Bethe-Peierls approximation for linear monodisperse polymers re-examined

Abstract

Bethe-Peierls approximation, as it applies to the thermodynamics of polymer melts, is reviewed. We compare the computed configurational entropy of monodisperse linear polymer melt with Monte Carlo data available in the literature. An estimation of the configurational contribution to the total liquid's C(p) is presented. We also discuss the relation between the Kauzmann paradox and polymer semiflexibility.

Theoretical estimation of density profile of semiflexible polymers adsorbed on a surface and thermodynamic glass transition scenario by means of the Bethe-Peierls approximation

“…where Ψ i = 1 + λξ i . As we have shown in our previous work, 37 the derived approximation for the partial partition function is equally applicable to the Cayley tree of x generations capturing a chain connected to its z ′ = 2(z − 1) + (x − 2)(z − 2) nearest neighbor sites.…”

“…Along with using more advanced in terms of correlations taken into account approximation, the present study remedies this omission by using the modified lattice coordination number that distinguishes between trans and gauche configurations of the polymer chain, as has been suggested previously by Silberberg. 33 In our former study, 37 we applied the Bethe-Peierls approximation 38,39 to the study of the uniform polymer melts and demonstrated the complete agreement of this approach with quasi-chemical approximation. The present work describes an extension of our earlier studies to the case of non-uniform polymer melts in the presence of adsorbing surface.…”

“…The latter provides the value of the bulk segment activity λ obtained in Ref. 37 and reproduced here for convenience:…”

“…In the present study, we will take the stiffness of a chain into account by employing the Flory lattice model Ref. 37. The essence of the approximation is to distinguish between trans and gauche states of the model chain: The latter can pass from any lattice site to the directions of the nearest-neighbor sites.…”

“…This PPF describes configurations of a part of the chain consisting of k bonds extending outside a first generation sites of the Cayley tree and i being the number of layers that separate the selected layer from the adsorbing surface. In terms of functions χ k,i , the contribution to the partition function coming from the aggregates with the occupied central site can be written 37 as…”