Density functional theory for polymeric systems in 2D

Abstract

We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.

New developments in classical density functional theory

“…Wertheim's approach [34,35] is developed for 2D polymers by Słyk et al [38]. The resulting DFT is used to investigate the adsorption of polymeric monolayers, making connections with self-consistent field theoretical treatments.…”

Semiflexible Polymers in the Bulk and Confined by Planar Walls

“…The latter approach is considered in general the most powerful version of mean field theory to describe ordering phenomena in condensed matter and has seen broad and significant progress in recent years [34,35,36,37], but for the most part, this technique is concerned with simple liquids (described by point-like particles interacting via isotropic potentials). Both the generalization to anisotropic particles, whose interactions depend on their mutual orientations (see, e.g., [38]) and the generalization to flexible (e.g., [39]) and semiflexible polymers (e.g., [40,41]) are highly nontrivial and are still subjects of ongoing research. While for simple fluids, the basic object of the theory is the spatially nonuniform density ρfalse(boldrfalse), for semiflexible macromolecules, one needs to operate with a function ρmol(r,ω), which depends not only on the particle position r, but also on the local orientation ω ( ω is a shorthand notation for the polar angles θ , ϕ of the molecular bonds).…”

A density functional approach to ferrogels

“…We remark at this stage that the problem of mapping from distinguishable to indistinguishable particles also occurs in density functional descriptions of polymeric bead models [49,50]. Typically, in tangential bead models for hard spheres [51,52], one neglects the linking constraints of the chain and maps the excess free energy of the system onto an unconstrained hard-sphere fluid.…”