Abstract
We present Monte Carlo (MC) simulations of the crystallisation transition of single-chain square-well homopolymers, with a continuous description of monomer positions. For long chains with short-ranged interactions this system shows a strong configurational bottleneck, which makes it difficult to explore the whole configuration space. To surmount this problem we combine parallel tempering with a non-standard choice of tempering levels, a bespoke biasing strategy and a method to map results between different temperatures. We verify that our simulations mix well when simulating chains of 128 and 256 beads. Our simulation approach resolves issues with reproducibility of MC simulations reported in prior work, particularly for the transition region between the expanded coil and crystalline region. We obtain highly reproducible results for both the free energy landscape and the inverse temperature, with low statistical noise. We outline a method to extract the free energy barrier, at any temperature, for any choice of order parameter, illustrating this technique by computing the free energy landscape as a function of the Steinhardt-Nelson order parameter for a range of temperatures.
Highlights
The collapse of a single polymer chain into a crystal state provides a fundamental model problem for polymer crystallization and protein folding
We show that an algorithm combining Monte Carlo (MC) simulation, carefully chosen biasing functions and parallel tempering, when combined with a method to extract the density of states, delivers all of the above points
Our simulation approach resolves reproducibility issues reported in previous MC simulations, for the transition region between the expanded coil and crystalline region
Summary
The collapse of a single polymer chain into a crystal state provides a fundamental model problem for polymer crystallization and protein folding. Monte Carlo (MC) simulations of the freely-jointed square well polymer chain have been carried out by Taylor and collaborators[11,19,20,21,22] They used Wang-Landau sampling[23] to comprehensively investigate the temperature-interaction range (T -λ) phase diagram[11]. Ruzicka et al.[24,25] investigated single square well chains in which the bond length can flex over a very small range They studied the phase transition dynamics using collision dynamics and forward flux sampling, and compared results to their Wang-Landau simulations of the same system. The computer code for our algorithm is publicly available[28]
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