Dynamics of phase separation: Cluster kinetics and self-similarity property of the structure function

Marro, Joaquín; Toral, Raúl

doi:10.1016/0378-4363(86)90021-5

Cited by 4 publications

(3 citation statements)

References 45 publications

(78 reference statements)

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“…In addition, for a lattice model it is no problem to define 'clusters' of reversed spins in terms of closed contours separating them from the surrounding up spins. Consequently the study of such clusters in the Ising model both for d = 2 and d = 3 has had much attention (Fisher 1967, Stoll et a1 1972, Muller-Krumbhaar 1974a,b, Muller-Krumbhaar and Stoll 1976, Binder 1976, Coniglio and Klein 1980, Binder et a1 1975, Stauffer et a1 1982, Dickman and Schieve 1982, Marro and Toral 1983, Jacucci et a1 1983, Hu 1984, Heermann et a1 1984, Binder and Heermann 1985, Heermann and Klein 1983a,b, Nauenberg and Cambier 1986. Despite this large activity, clusters in the Ising model are still incompletely understood, and hence our discussion will focus on a few aspects of this problem only.…”

Section: A F ( P ) = H ( 4 Y " " -4 F " " " ) P D V D + S D P D -' L N Tmentioning

confidence: 99%

Theory of first-order phase transitions

1987

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An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order are discussed, as well as exceptions to these rules. Attention is drawn to the rounding of first-order transitions due to finite-size or quenched impurities. Computational methods to calculate phase diagrams for simple model Hamiltonians are also described.Particular emphasis is laid on metastable states near first-order phase transitions, on the 'stability limits' of such states (e.g. the 'spinodal curve' of the gas-liquid transition) and on the dynamic mechanisms by which metastable states decay (nucleation and growth of droplets of a new phase, etc).

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Section: A F ( P ) = H ( 4 Y " " -4 F " " " ) P D V D + S D P D -' L N Tmentioning

confidence: 99%

Theory of first-order phase transitions

1987

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“…Different theories lead to different expressions for C , ( t ) and C,, and recent Monte Carlo work has been carried out to distinguish between the different theoretical approaches, both for the dynamical properties (Penrose et a1 1978, Marro and Toral 1986, Toral and Marro 1987 and the equilibrium properties (Jan er al 1982, Marro and Toral 1983, Cambier and Nauenberg 1986. Series expansions have also been used for the same purpose (Sykes andGaunt 1976, Gaunt andBrak 1985).…”

Section: Introductionmentioning

confidence: 99%

“…d = 2 or 3. Previous work (Marro and Toral 1983) suggested that Binder's theory can provide a correct description of clusters in the three-dimensional Ising model outside the percolation region. Recent work by Cambier and Nauenberg (1986) also seemed to confirm these results in three dimensions but with different values for the critical exponents; their results for d = 2 were interpreted as showing a complete failure of the microscopic (Bruce and Wallace) model, but this was in contradiction with other computer simulations (Jan et a1 1982) and results obtained from the series expansions (Gaunt and Brak 1985).…”

Section: Introductionmentioning

confidence: 99%

Finite-size scaling study of the equilibrium cluster distribution of the two-dimensional Ising model

Toral¹,

Wall²

1987

J. Phys. A: Math. Gen.

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We use a very fast and efficient algorithm to study by Monte Carlo methods the equilibrium cluster distribution C,(L) , the mean number of clusters per lattice site containing I particles in a square lattice of L2 sites, of the two-dimensional fsing model at the critical point. Finite-size scaling theory is then used to analyse the scalingansatz C,(L) = [-If(2'/L), T and s being critical exponents. The second moment of the cluster distribution pz(L) = I I'C, is shown to behave as p 2 (L)-Lo with fJ = 1.89510.010, The effect of corrections to scaling is also discussed.

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Adsorbate islanding in surface reactions: A combined Monte Carlo-lattice gas approach

Silverberg¹,

Ben‐Shaul²

1987

The Journal of Chemical Physics

115

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The effects of reactant aggregation and lateral interactions on bimolecular surface reactions A+B→AB are studied using a theoretical model combining Monte Carlo simulations with (modified) lattice gas approximations, with special reference to temperature programmed reactions. A and B are chemisorbed species yielding a rapidly desorbing product AB. We are particularly interested in systems where one reactant (A) tends to organize in ordered domains, as a result of strong A–A attractive forces. Our modeling scheme consists of two stages. First, A is randomly adsorbed at a temperature lower than the critical temperature of the gas–solid transition, and phase separation (i.e., A aggregation) starts taking place. This process is modeled by (conserved) Monte Carlo dynamics. As in previous studies, we find that after a while the A atoms form finite, metastable, often highly ramified islands, whose further growth is a very slow process. At this stage, or earlier, B is adsorbed on the A-free lattice sites, T is raised (linearly) and reaction begins. It is assumed that A is stationary while B is highly mobile and that B diffusion is much faster than A+B reaction. Thus, the distribution of B on A-free sites is always in equilibrium, but it depends on A–B and B–B interactions, as well as on coverage, temperature, and, in particular, the given distribution of A atoms. To calculate the B distribution we formulate and employ two lattice gas models, which are appropriately modified versions of the mean-field and the quasichemical approximations. To follow the time-space evolution of the system we use Monte Carlo methods to simulate the slow processes, A aggregation and AB formation, and (one of the) lattice gas models for B distribution. Calculations of thermal desorption spectra are performed for A and B adsorbed on a 500×500 square lattice (with periodic boundary conditions) assuming nearest-neighbor lateral interactions wAA, wBB, and wAB. The results reveal nontrivial kinetic behaviors, which depend strongly on initial conditions (coverages, dosing sequence) and interaction parameters. These are reflected in the temperature programmed spectra and the apparent (coverage dependent) activation energies derived from them. It is shown, for example, that the major effect of A–B interactions on the rate is via their influence on local concentration of B’s near A’s. B–B interactions affect directly the reaction activation barrier. A–A interactions show both ‘‘topological’’ and ‘‘energetic’’ effects.

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Dynamics of phase separation: Cluster kinetics and self-similarity property of the structure function

Cited by 4 publications

References 45 publications

Theory of first-order phase transitions

Theory of first-order phase transitions

Finite-size scaling study of the equilibrium cluster distribution of the two-dimensional Ising model

Adsorbate islanding in surface reactions: A combined Monte Carlo-lattice gas approach

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