temporal analysis of products(tap)- approach: theory and ...temporal analysis of...
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Temporal Analysis of Products(TAP)-Approach: Theory and Application
Gregory Yablonsky,
Parks College of Engineering, Aviation and Technology,
Department of Chemistry, Saint Louis University
(Missouri, USA)
or Chemical Calculus
Gregory YablonskyParks College, Department of Chemistry, Saint Louis University
OUTLINE
• Concepts and history• Experimental devices of chemical kinetics• TAP-apparatus: principle• Qualitative analysis of data• Quantitative analysis of data(a) Fitting(b) Moments(c) Kinetically mode-free analysis ( Y-procedure)• Future: Rate-Reactivity Model• Back to History and Conclusions
• Experimental Devices of Chemical Kinetics
temporal change of transport change due to
amount of component change reaction
Typical Requirements to Kinetic Experiments:
• Isothermicity
• Intensive heat exchange with surroundings
• Dilution of reactive medium
• Rapid recirculation
• Uniformity of the chemical composition
• Intensive mixing
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding
Complexity 7
Reactors for Kinetic Experiments
feed product feed product
recycle
feed product feed product
catalyst zone
Batch reactor CSTR Continuous-flow reactor with
recirculation
PFR Differential PFR
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding
Complexity 8
Reactors for Kinetic Experiments
catalyst zone
inert
zone
Convectional pulse
reactor
Diffusional pulse
reactor / TAP
reactor
Thin-zone TAP
reactor
What are we measuring as a rate in Chemical Kinetics?
CHANGE IN SPACE OR IN TIME- Algebraic difference of inlet and outlet
concentrations (CSTR)
- First time derivative of the concentration dependence (batch reactor)
- First time derivative of the outlet concentration dependence
on the residence time (plug-flow reactor, PFR)
- First longitudinal derivative of the concentration dependence
(some plug-flow reactors)
- Second longitudinal derivative of the concentration dependence
(Temporal Analysis of products, TAP)
10
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
c
t
c
t
slowintermediate
fast
Simple exponential relaxation Relaxation with induction period
Relaxation of different components at different time scales
11
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
3
2
1
Relaxation with “overshoots” (1) & (3) and start in “wrong” direction
(2)
12
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
I
II
c
t
Relaxation with different steady states
Damped oscillations
Belousov-Zhabotinsky reaction
14
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical
Reactions. Decoding Complexity
Types of Temporal Evolution Relaxation
c
t
c
t
Regular oscillations around a
steady state
Chaotic oscillations
Anatoly Zhabotinsky (1938 – 2008)
Gerhard Ertl (1936 - )
Progress in time resolutionfor 150 years
• From second to femptoseconds (10 -15 sec)
G.B. Marin & G.S. Yablonsky (2011). Kinetics of Chemical Reactions. Decoding
Complexity 18
Non-Steady-State Models
,d
fdt
c
c k
describes the temporal evolution of a chemical reaction mixture from an initial state
to a final state
• closed system: equilibrium
• open system: steady state
Three methods for studying non-steady-state behavior:
• change in time t: change in dynamic space (c,t)
• change of parameters k: change in parametric space (c,k)
• change of a concentration with respect to others: change in phase space
Rutherford Aris (1929 – 2005)
Calculus’ foundation: Cavalieri is a precursor of infinitesimal calculus
In Europe, the foundational work was a treatise due to Bonaventura Cavalieri, who argued that volumes and areas should be computed as the sums of the volumes and areas of infinitesimal thin cross-sections
Founders of infinitesimal calculus: Newton and Leibnitz
Isaac Newton (1743-1727)
Gottfried Wilhelm Leibnitz (1646-1716)
‘Drop-by-drop’: titration,determination of the equivalent point
The origins of volumetric analysis are in late-18th-century French chemistry. Francois Antoine Henri Descroizilles developed the first burette (which looked more like a graduated cylinder) in 1791. Joseph Louis Gay-Lussac developed an improved version of the burette that included a side arm, and coined the terms "pipette" and "burette" in an 1824 paper on the standardization of indigo solutions
Manfred Eigen (1927): Chemical relaxation, but not calculus
Experimental calculus in chemistry: John T. Gleaves
• Temporal Analysis of Products (TAP),
a vacuum transient response experiment performed by injecting a small number of gas molecules into an evacuated reactor containing a solid sample, which provides precise kinetic characterization of gas- solid interactions with submillisecond time resolution (developed by J.T. Gleaves in 1988)
TC
Pulse valve
Microreactor
Mass spectrometer
Catalyst
Vacuum (10-8 torr)
Reactantmixture
0.0 time (s) 0.5
Exit
flo
w (
F A)
Inert
Reactant
Product
Continuous flow valve
TAP Reactor System-Overview
TAP-3 System
IR Probe
and
Reactor
New Developments in TAP Instrumentation
Aiming
towards
‘kinetically
appropriate’
operando
reactors
Measuring Intrinsic Kinetic Characteristicswith Probe Molecules
Pulse valve
Mass spectrometer
Molecular beam
Scattered beam
P ≈ 10-9 Pa
Target
(a)
Differentially pumped
vacuum system
Molecular Beam Scattering – MBS experiment – Inspiration for TAP
Sticking probability of H2 on different
surfaces. Data of Rendulic and Winkler , Int. J. Mod.
Phys. B 3, 941, 1989.
Measuring Intrinsic Kinetic Characteristicswith Probe Molecules
Pulse valve
Mass spectrometer
Molecular beam
Scattered beam
P ≈ 10-9 Pa
Target
(a)
Differentially pumped
vacuum system
Molecular Beam Scattering – MBS experiment – Inspiration for TAP
Multi-component
Polycrystalline
Multiphasic
Heterogeneous Surface
Defects
Changes with Reaction
Practical Catalyst
(Complex Particles)
Measuring Intrinsic Kinetic Characteristicswith Probe Molecules
Pulse valve
Mass spectrometer
Molecular beam
Scattered beam
P ≈ 10-9 Pa
Target
(a)
Differentially pumped
vacuum system
Pulse valve
Mass
spectrometer
Reaction zone
Catalyst sampleExit flow
P ≈ 10-7 Pa
(b)
Input pulse
Molecular Beam Scattering – MBS experiment
Temporal Analysis of Products - TAP experiment
Insignificant change
Small number of pulses1 32 4
Key Features of TAP Pulsing
Significant change
1 50002500 7500Large number of pulses
Key Advantages:Small pulse size
Low adiabatic temperature rise
Isothermal experiments
Minimal surface reconstruction
No mass transfer limitations
Millisecond time resolution
Oxidation state can be
manipulated
Inert Reactant ProductInert Reactant Product
Small number of pulses
Insignificant change
0.0
State-defining Experiment
State-Defining & State-Altering Experiment
Inert Reactant Product
Large number of pulses0.0
State-altering Experiment
TAP Multipulse Experiment Combines
TAP-results
• About 20 machines working in the world• About 10 research groups
US-St. Louis, HoustonEurope – Belgium, Ghent; Netherlands, Delft ; N.Ireland, UK, Belfast; Germany – Ulm, Rostock, Bohum; France –Lyon; Spain; Switzerland –Zuerich;Asia- Japan – Tokyo, Toyota City;Thailand – Bangkok.Many catalytic reactions: oxidation of simple molecules, many reactions of complete and selective oxidation of hydrocarbons
• Interrogative kinetics, a systematic approach combining small stepwise changes in catalyst surface composition with precise kinetic characterization after each change to elucidate the evolution of catalyst properties and provide information on the relationship between surface composition and kinetic properties. (developed by J.T. Gleaves and G. Yablonsky in 1997)
The main idea is to combine two types of experiments:
Was firstly introduced in the paper:Gleaves, J.T., Yablonskii, G.S., Phanawadee, Ph., Schuurman, Y.
“TAP-2: An Interrogative Kinetics Approach” Appl. Catal., A: General, 160 (1997) 55.
A state-defining experiment in which the catalyst composition
and structure change insignificantly during a kinetic test
A state-altering experiment in which the catalyst composition
is changed in a controlled manner
Interrogative Kinetics (IK) Approach
Principles of the TAP-experiment
• 3 principles:
• (1) Insignificant change of catalyst composition during the single pulse
• (2) Controlled change of catalyst composition during the series of pulses
• (3) Uniformity of the active zone regarding the composition
=========
And… Transport is well-defined: Knudsen diffusion
Thin Zone TAP experiments
Thin-zone and Single Particle Reactor Configurations
Thin-zone
Single-particle
QUALITATIVE ANALYSIS
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-0.1
0.1
0.3
0.5
0.7
0.9
1.1
0.0 0.1 0.2 0.3 0.4 0.50.5time(s)
Argon
Butane Response after Reaction
Rel
ativ
e Fl
ow
Experimental and Predicted ResponsesArgon and Butane Pulsed over VPO
0.5time(s)
No
rmal
ized
Flo
w
Experimental and Predicted Responses Argon Pulsed over Quartz Particles
440400
360320
280
Temp.time (s)
1.0
Rel
ativ
e In
ten
s.
0.0
0.1
Non-uniformity along the catalyst bed was produced in multi-pulse experiment
porosity
bCA
t DeA
2CA
z2 ka CA*
Transport + Irreversible Adsorption
Standard Diffusion Curve
diffusivity
Experimental and predicted responsesButane pulsed over oxygen treated VPO
TAP-data qualitative analysis
• Distinguishing irreversible and reversible adsorption and interaction processes.
• Different “pump-probe” experiments• Testing of the temperature influence• Testing of the catalyst pretreatment• Change of pulse parameters (pulse intensity, time
interval between pulses etc)
Preliminary result: some hypotheses about thedetailed mechanism (types of adsorption and interactions, diffusion into the catalyst bulk etc)
Probe Molecules:TAP as a Surface Sensitive Materials Characterization Tool
Spectroscopic
TechniquesXPS, TEM, LEIS, etc.
Photons, electrons, ions
Near surface layers
Signal is proportional to
surface concentration
Well-defined (model)
materials
TAPProbe molecule pulsing
Reactants, products,
intermediates, bases, etc.
Exclusive to the surface
Signal follows exponential
kinetic dependence –
ultrasparse concentrations can
be detected
Real materials
Can distinguish active/inert
Wavelength time (s)
Vacuum Transformation of
Oxygen-treated (VO)2P2O7
Probe Molecules Indicate Kinetic Effects of
Structural Change
Activity-Structure Relationship for Complex Catalysts
Intrinsic kinetic
measurements
Techniques for Intraparticle Transport
• PFG NMR
• Quasi-elastic Neutron Scattering
• Single crystal membranes
• Zero Length Chromatography
• Frequency Response
• TAP
Techniques for Intraparticle Transport
• PFG NMR
• Quasi-elastic Neutron Scattering
• Single crystal membranes
• Zero Length Chromatography
• Frequency Response
• TAP
Diffusing species
must be in contact
with the
microporous
material for and
extended time.
Techniques for Intraparticle Transport
Microscopic Methods• PFG NMR• Quasi-elastic Neutron Scattering
Macroscopic Methods• Single crystal membranes• Zero Length Chromatography• Frequency Response• TAP
Diffusivity
measurements
polarized by two
orders of
magnitude.
TAP for Intraparticle Transport
• Millisecond time resolution
• Small quantity of sorbent, measurement at low pore occupancy
• No carrier gas which may influence mass transfer
• Knudsen regime, no external mass transport limitations
TAP for Intraparticle Transport
• Kinetic Processes • In the Porous Channel
– Adsorption/desorption into/from pore mouth
– Residence time in pores
– Diffusivity in microporous channel
• External Surface
• Activation energy 1/pore radius• Optimum pore size
• Catalyst coking studies• External plane vs. microporous channel
Unique Experiments with TAP
• Pump/Probe format
• Intraparticle transport at low pore occupancy
Pump/Probe FormatSeparation of 2 Reactants
Reactant A (e.g.
NO)
Reactant B (e.g. H2O)
Pulse response of
product at reactor
exit (e.g. N2O or N2)
How does H2O hinder the storage of NOx or facilitate its reduction?
New Pump/Probe Experiments for Multicomponent (Competitive)
Intraparticle TransportReactant A (e.g. CH4) Reactant B (e.g. CO)
Pulse response
of gas B at
reactor exit
Pulse response of
gas A at reactor exit
TAP-DATA QUANTITATIVE ANALYSIS
Inert zone Catalyst zone
Thin-Zone TAP -Reactor (TZTR) Idea
Dimensionless Axial Coordinate
Dim
en
sion
less
Gas
Con
cen
trati
on
0.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.00.00
.25
.50
.75
1.00
1.25
1.50
1.75
2.00
Vacuum
Thin-Zone TAP- Reactor (TZTR)
CI(x,t)xLTZ
CII (x,t)xLTZ
CTZ(t)
For concentrations
DCI (x,t)
x xLTZ
DCII (x,t)
x xL TZ
FluxI (x,t)xLTZ
Flux II (x,t)xLTZ
LcatRTZ(CS,CTZ ,TZ )
For flows
Inert zone Catalyst zone
TZTR vs CSTR
CSTR: SRVCVC 0 Uniformity is achieved by convective
mixing
X kappres, cat
diff
1 kappres, cat
diffConversion
Apparent rate constant
Diffusional residence time in catalyst zone
In TZTR uniformity is insured by diffusion
TZcat
Lx
II
Lx
I RLx
txCD
x
txCD
TZTZ
),(),(TZTR:
TZTR vs Differential PFR
TZTRDifferential PFR:
Conversion vs Non-Uniformity
x
Cx
C
Xg
g
g
g
C
CX
TAP: Diffusion SRx
CDV
t
CV rg
2
2
PFR: Convection SRx
Cv
t
CVg
Provides Uniformity at X ≤ 20% Provides Uniformity
at X ≤ 80%
Convectional Flow = Diffusional Flow = gVC
x
CD
g
Cg
Cg 2Lc
Lr
X
1 (1 X)LrLc
Shekhtman S.O., Yablonsky G.S. Ind. Eng. Chem. Res. 44 (2005) 6518-6522.
2) Moment analysis
1) Curve fitting
time
mol/s
× Loss of transient information Robust
3) ‘State-of-the-art’: Y-Procedure
× What about fast processes within the pulse?
Thin Zone TAP data analysis: Quantitative Analysis
× Relies on an a priori assumed mechanism
× Relies on an a priori assumed mechanism (ambiguous)
Curve Fitting
A drawback is that it relies on the
a priori assumed mechanism
MOMENT ANALYSIS
1000
2000
3000
4000
5000
6000
10000
time(s)
PulseNumber
M0 Fexit (t )dt
0
Zeroth Moment
Kinetic Characteristics from Pulse Response Moments
• Conversion (number of surfaceoxygen atoms and hydrocarbon)
• Selectivity• Product Yield• Residence time• Apparent rate constants• Apparent time delay
Quantities calculated from 0th, 1st, and
2nd moments
Shekhtman, S. Interrogative Kinetics A New Methodology or Catalyst Characterization. Doctoral Thesis, Washington University, 2003.
“State-by- state” kinetic catalyst screening:
“Show me state”Step 1 Introducing catalyst scale
Presenting conversions/yields vs amounts of consumed
/released reactants/removed oxygen/
via dimensionless scales (catalyst alteration degree; catalyst
oxidation/reduction degree
Step 2 Presenting catalyst state
Presenting kinetic characteristics(apparent kinetic constants and
time delays) as functions of catalyst scale (catalyst alteration degree, catalyst
oxidation/reduction degree)
Step 3 Revealing mechanism
Revealing mechanism of the complex reaction by comparison of different
kinetic characteristics (apparent kinetic constants, time delays)
Considerations for mechanism revealing
1) Routes:
Difference between apparent kinetic
constants of gas reactants is a fingerprint of
different reaction routes
2) Catalyst intermediates
Apparent time delay of gas reactant is a
fingerprint of the surface intermediate presence
==============================These characteristics depend on the catalyst state
Apparent Kinetic Constants and TOF
for Furan Oxidation as a Function of Oxidation State
0
200
400
600
800
1000
1200
1400
1600
00.20.40.60.81
Furan
MA
CO2
AC
Catalyst Oxidation Degree
Ap
pare
nt
Kin
eti
c C
on
sta
nt,
r0 , (
1/s
)
0
200
400
600
800
1000
1200
1400
1600
00.20.40.60.81
Furan
MA
CO2
AC
Catalyst Oxidation DegreeN
on
-Ste
ad
y-S
tate
TO
F,
Ap
pare
nt
Co
nsta
nt
/Ox
idati
on
De
gre
e,
(1/s
)
Non-steady-state TOF defined as the apparent
constant divided by the oxidation degree, for
furan and products (MA, CO2 and AC),
versus the catalyst oxidation degree.
All apparent kinetic constants are different
Apparent Time Delays
0.0
0.5
1.0
1.5
2.0
2.5
00.20.40.60.81
Furan
MA
CO2
AC
Catalyst Oxidation Degree
Appare
nt
Tim
e D
ela
y, |r
2/r
1|,
(s)
For all reactants, apparent time delays are different.
At least four intermediates can be involved
Detailed Mechanism of Furan Oxidation Over VPO
At least three independent routes
At least four specific intermediates
1) O2 + 2Z 2ZO;
2) Fr + ZO X;
3) Fr + ZO Y;
4) Fr + ZO U;
5) X MA+ Z + H2O;
6) YAC + Z + CO2 + H2O;
7) UZ + CO2+ H2O;
8) ZO + L LO + Z;
9) CO2 + Z1 Z1CO2.
where X, Y, U, Z1CO2 are different
surface intermediates, ZO and LO
– surface and lattice oxygen
respectively, Z and Z1 are different
catalyst active sites.Stoichiometric
coefficients of surface substances
will be specified in the course of
reaction. Steps 2-4 are supposed
to differ kinetically.
A drawback of the moment analysis
The moment analysis uses the
information which is averaged
within the pulse
Kinetically model-free analysis
Y-PROCEDURE
Kinetic Model-Free Analysis
Reactor Model:
Accumulation - Transport Term = Reaction Rate
Batch Reactor: Non SRdt
dCVg
CSTR: Convection SRCCVdt
dCVg )( 0
TAP: Diffusion SRx
CDV
t
CV rg
2
2
PFR: Convection SRx
Cv
t
CVg
The biggest methodologicaldifficulty in non-steady-state studies:
comparison with the steady-state experiment
1. CSTR-data provides the steady-state
reaction rate without assumptions on the
kinetic model (kinetic model – free data):
2. Presently all kinetic methods (CSTR,
PFR, TAP) do not provide data on the non-steady
state reaction rate in a kinetic model –free manner
• TWO IDEAS:
• I. Experimental idea: Thin-Zone TAP-Reactor (TZTR)
• 2. Theoretical Idea: Extracting the non-steady reaction rate in model-free manner
• (Y-procedure)
75AIChE Annual Meeting,
October 2012, Danckwerts Memorial Lecture
2
2
x
CD=
t
C
0=xδ=C(x,0) 0=t)(0,x
CD
0=t)C(L,t)(L,x
CD=F
0=x
L=x
Initial Pulse(Dirac delta)
Boundary Conditions
Closed valve
Vacuum
Observation(molecular flux)
Transport equation(Knudsen diffusion)
One zone: the diffusion equation requires an initial condition and two boundary conditions (as a second order PDE)
2
2
x
CD=
t
C
I
II)NR(C,=
x
CD+
x
CD Z
III
C=C=C III
)NR(C,=dt
dNZ
Z
0=xδ=C(x,0) 0=t)(0,x
CD
0=t)C(L,t)(L,x
CD=F
0=x
L=x
Initial Pulse(Dirac delta)
Boundary Conditions
Closed valve
Concentration continuity
TZ gas phasebalance
TZ surfacebalance
Vacuum
Observation(molecular flux)
Transport equation(Knudsen diffusion)
G. S. Yablonsky, D. Constales, et. al., Chem. Eng. Sci., 62, 6754 (2007)
Two zones: each zone requires two boundary conditions
Calculating surface concentrations (instantaneous storages)as a transient difference between total uptake and release
Uptake Release
dτ(τRνRelease(t)Uptake(t)(t)C
t
0 i
iiS )
Mathematical foundation of the Y-procedure:3 steps
• 1. exact solution in the Laplace domain;• 2. switching to the Fourier domain to allow sufficient
computation;• 3. introduction to discretization and filtering in the Fourier
domain to deal with the real data (in the time domain) subject to noise.Transposition to the Fourier domain combined with time discretization and filtering of the high-frequency noise leads to an efficient practical method for the reconstruction of gas-phase concentrations in a non-steady-state regime without any presuppositions about the kinetic dependence, that is, it is a model-free procedure.
The Y-Procedure analysis provides us with:
• 'Model free' transient kinetics
• Millisecond time resolution
• For complex multicomponent catalysts
• At the upper limit of the surface science range (10-6
torr)• Keeping high spacial uniformity for conversions up to 80% [1]
How do we deal with this information?
[1] - S. Shekhtman, et. al., Chem. Eng. Sci., 59, 5493 (2004)
Numerical solution(Method of Lines)
Y-Procedure(FFT)
Model mechanisms(set in advance)
Transient intrinsickinetics
(reconstructed)
?
Developing the Y-Procedure methodology: Numerical experiments
Simulateddata
• How do we extract a complex catalytic mechanism from corresponding transient kinetics?
• Which parameters we can extract from these data and how?
Irreversible adsorption: Simulation
A + Z → AZ k
AAZtotZ,A )CCk(C=R
k = 1000 m3/mol/s
CZ,tot = 5 nmol/m2
Np = 10-11 – 10-8 mol/pulse
Simu
lation
Reco
nstru
ctionExample (Np = 5·10-10 mol/pulse)
Irreversible adsorption: Trajectories in the rate/composition space,i.e R(t) vs. CA(t) vs. CZA(t), for different pulse intensities
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Reaction rate
Surface concentration
Gas concentration
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: State-defining experiment (small pulse)
Np = 1·10-10 mol/pulse
totZ,app kC=k
AtotZ,A CkCR
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: State-altering experiment (big pulse)
Np = 4·10-9 mol/pulse
AAZtotZ,A )CCk(C=R
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: State-altering experiment (big pulse)
Np = 4·10-9 mol/pulse
k
totZ,C
AZtotZ,
A
A kCkC=C
R
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: Multi-pulse experiment (series of small pulses)
Np = 1·10-10 mol/pulse
AappA CkR
ZAtotZ,app kCkCk
Np
↑
t
Characteristic surface defined by R(Cg,CS)
Irreversible adsorption: Multi-pulse experiment (series of small pulses)
Np = 1·10-10 mol/pulse
AappA CkR
ZAtotZ,app kCkCk
Reversible adsorption: Simulation
A + Z AZ k+
AZAAZtotZ,
+
A Ck)CC(Ck=R
→←k-
k = 10 1/s
CZ,tot = 0.5 nmol/m2
Np = 10-11 – 10-8 mol/pulse
k = 1000 m3/mol/s
Simu
lation
Reco
nstru
ction
Example (Np = 5·10-10 mol/pulse)
Reversible adsorption: Trajectories for different pulse intensities
Np
↑
t
Surface defined by R(Cg,CS)=0
Gas rate
Surface concentration
Gas concentration
Reversible adsorption: State-defining experiment (small pulse)
Np
↑
t
Surface defined by R(Cg,CS)=0
Np = 1·10-10 mol/pulse
Plane trajectory:
totZ,Ck
k
A
AZtotZ,
+
A
A
C
CkCk
C
R
Reversible adsorption: State-altering experiment (big pulse)
Np
↑
t
Surface defined by R(Cg,CS)=0
Np = 1·10-8 mol/pulse
k
totZ,C
Non-plane trajectory:
AZ
+
totZ,
+
A
AZA CkCk=C
CkR
Reversible adsorption: Transient Equilibrium
Np
↑
t
Surface defined by R(Cg,CS)=0
Isotherm (Rads = Rdes)
eqeqA,
eqA,totZ,
eqAZ,1/K+C
CC=C
The ‘menu’ of TAP experiments
How does pulse intensity affects the catalyst state for irreversible/reversible reactions?
Pulse Intensity
Irreversible
Reaction
Reversible
Reaction
Change within each pulse
Change from pulse to pulse
Change within each pulse
Change from pulse to pulse
Small pulse small controlled small Small
Big pulse big big big non
What parameters can we extract?
ExperimentIrreversible
Reaction
Reversible
Reaction
State-defining kapp = kCZ,tot k+app = k+CZ,tot and k-
State-alteringk and CZ,tot k+ and CZ,tot if k- is
known
CO + Z CO
ZCOCOZCOtotZ,
+
CO Ck)CC(Ck=R
k+
→←k-
Application to CO adsorption on Pd: Experimental results for a reversible adsorption
Np = 5·10-9 - 1·10-7 mol/pulse
Example (Np = 1·10-7 mol/pulse)
CO + Z COk+
→←k-
Application to CO adsorption on Pd: Experimental results for a reversible adsorption
7101
8105
8101
9105
3totZ,m
mol5C
40Keq
Isotherm fitting:
Decoding complex mechanisms:
Classical problem – Langmuir-Hinshelwood or Eley-Rideal?
For any combination of elementary steps, surface uptakes of CO and oxygen can be calculated as:
)dτ(τR(τ(R(t)C
t
0
COCOZCO 2))
t
0
COOZO dτ(τR(τ(2R(t)C22
)))
Step 1: Directly comparing rates in a state-defining experiment
Step 2: Testing coherency of the entire data set (time invariant parameters)
Apparent kinetic parameters:
ER+OAP
Step 2: Decision tree for oxygen pre-covered surface
Testing rates
Legend:
ER - Eley-Rideal LH - Langmuir-Hinshelwood OAP -Oxygen Additional ProcessBuffer - spectator CO
Testing parameters
TAP: New Results
• I. MOMENTARY EQUILIBRIUM:PULSE AND DIFFUSION (Ind. Eng. Chem. Res., 52 (44), 15417–15427 (2013) )
101AIChE Annual Meeting,
October 2012, Danckwerts Memorial Lecture
Thin-zone and Single Particle Reactor Configurations
Thin-zone
Single-particle
Inert zone Catalyst zone
Thin-Zone TAP -Reactor (TZTR) Idea
Dimensionless Axial Coordinate
Dim
en
sion
less
Gas
Con
cen
trati
on
0.0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.00.00
.25
.50
.75
1.00
1.25
1.50
1.75
2.00
Vacuum
The Y-Procedure analysis provides us with:
• 'Model free' transient kinetics
• Millisecond time resolution
•
Momentary equilibrium
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• Adsorption equilibrium is an essential step of catalytic processes,
which is often used to measure the total concentration of catalytic sites.
• The total concentration of sites
is typically determined by:
- Very sensitive pressure and microbalance
measurements in equilibrated closed system.
- Chemisorption of irreversibly adsorbing molecules.
- Chemisorption of reversibly adsorbing molecules
at low temperatures (much less than operating).
pi
Cs
Introduction
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• Adsorption equilibrium is an essential step of catalytic processes,
which is often used to measure the total concentration of catalytic sites.
• The total concentration of sites
is typically determined by:
- Very sensitive pressure and microbalance
measurements in equilibrated closed system.
- Chemisorption of irreversibly adsorbing molecules.
- Chemisorption of reversibly adsorbing molecules
at low temperatures (much less than operating).
• Measuring the concentration of adsorption sites by
reversible chemisorption under realistic operating temperatures and
non-steady-state conditions presents a significant challenge.
pi
Cs
Outline
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•
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
Outline
108NASCRE-3, Houston, TX,
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• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
Outline
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• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
Thin-Zone (TZ) Temporal Analysis of Products (TAP)
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timeQMStime
Inlet pulse Exit flow
pulse valve
catalyst
inert
thermocouple
Fexit(t)Finlet(t)
J. T. Gleaves et al. (2010)
Thin-Zone (TZ) Temporal Analysis of Products (TAP)
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timeQMStime
Inlet pulse Exit flow
pulse valve
catalyst
inert
thermocouple
Fexit(t)Finlet(t)
Cg(t)
Gas concentrationR(t)
Reaction rateCs(t)
Surface storage+
Y-Proc.
Kinetically “model-free” characteristics in the catalyst zone
stoichiometric
assumptions
G. S. Yablonsky et al. (2007)
Outline
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• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
Case study
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CO + Z ZCOk+
k-
𝐾𝑒𝑞 =𝑘+
𝑘−
Single-site CO adsorption:
Case study
114NASCRE-3, Houston, TX,
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CO + Z ZCOk+
k-
𝐾𝑒𝑞 =𝑘+
𝑘−
𝑅𝐶𝑂 = −𝑑𝐶𝐶𝑂𝑑𝑡= 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂 =
= 𝑘+(𝐶𝑍,𝑡𝑜𝑡−𝐶𝑍𝐶𝑂)𝐶𝐶𝑂 − 𝑘−𝐶𝑍𝐶𝑂
Single-site CO adsorption:
• Kinetics is governed by
Case study
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CO + Z ZCOk+
k-
𝐾𝑒𝑞 =𝑘+
𝑘−
We used numerical TZ TAP experiments with realistic noise model
to elucidate kinetic behavior during CO adsorption in TAP.
𝑅𝐶𝑂 = −𝑑𝐶𝐶𝑂𝑑𝑡= 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂 =
= 𝑘+(𝐶𝑍,𝑡𝑜𝑡−𝐶𝑍𝐶𝑂)𝐶𝐶𝑂 − 𝑘−𝐶𝑍𝐶𝑂
Single-site CO adsorption:
• Kinetics is governed by
• Surface CO uptake can be obtained as
𝐶𝑍𝐶𝑂(𝑡) = 0
𝑡
𝑅𝐶𝑂 𝑡′ 𝑑𝑡′
Intra-pulse kinetic characteristics
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Pulse-response experiment
in TZ TAP microreactor
RC
O,
(mm
ol/
kg
cat/s
)
CC
O,
(mm
ol/
m3)
CZ
CO,
(mm
ol/
kg
cat)
t, (s)
RCO
CZCO…
CCO
Momentary Equilibrium (ME)
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Pulse-response experiment
in TZ TAP microreactor
RC
O,
(mm
ol/
kg
cat/s
)
CC
O,
(mm
ol/
m3)
CZ
CO,
(mm
ol/
kg
cat)
ME
t, (s)
RCO
CZCO…
CCO
𝑅𝐶𝑂 𝑡 = 0 → 𝑟+ = 𝑟−
Momentary Equilibrium (ME)
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How do we use ME to obtain isotherms and
estimate the total concentration of sites?
Are the surface and gas concentrations in ME related
via the equilibrium constant?
Outline
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• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
Pulse-Intensity Modulation
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𝐶𝑍𝐶𝑂,𝑀𝐸 =𝐾𝑒𝑞𝐶𝑍,𝑡𝑜𝑡𝐶𝐶𝑂,𝑀𝐸
1 + 𝐾𝑒𝑞𝐶𝐶𝑂,𝑀𝐸
Langmuir isotherm:
Pulse-Intensity Modulation
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𝐶𝑍𝐶𝑂,𝑀𝐸 =𝐾𝑒𝑞𝐶𝑍,𝑡𝑜𝑡𝐶𝐶𝑂,𝑀𝐸
1 + 𝐾𝑒𝑞𝐶𝐶𝑂,𝑀𝐸
Langmuir isotherm:
Fexit(t)
t, (s)
Np,CO
Outline
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• Introduction
• TAP experiments and data analysis
• Momentary Equilibrium
• Pulse-Intensity Modulation
• Experimental example
• Conclusions
Experimental example
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CO adsorption on Pt/Mg(Al)Ox (1 wt. % Pt)
Pulse-intensity range: Np,CO = 1 – 14.5nmolCO
Temperature range: T = 50 – 140 °C
Experimental example
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Estimated concentration of adsorption sites: CZ,tot = 0.3-0.55 (mmol/kgcat)
Estimated heat of CO adsorption: ΔHads= - 17.9 (kJ/molCO)
Rate-concentration trajectories
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t, (s)
RCO
CZCO
CCO
State-defining trajectory
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𝑅𝐶𝑂 = 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂
𝑅𝐶𝑂𝐶𝐶𝑂≈ 𝑘+𝐶𝑍,𝑡𝑜𝑡 − 𝑘
−𝐶𝑍𝐶𝑂𝐶𝐶𝑂
State-altering trajectory
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𝑅𝐶𝑂 = 𝑘+𝐶𝑍𝐶𝐶𝑂 − 𝑘
−𝐶𝑍𝐶𝑂
𝑅𝐶𝑂 + 𝑘−𝐶𝑍𝐶𝑂𝐶𝐶𝑂
= 𝑘+𝐶𝑍,𝑡𝑜𝑡 − 𝑘+𝐶𝑍𝐶𝑂
Parameter estimation
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ME State-defining State-altering
N/A k+ k+
N/A k- k-
Keq Keq Keq
CZ,tot CZ,tot CZ,tot
Numerical example
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Experimental example
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CO adsorption on Pt/Mg(Al)Ox (1 wt. % Pt)
Pulse-intensity range: Np,CO = 1 – 14.5nmolCO
Temperature range: T = 50 – 140 °C
Experimental example
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Estimated concentration of adsorption sites: CZ,tot = 0.3-0.55 (mmol/kgcat)
Estimated heat of CO adsorption: ΔHads= - 17.9 (kJ/molCO)
Q&A
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TAP: New Results
• II. Independence of the final catalyst activity profile on the pulse procedure (AICHEJ, 2015,61,1, 31-35)
• The activity profile of a prepared catalytic system depends on the total amount of admitted substance. It does not depend on the pulse procedure whether it is a number of small pulses or one big pulse.
Uniqueness of the profile. It is based on two principles of uniqueness
• (I) At any position (longitudinal or radial) of the catalytic unit,
the final catalyst composition is uniquely defined by the
integral amount of gas substance concentrations related to the
given position.
This statement reflects a chemical feature. It is completely
independent of the fluid dynamics.
• (II) The integral amount of gas substance concentrations
related to the given position is uniquely defined by the total
amount of molecules admitted to the chemical reactor.
This statements reflects a specific hydrodynamic feature of our
device, viz the type of transport, boundary conditions etc
Computational and theoretical result
It was proven for different cases
• Longitudinal and radial profiles
• Non-porous and porous catalysts
• Mono-and bimolecular adsorption
• Different TAP-reactor configurations
(one zone; three-zone; thin-zone)
TAP: New Results on reaction-diffusion systems
(III) Optimal configuration of catalytic units
(Wallace, Feres, Yablonsky, 2015, submitted)
A. When catalytic activity (k) is sufficiently small, conversion is maximized by having all the catalytic particles (units) together right at the point of gas injection.
B. When k is very large, the optimal configuration for conversion approaches that in which the catalyst particles are equally spaced along the line of the reactor.
FUTURE
RATE–REACTIVITY MODEL
(Yablonsky, Redekop et al, submitted)
Rate-Reactivity Model (RRM):
a new basis for non-steady-state characterization of
heterogeneous catalysts
Catalysis is a complex phenomenon
• Multiple crystallographic phases
• Catalyst modifications by the reaction (phase transitions, coking, etc.)
• Emergent “true” active sites
• Hierarchy of meso- and nano-porous diffusions
The kinetic model must deal with two intersecting complexities:
Complexity of the material
Complexity of the reaction
• Multiple reaction pathways consisting of many reaction steps
• Energetically heterogeneous population of active sites
• Lateral interactions between adsorbed species
• Elemental transport at the molecular scale (spillover, surface/bulk exchange, etc.)
These interacting phenomena may not follow the “mass action law”
Catalytic kinetics: why?
mechanism
elucidation
materials
characterization
Kinetic data
kinetic
modeling
J. Hagens
G. B. Marin & G. S. Yablonsky
I. Chorkendorff & J.W. Niemantsverdriet
Edit. M. Che & J. C. Vedrine
Catalytic kinetics: how?
• Combinatorial screening
• High-throughput steady-state kinetics
• Non-steady-state (transient) kinetics
D. Farrusseng, Surface Science Reports 63 (2008) 487-513
M. Kramer, et al., Journal of Catalysis 251 (2007) 410
S. Senkan, Angewandte Chemie 40 (2001) 312-329
J.A. Moulijn, et al., Catalysis Today 81 (2003) 457-471
K. Metaxas, et al., Topics in Catalysis 53 (2010) 64-76
V. Prasad, et al., Chemical Engineering Science 65 (2010) 240-246
A.C. van Veen, et al., Journal of Catalysis 216 (2003) 135-143
R.J. Berger, et al., Applied Catalysis A: General 342 (2008) 3-28
G. Marin and G. Yablonsky, Kinetics of Chemical Reactions (2011) Wiley
Kinetic devices and the information they provide
feed product feed product
recycle
feed product
(a) (b) (c) (d)
feed product(e)
catalyst zone
(f) (g) (h)
catalyst zone
inert
zone
feed product feed product
recycle
feed product
recycle
feed product
(a) (b) (c) (d)
feed productfeed product(e)
catalyst zonecatalyst zone
(f) (g) (h)
catalyst zone
inert
zone
• Transport regimes:
Convection vs. diffusion
Well-defined vs. ill-defined
Achievable time resolution
Spatially uniform vs. non-uniform
Steady-state vs. non-steady-state
𝑗 = 𝑣𝐶
𝑗 = −𝐷𝛻𝐶
Kinetic devices and the information they provide
feed product feed product
recycle
feed product
(a) (b) (c) (d)
feed product(e)
catalyst zone
(f) (g) (h)
catalyst zone
inert
zone
feed product feed product
recycle
feed product
recycle
feed product
(a) (b) (c) (d)
feed productfeed product(e)
catalyst zonecatalyst zone
(f) (g) (h)
catalyst zone
inert
zone
• Observable characteristics:
Transformation rates (CSTR, TZ TAP via Y-Procedure)
Surface concentrations (SSITKA, operando surface spectroscopies, e.g. IR)
Gas concentrations (most devices)
Bulk material properties (operando bulk spectroscopies, e.g. XAS)
rarely
accessible
commonly used
Kinetic devices and the information they provide
feed product feed product
recycle
feed product
(a) (b) (c) (d)
feed product(e)
catalyst zone
(f) (g) (h)
catalyst zone
inert
zone
feed product feed product
recycle
feed product
recycle
feed product
(a) (b) (c) (d)
feed productfeed product(e)
catalyst zonecatalyst zone
(f) (g) (h)
catalyst zone
inert
zone
• Observable vs. non-observable surface characteristics:
Typically, many hypothetical intermediates are assumed (validity is questionable)
If non-steady-state rates are available, total surface uptakes can be computed
Chemical Kinetics.Textbook Knowledge
• Detailed mechanism is a set of elementary reactions. Typically, the mass-action-law is assumed.
• An example:Hydrogen Oxidation 2H2 +O2 = 2H2O
• 1)H2 + O2 = 2 OH ; 2) OH + H2= H2O + H ; 3) H + O2 = OH + O;
• 4) O + H2 = OH + H ; 5)O + H2O=2OH; 6) 2H + M = H2 + M ;7) 2O + M = O2 + M;
• 8)H + OH + M = H2O + M; 9) 2 OH + M = H2O2 + M;10) OH + O + M = HO2 + M;
• 11) H + O2 + M = HO2 + M; 12) HO2 + H2 = H2O2 + H;13)HO2 +H2 = H2O +OH;
Typical mechanism of the heterogeneous reaction
• Adsorbed mechanism (Langmuir’s mechanism)
• 1) 2 K + O2 2 KO
• 2) K + B KB
• 3) KO + KB 2 K + BO
• Overall reaction 2B+O2 KB (B is CO)
• Particular cases of this mechanisms are
Calculation of surface uptakes
• Instantaneous uptakes can be calculated from
the transient mass-balance of the catalyst surface
𝑼𝑿 𝒕 = 𝟎
𝒕
𝑹𝑿+ 𝝉 𝒅𝝉 −
𝟎
𝒕
𝑹𝑿− 𝝉 𝒅𝝉
• Uptakes are history-dependent and characterize the catalyst state
• «Observable» uptakes vs. hypothetical surface
intermediates
Calculation of surface uptakes (best case scenario)
CO + ½ O2 = CO2
Impact mechanism(a.k.a. Eley-Rideal)
Adsorption mechanism(a.k.a. Langmuir-Hinshelwood)
• Generally, it is not possible to express individual surface concentrations
through gaseous rates (uptake ≠ intermediate).
• But when all elementary steps:1) Exchange molecules with the gas phase
2) Certain connectivity condition are fulfilled
It is possible to express surface concentrations
through a linear combination of gaseous reaction rates (uptake =
intermediate):
Temporal Analysis of Products (TAP):
Experiments and
Data Analysis
time, s
norm. exit flow,mol/s
inert
reversible
irreversible
1. Primary information from moments:
𝑀𝑛 =
0
𝜏𝑒𝑛𝑑
𝐹𝑒𝑥𝑖𝑡 𝑡 ∙ 𝑡𝑛𝑑𝜏
• Conversion• Selectivity• Mean residence time• Apparent rate coefficients
3. Model-free analysis via the Y-Procedure:
2. Model regression:
• Parameter estimation for microkinetic models
Yablonsky, et al (2007), Redekop, et al (2011)
Balcaen, et al (2011)
Gleaves, et al (1997)
U(t)Surface uptake
Rate Reactivity Model (RRM)
Main idea
𝑹 𝒕 = 𝝍𝑪𝑪 𝒕 + 𝝍𝑼𝑼 𝒕 + 𝝍𝑪𝑼𝑪 𝒕 𝑼(𝒕)
• Phenomenological model relates rates, gas concentrations, and surface uptakes
• For one gas interacting with the catalyst:
gas-to-surface
«impact» interactions
surface-to-gas
«release» interactions(can have n>1 for uptake)
gas-to-surface
«complex» interactions
«Slow» or insignificant compositional changes are lumped into the reactivities 𝝍(slow intermediates, concentrations of active sites, other structural parameters)
«Fast» compositional changes are reflected for by the uptake terms
(short-lived and/or fast-accumulating intermediates)
Rate Reactivity Model (RRM)
Model properties
ALWAYS linear in parameters (i.e. empirical reactivities 𝝍)
Does not relay on detailed mechanism, but rather on general knowledge
(only monomolecular gas-to-surface steps, gas release from the surface)
Drastically simplified when the catalyst state is not changed
by the measurement (state-defining experiment)
The same (standard) form for all reactions
Shifts the focus from the process to material characterization
𝑹 𝒕 = 𝝍𝑪𝑪 𝒕 + 𝝍𝑼𝑼 𝒕 + 𝝍𝑪𝑼𝑪 𝒕 𝑼(𝒕)
gas-to-surface
«impact» interactions
surface-to-gas
«release» interactions(can have n>1 for uptake)
gas-to-surface
«complex» interactions
efficient parameter estimation using linear methods
Rate Reactivity Model (RRM)
Estimation of reactivities
𝑹 𝒕 = 𝝍𝑪𝑪 𝒕 + 𝝍𝑼𝑼 𝒕 + 𝝍𝑪𝑼𝑪 𝒕 𝑼(𝒕)
𝑹 (𝒕𝟏)𝑹 (𝒕𝟐)⋮𝑵𝒕×𝟏
=𝑪(𝒕𝟏) 𝑼(𝒕𝟏) 𝑪 𝒕𝟏 𝑼(𝒕𝟏)
𝑪(𝒕𝟐) 𝑼(𝒕𝟐) 𝑪 𝒕𝟐 𝑼(𝒕𝟐)⋮ ⋮ ⋮
𝑵𝒕×𝟑
∙
𝝍𝑪
𝝍𝑼
𝝍𝑪𝑼
𝟑×𝟏
𝑹 = 𝑨𝚿
SVD(A)
𝑹 = 𝑼𝚺𝑽𝑻𝚿 𝚿 = 𝑽𝚺−𝟏𝑼𝑻𝑹
• Matrix notation
• Linear estimation based on Singular Value Decomposition (SVD)
• Only the most important SVD components can be preserved for filtering out noise
R, m
ol/
kg
ca
t/s
time, s0.1 0.2 0.3 0.4 0.5
RRM example (state-defining)
Np, mol/pulse 1e-8
Ns, mol/kg 1e-3
kads, 100
kads*Ns, 0.1
kdes, 1/s 10
simulatio
n
• Kinetics: 𝑅𝐴 = 𝑘𝑎𝑑𝑠 𝑁𝑆 − 𝐶𝐴𝑍 𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍
• Single-site reversible adsorption: A + Z = AZ
• For small CAZ (state-defining): 𝑅𝐴 ≈ 𝑘𝑎𝑑𝑠𝑁𝑆𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍
R, m
ol/
kg
ca
t/s
time, s0.1 0.2 0.3 0.4 0.5
RRM example (state-defining)
Np, mol/pulse 1e-8
Ns, mol/kg 1e-3
kads, 100
kads*Ns, 0.1
kdes, 1/s 10
ψ0 2.3e-6
ψc 0.094
ψu -10.5
simulatio
n
estimated RRM
coeffs.
• Kinetics: 𝑅𝐴 = 𝑘𝑎𝑑𝑠 𝑁𝑆 − 𝐶𝐴𝑍 𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍
• Single-site reversible adsorption: A + Z = AZ
• For small CAZ (state-defining): 𝑅𝐴 ≈ 𝑘𝑎𝑑𝑠𝑁𝑆𝐶𝐴 − 𝑘𝑑𝑒𝑠𝐶𝐴𝑍
or in the RRM form 𝑅𝐴 ≈ 𝜓𝐶𝐶𝐴 + 𝜓
𝑈𝑈𝐴
𝑭𝑨 (𝒕)
𝑪𝑨 𝒕 ,
𝑹𝑨 (𝒕)
𝑼𝑨(𝒕)
Quantity
• For small perturbations,
only two RRM terms are required! 𝑅𝐴𝑑𝑡
𝑌
Operation
𝜳
𝑅𝑅𝑀
Rate Reactivity Model (RRM)
Generalization
𝑹𝒊 𝒕 =
𝒌=𝟏
𝑵
𝝍𝒊,𝒌𝑪 𝑪𝒌 𝒕 +
𝒋=𝟏
𝑴
𝝍𝒊,𝒋𝑼𝑼𝒋 𝒕 +
𝒌=𝟏
𝑵
𝒋=𝟏
𝑴
𝝍𝒊,𝒌,𝒋𝑪𝑼 𝑪𝒌 𝒕 𝑼𝒋 𝒕
• For many gases interacting with the catalyst:
The rate for every gas may depend on concentrations and uptakes of all
other gases Is it rigorously equivalent to microkinetics for (pseudo)monomolecular
mechanisms?
RRM example (complex)
Rate Reactivity Model (RRM)
Further generalization
𝑹𝒊 𝒕 =
𝒌=𝟏
𝑵
𝝍𝒊,𝒌𝑪 𝑪𝒌 𝒕 +
𝒋=𝟏
𝑴
𝝍𝒊,𝒋𝑼𝑼𝒋 𝒕 +
+
𝒌=𝟏
𝑵
𝒋=𝟏
𝑴
𝝍𝒊,𝒌,𝒋𝑪𝑼 𝑪𝒌 𝒕 𝑼𝒋 𝒕 +
𝒍=𝟏
𝑴
𝒋=𝟏
𝑴
𝝍𝒊,𝒍,𝒋𝑼𝑼𝑼𝒍 𝒕 𝑼𝒋 𝒕 + 𝝍𝒊,𝟎
surface-surface
interactions
zeroth term
constant emmision of the gas
(e.g. catalyst decomposition)
General strategy for systematic characterization
1. Individual reactants and products
2. Multiple reactants and reactants/products together
• Simultaneous pulsing of multiple gases
• Controlled time delay (pump-probe)
• Isotopic labeling
• State-defining experiments
• Titration and state-altering experiments (e.g. Momentary Equilibrium)
• Variable pulsing frequency (exchange with the bulk? spillover?)
• The influence of pretreatments
• Establish the scale of catalyst states (oxidation degree, coking, etc.)
3. Incremental characterization and mechanism refinement
• Coherency between different characteristics
• Decision trees to guide further experiments
• Classical parameter estimation and model discrimination
Conclusions
1. A novel phenomenological form of kinetic models is suggested
for systematic non-steady-state catalyst characterization
2. This Rate-Reactivity-Model (RRM) is always linear in parameters
3. The focus is on the material characterization,
one well-defined catalyst state at the time
4. The model is drastically simplified for state-defining experiments
5. Numerical examples are given for reversible adsorption
Strategies of Catalyst Kinetic Characterization
PropertiesApplied Kinetics
Surface Science
TAP State-by-State
Transient
ScreeningCSTR PFR
Domain of
working
conditions
Normal Conditions
High and ultra-
high vacuum
conditions
The top of the
surface science
domain
(10-1-10-2 Pa)
Information
about multi-
component
industrial
catalysts
provides provides does not provide provides
Observation
Regimesteady-state
steady-state and
unsteady-state
steady-state and
unsteady-stateunsteady-state
Separation of
the chemical
reaction and
transport
Well-defined
convection and
perfect mixing are
assumed (the validity
domains are
discussed)
Well-defined
convection
Direct
measurements of
the chemical
reaction rate
(convective
transport is
eliminated)
Well-defined
diffusion
Knudsen diffusion
regime
(convection is
eliminated)
PropertiesApplied Kinetics
Surface Science
TAP State-by-State
Transient
ScreeningCSTR PFR
Catal. Compo-
sition in a sin-
gle unsteady-
state exp.
The catalyst composition does change, but
this change is not measured
The change of
catalyst com-
position is directly
observed
Insignificant change
of the catalyst
composition
Uniformity of
the catalyst
composition
within the
reaction zone
Uniformity is
assumed under
steady-state
conditions
There is axial non-
uniformity
(radial non-
uniformity is
neglected)
Surface
concentration
profiles can be
directly
characterized
The catalyst
composition is
uniform
Amount of gas
reactants stored
or released by
the catalyst
Are measured by
SSITKA-method
(typically, not
reliable)
Are measured by
SSITKA-method
(reliable for the
steady-state)
Directly measured
Directly measured in
a multi-pulse TAP
experiment
Model-free
analysis (no
assumption
about detailed
kinetic model)
Steady-state data can be analyzed in a
model-free manner, but
nonsteady-state data cannot be
For different
techniques, the
analysis can be
either model-free
or not
Model-free analysis
is possible
Strategies of Catalyst Kinetic Characterization
continued
CONCLUSIONS
A BRIDGE ACROSS THE “PRESSURE-GAP”:
TAP is waiting for you at this BRIDGE !
• BACK TO HISTORY…
• BACK TO CELEBRITIES…
Isaac Newton (1743-1727)
Gottfried Wilhelm Leibnitz (1646-1716)
‘Drop-by-drop’: titration,determination of the equivalent point
The origins of volumetric analysis are in late-18th-century French chemistry. Francois Antoine Henri Descroizilles developed the first burette (which looked more like a graduated cylinder) in 1791. Joseph Louis Gay-Lussac developed an improved version of the burette that included a side arm, and coined the terms "pipette" and "burette" in an 1824 paper on the standardization of indigo solutions
Manfred Eigen (1927): Chemical relaxation, but not calculus
Experimental calculus in chemistry: John T. Gleaves
Gregory S. Yablonsky
“It has seen further it is by standing on the
shoulders of giants”
(Isaac Newton,
Letter to Robert Hook, February 1676)
Acknowledgements
John Gleaves
Denis Constales
Guy Marin
THANK YOU
FOR YOUR ATTENTIVE PATIENCE !
Questions & Answers
177
178
Cg = 0
Fexit (t)
Finlet(t)
CgTZ(ω)RTZ(ω)
Fre
qu
en
cy d
om
ain
Thin catalytic zone
Inert zone Inert zone
CgTZ(t)RTZ(t)
F F T F F T F F T
I F FT I F FT
Solving inverse diffusion problemin two inert zones
Reconstructed kinetically model-freecharacteristics in the time domain
4 linear eqns. (2 for each zone)7 vector-variables (4 unknowns)
Yablonsky et al. Chem. Eng. Sci., 2007, 62, 6754-6767
Phenomenological representation of the transformation rate
The ‘Rate-Reactivity’Model (RRM)Rgi = ∑Rj (CM, , CMOx, Cad, NS, T) Cgj
+ Roj (CM, CMOx, Cad, NS, T) Ri, Roj are catalyst reactivities.Catalyst reactivities Ri and Roi are functions of intermediate concentrations. The last ones can be estimated as (Integral uptake ofreactants – Integral release of products)
Strategies of Catalyst Kinetic Characterization
PropertiesApplied Kinetics
Surface Science
TAP State-by-State
Transient
ScreeningCSTR PFR
Domain of
working
conditions
Normal Conditions
High and ultra-
high vacuum
conditions
The top of the
surface science
domain
(10-1-10-2 Pa)
Information
about multi-
component
industrial
catalysts
provides provides does not provide provides
Observation
Regimesteady-state
steady-state and
unsteady-state
steady-state and
unsteady-stateunsteady-state
Separation of
the chemical
reaction and
transport
Well-defined
convection and
perfect mixing are
assumed (the validity
domains are
discussed)
Well-defined
convection
Direct
measurements of
the chemical
reaction rate
(convective
transport is
eliminated)
Well-defined
diffusion
Knudsen diffusion
regime
(convection is
eliminated)