Application to a Pure Model Polymer

In the previous section we have described how to implement TPTl for a mixture of Lennard-Jones chains with a FENE bonding potential. Before considering binary mixtures, however, we shall restrict our attention to the particular case of a one component system of polymers. In order to describe the thermodynamic properties of such a system, we will consider two TPTl implementations, which we denote TPTl-MSA and TPTl-RHNC. In TPTl-MSA, we employ the fiilly analytic equation of state described in the previous section. In TPTl-RHNC, the Lennard-Jones reference system is described by means of the Reference Hypernetted Chain theory (RHNC). This is an integral equation theory which can only be solved numerically. 

The liquid-vapor coexistence curve of the 10-mer as obtained from simulation and theory is shown in Fig. 23. Both the RHNC and MSA versions overestimate the critical temperature as obtained from simulation by about 15%. Of course, this is expected for any classical theory. On the other hand, far away from the critical point, results from both versions of the theory yield good agreement with simulation. The MSA version is somewhat more convenient, however, because it allows us to calculate the coexistence at low temperatures with no additional cost, while it becomes rather problematic to calculate the coexistence for the RHNC version below 

We have also investigated the critical points of chains with N = 20,40, and 60. Table 3 gives a summary of the simulation results, obtained by finite size scaling. 

Although the calculation of the critical point of fluids larger than about 100 monomers by computer simulation becomes prohibitively expensive, we can estimate the 0 point of our polymer model by an analysis of the temperature dependence of the polymer extension [238]. Extrapolation of the results gives as an estimate 0 = 3.32. As to the theory, fitting the critical temperature predicted by TPTl-RHNC to a power law of the form Tent = T + + cN in the range 10 to 

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