Depletion from a hard wall induced by aggregation and gelation

Diffusion-limited cluster aggregation and gelation of hard spheres is simulated using off-lattice Monte Carlo simulations. A comparison is made of the wall-particle correlation function with the particle-particle correlation function over a range of volume fractions, both for the initial system of randomly distributed spheres and for the final gel state. For randomly distributed spheres the correlation functions are compared with theoretical results using the Ornstein-Zernike equation and the Percus-Yevick closure. At high volume fractions (φ > 40%) gelation has little influence on the correlation function, but for φ < 10% it is a universal function of the distance normalized by correlation length (ξ) of the bulk. The width of the depletion layer is about 0.5ξ. The concentration increases as a power law from the wall up to r ≈ ξ, where it reaches a weak maximum before decreasing to the bulk value.     

Influence of the Brownian step size in off-lattice Monte Carlo simulations of irreversible particle aggregation

The influence of the Brownian step size in off-lattice Monte Carlo simulations of the aggregation and gelation of spheres is studied. It is found that the kinetics are strongly influenced if the step size is larger than the mean smallest distance between the sphere surfaces. The structure of the clusters and the gels is influenced, but only over length scales smaller than the step size. Using large step sizes leads to a narrower size distribution of the clusters. Implications of the present results are discussed for simulations reported in the literature in which the Brownian step size was chosen equal to the sphere diameter.     

Monte-Carlo simulation of transient gel formation and break-up during reversible aggregation

Monte-Carlo simulations of reversible aggregation on a cubic lattice were done by introducing a finite probability (P) of nearest neighbours to form a bond. Depending on the volume fraction of occupied sites (φ) and P we observed different phenomena by monitoring as a function of time the space filling and the distribution of the aggregates and the gel fraction. At smaller values of P the system develops into an equilibrium distribution of aggregates of which the average size increases with increasing φ until above a critical value the system percolates. At larger values of P the system phase separates into two phases with different densities. Above a critical value of φ the system percolates during a finite time. The life time of the gel and the maximum gel fraction were studied as a function of P. Received 1st March 2001 and Received in final form 24 April 2001     

Monte Carlo method for neutron spectrum recovery - a new approach based on the accelerated ions distribution

New method of neutron spectrum recovery described in the paper involves accelerated deuterons (that produce neutrons in DD reaction) and allows getting neutron spectrum in any direction from computed time-velocity characteristics of deuterons. Time of flight signals registered in various distances and directions are used, that makes information involved in the recovery process (Monte-Carlo simulation) more complete than in a one-directional case, although additional assumption about axial symmetry of deuterons motion, is required. In the paper recent results of two standard tests of the proposed method are presented demonstrating its capability to recover neutron spectrum from time-of-flight signals.     

Multicanonical Monte Carlo simulations on intramolecular micelle formation in copolymers

The formation of intramolecular micelles in copolymers with periodic sequence, where hydrophobic units (stickers) are periodically placed along the chain, is studied by using multicanonical Monte Carlo computer simulations for an off-lattice bead-rod model in three dimensions. With decreasing the temperature, a transition from random-coil conformations to micelles occurs and flower-type micelles are formed via the transition. The number of stickers forming a micelle core is limited by the excluded-volume effect of loop chains around micelle cores. By this effect, two intramolecular micelles are formed for long polymer chains with 60 bonds via the coil-to-micelle transition. By further decreasing the temperature, we find that another transition, i.e., a micelle-to-micelle transition, takes place. At this transition point, the two intramolecular micelles merge into one micelle. Furthermore, we extend the multicanonical MC method to study elastic properties of single polymer chains with strong attractive interactions under external force fields, and study how the intramolecular micellization affects the elastic property of single polymer chains.     

Phase diagram of a 2D Ising model within a nonextensive approach

In this work we report Monte Carlo simulations of a 2D Ising model, in which the statistics of the Metropolis algorithm is replaced by the nonextensive one. We compute the magnetization and show that phase transitions are present for q ≠ 1. A q - phase diagram (critical temperature vs. the entropic parameter q) is built and exhibits some interesting features, such as phases which are governed by the value of the entropic index q. It is shown that such phases favors some energy levels of magnetization states. It is also shown that the contribution of the Tsallis cutoff is capital to the existence of phase transitions.     

Pattern formation in the reaction with anisotropic lateral adsorbate-adsorbate interactions

We present Monte Carlo simulations of the formation of (1×2) islands in the case of the 2 A + B ₂ → 2 AB reaction occurring via the Langmuir-Hinshelwood mechanism on a square lattice under steady-state conditions. The model employed takes into account the effect of anisotropic lateral B-B interactions on the rates of B diffusion and elementary reaction events. The results obtained with qualitatively realistic ratio of the rate of elementary reaction steps indicate that the average island size depends on the details of diffusion and reaction dynamics in a similar way as in the earlier studied case of the simplest A + B reaction running via the Eley-Rideal mechanism. Received 4 January 2002 and Received in final form 2 April 2002 Published online 25 June 2002