A single flexible homopolymer chain can assume a variety of conformations which can be broadly classified as expanded coil, collapsed globule, and compact crystallite. Here we study transitions between these conformational states for an interaction-site polymer chain comprised of N=128 square-well-sphere monomers with hard-sphere diameter sigma and square-well diameter lambdasigma. Wang-Landau sampling with bond-rebridging Monte Carlo moves is used to compute the density of states for this chain and both canonical and microcanonical analyses are used to identify and characterize phase transitions in this finite size system. The temperature-interaction range (i.e., T-lambda) phase diagram is constructed for lambda1.06 these two states are separated by an intervening collapsed globule phase and thus, with decreasing temperature a chain undergoes a continuous coil-globule (collapse) transition followed by a discontinuous globule-crystal (freezing) transition. For well diameters lambda<1.06 the collapse transition is pre-empted by the freezing transition and thus there is a direct first-order coil-crystal phase transition. These results confirm the recent prediction, based on a lattice polymer model, that a collapsed globule state is unstable with respect to a solid phase for flexible polymers with sufficiently short-range monomer-monomer interactions.

Here we report a first-order all-or-none transition from an expanded coil to a compact crystallite for a flexible polymer chain. Wang-Landau sampling is used to construct the complete density of states for square-well chains up to length 256. Analysis within both the microcanonical and canonical ensembles shows a direct freezing transition for finite length chains with sufficiently short-range interactions. This type of transition is a distinctive feature of "one-step" protein folding and our findings demonstrate that a simple homopolymer model can exhibit protein-folding thermodynamics.

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A variety of molecules revenibly self-assemble in solution. forming noncovalently bonded molecular aggregates. In many cases these aggregales are asymmetric in shape and are observed to form liquid-crystal phases. The nature of and mechanisms for liquidcrystalline ordering in such self-assembled systems is the focus of lhis review. Contents 1. Introduction 2. Entropically driven ordering 2.1 Onsager model for orientational ordering 2 2 Cell model for positional ordering 3.1 Phenomenological description 3.2 Ideal-solution behaviour 4.1 Second vinal description 4.2 Lanice models 4.3 Scaled particle theory 5.1 A model rod-like system 5.2 The TP6EOZWwater and related systems 5.3 A model disc-like system 5.4 The CsPFO/water and related systems 3. The self-assembly process 4. Orientational ordering in surfactant and protein systems 5. Translational ordering in simple self-assembled systems 6. Conclusions