92
Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia Breitkopf Institut für Technische Chemie Universität Leipzig

TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

  • Upload
    others

  • View
    0

  • Download
    0

Embed Size (px)

Citation preview

Page 1: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Lecture Series at Fritz-Haber-Institute Berlin„Modern Methods in Heterogeneous Catalysis“

24.11.2006

TAPTemporal Analysis of Products

Cornelia BreitkopfInstitut für Technische Chemie

Universität Leipzig

Page 2: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Transient methods are a powerful tool for gaining insights into the mechanisms of

complex catalytic reactions.

Page 3: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Dimensions in Heterogeneous Catalysis

Page 4: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Macrokinetics and Microkinetics

Page 5: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Kinetic measurements

Complexity of heterogeneously catalyzed reactions –Macrokinetics and Microkinetics

O. Deutschmann, XXXIV. Jahrestreffen Deutscher Katalytiker/ Fachtreffen Reaktionstechnik, Weimar 21.-23.3.2001

Page 6: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Kinetic measurements in practise

Tasks of lab investigations

o catalyst preparation

o catalyst screening

o activity

o selectivity

o stability

o scale-up

o process optimization

Laboratory reactors

o microcatalytic pulse reactor

o gaschromatographic reactor

o single pellet diffusion reactor

o catalytic fixed bed reactor

o recycle reactor

o TAP

Page 7: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Questions

• What distinguishes TAP from other lab reactors ?

• Which information do we need to understand TAP ?

• How can TAP applied in heterogeneous chemistry?

Page 8: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Outline

• Steady state and unsteady state experiments

• Diffusion and mathematics

• TAP-Method and modeling

• Applications

Page 9: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Recommended literature and books

• Gleaves JT et al. Appl. Cat. A 160 (1997) 55-88.• Phanawadee P. PhD thesis Washington 1997.• Chen S. PhD thesis Washington 1996.• Yablonsky GS et al. J. Catal. 216 (2003) 120-134.• Gleaves JT et al. Cat. Rev.-Sci. Eng. 30 (1988) 49-116.• Dumesic JA et al (Ed) „The Microkinetics of Heterogeneous Catalysis“ ACS, Washington 1993.• Stoltze P. Progress in Surface Science 65 (2000) 65-150.• Kobayashi H et al.. Cat. Rev.-Sci. Eng. 10 (1974) 139-176.• Engel T, Ert G. Adv. Catal. 28 (1979) 1-78.• Ertl G. The dynamics of interactions between molecules and surfaces. Berichte Bunsengesellschaft

für Physikalische Chemie 99 (1995) 1282.• Creten G et al. J. Catal. 154 (1995) 151-152.• Haber J. 1983. Concepts in catalysis by transition metal oxides. Bonelle JP et al. (Ed.) D. Reidel

Publishing Company. Surface Properties and Catalysis by Nonmetals. 45, 1-45.• Hinrichsen O. DECHEMA-Kurs „Angewandte Heterogene Katalyse“, Bochum 2001.• Dewaele O, Froment GF. J. Catal. 184 (1999) 499-513.• Christoffel EG „Laboratory Studies of Heterogeneous Catalytic Processes“ Stud.Surf.Sci.Catal. 42. • Müller-Erlwein E. Chemische Reaktionstechnik, Teubner Stuttgart-Leipzig, 1998, 237.

Page 10: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

…continued

Jens Hagen

- Emig G., Klemm E.. Technische Chemie. Springer 2005.- Baerns M., Behr A., Brehm A., Gmehling J., Hofmann H., Onken U., Renken A.. Technische Chemie, Viley VCH 2006.

Page 11: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Steady state and unsteady state experiments

Page 12: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Kinetic investigations

Constructing of a mathematical model

Evaluation of thereaction mechanism

Parameter estimation

How to do…?

• Steady-state or unsteady-state experiment ?• Quantitative evaluation of kinetic data ?

Page 13: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Steady-state experiments

• Most common reaction technique used in heterogeneous catalysis

• Achieved by operation such that temperature, pressure, concentration, and flow rate at anypoint in the reactor is time invariant

• Access to activity, selectivity, reaction order, activation energy

Page 14: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Steady-state experiments

• Advantages:- Easy to build and operate- Results can be described with mathematical

models based on algebraic equations- Most industrial processes are operated under

steady-state conditions

• Disadvantages:- Provide global kinetic parameters, limited

information on individual reaction steps- Interpretations often based on „simple“

assumptions

Page 15: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Unsteady-state experiments

• Transient techniques provide information on

- Reaction intermediates (pulse response) (Gleaves 1988)

- Reaction sequence in a multistep reaction(Kobayashi 1975)

- Rate constants of elementary steps(Ertl 1979, Creten 1995)

Page 16: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Unsteady-state experiments

• Transient techniques provide information on

- Investigation of complex kinetic phenomena(oscillating chemical reactions, hysteresis) that are not observable under steady-stateconditions

- Probe of catalyst surfaces that are not easilyobserved under steady-state conditions(oxidation catalysis) (Haber 1983)

Page 17: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Unsteady-state experiments

• Disadvantages

- Not easy to build up, expensive

- Main problem: theory is very complex

Page 18: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Steady-state and transient methods

Steady-state methods

• measure overall performance

• give integrated picture of reaction system

• have minimum reactor residence time of 1 s

Transient methods

• give information on individual steps

• operate in millisecond time regime; resolution increase

Page 19: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Pulse methods

• response to pertubations describe mathematically thetransient behaviour

• evaluation of rate parameters from responsemeasurements, such as mass transfer coefficients, diffusivities, and chemical kinetic constants

• use of: - fixed-bed (column) chromatography- isotope technique- slurry adsorber- single-pellet

Page 20: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Pulse methods

Page 21: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Diffusion and mathematics

Page 22: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Diffusion in porous solids

Characteristic value to characterize the influence of internal transport phenomena of heterogeneous reactionson the surface between a fluid phase and a porous solid is DaII (see textbooks)

DaII = f (k, cexternal, lcharacteristic, Deff)

if fluid is gaseous: diffusion in pores depends ondimensions of pore system

Page 23: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Diffusion mechanisms

Transport mechanisms in porous solids

Pore diffusion dependingon pore diameter

Page 24: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Molecular diffusion

Atkins

Page 25: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Molecular diffusion

• mixture of two components A and B,concentration gradient (in one dimension y): under steady-state conditions the diffusional flow of onecomponent is described by 1. Fick law

• DAB ...binary molecular diffusion coefficient of component A diffusing through B

• DAB = f( molecular properties of A and B, T, c or p)

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

dydcDJ A

ABA

Page 26: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

General view to transport equations for gases

Transport

Mass Heat Energy

Flux of mass density

Flux ofheat density

Flux of momentum

⎟⎠⎞

⎜⎝⎛−=

dzdcDj in ⎟

⎠⎞

⎜⎝⎛−=

dzdTjQ λ ⎟⎟

⎞⎜⎜⎝

⎛−=

dyduj z

P η

Fourier´s Law Newton´s Law(viscosity)

Fick´s Law

Page 27: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

General view to transport equations for gases

Atkins

Page 28: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Molecular diffusion coefficient for gases

• Hirschfelder/Curtiss/Bird oder Chapman-Enskog relationfor gases at low T, p (± 10% accuracy; extrapolation possible)

122

,,

,,3

,2

001834.0 −

Ω

+

= smp

MMMM

TD

DAB

BrAr

BrAr

gsAB σ

constantsforcetorespectwithintegralCollisionΩBandAgasesoffactorcollisionAverageσ

BandAmoleculesofmassesmolecularRelativeM,M[bar] Pressure p

[K]eTemperaturT

D

2AB

Br,Ar,

Ω = f(kB*T / εAB) kB…Boltzmann constantεAB..force constant(see tables in textbooks)

Page 29: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Molecular diffusion coefficient for gases

Ω = f( kB*T / εAB)

Page 30: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Knudsen diffusion

• under low pressure conditions and/or for small pores:collision of gas with pore wall > collision of gas with gas

• mean free path length of molecule > pore diameterΛ …mean free path lengthσ2…molecular cross-sectionV… gas molar volume at p

• NA/V at 298 K : cges ≈ 3.1019 *p (molecules/cm3) (dimension of p 105 Pa)

• mean free path length with typical σ (9-20*10-16 cm2)

ANV

221πσ

)(102

nmp

≅Λ

Page 31: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Knudsen diffusion

)(102

nmp

≅Λ

• Conditions for Knudsen diffusion

dpore [nm] <1000 <100 <10 <2p [bar] 0.1 1 10 50

Page 32: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Knudsen diffusion

• Knudsen flow through one zylindrical pore

• for porous solids, the relative pore volume εb and thetortuousity factor τK have to be considered

• estimation of τ is a complex procedure (see literature)

)01.0,293(1083

26

, MPaKats

mMRTd

D piK

−≈=π

MRTd

D p

K

PiK

eff

πτε 8

3, = effective diffusion coefficient

Page 33: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Effective diffusion coefficients

• diffusional flow in the pores may be described byan effective diffusion coefficient

• relation to surface: surface of pore mouths is representingonly a part of the outer surface of a particle

• pores are not ideally cylindrical

• pores are connected by a network

ε

τ

Page 34: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Characterization of porous structures

• Porosity

• Pore radius, pore diameter• Pore radius distribution, -density

• Specific surface area• Tortuousity factor

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡kgm

mm 3

3

3

,mass- volume,total

volumepore

p

ppp

r

rpp dr

rHdrhrdrhrH

p

p

)()(;)()(

min,

== ∫

Page 35: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Transition region of diffusion

• for heterogeneous reactions in a porous solid, theconditions of pressure or pore diameter may be such that the system is between Knudsen and moleculardiffusion

• mean free path length ≈ pore diameter

• both equations for DM and DKn apply

KnM* D

1D1

D1

+=

Page 36: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

• for porous solids experimental evaluation of diffusioncoefficients

Knudsen and molecular diffusion

Emig, Klemm

Page 37: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Background - Mathematics

• Delta function f(x) = δ (x-a)

- functional which acts on elements of a function

- integral

- multiplication with a function f(x)

yxforayxa

yaxdtat

y

x

<<<<<

⎩⎨⎧

=−∫ ,01

)(δ

∫+∞

∞−

=− )()()( afdxaxxf δ

Page 38: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Background - Mathematics

• Delta function

- graphical representation as „Sprungfunktion“ (limes)

- graphical representation as „Pulsfunktion“

x

u(x-a)

1

a

)(sin)(

1lim)( axnax

axn

−−

=−∞→ π

δ

)()( axdx

axdu−=

− δ

1

x

u(t-a)

a

∫⎩⎨⎧

=−01

)( dtatδ

Page 39: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Background - Mathematics

• Laplace transformation- aim: transformation of differential and integral

expressions into algebraic expressions- definition

- examplesdttFesf ts )()(

0∫∞

−=

[ ]s

es

dteLsf tsts 111)(00

=−===∞

−∞

−∫

[ ]s

dteeeLsf ttst

−=== ∫

∞−

ααα 1)(

0

Page 40: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – method and modeling

Page 41: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Transient experiments

• Transients are introduced into a system byvarying one or more state variables (p, T, c, flow)

• Examples:

- Molecular beam experimentspressure change

- Temperature-programmed experimentstemperature change

- Step change experimentsconcentration change

Page 42: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – A transient technique

• The key feature which distinguishes it from otherpulse experiments is that no carrier gas is usedand, gas transport is the result of a pressuregradient.

• At low pulse intensities the total gas pressure isvery small, and gas transport occurs via Knudsen diffusion only.

• Pulse residence time under vacuum conditions ismuch shorter than in conventional pulse experiments. Thus a high time resolution isachievable.

Page 43: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Features

• Extraction of kinetic parameters differs compared to steady-state and surface science experiments

- Steady-state: kinetic information is extracted fromthe transport-kinetics data by experimentallyeliminating effects of transport

- Surface science: gas phase is eliminated

- In TAP pulse experiments gas transport is noteliminated. The pulse response data provides in-formation on the transport and kinetic parameters.

Page 44: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Features

• TAP pulse experiments are state-defining

- Typical pulse contains ≈ 1013 – 1014 moleculesor 1010 - 109 moles

- Example:

- Sulfated zirconia: 100 m2/g with 3 wt-% S,5*1018 S/m2

- 1 pulse of n-butane: 1*1014 molecules- per pulse 1/50000 of surface addressed

Page 45: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – System hardware

Simplified schematic of a TAP pulse response experiment

DetectorGas pulseReaction zone

• Injection of a narrow gas pulse into an evacuated microreactor

• Gas pulses travel through the reactor• Gas molecules (reactant and product)

are monitored as a function of time and produce a transient response at the MS

Page 46: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – System hardware

Page 47: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – System hardware

Page 48: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – System hardware

1) High speed pulse valve2) Pulse valve manifold3) Microreactor4) Mass spectrometer5) Vacuum valve6) Manual flow valve7) Mosfet switch

Page 49: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Response curves

Typical pulse response experimental outputs

Page 50: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Multipulse experiment

• Key features of input:- typical pulse intensity rangefrom 1013 to 1017

molecules/pulse- pulse width 150-250 µs- pulse rates 1-50 s-1

• Key features of output:- different products havedifferent responses- individual product responsecan change with pulse number

Page 51: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Pump probe experiment

• Key features of input:- different reaction mixturesare introduced sequentiallyfrom separate pulse valves

• Key features of output:- output transient responsespectrum coincides withboth valve inputs

Page 52: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transient response data

In contrast to traditional kinetic methods, that measureconcentrations, the observable quantity in TAP pulse response experiments is the time dependent gas flowescaping from the outlet of the microreactor.

The outlet flow is measured with a MS (QMS) that detectsindividual components of the flow with great sensitivity.

The composition of the flow provides information on thetypes of chemical transformation in the microreactor.

The time dependence of the flow contains information on gas transport and kinetics.

Page 53: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Theory

Goal

• Interpretation of pulse response data- determine typical processes- find parameters for these processes- develop a model

• Analyzation of experiments that provideparameters of diffusion, irreversible adsorption or reaction and reversible reaction

Page 54: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – General models

Currently there are three basic models in applicationbased on partial-differential equations.

- One-zone-model- Three-zone-model- Thin-zone-model

The mathematical framework for the one-zone-modelwas first published in 1988 (Gleaves).

Basic assumptions of one-zone-model:- catalyst and inert particle bed is uniform- no radial gradient of concentration in the bed- no temperature gradient (axial or radial)- diffusivity of each gas is constant

Page 55: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Gas transport model

The gas transport is the result of Knudsen diffusion.

An important characteristic of this tranport process is thatthe diffusivities of the individual components of a gas mixture are independent of the presssure or the compositionof the mixture.

De,i …effective Knudsen diffusivityMi …molecular weightTi …temperature1,2 …gas 1, gas 2

2

22

1

11 T

MD

TM

D ee =

Page 56: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

(1) Diffusion only case –Mass balance for a non-reacting gas A transported byKnudsen diffusion

CA … concentration of gas A (mol/cm3)DeA … effective Knudsen diffusivity of

gas A (cm2/s)t … time (s)z … axial coordinate (cm)εb … fractional voidage of the packed

bed in the reactor

2

2

zCD

tC A

eAA

b ∂∂

=∂∂ε

Page 57: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

The equation can be solved using different sets of initial and boundary conditions that correspond to different physical situations.

initial conditions: 0 ≤ z ≤ L , t = 0 , A

NC

b

pAzA ε

δ=

0=∂∂

zCAboundary conditions: z = 0 ,

z = L , 0=AC

NpA … number of moles of gas A in one pulseA … cross-sectional area of the reactor (cm2)L … length of the reactor (cm)

Page 58: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

The gas flow at the reactor exit FA (mol/s) is described by

LzA

eAA zCDAF =∂∂

=

and the gas flux (mol/cm2 s) by

AFA=AFlux

To solve for the gas flow it is useful to express initialand boundary conditions in terms of dimensionlessparameters.

Page 59: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Transport model

Use of dimensionless parameters

… dimensionless axial coordinate

… dimensionless concentration

… dimensionless time

Lz

LANCC

bPA

AA ε=

2LDt

b

eA

ετ =

Page 60: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

Dimensionless form of mass balance

2

2

ξτ ∂∂

=∂∂ AA CC initial conditions: 0 ≤ ξ ≤ 1 , t = 0 , ξδ=AC

boundary conditions: ξ = 0 ,ξ = 1 ,

0=∂∂ξ

AC

0=AC

Solution:- analytical a) method of separation of variables

b) Laplace transformation- numerical for more complex problems

Page 61: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

Method of separation of variables:

solution for dimensionless concentration

( ) ( )τππξτξ 22

0

)5.0(exp)5.0(cos2),( +−+= ∑∞

=

nnCn

A

solution for dimensionless flow rate

( ) ( )τππξπξτξτξ 22

0)5.0(exp)5.0(sin)12(),(),( +−++=

∂∂

−= ∑∞

=

nnnCFn

AA

dimensionless flow rate at the exit (ξ=1)

( )τππ 22

0)5.0(exp)12()1( +−+−= ∑

=

nnFn

nA

Page 62: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

( )τππ 22

0)5.0(exp)12()1( +−+−= ∑

=

nnFn

nA

Expression for the dimensionless exit flow rate as a function of dimensionless time

Standard diffusion curve

For any TAP pulse response experiment that involves onlygas transport, the plot of the dimensionless exit flow rateversus dimensionless time will give the same curveregardless the gas, reactor length, particle size, or reactortemperature.

Page 63: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

Due to initial condition the surface area under SDC is equal to unity – flow rate in dimensional form

⎟⎟⎠

⎞⎜⎜⎝

⎛+−+−= ∑

=2

22

02 )5.0(exp)12()1(

LDtnn

LD

NF

b

eA

n

n

b

eA

pA

A

επ

επ

An important property of this dimensional dependenceis that its shape is independent on the pulse intensity ifthe process occurs in the Knudsen regime.

Page 64: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

⎟⎟⎠

⎞⎜⎜⎝

⎛+−+−= ∑

=2

22

02 )5.0(exp)12()1(

LDtnn

LD

NF

b

eA

n

n

b

eA

pA

A

επ

επ

Characteristics of standard diffusion curve

… peak maximum

… corresponding height

… „fingerprint“ for Knudsen regime

eA

bpp D

Lt2

61,

61 ετ ==

2, 85.1,85.1L

DHFb

eAppA ε==

31.0, ≈= ppppA tHF τ

Page 65: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport model

a) Standard diffusion curve showing key time characteristics and the criterion for Knudsen diffusion

b) Comparison of standard curve with experimental inert gas curveover inert packed bed

Page 66: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport + adsorption model

(2) Diffusion + irreversible adsorption

(adsorption is first order in gas concentration)

AabvsA

eAA

b CkSazCD

tC )1(2

2

εε −−∂∂

=∂∂

AaA Ck

t=

∂∂θ

as … surface concentration of activesites (mol/cm2 of catalyst)

ka … adsorption rate constant(cm3 of gas/mol s)

Sv … surface area of catalyst per volume of catalyst (cm-1)

θA … fractional surface coverage of A

Page 67: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Transport + adsorption model

(2) Diffusion + irreversible adsorption

Flow rate FA at reactor exit

⎟⎟⎠

⎞⎜⎜⎝

⎛+−+−−= ∑

=2

22

0

´2 )5.0(exp)12()1()exp(

LDtnntk

LD

NF

b

eA

n

na

b

eA

pA

A

επ

επ

withb

abvsa

kSakε

ε )1(´ −=

Exit flow curve for diffusion+irreversible adsorption- is smaller than SDC by a factor of exp(-ka´t)- is always placed „inside“ the SDC (fingerprint)

Page 68: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Transport + adsorption model

Exit flow curve for the diffusion+irreversible adsorption case

Comparison of irreversible adsorptioncurves with standard diffusion curve(A) ka=0 (SDC), (B) ka=3 (C) ka=10

Page 69: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport and adsorption model

(3) Diffusion + reversible adsorption

Mass balances- for component A in gas phase

)()1(2

2

AdAabvsA

eAA

b kCkSazCD

tC θεε −−−

∂∂

=∂∂

- for component A on the catalyst surface

AdAaA kCk

tθθ

−=∂∂

kd …desorption rate constant (s-1)

Page 70: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Transport + adsorption model

Exit flow curve for the diffusion+reversible adsorption case

Comparison of reversible adsorptioncurves with standard diffusion curve(A) ka=0 (SDC), (B) ka=20, kd=20 (C) ka=20, kd=5

Page 71: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport, adsorption, reaction

(3) Diffusion + reversible adsorption + irreversible reactionA(gas) B(gas)

A(ads) B(ads)kr

)()1(2

2

AdAAaAbvsA

eAA

b kCkSazCD

tC θεε −−−

∂∂

=∂∂

ArAdAAaAA kkCk

tθθθ

−−=∂∂

)()1(2

2

BdBBaBbvsB

eBB

b kCkSazCD

tC θεε −−−

∂∂

=∂∂

BdBBdBArB kCkkt

θθθ+−=

∂∂

Page 72: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport, adsorption, reaction

(3) Diffusion + reversible adsorption + irreversible reaction

The initial and boundary conditions used in thetransport-only case can be applied to thetransport+reaction case as well.

Initial condition t = 0 , CA = 0

Inlet boundary condition )(,0 1,1, t

zC

Dz AeA δ=

∂∂

−=

Page 73: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Transport, adsorption, reaction

(3) Diffusion + reversible adsorption + irreversible reaction

)(1,1, t

zC

D AeA δ=

∂∂

The inlet flux is respresented by a delta function. With this combination, analytical solutions in theLaplace-domain can be easily derived when theset of differential equations that describe the modelis linear.

Page 74: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Characteristic values

Use of dimensionless parameters

eA

baa D

Lkk2

´ ε= dimensionless apparent adsorptionrate constant

b

abvsa

kSakε

ε )1(´ −=with

ka´ contains:

- the kinetic characteristics of the active site (ka)- the structural characteristics of the wholecatalytic system

b

bvs Saε

ε )1( −

Page 75: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Extended models

Three-zone-model

Additional boundary conditions between the different zones have to be applied

catalystinert inert

zone 1 zone 2 zone 3

pulse outcome to QMS

Evaluation of curve shapes and „fingerprints“ arebasicly the same as for the one-zone-model

Page 76: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Theory

Moment-based quantitative descriptionof TAP-experiments

• idea behind: observed TAP data consist of a set of exitflow rates versus time dependencies

• analytical solutions in integral form can be usuallyobtained

• analysis of some integral characteristics (moments) of theexit flow rate

• moments reflect important primary features of theobservations

Page 77: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Theory - Moments

• moment Mn of the exit flow rate (i.e. not of concentration)

n…order of moment

• representation in dimensionless form

dttFtMt

nn )(

0∫=

)/(with 2

0 eAbA

nn DL

tdFmε

τττ == ∫∞

Page 78: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Theory - Moments

Application to TAP experiments:- for irreversible adsorption / reaction

DaI … Damköhler number I

- mean dimensionless residence time

eA

baI

I DLkDa

DaXm

0 withcosh

11 ε==−=

[ ]Dif

n I

n Ires

DanBnADanB

nA

mm ττ

∑∞

=

=

+

+==

0

0

0

1

)()(

)()(

)12()1()( +−= nnnA22)5.0()( π+= nnB

Ae

bDif D

L

,

2ετ =

Page 79: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Applications

Page 80: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Examples

Mechanism and Kinetics of the Adsorption and Combustionof Methane on Ni/Al2O3 and NiO/Al2O3 (Dewaele et al. 1999)

- Supported Ni catalysts for steam reforming of natural gasto synthesis gas

- Combination of TPR with single pulse experiments

Page 81: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Examples

Selective oxidation of n-butane to maleic anhydride (MA) over vanadium phosphorous oxide (VPO)

(Gleaves et al. 1997)

• important heterogeneous selective oxidation• complex reaction (electron transfer, fission of C-H-bonds, addition of oxygen, ring closure)

• literature: (VO)2P2O7-lattice as active-selective phase, but itis not clear how the lattice supplies the oxygen

- possible involvation of oxygen adspecies adsorbed on vanadium surface sites

- possible involvation of bulk oxygen- possibly other crystal phases are active

Page 82: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Examples

Selective oxidation of n-butane to maleic anhydride (MA) over vanadium phosphorous oxide (VPO)

• Steady-state kinetic studies yielded different rate expressions and kinetic parameters – this may be relatedto differences in c. composition, c. structure, c. oxydationstate, etc. no unique information

• Aim of TAP investigations:Relate changes in kinetic dependencies to changes inthe catalyst

• How to do ? Systematic alteration of the state of thecatalyst and measuring kinetic dependencies

Page 83: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Examples

Selective oxidation of n-butane to maleic anhydride (MA) overvanadium phosphorous oxide (VPO)

Kinetics of n-butane conversion over VPO in the absenceof gas phase oxygen

- n-butane curve lies completelywithin the generated diffusioncurve irreversible process

- initial step is irreversible (fissureof CC or CH bond)

Page 84: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP - Examples

Selective oxidation of n-butane to maleic anhydride (MA) overvanadium phosphorous oxide (VPO)

Kinetics of n-butane conversion on oxygen-treated VPO

- values of apparent activationenergy is strongly dependenton the VPO oxidation state

- decreasing number of activecenters

- TAP + Raman: V4+ V5+Arrhenius plots for pulsed n-butane conversionover an oxygen-treated VPO catalyst sampleas a function of oxidation state

Page 85: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – sulfated zirconia (SZ)

TAP investiagtions on sulfated zirconias

C. Breitkopf. J. Mol. Catal. A: Chem. 226 (2005) 269.

X. Li, K. Nagaoka, L. Simon, J.A. Lercher, S. Wrabetz, F.C. Jentoft, C. Breitkopf, S. Matysik, H. Papp. J. Catal. 230 (2005) 214-225.

C. Breitkopf, S. Matysik, H. Papp. Appl. Catal. A: Gen. 301 (2006) 1.

C. Breitkopf, H. Papp. Proceedings of The 1st International Conference on Diffusion in Solids and Liquids DSL-2005, July 6-8, 2005, Aveiro, Portugal, 67. (oral presentation)

Page 86: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – Investigation of poisoned samples

Comparison of active sample Kat1 with samples of Na-modified surfaces

3 % of active centres poisoned40 % of active centres poisonedall centres poisoned

Sulfation Step: 5.7x10-3 mol (NH4)2SO4 Kat1

5x10-5 mol Na2SO4 + 5.7x10-3 mol (NH4)2SO4 SZ-Na15x10-4 mol Na2SO4 + 5.2x10-3 mol (NH4)2SO4 SZ-Na25x10-3 mol Na2SO4 + 0.7x10-3 mol (NH4)2SO4 SZ-Na3

Calcination @ 873 K for 3 h

Page 87: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Characterization

Sample Kat1 SZ-Na1 SZ-Na2 SZ-Na3

BET [m2/g] 103 76 45 10

Pore diameter [Å] 35 50 94 135

Pore volume[cm3/g]

0.08 0.11 0.11 0.04

SO4 content w.% 9.0 9.9 7.5 5.1

S atoms/m2 5.3*1018 7.8*1018 1.0*1019 2.9*1019

Na+ ions/m2 - 2.2*1017 3.7*1018 1.6*1020

S/Na+ - 35.4 2.7 0.29

Page 88: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Catalysis and TPD

Activation: 2 h at 600°C in air, 30 ml/minReaction: 5 % n-butane (99.95 % purity) in N2, 20 ml/min

Poisoning of 3 % of active Brønsted centres led to significant decrease in activity, loss of Brønsted centres led to inactive samples

0 50 100 150 200 2500

5

10

15

20

SZ-Na1 SZ-Na2 SZ-Na3 Kat1

150 °C

yiel

d i-b

utan

e / %

time on stream / min

TPD

100 200 300 400 500 600

Kat1

Na2

Temperatur [°C]

Page 89: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

DRIFTS

Sample L/B Ratio (by pyrads.) at 323 K

Surface ContentNa [%]

S=O mode [cm-1] at 673 K

Kat1 0.9 - 1402SZ-Na1 1.1 not detectable 1397SZ-Na2 1.7 3.5 1389SZ-Na3 13.0 8 -

L/B ratio determined according to Platon A, Thomas WJ. Ind. Engin. Chem. Res. 24 (2003) 5988.

Page 90: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

TAP – n-butane single pulses

SZ-Na1 SZ-Na2Kat1

0 1 2 3 4 5

0,0

0,2

0,4

0,6

0,8

1,0

H

öhen

norm

. Int

m/e

43

[w.E

.] 448 K 423 K 398 K 373 K 348 K

Zeit [s]0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0

Höh

enno

rm. I

nt. m

/e 4

3 [w

.E.] 448 K

423 K 398 K 373 K 348 K

Zeit [s]0,0 0,2 0,4 0,6 0,8 1,0

0,0

0,2

0,4

0,6

0,8

1,0 448 K 423 K 398 K 373 K 348 K

Höh

enno

rm. I

nt. m

/e 4

3 [w

.E.]

Zeit [s]

τ (348 K) = 0.47 sτ (423 K) = 0.16 s

τ (348 K) = 1.58 sτ (423 K) = 0.49 sτ … residence time

τ (348 K) = 0.20 sτ (423 K) = 0.11 s

Interaction of n-butane single pulse with surface decreaseswith increasing amount of sodium

Page 91: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Kinetic modeling

Page 92: TAP Temporal Analysis of Products · Lecture Series at Fritz-Haber-Institute Berlin „Modern Methods in Heterogeneous Catalysis“ 24.11.2006 TAP Temporal Analysis of Products Cornelia

Thank you for your attention!