Bethe Approximation for a Semi-flexible Polymer Chain

Abstract

We present a Bethe approximation to study lattice models of linear polymers. The approach is variational in nature and based on the cluster variation method (CVM). We focus on a model with $(i)$ a nearest neighbor attractive energy ${\epsilon }_v$ between pair of non--bonded monomers, $(ii)$ a bending energy ${\epsilon }_h$ for each pair of successive chain segments which are not collinear. We determine the phase diagram of the system as a function of the reduced temperature $t=\frac{T}{{\epsilon }_v}$ and of the parameter $x=\frac{{\epsilon }_h}{{\epsilon }_v}$. We find two different qualitative behaviors, on varying $t$. For small values of $x$ the system undergoes a $\theta$ collapse from an extended coil to a compact globule; subsequently, on decreasing further $t$, there is a first order transition to an anisotropic phase, characterized by global orientational order. For sufficiently large values of $x$, instead, there is directly a first order transition from the coil to the orientational ordered phase. Our results are in good agreement with previous Monte Carlo simulations and contradict in some aspects mean--field theory. In the limit of Hamiltonian walks, our approximation recovers results of the Flory-Huggins theory for polymer melting.

8 pages, 3 eps figures

References in corpus (2)

• Phase Transitions of Single Semi-stiff Polymer Chains
• The effect of chain stiffness on the phase behaviour of isolated homopolymers

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