubble points for the considered compounds and porosities

CompoundDiffusion

coefficientcm/s2

Porosityµm

Bubble pointmbars

Pentane 0.0888 0.5 86.95Benzene 0.0916 1 79.23

n-Heptane 0.0782 3 52.07n-Octane 0.0720 5 44.62

Ethyl-benzene 0.0767 10 21.84m,p-Xylene 0.0694 20 13.84

o-Xylene 0.0677Toluene 0.0852

Table S- 7.- Correlation coefficients for Eq. (8).

Parameter Uncertainty

a0 159.34 stdev a0 2.792b0 4.191 Stdev b0 0.221c0 100.97 Stdev c0 0.094

cov (a0 ,b0) 0.0044

Table S- 8.- Correlation coefficients for Eq. (10)

Coefficient

Value UncertaintyStandard deviation

α 16.78944 0.242993β 0.17647 0.001027γ 0.00032 0.000005δ -0.38920 0.005000ε 0.00225 0.000027

ξ -3.85584 0.058247

θ 0.31163 0.003422ϑ -0.01735 0.000132μ -0.00190 0.000012π 0.05237 0.000593ρ 0.00001 0.000002

Figure S- 12.- Uncertainty contributions to the sampling rate at reference temperature (20 °C).

Figure S- 13.- Uncertainty contributions to the sampling rate at different temperatures

Figure S- 14.- Relative uncertainties for the input variables of the model (Diffusivity, porosity and temperature)

S-G.- Additional Figures

Figure S- 15.-Sampling rates determined for different diffusion body porosities

Figure S- 16.- Correlations SR0,avs Da. and SR0,a vs ka

Figure S- 17.- Experimental versus estimated sampling rates for all the compounds and the whole set tests at different temperatures.

Figure S- 18.- Individual compound correlations for concentrations determined by canisters and POD samplers in field conditions.

S-H.- Additional Tables

Table S- 9.- Sampling rate and temperature tests

Temperature Exposure time Wind velocity SR (20 °C) SR (20 °C) SR (20 °C)°C h m/s cm3/min cm3/min cm3/min

n-pentane 5.85 8.49 0.37 5.42 0.19 2.4 0.04benzene 5.01 9.44 0.47 5.78 0.19 2.57 0.04n-heptane 1.25 - - - - - -toluene 9.88 6.67 0.2 4.47 0.34 2.08 0.05n-octane 1.05 - - 3.44 0.3 1.67 0.09ethyl-benzene 2.31 3.37 0.27 2.75 0.58 1.51 0.14m,p-xylene 1.98 2.88 0.18 2.21 0.63 1.31 0.18o-xylene 2.29 3.02 0.09 2.35 0.62 1.38 0.19n-pentane 5.74 8.11 0.09 5.33 0.09 2.43 0.03benzene 4.96 9.18 0.28 5.8 0.11 2.62 0.09n-heptane 1.21 5.91 0.3 - 0.37 - 0.56toluene 9.72 6.54 0.26 4.53 0.08 2.08 0.08n-octane 1 4.71 0.32 3.46 0.18 1.62 0.03ethyl-benzene 2.2 3.29 0.48 2.89 0.43 1.39 0.11m,p-xylene 1.88 3.05 0.32 2.55 0.39 1.35 0.07o-xylene 2.15 3.16 0.34 2.69 0.44 1.36 0.09n-pentane 6.22 8.35 0.27 5.07 0.14 2.2 0.12benzene 5.23 9.32 0.35 5.69 0.14 2.32 0.18n-heptane 1.31 - - 4.36 0.48 1.7 0.22toluene 10.23 7.39 0.72 4.27 0.25 1.77 0.12n-octane 1.17 4.92 0.95 2.88 0.22 1.29 0.07ethyl-benzene 1.98 6.13 2.07 3.16 0.5 1.5 0.17m,p-xylene 2.08 4.66 1.87 2.19 0.35 1.06 0.19o-xylene 2.47 4.68 1.92 2.19 0.36 1.08 0.17n-pentane 1.88 - 5.31 7.37 0.08 5.12 0.5 2.4 0.98benzene 1.59 - 4.31 8.8 1.29 5.83 0.44 2.69 0.07n-heptane 0.38 - 1.08 5.72 0.73 3.62 0.3 1.81 0.09toluene 2.92 - 8.34 6.73 0.95 4.26 0.28 2.06 0.1n-octane 0.36 - 0.93 4.43 0.71 2.79 0.29 1.49 0.1ethyl-benzene 0.68 - 1.99 4.4 0.27 - - 1.53 0.12m,p-xylene 0.58 - 1.75 4.2 0.56 2.82 0.24 1.53 0.15o-xylene 0.76 - 2.02 3.95 0.52 2.43 0.23 1.5 0.13n-pentane 5.65 7.36 0.79 4.96 0.84 2.02 0.15benzene 4.73 8.74 0.53 5.85 0.87 2.25 0.23n-heptane 1.13 5.61 0.31 3.33 0.48 1.4 0.14toluene 9.1 5.92 0.39 3.76 0.46 1.56 0.12n-octane 0.93 3.88 0.35 2.24 0.54 - -ethyl-benzene 2.06 - - - - - -m,p-xylene 1.78 - - 1.86 0.63 1.04 0.14o-xylene 1.47 3.75 0.79 2.51 0.79 1.42 0.2n-pentane 2.31 - 31.16 7.96 0.55 5.06 0.35 2.2 0.11benzene 1.85- 26.4 8.88 0.61 5.54 0.41 2.39 0.14n-heptane 0.49 - 6.52 6.63 0.38 4.17 0.29 1.8 0.08toluene 3.49 - 51.02 7.69 0.51 4.85 0.39 2.07 0.15n-octane 0.48 - 6.46 5.79 0.45 3.66 0.33 1.58 0.13ethyl-benzene 0.52 -12.21 6.41 0.55 4.06 0.44 1.73 0.19m,p-xylene 0.93 - 10.62 5.96 0.58 3.33 0.78 1.47 0.31o-xylene 1.08 - 12.14 5.84 0.72 3.56 0.39 1.57 0.26n-pentane 5.09 8.08 0.23 5.45 0.18 2.38 0.08benzene 4.38 9.1 0.26 6.14 0.25 2.62 0.08n-heptane 1.2 6.13 0.29 5.02 1.58 1.66 0.06toluene 8.47 7.97 0.25 5.15 0.13 2.14 0.06n-octane 0.93 5.88 0.23 3.71 0.15 1.58 0.07ethyl-benzene 2.11 6.53 0.43 4.07 0.11 1.65 0.03m,p-xylene 1.99 5.92 0.58 3.9 0.13 1.66 0.07o-xylene 2.22 5.62 0.53 4 0.1 1.56 0.04n-pentane 17.73 - - - - - -benzene 13.4 8.63 0.26 5.4 0.38 2.45 0.09n-heptane 3.24 7.13 0.12 4.33 0.28 1.88 0.04toluene 25.05 8.12 0.12 4.92 0.29 2.15 0.07n-octane 3.04 6.34 0.11 3.84 0.21 1.66 0.09ethyl-benzene 5.82 6.94 0.37 4.18 0.18 1.78 0.13m,p-xylene 5.84 6.6 0.49 3.91 0.18 1.67 0.21o-xylene 5.72 6.69 0.48 3.63 0.18 1.74 0.22n-pentane 4.2 - 1.07 4.89 0.32 2.33 0.17benzene 4.7 8.78 0.62 6.79 0.26 2.43 0.36n-heptane 1.06 - - - - - -toluene 8.33 8.1 0.5 5 0.3 1.99 0.16n-octane 0.87 6.28 0.5 4.25 0.39 1.63 0.24ethyl-benzene 3.11 6.96 0.66 4.33 0.36 1.63 0.21m,p-xylene 5.64 6.66 0.85 4.56 0.43 1.53 0.27o-xylene 3 6.8 0.94 4.82 0.52 1.61 0.32

40.5 24.18 0.5 67.7

30 23.9 0.5 50.1

800.523.1735

10.2

20 24 0.5 50

51.70.522.4

-4.8 22.4 0.5 9.4

25-50 0.5~ 24 5.1

-28 24 0.5 11

8.50.524-14.5

Compound Concentration µg/m3 Relative humidity, % Stdev Stdev Stdev

Porosity (µm) Porosity (µm) Porosity (µm)20 5 1