Phase coexistence in the hard-sphere Yukawa chain fluid with chain length polydispersity: dimer thermodynamic perturbation theory.

An extension of the dimer version of Wertheim's thermodynamic perturbation theory is proposed and used to treat polydisperse mixture of the hard-sphere Yukawa chain fluid with chain length polydispersity. The structure and thermodynamic properties of the reference system, represented by multicomponent mixture of the Yukawa hard-sphere dimers, are described using polymer mean spherical approximation. Explicit analytical expressions for the Helmholtz free energy, chemical potential, and pressure in terms of the two chain length distribution function moments are derived. The theory is used to calculate the full liquid-gas phase diagram, including critical binodal, cloud and shadow curves, and distribution functions of the coexisting phases. Effects of fractionation in terms of the distribution function and its first and second moments are studied. Predictions of the theory for these effects are in qualitative agreement with the corresponding experimental predictions, obtained recently for the polydisperse mixture of polymers in a single solvent. In particular, both theory and experiment predict that longer chain polymers equilibrate to the liquid phase while shorter chain polymers are predominantly encountered in the gas phase.