Extension of lattice cluster theory to strongly interacting, self-assembling polymeric systems

Abstract

A new extension of the lattice cluster theory is developed to describe the influence of monomer structure and local correlations on the free energy of strongly interacting and self-assembling polymer systems. This extension combines a systematic high dimension (1/d) and high temperature expansion (that is appropriate for weakly interacting systems) with a direct treatment of strong interactions. The general theory is illustrated for a binary polymer blend whose two components contain “sticky” donor and acceptor groups, respectively. The free energy is determined as an explicit function of the donor-acceptor contact probabilities that depend, in turn, on the local structure and both the strong and weak interactions.

Lattice cluster theory of associating polymers. I. Solutions of linear telechelic polymer chains

“…(20)-(22) by collecting terms corresponding to a given power of y. The quantity y is determined by the maximum term method, i.e., by applying the condition,102 …”

Lattice cluster theory of associating polymers. IV. Phase behavior of telechelic polymer solutions

“…(5) depends for a given lattice type only on the chain index M (the number of united atom groups) and the monomer molecular structure of the telechelic polymer chains. 12,20 The effective value y * for the volume fraction y in Eqs. (2) and (3) is determined through maximizing the free energy f s with respect to y, which leads to the relation, 12,20 …”

“…Previous studies 18,19 of this phenomenon are based on the principles of mass action or, more generally, on simple FH type theories. The recent extension 12,20 of the LCT to strongly interacting polymer systems significantly enhances the predictive capacity of the analytical modeling of self-assembly by incorporating the molecular details of internal monomer structure and short range structural correlations (that arise from bonding constraints and interactions) 21 into the thermodynamic description of these systems. Our short communication 22 highlights the much richer coupling between phase separation and self-assembly that is obtained from our new theory.…”

Liquid–liquid phase equilibria of hyperbranched polymers—Experimental study and modeling

“…Freed et al [28][29][30][31][32][33][34][35][36][37][38][39][40][41] introduced the lattice-cluster theory (LCT) that considers the architecture of the molecules of the components. For a solution of a hyperbranched polymer (B) in a solvent (A) the Helmholtz free energy is expanded in a double power series of 1/z and ε/(k B T).…”

“…The FH theory ignores the details of chain connectivity and therefore cannot distinguish between linear, star, branch or comb polymer architecture. The lattice-cluster theory (LCT) developed by Freed and co-workers overcomes this problem [28][29][30][31][32][33][34][35][36][37][38][39][40][41]. It is very suitable for HPBs because it can describe how the architecture of the molecules influences Gibbs free energy and phase equilibrium.…”