General Expression for Pure Polymers and Mixtures

Previously we have seen a heuristic derivation of TPTl for the special case of a pure polymer with fixed bond length. Actually, TPTl is a much more general theory which allows to describe a wide variety of systems. We will henceforth restrict our attention to the special case of multicomponent mixtures. We will assume that each of the components is a chain molecule, described as an ensemble of A,- identical beads, which interact with each other and with any other bead in the system by means of a site-site potential, Vtj. Furthermore, adjacent beads on the same molecule interact by means of a bonding potential,. The composition of the mixture may be described by means of the total molecular density, p, and the molar fractions of each component, Xj. According to TPTl, the total Helmholtz free energy of the multicomponent mixture may be described in terms of three different contributions [237, 253]  

Ideal contribution The Helmholtz free energy of an ideal gas of molecules is given 

Monomer contribution The residual monomer contribution to the free energy is given by  

Chain contribution The free energy required to form the chain fluid from the reference fluid of unbonded monomers is given by  

Note that within the TPTl theory, the problem of describing the thermodynamics of a system of chain molecules is converted into a much simpler problem, namely. 

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