Wang-Landau simulations of thermodynamic behavior in homopolymer systems

Abstract

This work focuses on the thermodynamic behavior of both flexible and semi-flexible homopolymer systems through the application of the Wang-Landau algorithm. Coarse-grained homopolymer systems are simple models used to understand complex phenomena in polymer and protein systems. The free energy landscape associated with these systems is similar to, yet less complex than those of real polymers and proteins, providing a tractable system for studying thermodynamic and conformational behavior. The results of these investigations can be divided into two separate sections, one studying the behavior of fully-flexible homopolymers for chain lengths up to N=561, and the other mapping out similar conformational and transition behavior in semi-flexible homopolymers up to N=55.

In the case of fully flexible homopolymers, results are generated using a one-dimensional implementation of the Wang-Landau algorithm. Investigations of transition phenomena are performed, with particular attention given to the infinite-chain behavior of the coil-globule and liquid-solid transitions. In addition, analysis of finite chains has revealed unique behavior in regard to solid-solid transitions occurring in the crystalline region of phase space. These features can be understood by considering the behavior of certain ``magic number' chain lengths (N=13,55,147,309,561,...), for which perfect icosahedral geometries form. The low temperature properties of other chain lengths can be correlated to this magic number behavior using packing considerations.

The conformational behavior of semi-flexible polymers is an extension of these results and methodology, with a key difference being the application of multi-dimensional Wang-Landau sampling. Using the energy and stiffness of the chain as sampling directions, three primary conformational regions occurring at low temperatures are described, namely, solid-globular, rod-like, and toroidal states. The existence of icosahedral ordering within the solid-globular region is of principal interest, and results showing Mackay and Anti-Mackay behavior are presented. The tendency for chains to fold into icosahedral geometries reduces as stiffness is increased, giving way to the less-ordered rod-like and toroidal structures at low temperatures. The overall conformational behavior is mapped out as a function of chain length and stiffness using various thermodynamic and structural quantities. Investigations of both flexible and semi-flexible homopolymers have been aided by the introduction of unique Monte Carlo trial moves, as well as algorithmic improvements, all of which are discussed in detail.