Deviation from Corresponding States for a Fluid of Square Well Spherocylinders

Abstract

The nonconformal behavior of a fluid of hard spherocylinders with a spherocylindrical square well attraction is examined using a simple perturbation theory in which the thermodynamics of the anisotropic fluid is mapped to that of an equivalent spherical system. This theory was shown to give a good description of the thermodynamic properties of the isotropic phase of a fluid of hard core aspect ratio 5:1 and square well range λ ) 1.5. To date no simulation data exists for the vapor-liquid region of this model; however, the theoretical predictions are compared with Gibbs ensemble Monte Carlo simulation data for the linear Kihara potentials. A strong similarity is observed. in the phase behavior of both fluids. The square well system has the advantage that there is a good theoretical equation of state in which the range parameter can be varied without extra computational difficulty. Finally, despite the simplicity of the square well model, we demonstrate that this model can be used to describe the vapor-liquid coexistence of the alkane chain series from ethane to octane.

Advances in generalised van der Waals approaches for the isotropic–nematic fluid phase equilibria of thermotropic liquid crystals–an algebraic equation of state for attractive anisotropic particles with the Onsager trial function

“…The fluid phase behaviour for the system of L/D = 5 hard spherocylinders with isotropic square-well attractions of range λ = 6 is presented as a temperature-density projection of the phase diagram in Figure 2. In keeping with the previous theoretical studies for this type of model (see References 48,49,52,53,68,70,72,73,79,80,95,96,99,109 as typical examples), three-regions of fluid phase equilibria are apparent. This type of vapour-liquid-nematic (V-L-N) phase behaviour has also been observed in simulations of Gay-Berne particles 165 , and of hard spherocylinders with isotropic (depletion) 171 and anisotropic 93 attractive interactions for appropriate choices of the molecular aspect ratio and attractions.…”

“…Does the phase behaviour of such a model conform to the van der Waals principle of corresponding states 172 ? In order to answer this question we have replotted the fluid phase equilibria in terms of a temperature which is reduced in a van der Waals dimensionless form in terms of the inte- Figure 4, that as the range of the isotropic attraction is increased the vapour-liquid coexistence of the system converges onto a universal correspondingstates curve (also see the work by Williamson and Guevara 96 ). This is expected as we are modelling the fluid phase equilibria with an augmented van der Waals equation of state; for large ranges of the attractive interactions one tends to the mean-field limit.…”

Modeling the phase behavior of polydisperse rigid rods with attractive interactions with applications to single-walled carbon nanotubes in superacids

“…23,24 Because of the shorter aspect ratio and the importance of temperature, these types of simulations are often applied to alkanes, 25,28 far smaller than LC polymers or nanotubes; these simulations have also detected the existence of a nematic-liquid-vapor triple point for these shorter spherocylinders. 25,27 Particle-based simulations provide a useful means of evaluating approximations in Onsager-type frameworks; for instance, Samborski et al 22 used Monte Carlo simulations as a point of comparison for various techniques of computing higher order virial coefficients for the Onsager theory.…”

Understanding and Describing the Liquid-Crystalline States of Polypeptide Solutions: A Coarse-Grained Model of PBLG in DMF

“…A number of studies have been carried out after the early attempts by Kimura 71 to describe the properties of a system which combines Onsager's hard-rod model with anisotropic dispersion forces. [72][73][74][75][76][77][78][79][80][81][82][83] Some progress has also been made in introducing dipolar [84][85][86][87][88][89] or chiral [90][91][92][93] interactions between LC molecules. Of particular relevance to our current work is the closed-form algebraic equation of state developed within a van der Waals-Onsager treatment for systems of attractive hard-core particles, 94 in which the attractive potential is expanded in spherical harmonics 95 representing different multipolar contributions to the anisotropic attractions.…”