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PubMed2001

Extended state-space Monte Carlo methods.

In this paper various extensions of the parallel-tempering algorithm are developed and their properties are analyzed. The algorithms are designed to alleviate quasiergodic sampling in systems which have rough energy landscapes by coupling individual Monte Carlo chains to form a composite chain. As with parallel tempering, the procedures are based upon extending the state space to include parameters to encourage sampling mobility. One of the drawbacks of the parallel-tempering method is the stochastic nature of the Monte Carlo dynamics in the auxiliary variables which extend the state space. In this work, the possibility of improving the sampling rate by designing deterministic methods of moving through the parameter space is investigated. The methods developed in this article, which are based upon a statistical quenching and heating procedure similar in spirit to simulated annealing, are tested on a simple two-dimensional spin system (xy model) and on a model in vacuo polypeptide system. In the coupled Monte Carlo chain algorithms, we find that the net mobility of the composite chain is determined by the competition between the characteristic time of coupling between adjacent chains and the degree of overlap of their distributions. Extensive studies of all methods are carried out to obtain optimal sampling conditions. In particular, the most efficient parallel-tempering procedure is to attempt to swap configurations after very few Monte Carlo updates of the composite chains. Furthermore, it is demonstrated that, contrary to expectations, the deterministic procedure does not improve the sampling rate over that of parallel tempering.

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PubMed2001

Monte Carlo studies of model Langmuir monolayers.

This paper examines some of the basic properties of a model Langmuir monolayer, consisting of surfactant molecules deposited onto a water subphase. The surfactants are modeled as rigid rods composed of a head and tail segment of diameters sigma(hh) and sigma(tt), respectively. The tails consist of n(t) approximately 4-7 effective monomers representing methylene groups. These rigid rods interact via site-site Lennard-Jones potentials with different interaction parameters for the tail-tail, head-tail, and head-head interactions. In a previous paper, we studied the ground-state properties of this system using a Landau approach. In the present paper, Monte Carlo simulations were performed in the canonical ensemble to elucidate the finite-temperature behavior of this system. Simulation techniques, incorporating a system of dynamic filters, allow us to decrease CPU time with negligible statistical error. This paper focuses on several of the key parameters, such as density, head-tail diameter mismatch, and chain length, responsible for driving transitions from uniformly tilted to untilted phases and between different tilt-ordered phases. Upon varying the density of the system, with sigma(hh)=sigma(tt), we observe a transition from a tilted (NNN)-condensed phase to an untilted-liquid phase and, upon comparison with recent experiments with fatty acid-alcohol and fatty acid-ester mixtures [M. C. Shih, M. K. Durbin, A. Malik, P. Zschack, and P. Dutta, J. Chem. Phys. 101, 9132 (1994); E. Teer, C. M. Knobler, C. Lautz, S. Wurlitzer, J. Kildae, and T. M. Fischer, J. Chem. Phys. 106, 1913 (1997)], we identify this as the L'(2)/Ov-L1 phase boundary. By varying the head-tail diameter ratio, we observe a decrease in T(c) with increasing mismatch. However, as the chain length was increased we observed that the transition temperatures increased and differences in T(c) due to head-tail diameter mismatch were diminished. In most of the present research, the water was treated as a hard surface, whereby the surfactants are only allowed to move within the plane of this surface. However, we have also utilized a more realistic model for the surfactant-water interactions, developed by Karaborni and Toxvaerd, in order to examine the role which the coupled effects of head group size and head group-subphase interactions plays in determining tilt ordering and on the stability of the monolayer. It is found that increasing the head diameter results in a widening of the air-water interface and an associated destruction of orientational order. Furthermore, the onset of capillary waves at lower temperatures for larger head diameters implies that the L2-L1 phase boundary for acids and acetates should move to lower temperatures relative to the L'(2)/Ov-L1 phase boundary for alcohols and esters. This feature has yet to be seen in experimental studies.

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