# Isotropic-nematic phase separation in asymmetrical rod-plate mixtures

### Full-text

Henricus Herman Wensink, Jul 04, 2015 Available from:- [Show abstract] [Hide abstract]

**ABSTRACT:**The phase behavior of a liquid-crystal forming binary mixture of generic hard rodlike and platelike particles is studied with the theory of Onsager [L. Onsager, Ann. N. Y. Acad. Sci. 51, 627 (1949)] for nematic ordering. The mixture is chosen to be symmetric at the level of the second virial theory, so that the phase behavior of the two pure components is identical. A parameter q is used to quantify the effect of the unlike rod-plate excluded volumes on the phase behavior; a value of q>1 indicates that the unlike excluded volume is greater than the like excluded volume between the rods or plates, and a value of q<1 corresponds to a smaller unlike excluded volume. Two methods are used to solve the excluded volume integrals: the approximate L2 model [A. Stroobants and H. N. W. Lekkerkerker, J. Phys. Chem. 88, 3669 (1984)], in which a second-order Legendre polynomial is used; and a numerical method where the integrals are solved exactly. By varying the unlike excluded volume interaction q, the isotropic phase is seen to be stabilized (small q) or destabilized (large q) with respect to the nematic phase for both models. Isotropic-isotropic demixing is also observed for the largest values of q due to the unfavorable contribution of the unlike excluded volume to the entropy of the system. A second-order nematic-biaxial nematic phase transition is observed for small values of q in the L2 approximation, and for all q in the exact calculation; in the latter case the stability of the biaxial phase is enhanced by increasing q, while in the L2 approximation nematic-nematic phase separation is favored. This result is the most striking difference between the two methods, and is in contrast with the results of previous studies. We show that the accuracy of the L2 expansion is particularly poor for parallel and perpendicular particle orientations.Physical Review E 08/2002; 66(1 Pt 1):011707. DOI:10.1103/PhysRevE.66.011707 · 2.33 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The phase behavior of a liquid-crystal forming model colloidal system containing hard rodlike and platelike particles is studied using the Parsons–Lee scaling [J. D. Parsons, Phys. Rev. A 19, 1225 (1979); S. D. Lee, J. Chem. Phys. 87, 4972 (1987)] of the Onsager theory. The rod and plate molecules are both modeled as hard cylinders. All of the mixtures considered correspond to cases in which the volume of the plate is orders of magnitude larger that the volume of the rod, so that an equivalence can be made where the plates are colloidal particles while the rods play the role of a depleting agent. A combined analysis of the isotropic–nematic bifurcation transition and spinodal demixing is carried out to determine the geometrical requirements for the stabilization of a demixing transition involving two isotropic phases. Global phase diagrams are presented in which the boundaries of isotropic phase demixing are indicated as functions of the molecular parameters. Using a parameter z which corresponds to the product of the rod and plate aspect ratios, it is shown that the isotropic phase is unstable relative to a demixed state for a wide range of molecular parameters of the constituting particles due to the large excluded volume associated with the mixing of the unlike particles. However, the stability analysis indicates that for certain aspect ratios, the isotropic–nematic phase equilibria always preempts the demixing of the isotropic phase, irrespective of the diameters of the particles. When isotropic–isotropic demixing is found, there is an upper bound at large size ratios (Asakura and Oosawa limit), and a lower bound at small size ratios (Onsager limit) beyond which the system exhibits a miscible isotropic phase. It is very gratifying to find both of these limits within a single theoretical framework. We test the validity of the stability analysis proposed by calculating a number of phase diagrams of the mixture for selected molecular parameters. As the hard rod particles promote an effective attractive interaction between the hard-plate colloidal particles, the isotropic–isotropic demixing usually takes place between two rod-rich fluids. As far as the isotropic–nematic transition is concerned, a stabilization as well as a destabilization of the nematic phase relative to the isotropic phase is seen for varying rod–plate size ratios. Moreover, isotropic–nematic azeotropes and re-entrant phenomena are also observed in most of the mixtures studied. We draw comparisons between the predicted regions of stability for isotropic demixing and recent experimental observations. © 2002 American Institute of Physics.The Journal of Chemical Physics 10/2002; 117(15):7207-7221. DOI:10.1063/1.1507112 · 3.12 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The isotropic-nematic phase behavior of a binary mixture of rodlike and platelike particles is studied within Onsager's second virial theory. The phase behavior is obtained from the numerically exact equilibrium orientational distribution functions for both uniaxial and biaxial nematic phases. Inspired by recent experimental work on these systems we concentrated on asymmetric mixtures in which the excluded volume between the plates v(pp)(ex) is larger than that between the rods v(rr)(ex). Starting from the symmetric case (v(pp)(ex)/v(rr)(ex)=1) and increasing the rod-plate excluded volume ratio we scrutinized the phase behavior, in particular focusing on the stability of the biaxial nematic phase. We observe that, at a certain asymmetry, the characteristic bicritical point is replaced by a two-phase region marking first order isotropic-biaxial transitions. Increasing the asymmetry even further leads to several demixing scenarios. First, there is a uniaxial-biaxial (N+-B) demixing scenario with an associated isotropic-uniaxial-biaxial (I-N+-B) triple equilibrium. Second, a uniaxial-uniaxial (N+-N-) demixing occurs in case of strongly asymmetric mixtures indicating that the biaxial nematic phase may become fully metastable. Since all predicted demixing scenarios lie in the experimentally accessible regime, there is a possibility of finding biaxial nematic structures in lyotropic colloidal rod-plate mixtures.Physical Review E 11/2002; 66(4 Pt 1):041704. DOI:10.1103/PhysRevE.66.041704 · 2.33 Impact Factor