The results of the thermodynamic integration are displayed in figure 6.5 for different values of . The graphs are plotted in the plane instead of the usual plane because the well depth is more directly related to the fugacity of the polymers in the system. In this way one can compare the phase diagrams with those of section 6.2. We note, however, that the pair potential that we use is not completely equivalent to the Asakura-Oosawa interaction. For this reason we focus on the qualitative features of the phase diagram. For q=1 the range of the potential is equal to the diameter of the spherocylinder and we see a phase separation between two isotropic phases ending in a critical point. The isotropic-isotropic phase separation is similar to the fluid-fluid coexistence in chapter 2. The density region where the nematic phase is stable becomes narrower as increases and it ends in an isotropic-nematic-smectic triple point at a fugacity of 0.23. This is lower than the location of the -- triple point at 0.34. In contrast, the results of the perturbation theory in section 6.2 indicate that for q=1 the I-N-SmA triple point has a higher fugacity than the -- one. Apparently, the attractive pair potential destabilizes the nematic phase with respect to the smectic phase.
At higher fugacity the smectic phase is expected to become metastable with respect to the solid. Although we have not included the solid in our simulation, it is likely that the general picture is similar to that found in section 6.2.

The perturbation theory of section 6.2 predicts that, for smaller values of q, the isotropic-isotropic transition will shift to higher fugacity and density and will, eventually be preempted by the isotropic-nematic transition. Indeed, for q=0.5 we find that the I-I transition has already disappeared. The I-N and N-SmA transitions widen at higher . The I-N-SmA triple point is located at =0.3. For still smaller q, the picture remains much the same. The I-N and N-SmA transitions widen at high , the triple point moves to higher and lower . This last feature was not predicted by the perturbation theory.

We do not observe a nematic-nematic or smectic-smectic phase separation. In section 6.2, we argued that a nematic-nematic or smectic-smectic transition will, most likely, be preempted by a transition to a phase with a different symmetry. However, for large , the range of stability of the nematic phase will become very large. Under those circumstances, it is likely that a N-N phase-transition becomes possible