Phase behavior of binary mixtures of thick and thin hard rods

Abstract

Using a straightforward extension of the Onsager-theory for hard rods, we consider the thermodynamic stability of the isotropic (I) and nematic (N) phase of binary mixtures of thick and thin hard rods of the same length. We show that such mixtures not only exhibit the expected I-N ordering transition and the previously predicted depletion driven I-I demixing transition, but also a N-N demixing transition driven by the orientation entropy of the thinner rods. For various values of the diameter ratio of the two species we present the phase diagrams, which exhibit I-N, I-I and N-N coexistence, I-N-N and I-I-N triple points, and I-I and N-N critical points. We also present the results of computer simulations of the I-I and I-N coexistence for diameter ratio 1 : 10, which are in good agreement with the theory.

Global fluid phase behavior in binary mixtures of rodlike and platelike molecules

“…͑6͔͒. In order to avoid the uncertainties that arise when using the series-expansion methods, 30 we solve the coupled integral equations ͓Eqs. ͑11͒ and ͑12͔͒ numerically.…”

“…The nematic-nematic transition usually occurs at very high pressure, hence involving highly ordered phases; one also finds upper and lower critical points which are associated with this demixing transition. It is interesting to note that upper critical pressures have been obtained for nematic demixing in mixtures of hard rodlike particles, [29][30][31] while lower critical pressures are seen as the limit of nematic demixing in mixtures platelike particles. 32 In hard rod-plate mixtures, the nematic directors of the rod-rich and plate-rich coexisting phases are always perpendicular to each other, so that high-pressure nematic-nematic critical points have not been observed.…”

“…The necessary conditions for isotropic-isotropic coexistence in mixtures of nonspherical hard particles have been previously investigated for a number of special cases. 30,[33][34][35][36] It is known, for example, that mixtures of rodlike particles of different lengths but equal diameters do not exhibit this phase separation, 33 and that when the diameters are different, a critical volume ratio determines the stabilization of the transition. 30,34,35 In the limit of very large size ratios, the smaller particles can be treated as ideal as far as the pure component interactions are concerned, although in the mixture the interactions between the small and large particles must be incorporated.…”

Isotropic−Nematic Density Inversion in a Binary Mixture of Thin and Thick Hard Platelets

“…As in ref 17, we use Gaussian trial ODFs with variational parameter R j to describe the angular distribution of the platelets j in the nematic state A great advantage of using a Gaussian trial ODF is that σ j and F jk are now analytically tractable. Substituting (11) in (1) gives us for the orientational entropy. For the excluded volume entropy in the nematic phase, we will only retain the leading order terms…”

Entropy-Driven Triple Point Wetting in Hard-Rod Mixtures

“…The depletion effect, whereby two large hard-core particles attract each other effectively due to the presence of a "sea" of smaller ones, is perhaps the best known entropic demixing mechanism; it can, e.g., drive a gasliquid transition in colloid-polymer mixtures [5]. In mixtures of hard rods, the object of study in this Letter, another entropic demixing mechanism is at work: the orientation entropy can drive an immiscibility gap in the nematic phase if the two rod species are sufficiently dissimilar [6,7]. The bulk phase diagram of such mixtures not only features isotropic-nematic coexistence, but also nematic-nematic coexistence and an isotropic-nematicnematic triple point (see Fig.…”