| The present work deals with the statistical mechanical lattice investigation of the effects of free volume in polymers. The free volume is represented as “voids” (0), and considered a separate species. We use the recursive lattice approach, which was initiated in our group, throughout this work. The work is limited to the following four aspects of free volume. (i) In chapter III, a lattice model of a polymer melt in which we distinguish between the end (E) and the middle (M) groups is used to study the free volume distribution between the two groups. We define the free volume vj associated with the species j = M or E, as the average number of voids that are nearest neighbors to j. We demonstrate that when the end-group is chemically dissimilar from the middle-group, we may have VM > VE, in contrast to popular belief. (ii) In chapter IV, we calculate the cluster size distribution and average cluster size of voids in a polymer melt. The effects of interactions, the pressure, the degree of polymerization (DP), the coordination number q, and the possibility of void percolation on the above properties are evaluated. (iii) In chapter V, the procedure of extracting dressed chi's for compressible blends from small angle neutron scattering data is critically evaluated. A compressible binary blend of species 1 and 2 is characterized by three bare chi parameters: χ01, χ 02, and χ12. New (bar and unbar) definitions of the dressed chi's are introduced by considering different reference states. Our calculations show that for weakly interacting asymmetric blends, thermodynamic effects arising from interactions with the free volume become very strong and the unbar dressed chi loses correlation with χ12; it may even become negative for a positive χ12. But the bar dressed chi's provide a reliable estimate of χ12; however, they cannot be extracted, at least at the present time. Strongly interacting or symmetric blends pose no problem in determining chi. (iv) In chapter VI, we present a new lattice theory of a multi-component mixture in which the monomer of different species can have different sizes, with respect to the void size. |
