Density functional theory for hard spherocylinders: phase transitions in the bulk and in the presence of external fields

Abstract

The phase behaviour of hard spherocylinders is calculated using the classical density functional theory of freezing. In particular, we construct a modified weighted-density approximation and calculate the bulk phase diagram. While the stability regime of the isotropic, nematic and smectic-A phases is in reasonable agreement with computer simulation data, the theory fails to describe the correct stability of the crystalline phases. Furthermore, we investigate the phase behaviour in an external field coupling to the orientational degrees of freedom. As a result, bulk phases which have the same translational symmetry but a different orientational symmetry can be transformed continuously into each other above a critical strength of the external field.

Dynamical density functional theory for colloidal particles with arbitrary shape

“…Our results constitute an important framework for further numerical explorations. This is in particular appealing as since recently an equilibrium density functional is known for arbitrarily shaped hard colloids [6,80,81] which can serve as an input for the dynamical density functional theory. Another possibility to construct a density functional for biaxial particles is a mean-field approximation for repulsive segment potentials [4], which works for soft interactions [82], or a perturbation theory [83,84] for anisotropic attractions around a spherical reference system.…”

A generalisation of the Onsager trial-function approach: describing nematic liquid crystals with an algebraic equation of state

“…This is due in part to the lack of transparency in the description that Onsager provides in his well-known appendix [37]. In the majority of studies that have been made with the OTF [52,[104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119], the Onsager expressions are employed as originally quoted. Significant effort has to be expended to recognise the general aspects of the Onsager approach in describing the ordering transition of more-complex molecules and mixtures with simple algebraic equations.…”

“…The last three (concise) pages of Onsager's long paper [37] are dedicated to the use of a single-parameter hyperbolic trial function to develop an analytical representation of the free energy for the nematic phase of hard rod-like particles. Considering the large number of studies that have made use of the generic form of the Onsager free-energy functional for anisotropic phases, it is surprising that his trial function has been employed far less frequently (see, for example, references [52,[104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119]). As far as we are aware only the explicit analytical forms of the free energy derived by Onsager for the leading term of the second virial coefficient of rod-like particles have been used thus far; no attempt has been made to generalise the treatment to more complicated mathematical forms of the excluded volume.…”

Differently shaped hard body colloids in confinement: From passive to active particles

“…The work of Bolhuis and Frenkel [62] thus provides excellent benchmark data to test density functional theories for rodlike colloids [63]. The recently developed E-FMT has been applied to inhomogeneous isotropic and nematic phases [32] but the computation of the full phase diagram is still hampered by the enormous numerical effort required to evaluate the functional for structured phases such as smectic A and plastic crystal.…”

“…The numerical burden can be significantly reduced by applying E-FMT to spherocylinders in strong aligning fields which only couple to the orientational degrees of freedom [63]. Numerical results for the isotropic and nematic fluids of spherocylinders and their coexistence are presented in [32].…”