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

The Journal of Chemical Physics (Impact Factor: 2.95). 10/2001; 115(15):7319-7329. DOI: 10.1063/1.1403686

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**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. - [Show abstract] [Hide abstract]

**ABSTRACT:**The molecular requirements for the stabilization of an isotropic demixing transition in mixtures of plate- and rodlike particles were considered. Based on a comparison of the critical pressure of the isotropic demixing transition and the lowest pressure of the isotropic-nematic bifurcation curve, a global phase diagram in terms of the molecular parameters were obtained which indicates the regions with and without isotropic demixing. The stability analysis proposed was very simple but it was also approximate, as the isotropic-nematic bifurcation pressure rarely coincides with the coexistence pressure in first-order transitions. - [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.