INTRODUCTION

For over half a century, experimentalists have known that the isolation and purification of rodlike viruses, such as the tobacco-mosaic virus (TMV), can be facilitated by addition of non-adsorbing polymers [114]. As purification of the virus was the central theme of these experiments, little attention was paid to the underlying physics of such mixtures of polymers and rodlike colloids. Yet, TMV dispersions provide excellent model systems to study colloidal liquid crystalline phases [100]. However, a limitation of the TMV system is that the length of the particle cannot be varied at will. Less seriously, the rod-rod interaction is predominantly electrostatic. This complicates a direct comparison to theories for hard rod suspensions. In recent years, much effort has been invested in the development of reliable techniques to synthesize sterically stabilized rodlike colloidal boehmite needles [115]. Dispersions of such particles could serve as a model system for rodlike colloids, much in the same way as dispersions of spherical latex and silica particles act as proto-typical experimental realizations of hard-sphere fluids. The boehmite rods have the added advantage that the length-to-width ratio can be varied. Thus far, these boehmite suspensions are still fairly polydisperse, but the situation is likely to improve as more sophisticated colloid synthesis techniques are developed. Buitenhuis et al.[116] conducted experiments on a mixture of polystyrene and boehmite rods with an aspect ratio =6.4, sterically stabilized with poly-isobutene [117] and dispersed in an organic solvent. For a polymer radius of gyration which was about 80% of the rod diameter they observed phase separation into two isotropic phases at sufficiently high polymer concentration.
The phase behavior of rod-polymer mixtures has been studied theoretically in the context of the Asakura-Oosawa (AO) model. As explained in chapter 1, the AO model describes the polymer as a sphere that has a hard core interaction with the rods, but is completely penetrable to other polymer spheres. Lekkerkerker and Stroobants [113] have used the formalism described in chapter 1 in combination with scaled particle theory to predict the phase diagram for mixtures of spherocylinders with an aspect ratio =5 and polymers with q= 1.0, 0.8, 0.5 and 0.1, where q is defined as the ratio of the (hard sphere) polymer diameter and the spherocylinder hard core diameter (). Scaled particle theory provides the equation of state for pure hard spherocylinder systems and the free volume fraction required in the perturbation theory. The free energy of the nematic phase depends functionally on the orientational distribution function. The equilibrium orientational distribution minimizes the free energy. Figure 6.1 shows the results of the calculations of Lekkerkerker and Stroobants in the plane. Here z, the polymer fugacity of the reservoir is related to the reservoir polymer number density by . As can be seen from the figure, the theory predicts that for long polymers (0.8), demixing will occur in the isotropic phase: this corresponds roughly to the results of the experiments on boehmite rods, mentioned above [116]. The critical point of the binodal in figure 6.1 shifts to higher density as q is lowered. For shorter polymers, this I-I transition disappears. For instance, for q=0.5, the I-I binodal is metastable with respect to the I-N transition. And for short polymers (0.1) a demixing transition is found in the nematic phase. It should be stressed that the theoretical prediction of the existence of a nematic-nematic phase separation should be treated with some caution: in the SPT approach of ref. [113], the smectic-A and solid phases are not considered, because the approximations that are used to compute the free-volume fraction by scaled-particle theory, are expected to break down in translationally ordered phases. However, as Lekkerkerker and Stroobants already noted, it is unlikely that the neglect of the smectic A and the solid phase is justified. There might, for instance, be a nematic-smectic (or smectic-smectic) phase transition, preempting the nematic-nematic transition. Even a solid-solid phase transition, as was discussed in chapter 3 belongs to the possibilities. In this chapter we will therefore also consider the influence of polymer addition on the location of the N-SmA and the SmA-S transition.
In the following section we use the results of numerical simulations on hard spherocylinders with aspect ratio =5, to compute the free-volume fraction that plays a crucial role in the thermodynamic perturbation theory as applied to the Asakura-Oosawa model. Using this perturbation theory, we arrive at a prediction of the phase diagram of the polymer-colloid mixture. It would be natural to compare the theoretical predictions with a direct simulation of the full AO model, at finite polymer fugacity z. However, such simulations would be computational quite expensive. In section 6.3, we therefore explore an alternative approach: we replace the polymer-induced depletion force by an angle dependent attractive pair potential. In section 6.4 we study the possibility of nematic-nematic phase transitions in the limit of large .