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FROM ATOMIC SCALE ORDERING TO MESOSCALE SPATIAL PATTERNS IN SURFACE REACTIONS: HCLG

FROM ATOMIC SCALE ORDERING TO MESOSCALE SPATIAL PATTERNS IN SURFACE REACTIONS: HCLG. MULTISCALE MODELING WORKSHOP II (KRATZER, RATSCH, VVEDENSKY) IPAM - UCLA OCT 2005. Jim Evans 1,2 , Dajiang Liu 1 : Stat Mech & Multiscale Modeling 1 Chemical Physics Program, Ames Laboratory USDOE

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FROM ATOMIC SCALE ORDERING TO MESOSCALE SPATIAL PATTERNS IN SURFACE REACTIONS: HCLG

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  1. 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

  2. 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

  3. 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 CO(ads)+O(ads)  CO2(gas) +2CO+O REACTION CO(ads)  CO(gas) +  CO-DESORPTION CO(ads) +  + CO(ads) RAPID CO-DIFFUSION PCO PO2 k d h MEAN-FIELD RATE AND REACTION-DIFFUSION EQUATIONS /t CO = PCOSCO - RCO+O - d CO + DCO2CO /t O = 2PO2SO2 - RCO+Owhere  = surface coverages SCO,O2 = sticking coeffts, RCO+O = reaction rate  k COO or… DCO h REFINEMENTS: SURFACE RECONSTRUCTION PROVIDES ADDITIONAL DEGREE OF FREEDOM

  4. Stable Inactive State …near CO-poisoned CO CO  BISTABILITY OF STEADY-STATES PCO Stable Reactive State …low CO coverage CO-partial pressure PCO PREDICTIONS OF MF RATE & RD EQUN: CO-OXIDATION CO(gas) +   CO(ads); O2(gas) + 2  2O(ads); CO(ads) + O(ads)  CO2(gas) + 2 Increase d, T Non-Equilibrium Critical Point: Bistability  Monostability Reaction-Diffusion Phenomena: Front Width & Velocity  (DCO)1/2 CO Inactive REACTION FRONT Spatial Non-Uniformity @ fixed (small) PCO Reactive x

  5. CO LOW T CO HIGH T PCO PCO EXPT STUDIES OF REACTION KINETICS: CO-OXIDATION ON Pt(111) Berdau et al. J. Chem. Phys. 110 (1999) 11551

  6. 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) • system with oscillatory kinetics • due to surface reconstruction • Temperature = 400 K 400 m Review: Imbihl & Ertl, Chem. Rev. 1995

  7. O 25 m CO SHORTCOMINGS OF MEAN-FIELD RDE TREATMENT LEEM IMAGE 300 K CO O KMC 300 K “COMPLEX” REACTION FRONTS: TITRATION OF PREADSORBED CO ON Pt(100) BY EXPOSURE TO O Tammaro, Evans, …Bradshaw, Imbihl, Surf Sci 407 (1998); also 307 (1994) ISLANDING & ORDERING IN REACTIVE STEADY-STATES: CO-OXIDATION ON Pd(100) @ 300K Realistic atomistic lattice-gas modeling Liu and Evans, PRB (04); JCP (05) • Adspecies are not well-stirred or • Randomly distributed (interactions) • Reaction rate  kCOO, etc. cf. Engel & Ertl. J. Cat. (1981) Fronts do have smooth tanh–form of MF RDE due to ordering & due to COMPLEX NATURE OF CHEMICAL DIFFUSION IN MIXED ADLAYERS

  8. 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)

  9. “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 COfor 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

  10. 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 

  11. STEADY-STATE BEHAVIOR d=0 OXYGEN ADATOMS 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) SYMMETRY-BREAKING TRANSITION FOR CHECKERBOARD ORDERING …TO UNEQUAL POPULATIONS OF THE TWO SUB-DOMAINS

  12. 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

  13. DCO DIFFUSION PATH for CO * 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] Lifshitz-Sepanova-type density expansion a1(monomer)=-1=2.14 (Ernst et al.) 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) O O 0

  14. 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

  15. 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)]

  16. SCALED VELOCITY (changes sign @ equistability) DIRECT SIMULATION HCLG DIFFUSION PATH for CO PROPAGATION VELOCITY OF REACTION FRONTS IN THE BISTABLE REGION EQUISTABILITY POINT HCLG MF CONST. Dco DIRECT SIMULATION with incr. hCO SIMPLE RDE ANALYSIS OF PERCOLATIVE TRANSPORT OF CO(ads) THRU COADS. O(ads) DCO,CO(O) See also: Liu & Evans, PRL 84 (00) 955; JCP 113 (00) 10252

  17. 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) *QADS(King et al 97) EQUILIBRIUM ORDERING: O/Pd(100) p(22) and c(22) O @ 4f hollow sites …O<0.5 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 2 a 3o = -0.02 eV (3NN attraction)GGA-PBE= -0.04eV LEED, TPD (Chang, Evans & Thiel, SS 89, Chang & Thiel JCP 88) c(22)-O p(22)-O LG MODEL ANALYSES: KMC, Transfer Matrix – Finite Size Scaling

  18. 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 ECO+O=0.73eV =big 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 CO O O “Typical” High-Coverage Reaction Config. 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)

  19. “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 PCO=0.07 Reactive state =p(2x2)-O + CO Inactive state = c(222)R45 CO + small holes • PARAMETERS: • Total Pressure • ~ 10-3 Torr • Tot. Ads. Rate PCO + PO2  1 s-1 REACTIVE STATE INACTIVE STATE

  20. 300 K Reactive State (O = 0.39ML) 300 K Reactive State (O = 0.28ML) 300 K Reactive State (O = 0.16ML) 300 K Near-CO-Poisoned State ? (O = 0.02ML)

  21. co,o CO O ~0.5 ML ~0.08 ML ~0.28 ML ~0 ML JCO’s -COCO -DCO,COCO -DCO,OO CO 0.13  max for 0 0  max x RESULTS OF HCLG ANALYSIS: FRONTS AND TRANSPORT INACTIVE STATE REACTIVE STATE “Complex” profile shape differs from tanh - form of standard MF RDE Latter = analogue of tanh-profile of Cahn - Allenphase bndries HCLG results validated by comparison with direct “brute force” KMC (scaling up simulations for lower CO hop rate) SIMULATION CONDITIONS: Temperature = 380 K Adsorption rates: PCO = 0.17 ML/s PO2 = 1 ML/s (equistability between reactive & inactive states  stationary front) CO mobility

  22. 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

  23. 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) TPR SIMULATIONS: CO2PRODUCTION ATOMISTIC LG REACTION MODEL O = 0.25 ML 360K peak O = 0.25 CO = 0.80 0.75 0.55 405 O = 0.25 CO= 0.24 0.11 0.05 0.03 0.01 0.005 405K peak CO = 0.40 0.28 0.19 0.10 0.050 low-T peak O PROCEDURE: 300K deposit 0.25ML O  p(22) 100K deposit various CO amounts Heat @ ~10K/s Monitor CO2production versus T CO High CO>0.25: Eact=0.73 Low CO: Eact=1.0 CO>0.1: Eact=1.0+=1.2

  24. 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, withm  0.6  1/2 CO STM Wintterlin et al. Science 278 (1997) JCP 114 (2001) Chaos 12 (2002) CO CO+O/Pt(111) @ 300K O

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