Titles and Abstracts
Desorption processes in 1D: A mesoscopic approach (2 talks)
by Enrique Abad and Fotis Vikas
Universite Libre de Bruxelles, Belgium
Lattice dynamics of the desorption reaction
A + A -> A + S: Role of diffusion (E. Abad)
A Boolean cellular automaton model is developed to describe the 1D lattice
dynamics of the irreversible desorption process A + A -> A + S.
The underlying classical rate equation predicts a $t^{-1}$ decay to a
zero-density state. We
study both the no-diffusion limit (immobile reactants) and the
diffusion-controlled case on an infinite lattice. In the absence
of diffusion,
deviations from mean field
behavior are observed both in the dynamics and in the steady states.
The long time behavior is characterized by relaxation toward a
nonvanishing
invariant state which depends on the initial conditions. If particles
are allowed to diffuse,
the density shows an anomalous $t^{-1/2}$ approach to the mean field
steady state, in agreement with the off-lattice solution. The early
time behavior, however, predicts a slower decay of the density, due
to the finite propagation velocity of a local density perturbation,
as opposed to the infinite propagation velocity characteristic of
diffusion.
A three-state model for reaction controlled cooperative
desorption on a one-dimensional lattice (F. Vikas)
We present a master equation approach for the analysis of the dynamics of
immobile reactants on a one-dimensional lattice, involving two reactive
species and vacant sites. A common feature of all the studied schemes is
the strong
dependence of the final coverage on the initial conditions, associated
with the lack of ergodicity of the invariant state. Our approach leads
to full agreement with Monte-Carlo simulations, both asymptotically and
dynamically.
A mean-field kinetic lattice gas model of
electrodeposition
by Marc-Olivier Bernard and Jean-Francois Gouyet
Laboratoire PMC, Ecole Polytechnique, 91128 Palaiseau cedex, France
Abstract
The arborescent growth of an electrode due to the reduction of an
electroactive cation (electrodeposition) was experimentally and
theoretically studied in a mesoscopic frame in the early 90's (see [1] as an
example).
Our aim is to generalize existing models of Mean Field Kinetic Equations
(MFKE, Martin [2] Gouyet [3]), previously applied to various physical
systems, such as intercalation [4], dentritic growth and spinodal
decomposition in alloys [5], in order to address electrochemical problems.
Electrochemical MFKEs involve solving the Poisson equation to determine the
electrostatic potential at any point of the system and to build a plausible
microscopic model for reduction at the cathode and dissolution at the anode.
We thus hope to obtain a better understanding of dendritic growth in
electrodeposition problems; in particular, the effects of crystal
anisotropy, rate of electronic transfer, the mobility of the ions and
nearest neighbour interactions.
References:
[1] V. Fleury, Croissance par voie electrochimique d'agregats metalliques
ramifies, te?se de l'Ecole polytechnique, 13 decembre 1991.
[2] G. Martin, Phys. Rev. B, 41 2279 (1990).
[3] J.F. Gouyet, Europhys. Lett., 21 [3], pp. 335-341 (1993).
[4] R. Nassif, Y. Boughaleb, A. Hekkouri, J.F. Gouyet and M. Kolb, Eur.
Phys. J. B, 1 453-464 (1998).
[5] M. Plapp, Phys. Rev. Lett. 78,26 p. 4970 (1997).
Simple reactions involving structured molecular systems: influence of the
internal dynamics
by Alexander Blumen and Gleb Oshanin,
University of Freiburg, Germany
Abstract
As is well known from polymer physics, even in the simplest Rouse-model
(involving point-like molecules connected to each other through springs) the
dynamics of the whole object may be quite complex. Thus even a single monomer
in a linear chain experiences first a sublinear motion, proportional to the
square-root of time, followed later by regular diffusion.
Such features effect drastically even the simplest decays, such as found for
trapping or for target annihilation [1].
In this talk we will focus on such simple A+B->B reactions, when the
particles under investigation have an internal structure. Examples will
involve, among others, dendrimers and star-like molecules [2,3]. As we will
show, this leads to quite complex dynamical patterns, and not in all cases
regular scaling laws are obeyed. Furthermore, the introduction of
hydrodynamic interactions (which must be accounted for in dilute solutions)
adds additional features to the decay laws.
References:
[1] S. Nechaev, G. Oshanin and A. Blumen, J.Stat.Phys.98, 281 (2000).
[2] P. Biswas, R. Kant and A. Blumen, Macromol.Theory Simul.9, 56 (2000).
[3] R. Kant, P. Biswas and A. Blumen, Macromol.Theory Simul., submitted.
Chemical Wave propagation in lattice-gas
models for surface reactions: Analysis of the hydrodynamic limit
by Jim Evans
Ames Laboratory and Dept of Mathematics, Iowa State University, USA
Abstract
We develop exact (non-mean-field) reaction-diffusion equations (RDE's) to
describe chemical or trigger wave propagation in a simple model for
CO-oxidation,
and front propagation in a simple model for the reactive removal of unstable
mixed NO+CO adlayers. Particular emphasis is placed on the appropriate
description of chemical diffusion in mixed adlayers, a key ingredient in
these RDE's. Results from the exact RDE's match direct KMC simulations.
References:
[1] M. Tammaro and J.W. Evans, J. Chem. Phys. 108, 762 (1998).
[2] M. Tammaro and J.W. Evans, J. Chem. Phys. 108, 7795 (1998).
[3] M. Tammaro and J.W. Evans, in "Computer Simulation Studies in CMP"
D.P. Landau & H.-B. Schuettler, Eds. (Springer, Berlin, 1999).
First-principle electronic structure
calculations as a tool for modelling surface reactions
by Fabio Finocchi
Laboratoire de Physique des Solides, Batiment 510, Universite Paris-Sud, Orsay,
F-91405, France
Abstract
The Density Functional Theory (DFT) has become a "standard" approach to
evaluate, from first principles,
the interaction energy between atoms in different physical states
(molecules, clusters, surfaces,
and solids) without making any "a-priori" approximation on the nature of the
chemical bond.
We review the theoretical basis of the DFT, with special emphasis on the
currently used approximations of the exchange-correlation energy functional.
We discuss how energy surfaces can be computed as a function
of the ionic coordinates, and stress the limitations and the accuracy of the
method. Presently, systems of few hundreds atoms can be studied, and their
dynamics followed for some tens of picoseconds.
Therefore, energy surfaces computed from first principles can be used as
input for other numerical approaches - such as kinetic Monte Carlo - able to
cope with larger length scales and longer simulation times. Moreover,
ab-initio molecular dynamics provides an unique way to look into atomic
scale
complex phenomena, such as bond breaking and reforming, often associated to
chemical reactions at surfaces.
As an illustration, we describe the interaction of water molecules with
MgO(100) surfaces, either
perfectly planar or containing defects, such as steps, edges, and vacancies.
Fluctuations in catalytic CO oxidation
by Ronald Imbihl
Institut fuer Physikalische Chemie
und Elektrochemie,
Universitaet Hannover, Germany
Abstract
A Dynamic Monte Carlo Method for Systems of Any Size?
by Tonek Jansen
Schuit Institute of Catalysis,
Eindhoven University of Technology,
P.O. Box 513,
5600 MB Eindhoven, The Netherlands
Abstract
I will discuss the idea of a Monte Carlo method in which a lattice-gas
model of a catalyst's surface is used with each grid point corresponding
to a block of sites. The number of adsorbates of each type is known for
each block, but not the adlayer structure within a block. By choosing
large blocks large systems can be simulated. As diffusion within a block
does not change the number of adsorbates in a block, the amount of
computer time spent on simulating diffusion can be substantially
reduced. The method can be speeded up even more by using a reduced
number of effective adsorbates instead of the number of real
adsorbates. One problem with the method is how to incorporate the
influence of structure of adlayer within the blocks on the
kinetics. Another is that with the effective adsorbates fluctuations may
not be taken into account correctly.
Mesoscale Dynamics of Reaction-Diffusion
Systems
by Raymond Kapral
Chemical Physics Theory Group, Department of Chemistry,
University of Toronto,
Toronto, Ontario M5S 3H6, Canada
Abstract
A mesoscale Markov chain description of reaction-diffusion media will
be used to explore the effects of fluctuations and correlations on
chemical oscillations and chemical waves. The range of
validity of macroscopic mass-action or reaction-diffusion models
and the consequences of their breakdown will be discussed. Simulations
and kinetic theory analyses on a number ofchemical models will be used
to illustrate the phenomena.
Adsorbate island formation and dynamics
at nanoscale resolution: Experiments and Simulations
by Norbert Kruse*, Christian Voss*, Valentin Medvedev*+,
Christopher Bodenstein#, David Hanon#, and Jean-Pierre Boon# (2 talks)
*Chemical Physics at Surfaces and Heterogeneous Catalysis, CP 243,
Universit\'e Libre de Bruxelles, 1050--Bruxelles, Belgium
#Center for Nonlinear Phenomena and Complex Systems, CP 231,
Universit\'{e} Libre de Bruxelles, 1050--Bruxelles, Belgium
+Department of Chemical Engineering, University of Washington, Seattle,
WA 98195-1750, USA
Abstract
Surface catalytic processes produce, under certain conditions, small
clusters of adsorbed atoms or groups, called {\em islands} which,
after they have been formed, move as individual entities. Here we
consider the catalytic reduction of NO with hydrogen on platinum.
(i) Using video field ion microscopy, we observe the dynamic motion of
small hydroxyl islands on the Pt(001) plane; despite changes in their
morphology, the islands dimensions are confined to values corresponding
to 10 to 30 Pt atoms suggesting cooperative effects to be in operation.
(ii) We construct an automaton (or lattice Monte-Carlo) model on the
basis of a set of elementary processes governing the microscopic
dynamics. The agreement between the simulation results and the
experimental observations suggests a possible mechanism for the
formation and dynamics of hydroxyl islands.
Reference:
[1] N. Kruse, C. Voss, V. Medvedev,
C. Bodenstein, D. Hanon, and J.-P. Boon, J. Stat. Phys. (to appear
June 2000).
New insights for the A+A -> 0 problem in one dimension
by Katja Lindenberg
University of California - San Diego, USA
Abstract
Recent work on the dynamical aspects of the A+A-> 0 reaction
(in particular the effect of the distribution of sources)
is presented. Our approach is
mesoscopic, but the inspiration and results come from a microscopic
simulation of a kink-antikink problem.
Ordering, percolation and diffusion
in a lattice gas model for co-oxidation with superlattice ordering of
oxygen
by Da-Jiang Liu
Ames Laboratory, Iowa State University, USA
Abstract
An order-disorder transition is found in a nonequilibrium surface reaction
model for CO-oxidation with superlattice ordering of adsorbed oxygen. This
ordering transition strongly influences the percolation properties of
superlattice domains of oxygen, which in turn are shown to control the
chemical diffusion of coadsorbed CO. The latter constitutes a new type
of problem involving transport in disordered media, which is important as
CO-diffusion controls spatial pattern formation in the reaction system.
Reference:
[1] D.-J. Liu and J.W. Evans, Phys. Rev. Lett. 84, 955 (2000).
Landau-type mean-field theory of the Langmuir-Hinshelwood reactions
between interacting particles on heterogeneous catalytic substrates
by Gleb Oshanin
Laboratoire de Physique
Theorique des Liquides,
Universite Paris VI,
T.16, 4 place Jussieu,
75252 Paris, France
Abstract
Reactive dynamics on low dimensional
supports: A Lattice Limit Cycle model
by Astero Provata
National Research Center "Demokritos", Athens, Greece
Abstract
The Lattice Limit Cycle (LLC) model is proposed as
a lattice compatible reactive mechanism which in the
mean field limit gives rise to sustained limit cycle oscillations.
The LLC model concerns an open process and involves reaction,
adsorption and desorption mechanisms.
The same model, realised by Monte-Carlo simulations on a 2-d lattice
gives rise to sustained oscillations of the local concentrations
on the lattice. These local
oscillations are due to a) local fluctuations
and b) competition between domains of different species.
The oscillator characteristics depend on the system parameters and
on the lattice geometry.
Such surface concentration oscillations
are observed in catalytic process eg. the CO oxidation on Pt surface.
References:
[1] A. Provata, G. Nicolis and F. Baras,
J. Chem. Phys. 110 (1999) 8361.
[2] A. Shabunin, F. Baras and A. Provata (submitted).
Reaction fronts in hydrogen oxidation on Pt(111); modelling and
quantitative description of STM experiments
by Christian Sachs, M. Hildebrandt, S. Völkening, J. Wintterlin and G.
Ertl
Fritz-Haber-Institut der Max-Planck-Gesellschaft, Abt. PC
Faradayweg 4-6 14195 Berlin, Germany
Abstract
Recently we suggested an autocatalytic mechanism for the oxidation
of hydrogen on Pt(111) below the desorption temperature of H2O [1,2]:
O + H -> OH (I)
OH + H -> H2O (II)
2 H2O + O -> 3 OH + H (III)
This autocatalytic meachanism leads to the formation of reaction
fronts on a 100 to 1000 Å scale that were observed by STM over a
range of temperatures. Because water is mobile under these conditions
the combined reactions II and III represent a reaction diffusion
system. The front velocity, obtained from an analytical treatment
and also from numeric simulations, depends on the two reaction rates
and the diffusion constant of water. LEED and STM experiments were
performed in order to measure these parameters. The front velocities
evaluated on the basis of these data agree with those
determined by the STM experiments. Additionally it is possible to
derive their temperature dependence.
References:
[1] S. Völkening, K. Bedürftig, K. Jacobi, J. Wintterlin, and
G. Ertl, Phys. Rev. Lett. 83, 2672 (1999).
[2] K. Bedürftig, S. Völkening, Y. Wang, J. Wintterlin, and G.
Ertl, J. Chem. Phys. 111, 11147 (1999).
Exact solution for front propagation in a one-dimensional epidemic model
by C. Warren, E. Somfai*, and Leonard Sander
Dept. of Physics, The University of Michigan,
Ann Arbor, MI 48109-1120, USA
Abstract
We study the discrete model of the irreversible autocatalytic reaction
A + B -> 2A in one dimension, which is a version of the model of
J. Mai, I.M. Sokolov and A. Blumen, Phys.Rev.Lett. vol. 77, 4462 (1996),
which can also be regarded as the simplest way to look at the spread of an
epidemic. We are able to solve the model exactly in one dimension for low
concentrations. We find that in the low-concentration limit the average
velocity of propagation approaches c/2 where c is the concentration. The
front propogation is entirely dominated by fluctuations in the density: the
front spends most of its time pinned behind gaps in the density. We have
numerical results to indicate that this behavior is preserved in two
dimensions, and thus may give some guidance for the behavior of real surface
reactions, and even epidemics in populations that are not well mixed.
Supported by DOE grant DEFG-02-95ER-45546.
*Current address: Instituut Lorentz, Leiden, NL-2333
Chemoconvection: A fluid instability driven by a surface chemical reaction
by Francesc Sagues
Departament de Quimica Fisica,
Universitat de Barcelona, Spain
Abstract
We will report a systematic experimental study of pattern formation in
a thin fluid layer driven by a simple surface chemical reaction. The hydrodyn
amic instability arises due to the increase of fluid density in the sub-
surface layer caused by the oxidation of glucose to gluconic acid with the
methylene blue as a catalyst. The role of different parameters (chemical con
centrations, temperature, layer thichness, etc) are analyzed. In addition a
theoretical model is developed based on the coupling of a simplified chemical
scheme with the Navier-Stokes equation. A linear stability analysis is
performed whose results are compared with the experimental observations.
Stochastic simulations of excitable dynamics with applications to
heterogeneous catalysis
by Lutz Schimansky-Geier
Institute of Physics, Humboldt-University at Berlin
Invalidenstr. 110, D-10115 Berlin, FR Germany
Abstract
It is well known that in systems far from
equilibrium an increasing noise may exhibit more ordered
state. Typical examples of this 'unusual` behavior are stochastic
resonance, noise induced directed motion and noise induced phase
transitions.
We apply noise to excitable systems which model a wide
class of dynamical behavior in biophysics and chemistry. First we
exemplify the ordering role of noise on behalf of a time-dependent
excitable dynamics. We calculate the output spectrum of the dynamics
and show that an increase of the noise level generates oscillating
outputs. If additionally a periodic force drives the excitable
dynamics stochastic resonance is supported by this oscillations.
In the second part distributed coupled excitable units under noise are
investigated. First we show that the presence of noise sustains moving
structures of excitations in the medium. Beginning with a certain
noise level the system of coupled units exhibits synchronized
collective oscillations. Applications to heterogeneous catalysis is
discussed and different simulation algorithms are presented.
Front propagation in one-dimensional autocatalytic systems
by I. M. Sokolov, J. Mai and A. Blumen
University of Freiburg, Germany
Abstract
We consider the front propagation in an autocatalytic reaction between
particles which perform random walks on a lattice and react on contact
according to the A+B -> 2A reaction scheme. The classical,
continuous-medium description of this reaction leads to a Fisher equation
whose front solutions can in principle propagate with any velocity $v>v_{c}=2%
\sqrt{kDc}$, with $k$ being the local reaction rate, $D$ the diffusion
coefficient and $c$ the particles' concentrations. The marginal stability
principle requires that for rather general initial conditions the minimal
velocity is the one really attained.
The discrete structure of real systems leads to strong departures from this
prediction, since it introduces new length-scales into the problem (e.g. the
interparticle distance $\lambda =c^{-1/d}$), which determine the local,
small-scale structure of the system. In a 1d system (where the classical
reaction scheme is absolutely inappropriate) this leads to a stable
propagation of the front with a velocity which is fully determined by local
ordering phenomena. This situation is modelled numerically under different
conditions, e.g. for equal and different diffusion coefficients of reacting
species and also taking the finite life-time of $B$-particles into account.
The discussion of the front structure assumes the introduction of a comoving
coordinate frame. This can either be taken to move with an average velocity,
or can be defined in each realization separately. Since different
definitions emphasise different aspects of the local ordering, the average
front forms obtained for different coordinate frames differ.
The results of our numerical simulations for the front velocity and of the
front forms are discussed within a theoretical framework based on a
Smoluchowski-like approximation and on the biased random-walk approach.
References
[1] J. Mai, I.M. Sokolov and A. Blumen, Phys.Rev.Lett. vol. 77,
4462 (1996).
[2] J. Mai, I.M. Sokolov, V.N. Kuzovkov and A. Blumen, Phys. Rev. E,
vol. 56, 4130 (1997).
[3] V.N. Kuzovkov, J. Mai, I.M.Sokolov, and A. Blumen, Phys. Rev. E,
vol. 59, 2561 (1999).
Molecular Dynamics
simulations of chemical reactions in condensed fluids
by Soeren Toxvaerd
University of Copenhagen, Denmark
Abstract
Simulations of three different reaction schemes for the isomerization
kinetics in a condensed fluid mixture between two species which only differ
marginally in pair energies show that the
mixture is bistable and that one of the species dominates
at late reaction times.
The kinetics are without random elements and are performed on the
basis of the steepest descent method in the potential energy. The
kinetics establish
a domain decomposition with critical fluctuations which ensure the
symmetry break.
The model(s) offers a possible explanation of origin of biomolecular
chirality.
Simulations of the reaction kinetics on nanometer
supported catalyst particles
by P. Thormahlen*, H. Persson*, B. Kassemo* and V. P. Zhdanov*#
*Competence Center for Catalysis and Department of Applied Physics,
Chalmers University of Technology, 41296 Goteborg, Sweden
# Boreskov Institute of Catalysis, Russian Academy of Sciences,
Novosibirsk 630090, Russia
Abstract
Real catalysts frequently consist of nm-sized (1-100 nm) metal particles
deposited on the internal surface of a more or less inactive porous support.
The complexity of such systems in combination with relatively high
(atmospheric) reactant pressures, typical for practical catalysis, hinders
the application of surface science methods to their full potential and
makes it difficult to interpret the measured reaction kinetics on the basis
of kinetic data for single-crystal samples.
To bridge these pressure and structure gaps and to form a conceptual basis
for the understanding of reactions occurring on supported catalyst,
we have performed simulations scrutinizing
qualitatively new effects in the reaction kinetics on the nm scale.
The attention is focused on the particle size range where the catalyst
particles have reached sufficient size to essentially have the electronic
properties of bulk crystals, but where they are still small enough that
the kinetic effects connected with the particle size are important.
We treat in detail such factors inherent for nm chemistry as reactant supply
via the support, interplay of the reaction kinetics on different facets
of supported particles due to interfacet diffusion, adsorbate-induced
reshaping of catalyst particles, and oscillation and chaos on the nm scale.
All these factors are demonstrated to be especially important in the case
of rapid catalytic reactions occuring far from the adsorption-desorption
equilibrium. As a general conclusion, we find that kinetic effects alone
(i.e. no special kinetic effects or "active sites") can cause large
differences in reaction kinetics on nm particles and single crystals.
In-situ dynamic study of hydrogen oxidation on rhodium
by Thierry Visart de Bocarme
Universite Libre de Bruxelles, 1050 Bruxelles, Belgium
Abstract