Transcript maws2 5461

FROM ATOMIC SCALE ORDERING TO MESOSCALE
SPATIAL PATTERNS IN SURFACE REACTIONS: HCLG
MULTISCALE MODELING WORKSHOP II (KRATZER, RATSCH, VVEDENSKY) IPAM - UCLA OCT 2005
Jim Evans1,2, Dajiang Liu1: Stat Mech & Multiscale Modeling
1Chemical Physics Program, Ames Laboratory USDOE
2Mathematics Dept., Iowa State University, Ames, Iowa
MULTISCALE MODELING
OF MESOSCALE REACTION
FRONT PROPAGATION IN
CO-OXIDATION ON Pd(100)
HETEROGENEOUS COUPLED
LATTICE-GAS (HCLG)
SIMULATION APPROACH
…parallel LG simulations coupled
via mesoscale CO surface diffusion
Phys. Rev. B 70 (2004) 193408; SIAM Multiscale Modeling Sim. 4 (2005) 424
OUTLINE
PART I:
CO-OXIDATION - KINETICS AND FRONTS
Traditional Modeling: mean-field rate equations & reaction-diffusion equations (RDE)
Expts: kinetics and steady-states, electron microscopy
 Limitations of mean-field !
PART II: CONNECTINGTHELENGTHSCALES FROM
LOCAL ORDERING TO MESOSCALE PATTERNS
HCLG Multiscale Modeling to describe spatial patterns & reaction fronts on a large
a characteristic length scale (microns) incorporating precise atomic scale information
Collective or chemical diffusion on surfaces: non-trivial Onsager transport problem
PART III: CANONICAL ATOMISTIC LATTICE-GAS MODEL
Adspecies ordering; kinetics & steady-states; percolative chemical diffusion; HCLG
PART IV: REALISTIC MODELING FOR CO+O/Pd(100)
Development of atomistic LG model; HCLG results
MEAN-FIELD RATE EQUATIONS & REACTION-DIFFUSION
EQUATIONS (RDE’s) FOR CO-OXIDATION ON SURFACES
CO(gas) +   CO(ads)
CO-ADSORPTION
O2(gas) + “ 2 ”  2O(ads)
O2-ADSORPTION
PCO
PO2
CO(ads)+O(ads)  CO2(gas) +2 CO+O REACTION
k
CO(ads)  CO(gas) + 
CO-DESORPTION
d
CO(ads) +    + CO(ads)
h
RAPID CO-DIFFUSION
MEAN-FIELD RATE AND REACTION-DIFFUSION EQUATIONS
/t CO = PCOSCO - RCO+O - d CO + DCO2CO
/t O = 2PO2SO2 - RCO+O
where  = surface coverages
SCO,O2 = sticking coeffts, RCO+O = reaction rate  k COO or… DCO  h
REFINEMENTS: SURFACE RECONSTRUCTION PROVIDES ADDITIONAL DEGREE OF FREEDOM
PREDICTIONS OF MF RATE & RD EQUN: CO-OXIDATION
CO(gas) +   CO(ads); O2(gas) + 2  2O(ads); CO(ads) + O(ads)  CO2(gas) + 2
CO
Stable Inactive State
…near CO-poisoned
CO

BISTABILITY
Increase d, T
OF STEADY-STATES
PCO
Stable Reactive State
…low CO coverage
Non-Equilibrium Critical Point:
Bistability  Monostability
CO-partial pressure PCO
CO
Spatial Non-Uniformity
@ fixed (small) PCO
Reaction-Diffusion Phenomena:
Front Width & Velocity  (DCO)1/2
Reactive
Inactive
REACTION
FRONT
x
EXPT STUDIES OF REACTION KINETICS: CO-OXIDATION ON Pt(111)
Berdau et al. J. Chem. Phys. 110 (1999) 11551
CO HIGH T
CO LOW T
PCO
PCO
PHOTO-EMISSION ELECTRON MICROSCOPY (PEEM) STUDIES: CO-OXIDATION
CO-OXIDATION ON Pt(111)
- a classic bistable system
Expansion of reactive state
into CO-poisoned state
facilitated by an “O-defect”
Temperature = 413 K
PEEM studies by Christmann &
Bloch groups, JCP 110 (99) 11551
380 m
CO-OXIDATION ON Pt(110)
Temperature = 400 K
Review: Imbihl & Ertl, Chem. Rev. 1995
400 m
- system with oscillatory kinetics
due to surface reconstruction
SHORTCOMINGS OF MEAN-FIELD RDE TREATMENT
CO
O
KMC
300 K
LEEM
IMAGE
300 K
O
25 m
CO
CO-OXIDATION ON Pd(100) @ 300K
“COMPLEX” REACTION FRONTS:
TITRATION OF PREADSORBED CO
ON Pt(100) BY EXPOSURE TO O
Realistic atomistic lattice-gas modeling
Liu and Evans, PRB (04); JCP (05)
Surf Sci 407 (1998); also 307 (1994)
ISLANDING & ORDERING IN
REACTIVE STEADY-STATES:
Adspecies are not well-stirred or
Randomly distributed (interactions)
Reaction rate  kCOO, etc.
cf. Engel & Ertl. J. Cat. (1981)
Tammaro, Evans, …Bradshaw, Imbihl,
Fronts do have smooth tanh–form
of MF RDE due to ordering & due to
COMPLEX NATURE OF CHEMICAL
DIFFUSION IN MIXED ADLAYERS
HETEROGENEOUS COUPLED LATTICE-GAS (HCLG) ANALYSIS
...for simple reaction model, J. Chem. Phys. (1995)
Exact Reaction-Diffusion Eqns
/t CO = RCO({CO,O}) - JCO
/t O = RO({CO,O})
where {CO,O} denotes the full
configuration of the adlayer
Simultaneous LG simulations distributed across reaction front.
Extract simultaneously reaction kinetics and CO chemical diffusivity.
CO(i) = “RCO t” + [JCO(i-1i) - JCO(ii+1)]t, O(i) = “RO t”
HCLG: Tammaro, Sabella, Evans JCP (95); Liu & Evans PRB (04); SIAM-MMS (05)
cf. Heterogeneous Multiscale Method E & Enquist (03); Gap-tooth Method Kevrekidis et al. (03)
“EXACT” TREATMENT OF CO SURFACE MASS TRANSPORT
EXTENSIVE STUDIES on CHEMICAL (COLLECTIVE) DIFFUSION in INTERACTING
SINGLE SPECIES ADLAYERS, e.g., Gomer, Rep. Prog. Phys. (1990), but here…
CHEMICAL DIFFUSION IN MIXED INTERACTING ADLAYERS
Low CO… percolative diffusion of CO(ads) through relatively immobile coads. O(ads)
JCO = -CO CO for Onsager coefft. CO= CO-conductivity/(kT)
…so in addition to reaction kinetics, parallel HCLG simulations must also
determine the (collective) CO mobility, CO, & CO chemical potential, CO
(e.g., via Widom insertion method). Numerical implementation via…
JCO(kk+1) = - CO(k+½)[CO(k+1)-CO(k)] with CO(k+½ )= ½ [CO(k)+CO(k+1)]
...fairly mobile O(ads)  local adlayer equilibration ?  CO= CO(CO, O)
…or no CO-CO or CO-O interactions  random CO  ditto
 JCO = - DCO,CO CO - DCO,O O
where DCO,CO & DCO,O = (thermodynamic factors)  CO
…second “cross-term” always ignored in traditional MF RDE modeling
CANONICAL ATOMISTIC LATTICE-GAS MODEL: CO-OXIDATION
PRL 82 (99) 1907; J Chem Phys 111 (99) 6579; PRL 84 (00) 955, JCP 113 (00); Chaos 12 (02); SIAM MSS 4 (05)
KEY MODEL FEATURES:
SQUARE-LATTICE OF
ADSORPTION SITES
FOR BOTH CO AND O

VERY STRONG NN
O-O REPULSION
 NO O-O NN PAIRS
 CHECKERBOARD
C(2X2) ORDERING
 EIGHT-SITE RULE
FOR ADSORPTION
CONSIDER REGIME OF
RAPID DIFFUSION OF
CO: h >> other rates
 CO IS RANDOMLY
DISTIBUTED ON SITES
NOT OCCUPIED BY O
REACTION KINETICS & STEADY-STATE BIFURCATIONS
d/dt CO = PCO(1-CO-O) - 4kOCOloc - dCO = RCO(CO,{O})
d/dt O = 2PO2SO2({O}, CO) - 4kOCOloc = RO(CO,{O}) where…
SO2= probability of 8-site ads ensemble; COloc=CO/(1-O)
STEADY-STATE BEHAVIOR
OXYGEN ADATOMS
d=0
SYMMETRY-BREAKING TRANSITION
FOR CHECKERBOARD ORDERING
…TO UNEQUAL POPULATIONS
OF THE TWO SUB-DOMAINS
SURFACE CHEMICAL DIFFUSION OF CO & EXACT RDE’S
/t CO = RCO(CO,{O}) - JCO, and /t O = RO(CO,{O})
where RCO = PCO(1-CO-O) - 4kOCOloc and RO = 2PO2SO({O}, CO) - 4kOCOloc and…
JCO = - DCO,COCO - DCO,O O (Onsager transport theory)
JCO = -CO CO for CO chem potential CO = kBT ln[CO/(1-CO-O)]
so… DCO,O
= CO(1-O)-1 DCO,CO = COloc DCO,CO
Also DCO,CO = DCO(O) is independent of CO but decreases with O
i.e., many-particle CO chemical diffusion problem
reduces to a problem of single-particle percolative
diffusion for CO through a labyrinth of coadsorbed O
ANALYSIS OF CO PERCOLATIVE DIFFUSION
LOW O: DIFFUSION AROUND ISOLATED OBSTACLES (ADSORBED O)
DCO = D0[1-a1 O - a2 (O)2 -…]  D0[1 - a1 O]
a1(monomer)=-1=2.14 (Ernst et al.)
Lifshitz-Sepanova-type density expansion
a1(dimer) = 2.96 (Liu & Evans)
HIGH O: PERCOLATIVE DIFFUSION (ALONG DOMAIN BOUNDARIES)
Cessation of diffusion  lack of percolation of domain boundary diffusion paths
 percolation of c(2x2) O-domains  symmetry-breaking in the O adlayer
DCO ~ D0 [*- O] where  = dynamic critical exponent for percolative transport
 = 1.3 (random percolation Alexander-Orbach)  = 1.4 (Ising HS: Liu & Evans)
DCO
O
*
DIFFUSION
PATH for CO
O
0
O
DIFFUSION PATH AT THE
PERCOLATION THRESHOLD
WHEN PERCOLATION OCCURS
AFTER SYMMETRY BREAKING
Dynamical Critical Exponent  = 1.3
DIFFUSION PATH AT THE
PERCOLATION THRESHOLD
FOR SIMULTANEOUS
PERC & SYMM-BREAKING
Dynamical Critical Exponent =1.4
HETEROGENEOUS COUPLED LATTICE-GAS SIMULATION
Liu and Evans, SIAM Multiscale Modeling Sim. 4 (2005) 424
CO
k-1
k
k+1
JCO(kk+1)= - DCO,CO(k+½)[CO(k+1)-CO(k)]/x - DCO,O(k+½)[O(k+1)-O(k)]/x
with D..(k+½ )= ½ [D..(k)+D..(k+1)]
PROPAGATION VELOCITY OF REACTION FRONTS IN THE BISTABLE REGION
EQUISTABILITY POINT
SCALED VELOCITY
(changes sign
@ equistability)
HCLG
MF CONST. Dco
DIRECT
SIMULATION
DIRECT
SIMULATION
with incr. hCO
HCLG
SIMPLE
RDE
ANALYSIS OF PERCOLATIVE TRANSPORT OF CO(ads) THRU COADS. O(ads)
DIFFUSION
PATH for CO
See also: Liu & Evans, PRL 84 (00) 955; JCP 113 (00) 10252
DCO,CO(O)
LATTICE-GAS MODEL DEVELOPMENT: CO+O/Pd(100)
CO
EQUILIBRIUM ORDERING: CO/Pd(100)
c(222)R45 CO @ bridge sites …CO<0.5
SEPN
REPULSION
a/2 1CO =  (exclusion)
a
2CO = 0.17 eV * # GGA-PBE=0.22eV
2 a
3CO = 0.03 eV # GGA-PBE=0.02eV
10 a/2 4CO  0
#LEED, TPD (Behm et al 80) *Q
ADS (King et al 97)
EQUILIBRIUM ORDERING: O/Pd(100)
p(22) and c(22) O @ 4f hollow sites …O<0.5
c(22)-O
SEPN INTERACTION
a
1o = 0.36 eV (NN repulsion) GGA-PBE=0.37eV
2 a 2o = 0.08 eV (2NN repulsion) GGA-PBE=0.10eV p(22)-O
2 a 3o = -0.02 eV (3NN attraction) GGA-PBE= -0.04eV
LEED, TPD (Chang, Evans & Thiel, SS 89, Chang & Thiel JCP 88)
LG MODEL ANALYSES: KMC, Transfer Matrix – Finite Size Scaling
LATTICE-GAS MODEL DEVELOPMENT: CO+O/Pd(100)
KINETICS OF ADSORPTION:
Steering of CO to on-top sites (allow occupation of bridge, hollow and on-top sites)
Eight-site rule for dissociative adsorption of O (2NN ads. sites with 6 NN free of O)
KINETICS OF CO DESORPTION:
EbCO = 1.6 eV from bridge (low CO) with b = 1016/s (Behm et al. 80) GGA-PBE=1.9 eV
KINETICS OF DIFFUSION:
EdO = 0.65 eV - non-equil. ordering (LEED) GGA-PBE = 0.35 eV; EdCO ~ 0.2 eV (rapid CO diffusion)
ECO+O=1.0eV =0.19eV
CO+O INTERACTION & REACTION:
Low coverages: CO(br)+O(4fh)CO2(gas)
High coverage reaction: CO forced to 4fh
site by p(2x2)- or c(2x2)-O …lower barrier
CO
ECO+O=0.73eV =big
CO
O
“Typical”
Reaction Config.
O
High-Coverage
Reaction Config.
Zhang & Hu JACS 123 (2001) 1166 DFT
References:
CO/Pd(100):
Liu, JCP 121 (04); Eichler & Hafner, PRB 57 (98) ; Behm et al. JCP (80)
O/Pd(100):
Liu & Evans, SS 563 (04); Chang & Thiel, PRL (87) JCP (88); Evans, JCP (87)
CO+O/Pd(100): Liu & Evans, PRB 70 (04); JCP (05) submitted; Zhang & Hu, JACS (01)
“EXACT” STEADY-STATE BIFURCATION BEHAVIOR: BISTABILITY
STEADY-STATE BEHAVIOR (KMC)
for CO coverage vs. PCO for various T
BIFURCATION DIAGRAM (KMC)
for bistability region in (PCO,T)-plane
NON-EQUILIBRIUM CRITICAL POINT
(CUSP BIFURCATION)
STABLE INACTIVE STATES
Reactive
State only
UNSTABLE
STATES
Inactive
State only
PCO
STABLE REACTIVE STATES
CO =
O =
400K
PARAMETERS:
Total Pressure
~ 10-3 Torr
Tot. Ads. Rate
PCO + PO2  1 s-1
PCO=0.07
REACTIVE STATE
INACTIVE STATE
Reactive state = p(2x2)-O + CO
Inactive state = c(222)R45 CO
+ small holes
300 K Reactive State (O = 0.39ML)
300 K Reactive State (O = 0.16ML)
300 K Reactive State (O = 0.28ML)
300 K Near-CO-Poisoned State ? (O = 0.02ML)
RESULTS OF HCLG ANALYSIS: FRONTS AND TRANSPORT
co,o
INACTIVE STATE
CO
~0.5 ML
~0 ML
JCO’s
-COCO
REACTIVE STATE
“Complex” profile
shape differs from
tanh - form of
standard MF RDE
O
~0.08 ML
Latter = analogue of
tanh-profile of Cahn
- Allen phase bndries
~0.28 ML
-DCO,COCO
HCLG results validated
by comparison with
direct “brute force” KMC
(scaling up simulations
for lower CO hop rate)
-DCO,OO
CO
SIMULATION CONDITIONS:
0.13  max for 0
Temperature =
CO mobility
0  max
x
380 K
Adsorption rates:
PCO = 0.17 ML/s PO2 = 1 ML/s
(equistability between reactive &
inactive states  stationary front)
SUMMARY
♦ MULTISCALE HCLG MODELING EFFECTIVELY
INCORPORATES ATOMIC SCALE INFORMATION INTO
DESCRIPTION OF MESOSCALE FRONT PROPAGATION
…compare with similar applied math multiscale methods:
Gap-tooth methods for hydrodynamic systems – Kevrekidis
Heterogeneous Multiscale Methods (HMM) – E & Enquist
♦ KEY FACTOR: CORRECT TREATMENT OF DIFFUSIVE
TRANSPORT – non-trivial, collective diffusion in interacting,
mixed species lattice-gas models for surface adlayers
♦ APPLICATION TO SPECIFIC SYSTEM: CO+O/Pd(100)
Challenge: to describe complex adlayer ordering mediated
by weak adspecies interactions; determined from expt & DFT
TPR STUDIES: COMPARISON OF MODEL WITH EXPERIMENT
TPR EXPERIMENTS: CO2 PRODUCTION
Below: Stuve et al., Surf. Sci. 146 (1984)
Also: Zheng & Altman, JPC B 106 (2002)
405
O =
0.25
TPR SIMULATIONS: CO2 PRODUCTION
ATOMISTIC LG REACTION MODEL
O =
360K peak
0.25
CO =
O = 0.25 ML
405K peak
0.80
CO =
CO=
0.24
0.75
0.11
0.40
0.28
0.19
0.10
low-T peak
0.05
0.03
0.01
0.005
0.55
0.050
O
PROCEDURE:
300K deposit 0.25ML O  p(22)
100K deposit various CO amounts
Heat @ ~10K/s
Monitor CO2 production versus T
CO
High CO>0.25: Eact=0.73
Low CO: Eact=1.0
CO>0.1: Eact=1.0+=1.2
ATOMISTIC MODELING OF STM-BASED TITRATION STUDIES
Pre-deposit O at low T: create c(2x2) domains plus antiphase boundaries. Expt: Chang et al. PRL (87)
Then expose to CO @ 300K: titrates O(ads), initially preferentially reacting at domain boundaries.
KMC
CO+O/Pd(100) @ 300 K
O
Reaction rate ~ (O)m,
with m  0.6  1/2
CO
STM
Wintterlin et al.
Science 278 (1997)
JCP 114 (2001)
Chaos 12 (2002)
CO
O
CO+O/Pt(111) @ 300K