Dynamics at the Mesoscale:
Theory, Modelling and Experiments

September 8-11, 2004

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Scientific Background

Currently, processes taking place at the nano and meso-scales have attracted the interest of a large part of the scientific community because they are responsible for the macroscopic properties of materials. Detailed study of the mechanisms acting in these scales is essential for the design of new materials with prescribed physical, mechanical, thermal, transport and interfacial properties. Besides, the study of nanostructured systems addresses many important questions which require the development of specific analysis tools. Statistical physics and thermodynamics, nonlinear physics and stochastic processes, mesoscopic simulations and molecular dynamics are concerned since it is essential to adopt a multi-scale point of view.

At the mesoscopic level, only one hundred or one thousand of elementary constituents may adopt collective behavior and organize themselves into complex spatio-temporal structures. For such small systems, it is expected that the emergence of macroscopic properties are affected by intrinsic fluctuations and microscopic aspects such as local interactions. Sophisticated experimental techniques are becoming increasingly powerful and allow to perform real-time in-situ observations at the meso and nanometer scales. The resolution in time and space is so good that the mesoscopic properties are directly detectable on the experimental sample.

Numerous experiments have manifested the role of fluctuations [1]. In the case of surface reactions, transient effects associated with local pattern formation have been observed by applying scanning tunneling microscopy (STM) [2,3]. Field ion microscopy (FIM) is used to obtain nanoscale information on the occurrence of kinetic instabilities with sustained oscillations, propagating waves and explosive behavior on catalytic supports [4]. The coupling with atom probe method gives informations on the chemical nature of the processes involved. The novel technique of digital high-speed microscopic video recording allows in-situ observations of rapid processes such as high temperature heterogeneous reactions used in the synthesis of advanced materials [5]. Moreover, a large amount of work has been performed to extract the statistical properties of fluctuations thanks to appropriate treatment of collected experimental data [6,7].

The dynamical aspects of meso and nanophenomena are particularly interesting [8-11]. Numerous investigations have recently been developed to explain experimental results, to explore the applicability of theoretical approaches and to develop appropriate modeling [12-18]. In this respect, nanostructured chemical systems provide good examples for such study since reactive processes act as a generator of complexity. Moreover it is now well established that the stochastic approach of reactive systems and related numerical methods are well suited to treat these systems [19]. Problems related to transport phenomena are very significant at this scale. Understanding the diffusion process on the surface or in a solid, using an appropriate mesoscopic description and extracting kinetic pathways from microscopic information, explaining the growth of nanostructures by cluster deposition are challenging problems [20-25]. Another important problem is how to describe a porous nanostructured support using the standard tools of macroscopic theory for instance in the case of thermal conduction [26]. The relation between heterogeneity, stochasticity and transport has to be considered [27,28].

Discovering the microscopic mechanisms involved in meso and nanophenomena [29] and exploring the coupling between the mesoscopic level and the collective behavior are very actual problems to be addressed in this meeting.

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References

[1] R. Imbihl
" Fluctuations in catalytic surface reactions",
New J. Phys. , 5 , no. 62 (2003)

[2] S. V\"olkening and J. Wintterlin
"CO oxidation on Pt(111) - Scanning tunneling microscopy experiments and Monte Carlo simulations"
J. Chem. Phys. , 114 , 6382 (2001)

[3]B.L.M. Hendriksen et J.W.M. Frenken,
"CO oxidation on Pt(110): scanning tunneling microscopy inside high-pressure flow reactor",
Phys. Rev. Lett. , 89 , 04601 (2002)

[4] T. Visart de Bocarm\'e and N. Kruse,
" CO oxidation on Gold Surfaces Studied on the Atomistic Scale",
Catalysis Letters , 74 , 127 (2001)

[5] A. Varma, A.S. Rogachev, A.S. Mukaysan and S. Hwang,
"Complex behavior of self-propagating reaction waves in heterogeneous media",
Proc. Natl. Acad. Sci. , 95 , 11053 (1998)

[6] Yu. Suchorski, J. Beben and R. Imbhil,
"Spatio-temporal dynamics of fluctuations in a surface reaction by Karhunen-Loeve decomposition of field emission images"
Surface Science , 454-456 , 331 (2000)

[7] A.S. Mukaysan}, A.S. Rogachev and A. Varma,
"Mechanisms of reaction wave propagatoin during combustion synthesis of advanced materials",
Chem. Eng. Sc. , 54 , 3357 (1999)

[8] R. Reigada, F. Sagu\'es and A.S. Mikhailov,
"Traveling waves and nonequilibrium stationary patterns in two-component reactive Langmuir monolayers",
Phys. Rev. Lett. , 89 , 038301-1 (2002)

[9] M. Pagitsas, A. Diamantopoulou and D. Sazou,
"A point defect model for the general and pitting corrosion on Iron electrolyte interface deduced from current oscillations",
Chaos Soliton Fract. , 17 , 263 (2003)

[10] C. J. Hemming and R. Kapral
" Front explosions in three-dimensional resonantly-forced oscillatory systems",
Phys. Rev. E , 68 , 026203 (2003)

[11] P. Gaspard,
"The correlation time of mesoscopic chemical clocks",
J. Chem. Phys. , 117 , 8905 (2002)

[12] N. Pavlenko, J. W. Evans, D. J. Liu and R. Imbihl
" Catalytic CO oxidation on nanoscale Pt Facets: Effect of interfacet CO diffusion on bifurcation and fluctuation behavior",
Phys. Rev. E , 65 , 016121 (2002)

[13]S. Brosda and C.G. Vayenas
" Rules and mathematical modeling of electrochemical and classical promotion: modelling",
J. Catal. , 204 , 23 (2002)

[14] Y. De Decker, F. Baras, N. Kruse and G. Nicolis
"Modeling the $NO+H_2$ reaction on a Pt field emitter tip: Mean-field analysis and Monte Carlo simulations",
J. Chem. Phys. , 117 , 10244 (2002)

[15] A. Provata, G. A. Tsekouras, F. Baras, F. Diakonos, D. Frantzeskakis,A. Shabunin, V. Astakhov,
"Noise-induced local oscillators and fractal patterns in the Lattice Limit Cycle model",
Fluctuations and Noise Letters , 3 , 241 (2003)

[16] E. Abad, A. Provata and G. Nicolis
"Reactive dynamics on fractal sets: Anomalous fluctuations and memory effects",
Europhys. Lett. , 61 , 586 (2003)

[17] A. Provata and G. A. Tsekouras
"Spontaneous formation of dynamical patterns with fractal fronts in the cyclic Lattice Lotka-Volterra model",
Phys. Rev. E , 67 , 056602 (2003)

[18] A. S. Rogachev, A. S. Mukasyan and A. Varma
"Volume combustion models in heterogeneous reaction systems",
J. Mater. Synth. Proces. , 10 , 31 (2002)

[19] Stochastic processes in physics, chemistry and biology,
J.A. Freund and T. P\"oschel Eds
Lectures Notes in Physics 557, Springer (2000)

[20] J.V. Barth
"Transport of adsorbates at metal surfaces: from thermal migration to hot precusors",
Surf. Sc. Reports , 40 , 75 (2000)

[21] J. W. Evans, D. J. Liu and M. Tammaro
"From atomistic Lattice-gas Models for Surface Reactions to Hydrodynamics Reaction-Diffusion Equations",
Chaos, , 12 , 131 (2002)

[22] Y. Le Bouar and F. Soisson
"Kinetic pathways from embedded-atom-method potentials: Influence of the activation barriers",
Phys. Rev. B , 65 , 094103 (2002)

[23]P. Jensen
"Growth of nanostructures by cluster deposition: Experiments and simple models",
Rev. Mod. Phys. , 71 , 1695 (1999)

[24] H. Nakao and A. S. Mikhailov
"Statistics of rare strong bursts in autocatalytic stochastic growth with diffusion",
Chaos , 13 , 953 (2003)

[25] F. Coppex, M. Droz, and A. Lipowski
"Dynamics of the breakdown of granular clusters",
Phys. Rev. E , 66 , 011305 (2002)

[26] L.M. Sander, C.P. Warren and I.M. Sokolov {\bf 325}, 1 (2003)
"Epidemics, disorder and percolation",
Physica A , 325 , 1 (2003)

[27] P. Chantrenne and J.-L. Barrat
"Finite size effects in determination of thermal conductivities: comparing molecular dynamics results with simple models",
submitted to Journal of Heat Transfer

[28] N. Provatas et al.,
"Phase-field model for activated reaction fronts",
Phys. Rev. B , 53 , 6263 (1996)

[29] P. Kratzer
"Atomistic simulations of processes at surfaces"
in Challenges in Predictive Process Simulations, J. Dabrowski Ed., Springer Verlag (2003)