Abstract
Local stiffness of polymer chains is instrumental in all structure formation processes of polymers, from crystallization of synthetic polymers to protein folding and DNA compactification. We present Stochastic Approximation Monte Carlo simulations—a type of flat-histogram Monte Carlo method—determining the density of states of a model class of single semi-flexible polymer chains, and, from this, their complete thermodynamic behavior. The chains possess a rich pseudo phase diagram as a function of stiffness and temperature, displaying non-trivial ground-state morphologies. This pseudo phase diagram also depends on chain length. Differences to existing pseudo phase diagrams of semi-flexible chains in the literature emphasize the fact that the mechanism of stiffness creation matters.
Highlights
Local stiffness or semi-flexibility of polymer chains is probably by far the most important design concept for the creation of ordered polymeric structures
As we have shown here, the pseudo phase diagram, depends on chain length, such that structures which are dominant for one chain length might not be possible or be suppressed for another one
We have presented flat histogram Monte Carlo simulations using the SAMC approach to determine the pseudo phase diagram of single semi-flexible chains as a function of stiffness and temperature
Summary
Local stiffness or semi-flexibility of polymer chains is probably by far the most important design concept for the creation of ordered polymeric structures. The most important theoretical model is certainly the worm-like chain [6] with its prediction of an exponential decay of bond-orientation correlation along the chain on the scale of its persistence length. The property of this model, that the Kuhn-length of a chain is twice its persistence length, has become such common folklore that it is often taken as a general relation, it is only valid within this model of a persistent type of semi-flexibility. Orientational correlations within a chain asymptotically always decay algebraically [8,9,10,11,12] and not exponentially
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