Recent Developments in Monte Carlo Simulations of Lattice Models for Polymer Systems

Abstract

A brief review is given of methodological advances made during the past decade with the Monte Carlo sampling of equilibrium properties of simple lattice models of polymer systems, and representative applications of these new algorithms are summarized. These algorithms include Wang−Landau (WL) sampling, the pruned-enriched Rosenbluth method (PERM), and topology violating dynamic Monte Carlo algorithms such as combinations of local moves, slithering snake moves, and “double bridging” moves for the bond fluctuation model. The applications mentioned concern phase-transition-like phenomena of single chains (collapse and crystallization in bad solvents; interplay of collapse and adsorption; escape of chains from confining tubes; microphase separation in binary bottle brushes) and nontrivial correlation effects in dense systems of many chains (intramolecular long-range correlations in melts; fluctuation effects of micelles in homopolymer−block copolymer blends.) While all these examples refer to work on lattice models, these algorithms are useful for off-lattice models as well. Open problems and directions for future work are briefly addressed.

Polymer crystallization in the presence of “sticky” additives

“…Other algorithms such as the wormhole moves algorithm 20 are also not suitable for simulation of crystallization of a dense melt, where the same polymer chain could exist in amorphous and crystalline regions. Lattice simulations of dense systems are possible by the cooperative motion algorithm ͑CMA͒ by Pakula and co-worker 21,22 and the single site version of the bond fluctuation model [23][24][25][26] by Hu. 27,28 CMA has been employed for lattice systems with 100% occupancy.…”

“…The combination of these moves is known to produce faster relaxation in such a highly dense system. 26 We enforce excluded volume interactions and disallow bond crossings. 32,33 Such a scheme satisfies detailed balance and precludes "locked-in" states, which chain-growth selfavoiding walk algorithms may face.…”

Conformation and dynamics of a diluted chain in the presence of an adsorbing wall: A simulation with the bond fluctuation model

“…Phase transitions of single polymer chains in the bulk and in the presence of an adsorbing wall have been studied through model simulations [13][14][15][16][17]. In equilibrium states, the phase diagram as a function of temperature shows coil, liquid globule, solid globule, adsorbed coil (or adsorbed-extended) and adsorbed globule (or adsorbed compact) configurations, depending on the monomer wall attraction potential [13][14][15].…”

“…In equilibrium states, the phase diagram as a function of temperature shows coil, liquid globule, solid globule, adsorbed coil (or adsorbed-extended) and adsorbed globule (or adsorbed compact) configurations, depending on the monomer wall attraction potential [13][14][15].…”

“…We studied the adsorption with different values for the wall potential and different thermal treatments. As we are interested in chain dynamics, the BFM [25] with the Metropolis criterion [13] is preferred over other methods as the Wang-Landau, which is more appropriate for equilibrium properties or phase transition studies [19,26]. The main aim of this study is to analyze the behaviour of a semiflexible chain in a confined space and in presence of an adsorbing wall in order to obtain a deeper insight in the morphology of the system.…”