The isotropic-nematic phase transition of tangent hard-sphere chain fluids—Pure components

Abstract

An extension of Onsager's second virial theory is developed to describe the isotropic-nematic phase transition of tangent hard-sphere chain fluids. Flexibility is introduced by the rod-coil model. The effect of chain-flexibility on the second virial coefficient is described using an accurate, analytical approximation for the orientation-dependent pair-excluded volume. The use of this approximation allows for an analytical treatment of intramolecular flexibility by using a single pure-component parameter. Two approaches to approximate the effect of the higher virial coefficients are considered, i.e., the Vega-Lago rescaling and Scaled Particle Theory (SPT). The Onsager trial function is employed to describe the orientational distribution function. Theoretical predictions for the equation of state and orientational order parameter are tested against the results from Monte Carlo (MC) simulations. For linear chains of length 9 and longer, theoretical results are in excellent agreement with MC data. For smaller chain lengths, small errors introduced by the approximation of the higher virial coefficients become apparent, leading to a small under-and overestimation of the pressure and density difference at the phase transition, respectively. For rod-coil fluids of reasonable rigidity, a quantitative comparison between theory and MC simulations is obtained. For more flexible chains, however, both the Vega-Lago rescaling and SPT lead to a small underestimation of the location of the phase transition. © 2013 AIP Publishing LLC. [http://dx

The isotropic-nematic and nematic-nematic phase transition of binary mixtures of tangent hard-sphere chain fluids: An analytical equation of state

“…In our previous work, 33 an Onsager-like Helmholtz energy functional was derived to describe the isotropic-nematic ordering transition in pure component systems of tangent hard-sphere chain molecules. The resulting Helmholtz energy functional could be expressed in terms of an orientational distribution function only, leading to a unified description of linear and partially flexible (rod-coil) tangent hard-sphere chain fluids.…”

“…This model will be referred to as rod-coil fluid. 33,50,53 We employ a general m-m R notation to denote a rod-coil with a total number of m segments and a number of m R segments in the rigid block. A completely linear chain is referred to as a linear m-mer.…”

“…As a measure for the partial flexibility of a molecule, a dimensionless rigidity parameter is introduced, which, following our previous work, 33,50,53 is defined as the ratio of the total number of rigid bond-angles and the total number of bondangles in a molecule:…”

“…Here, ρ i = N i /V is the number density of molecules of component i, 3 i is a generalized De Broglie volume (which for partially flexible molecules incorporates a contribution due to the internal configurational degrees of freedom of a molecule 33 ) and the factor = dω ω ω = 4π is a normalization constant which ensures that the anisotropic part vanishes for an isotropic distribution of molecular orientations (since f i,iso (ω ω ω) = 1/ = 1/4π ).…”

Conformations and orientational ordering of semiflexible polymers in spherical confinement

“…[45][46][47] Of course, the choice of the details of coarse-grained models for semiflexible polymers is just a matter of computational convenience; other models have been used in the literature as well (see, e.g., Refs. [48][49][50][51][52][53][54]. Our model, however, has the distinct advantage that extensive results for confinement effects due to hard repulsive walls are already available.…”