Rod-like Colloids Plus Interacting Polymers

As we noted in Chap. 4, expression (6.33) just like (4.5) only holds for noninteracting depletants. The general expression for the semi-grand potential for hard spherocyhnders plus interacting depletants is 

6 Phase Transitions in Suspensions of Rod-Like Colloids Plus Polymers 

Expression (6.46) may be regarded as a generalized free volume theory (GFVT) semi-grand potential for rods plus interacting polymers. Subsequently, we can specify the quantities a and P for interacting polymers. 

While the formalism of (6.46) appears simple and does not present any particular problem, the computations of Q and especially the phase coexistence concentrations are involved. The reason for this is the combination of the numerical integration over the polymer concentration plus the minimisation of 2 for each rod and polymer concentration. Even within the Gaussian approximation, where the minimisation is relatively simple and there are explicit expressions for the variational parameter k, the calculations are demanding. 

For the free volume fraction a of interacting polymers in a suspension of hard spherocylinders we can write down a revised form of (6.39), 

---