Nikolai A. Volkov

Entropic sampling of simple polymer models within Wang–Landau algorithm

In this paper we apply a new simulation technique proposed in Wang and Landau (WL) (2001 Phys. Rev. Lett. 86 2050) to sampling of three-dimensional lattice and continuous models of polymer chains. Distributions obtained by homogeneous (unconditional) random walks are compared with results of entropic sampling (ES) within the WL algorithm. While homogeneous sampling gives reliable results typically in the range of 4?5 orders of magnitude, the WL entropic sampling yields them in the range of 20?30 orders and even larger with comparable computer effort. A combination of homogeneous and WL sampling provides reliable data for events with probabilities down to 10?35.For the lattice model we consider both the athermal case (self-avoiding walks, SAWs) and the thermal case when an energy is attributed to each contact between nonbonded monomers in a self-avoiding walk. For short chains the simulation results are checked by comparison with the exact data. In WL calculations for chain lengths up to N = 300 scaling relations for SAWs are well reproduced. In the thermal case distribution over the number of contacts is obtained in the N-range up to N = 100 and the canonical averages?internal energy, heat capacity, excess canonical entropy, mean square end-to-end distance?are calculated as a result in a wide temperature range.The continuous model is studied in the athermal case. By sorting conformations of a continuous phantom freely joined N-bonded chain with a unit bond length over a stochastic variable, the minimum distance between nonbonded beads, we determine the probability distribution for the N-bonded chain with hard sphere monomer units over its diameter a in the complete diameter range, 0 ? a ? 2, within a single ES run. This distribution provides us with excess specific entropy for a set of diameters a in this range. Calculations were made for chain lengths up to N = 100 and results were extrapolated to N ? ? for a in the range 0 ? a ? 1.25.

Phase transitions and thermodynamic properties of dense assemblies of truncated nanocubes and cuboctahedra

Inspired by recent advances on the self-assembly of non-spherical nanoparticles, Monte Carlo simulations of the packing and thermodynamic properties of truncated nanocubes and cuboctahedra have been performed. The ergodicity problem was overcome by a modified Wang-Landau entropic sampling algorithm and equilibrium structural and thermodynamic properties were computed over a wide density range for both non-interacting and interacting particles. We found a structural transition from a simple cubic to a rhombohedral order when the degree of truncation exceeds a value of 0.9.

Simulation of polymers by the Monte Carlo method using the Wang-Landau algorithm

Studies of several models of polymers with the use of a version of the Monte Carlo method—entropy sampling combined with the Wang-Landau algorithm—are presented. This approach allows derivation of the energy distribution function over a broad energy range. On the basis of this distribution various thermal characteristics of the systems are calculated in a wide temperature range: internal energy, free energy, heat capacity, average gyration radius, and mean end-to-end distance. For simple continuum and lattice models of free chains and rings we consider the athermal case, with eliminated overlaps, and the thermal case, when nonvalence interactions between units at finite distances are accounted for. In the framework of the proposed approaches, the models of alkanes and the simplest polypeptide, polyglycine, and the lattice model of flexible polyelectrolyte are investigated.

Diffusion in micellar systems: theory and molecular modelling

Recent development of experimental methods of investigation of diffusion in micellar systems and rethinking of the available material led to an increase in the number of theoretical studies in this field. This review summarizes the achievements in the general theory of micellization based on the law of mass action and in its applications to migration of surfactants in micellar systems. The law of mass action itself is modified to describe aggregative systems not only at low but also at moderate concentrations. New methods for calculating the concentrations of monomers and micelles in nonionic and ionic micellar systems are presented. Methods for estimating the micellar diffusion coefficient and the aggregation number from experimental data on surfactant diffusion are described. The theory of diffusion of electrically neutral micelles in concentrated ionic micellar solutions is developed. Computer simulation is an important tool complementing analytical and experimental methods of investigation of diffusion processes in micellar systems. The review addresses modern methods of molecular modelling of micellar systems, such as the all-atom molecular dynamics, molecular dynamics within coarse-grained models, and Brownian dynamics, which allow one to obtain a most detailed description of the structural and transport properties of micellar solutions. Various versions of cluster analysis and the role of this approach in calculations of surfactant diffusion coefficients in micellar solutions are discussed. The results of calculations of the diffusion coefficients of aggregates with different aggregation numbers, ions and water molecules from the data of all-atom molecular dynamics simulations at different total surfactant concentrations in the presence and in the absence of electrolyte are presented.The bibliography includes 77 references.

Kinetics of Aggregation and Relaxation in Micellar Surfactant Solutions

Theoretical results published in the last 17 years on the kinetics of aggregation and relaxation in micellar surfactant solutions have been reviewed. The results obtained by the analytical and direct numerical solution of the Becker–Döring kinetic equations and the Smoluchowski generalized equations, which describe different possible mechanisms of aggregation and relaxation on all time scales from ultrafast relaxation while reaching the quasi-equilibrium in the region of subcritical molecular aggregates to the last stage of slow relaxation of micelles to the final aggregated state, have been considered in detail. The droplet model and the model linear with respect to aggregation numbers have been used for the work of aggregation to describe the dynamics of the rearrangement of micellar systems consisting of only spherical, only cylindrical, and coexisting spherical and cylindrical aggregates, with the dynamics being both linear and nonlinear with respect to deviations from equilibrium. The results of molecular simulation of the rearrangement kinetics of micellar systems subjected to initial disturbance have been reviewed.

All-atom molecular dynamics analysis of kinetic and structural properties of ionic micellar solutions

All-atom molecular dynamics simulation results regarding aqueous sodium dodecyl sulfate (SDS) solutions have been presented. Both salt-free solutions with different SDS concentrations and those containing calcium chloride additives have been studied. The simulation has shown that surface-active SDS ions form stable premicellar aggregates. The obtained molecular dynamics trajectories have been used to describe both the kinetic and structural properties of solutions containing SDS molecular aggregates and the properties of individual aggregates. Aggregation kinetics has been investigated, and the characteristic sizes of the aggregates have been calculated by different methods. It has been found that the size of a premicellar aggregate with aggregation number n = 16 in a salt-free solution virtually does not depend on surfactant concentration. Radial distribution functions (RDFs) of hydrogen and oxygen atoms of water molecules relative to the center of mass of an aggregate have no local maxima near the aggregate surface; i.e., the surface is incompletely wetted with water. Corresponding RDFs of carbon atoms have one, two or three maxima depending on the surfactant concentration and the serial number of a carbon atom in the hydrocarbon radical of the surface- active ion. The study of the potentials of mean force for the interaction of sodium and calcium ions with an aggregate having aggregation number n = 32 shows that only calcium ions can be strongly bound to such an aggregate.

The Effect of Simulation Cell Size on the Diffusion Coefficient of an Ionic Surfactant Aggregate

Results of all-atom molecular dynamics simulation have been presented for salt-free aqueous solutions of sodium dodecyl sulfate at its fixed total concentration in a simulation cell containing one to four preliminarily formed quasi-stable ionic aggregates with equal aggregation numbers n = 32. The obtained molecular dynamics trajectories have been used to study the structural and transport properties of the micellar solution. The value of the counterion diffusion coefficient obtained using the Green–Kubo relation has turned out to be somewhat higher than the corresponding value calculated by the Einstein equation. The diffusion coefficients of the aggregates in the systems containing from two to four aggregates have appeared to be higher than the diffusion coefficient of a single aggregate in a cell. The mean force potential obtained for the interaction between the aggregates having aggregation number n = 32 as a function the distance between the aggregate centers of mass has a local minimum in the system containing four such aggregates.