Importance of interactions for free-volume and end-group effects in polymers: an equilibrium lattice investigation

We consider a lattice model of a polymer system in which we distinguish between the end (E) and the middle (M) groups. The free volume is represented as a "hole" or "void" (0), which constitutes a separate species in addition to the two "species" M and E. There are three different exchange interaction energies, and correspondingly three Boltzmann weights w(ij), i not equal j=0,E,M between different species. We define the free volume associated with the species j=M or E, as the average number of voids next to j. Using a recently developed equilibrium lattice theory, we calculate the free volume v(E) and v(M) associated with an end group and a middle group, respectively, and investigate the effects of interactions among them. Our calculations show that v(E) and v(M) are intricate functions of w(ij), the pressure and the molecular weight, and that their difference can change sign under certain conditions. These conditions are elucidated. We demonstrate that when the end group is chemically dissimilar from the middle group, the middle group may have more free volume than the end group. We find that the conditions that favor a middle group having more free volume over an end group are w(E0)<1, w(M0)<1, and w(ME)>1. The effect of pressure and molecular weight can be of either type and appears to be dependent on the interactions.