Significance of the free volume for metastability, spinodals, and the glassy state: An exact calculation in polymers

Abstract

A lattice model of semiflexible linear chains (with equilibrium polydispersity) containing free volume is solved exactly on a Husimi cactus. A metastable liquid (ML) is discovered to exist only at low temperatures and is distinct (and may be disjoint) from the supercooled liquid (SCL) that exists only at high temperatures. The free volume plays a significant role in that the spinodals of the ML and SCL merge and then disappear as the free volume is reduced. The Kauzmann temperature T(K) occurs in the ML without any singularity. At T(MC)>T(K), the ML specific heat has a peak. For infinitely long polymers, the peak height diverges and the free volume vanishes at T(MC), resulting in a continuous liquid-liquid transition. Contrary to the conventional wisdom, both T(K) and T(MC) occur in the ML and not in the SCL.

Percolation of particles on recursive lattices using a nanoscale approach. III. Percolation of polydisperse particles in the presence of a polymer matrix

“…The gelation of the polymer chains and the percolation of the filler particles are two independent processes but it is easy to understand how these two processes might strongly affect one another. Our polymer model has been recently implemented in order to describe the presence of finite polymer chains [23]. The current model describes a polydisperse polymer system with an equilibrium degree of polymerization but the model can be easily extended in order to be able to describe a monodisperse polymer system.…”

“…This polymer model, originally used to describe an infinite molecular weight incompressible polymer, has been recently implemented to take into account the finite length of many polymers and the presence of free volume [23,24]. The model developed in [22] is defined on a square lattice and solved exactly on a square Husimi lattice, part of which is shown in Figure 1.…”

“…In order to describe the percolation of particles of different sizes in the presence of a polymer matrix, we have used a model for a semiflexible polymer due to Flory [19,20], which has been extended and used previously in our research group [21,22,23,24]. This polymer model, originally used to describe an infinite molecular weight incompressible polymer, has been recently implemented to take into account the finite length of many polymers and the presence of free volume [23,24].…”

Entropy of polydisperse chains: Solution on the Husimi lattice

“…(10). The linearity of these recursion relations with respect to the ratios G i allows us to assure that a fixed point of the pair of recursion relations Eqs.…”

“…Thermal generalizations of the model, where energies are associated to different allowed configurations, were studied in the literature with techniques similar to the one we will use here, with focus on phase transitions, which occur in these models, as well as on metastable states and glass transitions. 10 Also, a model where the sets of connected sites are not linear chains, but objects with loops, was also considered before with emphasis on the percolation transition, 11 but in the particular case where this athermal model reduces to the one we study here no distinction is made between internal and endpoint monomers of the chains.…”