Adsorption time scales of cluster-forming systems

A microscopic model of adsorption in cluster forming systems with competing interaction is considered. The adsorption process is described by the master equation and modelled by a kinetic Monte Carlo method. The evolution of the particle concentration and interaction energy during the adsorption of particles on a plane triangular lattice is investigated. The simulation results show a diverse behavior of the system time evolution depending on the temperature and chemical potential and finally on the formation of clusters in the system. The characteristic relaxation times of adsorption vary in several orders of magnitude depending on the thermodynamic parameters of the final equilibrium state of the adsorbate. A very fast adsorption of particles is observed for highly ordered adsorbate equilibrium states

Equilibrium properties of the lattice system with SALR interaction potential on a square lattice: quasi-chemical approximation versus Monte Carlo simulation

The lattice system with competing interactions that models biological objects (colloids, ensembles of protein molecules, etc.) is considered. This system is the lattice fluid on a square lattice with attractive interaction between nearest neighbours and repulsive interaction between next-next-nearest neighbours. The geometric order parameter is introduced for describing the ordered phases in this system. The critical value of the order parameter is estimated and the phase diagram of the system is constructed. The simple quasi-chemical approximation (QChA) is proposed for the system under consideration. The data of Monte Carlo simulation of equilibrium properties of the model are compared with the results of QChA. It is shown that QChA provides reasonable semiquantitative results for the systems studied and can be used as the basis for next order approximations.Comment: 10 pages, 8 figure

The effect of short-range interaction and correlations on the charge and electric field distribution in a model solid electrolyte

A simple lattice model of a solid electrolyte presented as a xy-slab geometry system of mobile cations on a background of energetic landscape of the host system and a compensating field of uniformly distributed anions is studied. The system is confined in the z-direction between two oppositely charged walls, which are in parallel to xy-plane. Besides the long-range Coulomb interactions appearing in the system, the short-range attractive potential between cations is considered in our study. We propose the mean field description of this model and extend it by taking into account correlation effects at short distances. Using the free energy minimization at each of z-coordinates, the corresponding set of non-linear equations for the chemical potential is derived. The set of equations was solved numerically with respect to the charge density distribution in order to calculate the cations distribution profile and the electrostatic potential in the system along z-direction under different conditions. An asymmetry of charge distribution profile with respect to the midplane of the system is observed. The effects of the short-range interactions and pair correlations on the charge and electric field distributions are demonstrated

Statistical Method of Conditional Distributions

Within the framework of the method of unconditional distribution correlation functions the main problem seems to be unsolved: whether the Gibbsian statistical formalism contains one and the same description for solid and liquid phases, naturally including consideration of phase crystal-liquid, liquid-gas and crystal-gas transitions. The above difficulties forced the workers to search for a new formalism in the corre­lation functions theory which would be most suitable for description of condensed state. The method of conditional distribution correlation functions has been developed as a supplement to the BBGKY hierarchy. The present review is the first attempt to give a systematic description of the method of conditional distribution functions

Truncation procedure for high order reduced distribution functions

The concept of the average force potentials is used to develop the truncation procedure for an arbitrary equation of the chain. The closed system of integral equations for the average force potentials is formulated. In the case when the truncation approximation involves the four-particle distribution function the expression for the configurational integral is derived. The internal energy and the pressure calculated in terms of the binary distribution function are thermodynamically compatible