Lattice model of equilibrium polymerization. VI. Measures of fluid "complexity" and search for generalized...

Particle association in "complex" fluids containing charged, polar, or polymeric molecular species often leads to deviations from the corresponding state description of "simple" fluids in which the molecules are assumed to have relatively symmetric interactions and shapes. This fundamental problem is addressed by developing a minimal thermodynamic model of activated equilibrium polymerization solutions that incorporates effects associated with the competition between van der Waals and associative interactions, as well as features related to molecular anisotropy and many-body interactions. As a dual purpose, we focus on thermodynamic signatures that can be used to identify the nature of dynamic clustering transitions and the interaction parameters associated with these rounded thermodynamic transitions. The analysis begins by examining "singular" features in the concentration dependence of the osmotic pressure Pi that generically characterize the onset of particle association. Because molecular self-assembly can strongly couple with fluid phase separation, evidence is also sought for associative interactions in the behavior of the second A(2) and third A(3) osmotic virial coefficients. In particular, the temperatures T(Theta2) and T(Theta3) where A(2) and A(3), respectively, vanish are found to contain valuable information about the relative strength of the associative and van der Waals interactions. The critical temperature T(c) for phase separation, the critical composition phi(c), and the rectilinear diameter A(d), describing the asymmetry of the coexistence curve for phase separation, along with the average cluster mass L(c) and extent of polymerization Phi(c) at the critical point, further specify the relevant interaction parameters of our model. Collectively, these characteristic properties provide a thermodynamic metric for defining fluid complexity and in developing a theoretically based corresponding state relation for complex fluids.