Bela M. Mulder

Do cylinders exhibit a cubatic phase

We investigate the possibility that freely rotating cylinders with an aspect ratio L/D=0.9 exhibit a cubatic phase similar to the one found for a system of cut spheres. We present theoretical arguments why a cubatic phase might occur in this particular system. Monte Carlo simulations do not confirm the existence of a cubatic phase for cylinders. However, they do reveal an unexpected phase behavior between the isotropic and crystalline phase.

The excluded volume of hard sphero-zonotopes

Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as mo...Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as models for fluid and liquid crystalline behaviour e.g. spheres, cubes, sphero-cylinders, sphero-platelets. We discuss two explicit examples: sphero-cuboids, the 3D core generalization of the sphero-cylinder and the sphero-platelet, and hexagonal prisms that are models for the recently synthesized colloidal gibbsite platelets. Employing the fact that a cylinder is a zonoid, i.e. the limit of a sequence of right regular prisms, we are able to compute the excluded volume of the ‘true’ sphero-cylinder, a uniformly padded cylinder, of which the oblate-spherocylinder is a known example. Our approach en passant provides a relatively elementary rederivation of Onsagers classical result on cylinders.

Phase Diagram of Hard Ellipsoids of Revolution

Abstract We present the results of Monte Carlo simulations of the equation of state of hard ellipsoids of revolution with axial ratios a/b = 3, 2.75, 2, 1.25, 0.8, 0.5, 0.3636 and 0.3333. We identify four distinct phases, viz. isotropic fluid, nematic fluid, ordered solid and plastic solid. In all cases the thermodynamic phase transitions are located by free energy computation. We find nematic phases only for a/b ≥ 2.75 and a/b ≤ 1/2.75. A plastic solid phase is observed for 1.25 ≥ a/b / 0.8. It is found that the phase diagram is surprisingly symmetric under interchange of the major and minor axes of the ellipsoids.

ABSENCE OF HIGH-DENSITY CONSOLUTE POINT IN NEMATIC HARD ROD MIXTURES

In this paper we resolve a controversy related to the demixing transition in the nematic phase of binary hard rod mixtures. Previous analyses do not agree on the existence of a consolute point closing the nematic‐nematic coexistence region. We definitely rule out the existence of this critical point, at least in the Onsager theory. Our analysis requires the determination of self‐consistent orientation distribution functions, for which we develop an efficient numerical scheme. This scheme is based on the scaling properties of the high density limit of the stationarity condition on the free energy functional. We illustrate this method in some detail for the monodisperse thin hard rod system.

Cubatic phase for tetrapods

We investigate the phase behavior of tetrapods, hard nonconvex bodies formed by four rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.

Phase behaviour of a symmetric binary mixture of hard rods

The phase behaviour of long hard rods is independent of their length to breadth ratio in the limit that this ratio is very large. We form a binary mixture of rods with different length to breadth ratios but the same second virial coefficient. As the second virial coefficient is the same for both components, their phase behaviour in the pure state is identical. However, the difference in their shapes—one is longer and thinner than the other—results in an increased interaction between a pair of rods of different components. As the difference in shape of the two components is increased, first isotropic–isotropic coexistence is observed (with a critical point), then in addition nematic–nematic coexistence. At first there is a nematic–nematic critical point but this point reaches the isotropic–nematic transition, creating a four phase region. Gibbs’ phase rule, as usually stated, permits a maximum of three phases to coexist simultaneously in a binary athermal mixture. Here, the symmetry between the two compone...

RESEARCH NOTE Virial coefficients of Onsager crosses

Onsager crosses are particles formed by rigidly connecting three perpendicular, elongated rods of length L and diameter D. We have investigated the behaviour of the virial coefficients of Onsager crosses as a function of the aspect ratio L/D of the rods. The interest in these particles stems from the fact that they should exhibit a cubatic liquid crystalline phase in the limit (L/D) →∞. It is shown that in order for the theory predicting this phase to be strictly valid, the rod aspect ratio should be extremely large ((L/D) ≳ 1000).