Thermodynamics of a Compressible Maier-Saupe Model Based on the Self-Consistent Field Theory of Wormlike Polymer

Abstract

This paper presents a theoretical formalism for describing systems of semiflexible polymers, which can have density variations due to finite compressibility and exhibit an isotropic-nematic transition. The molecular architecture of the semiflexible polymers is described by a continuum wormlike-chain model. The non-bonded interactions are described through a functional of two collective variables, the local density and local segmental orientation tensor. In particular, the functional depends quadratically on local density-variations and includes a Maier-Saupe-type term to deal with the orientational ordering. The specified density-dependence stems from a free energy expansion, where the free energy of an isotropic and homogeneous homopolymer melt at some fixed density serves as a reference state. Using this framework, a self-consistent field theory is developed, which produces a Helmholtz free energy that can be used for the calculation of the thermodynamics of the system. The thermodynamic properties are analysed as functions of the compressibility of the model, for values of the compressibility realizable in mesoscopic simulations with soft interactions and in actual polymeric materials.

Temperature-Dependence of Persistence Length Affects Phenomenological Descriptions of Aligning Interactions in Nematic Semiconducting Polymers

“…MS models can be incompressible or compressible, in which case the anisotropic interactions are augmented by simple, isotropic repulsive potentials. , For multicomponent systems, additional isotropic interactions are included − to account for incompatibility of different monomers. Although MS models have been initially applied to thermotropic nematics, compressible variants are also applicable to lyotropic systems . In fact, the standard Onsager model for lyotropic nematics can be approximately , reduced to a compressible MS description.…”

“…Although MS models have been initially applied to thermotropic nematics, compressible variants are also applicable to lyotropic systems . In fact, the standard Onsager model for lyotropic nematics can be approximately , reduced to a compressible MS description.…”

“…Because the MS model is mesoscopic, its “potentials” are in fact free energies and the parameters are generally state-dependent, e.g., the MS parameter depends on temperature, T . Once the parameters are specified, the properties can be explored through various computational techniques: from numerical Self Consistent Field (SCF) theory ,− to particle-based simulations. ,,,, …”

Recent Progress in Processing Functionally Graded Polymer Foams

“…Recently, flexible polymers like compressible elastomers with different densities (graded materials) have been described by a worm-like chain model [ 74 ]. A self-consistent field theory (SCFT) was developed using thermodynamic calculations of the system based on Helmholtz free energy.…”

Nonequilibrium Molecular Conformations in Polymer Self-Consistent Field Theory

“…The functional integral over the symmetric, tensorial orienting field, , runs over the 6 independent component fields. Similar tensorial fields are employed in the field-theoretic treatments of Maier-Saupe interactions in liquid-crystalline polymers. − At the saddlepoint of the integral, the auxiliary collective fields Ω A , Ω B , and are real such that we recover the canonical ensemble form within a mean-field approximation (see below). The coefficient 3π 2 / R e 2 has been chosen such that is dimensionless and the eigenvalues of at the saddlepoint of the integral are smaller than 1…”