Finite-density Onsager-type theory for the isotropic-nematic transition of hard ellipsoids

Abstract

We propose a sim ple density-functional theory for the isotropic-nem atic transition of a System of hard ellipsoids which yields results in fair agreem ent with the com puter sim ulation studies and which reduces exactly to Onsager's theory in the lim it of infinitely dilute Systems of infinitely long ellipsoids. When the free energy is expanded with respect to the Maier-Saupe quadrupole order param eter an explicit Landau theory is produced which yields good results for sm all nonsphericities. The theory also predicts a Lindem ann ruie for orientational freezing.

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

“…The distribution function g(y) is then represented as a simple function such that the positional and orientational dependencies are decoupled and can be integrated separately. This type of decoupling approximation is commonly used to represent the structure of nonspherical molecules (e.g., see references [67,163,164]). Thereby, the compressibility factor (Equation (7)) becomes…”

“…This limits the applicability to the low-density region; as the F o r P e e r R e v i e w O n l y 3 aspect ratio of the rod-like particles increases, the system will exhibit an isotropic-nematic at progressively lower densities so the Onsager second-virial approach is exact in the limit of infinitely long and thin particles. A number of alternative approaches are available to incorporate the effect of higher-body contributions (which are important for molecules with more moderate aspect ratios) in an Onsager-like treatment: higher virial coefficients can be included in the density series of the free energy (often represented as a Padé approximant) [56][57][58][59][60]; the Onsager free energy can be reformulated as a scaled-particle theory [49,[61][62][63]; more-rigorous integral equation and density functional approaches can be used (see for example [10,12,[64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80]); scaling arguments and the decoupling approximation can be employed to express the free energy of the system in terms of that of an effective hard-sphere system (or of an isotropic fluid of the non-spherical particles) [81][82][83][84]. In our work we opt for a decoupling approximation of this type, as these have been shown to provide a very accurate representation of the isotropic-nematic transition for hard-core particles of moderate size asymmetry (e.g., [11,42]); further details of the methodology are presented in the following section.…”

Universality in the jamming limit for elongated hard particles in one dimension

“…1). Non-spherically symmetric hard particles [12][13][14][15][16][17][18][19][20][21][22][23][24] provide important perspectives into the phase behavior of liquid crystals. Indeed, following an approach outlined in Ref.…”

Effective-liquid approach to the generalized Onsager theories of the isotropic-nematic transition of hard convex bodies

“…The DFT of these phases can then be completed by parametrizing h(u) in terms of known functions [11] and minimizing P with respect to these (order) parameters for a given DCF. The latter function is however not known and diferent strategies can be followed in order to approximate its contribution to (4 cI (r;u, u;p)=cH~P UO a(r;u, u') (6) where r=r/~r~, and pvo is the packing fraction. Using (5) and (6) in (4) we obtain an expression for the excess ly proposed by Tjipto-Margo and Evans [12].…”

“…Here i)i = plvo denotes the packing fraction of the isotropic phase, b i) = i)~-gl, P* =Ppvo the reduced pressure, p, ""=Pp, ," the reduced excess chemical potential, and q = (P2(cos8) ) the quadrupole moment of the angular distribution of the nematic at coexistence. All the theoretical results have been obtained using the Carnahan-Starling HS equation of state [6] for QHs(7) l, the Maier-Saupe one orderparameter approximation [6] for h(u) and the Berne-Pechukas approximation [6] for the overlap distance o. (r;u, u') (rescaled in such a way as to restore the exact second virial coefficient [4] Eq.…”