Chain structure of homogeneous ethylene-propylene copolymers showing inversion, described on the basis of 13C-NMR data. I. Theory

A first-order Markovian terpolymer model is used to describe the arrangement of ethylene (1), inverted propylene (2), and normal propylene (3) units in an ethylene-propylene chain by means of chain propagation probabilities (P set) and corresponding reactivity ratios (r set). From nuclear magnetic resonance data on the weight fractions of methylene sequences, w1:m up to and including w5:m, P11 and the methylene, ethylene, and propylene sequence length distributions can be calculated, as well as the mole fraction of ethylene (x1) and the average sequence lengths sn, sw, sz. With the usual fitting procedures, these results can be obtained for quite different P sets and r sets. This unsatisfactory situation is characterized by the assignment of different values to the degree of inversion I = x2/(x2 + x3). Insight into this indeterminacy was obtained by distinguishing the methylene sequences (s : m) ending with 2 and sequences ending with 3 (s : m, 2 and s : m, 3, respectively), the weight fractions of which appear to be independent of I except for w1:m,2, and w1:m,3. In the constant sum w1:m, the ratio of the two is determined by I. The limit values of I (Imin and Imax) are fixed within the model used and are reached for w1:m,2 = 0 and w1:m,3 = 0, respectively. The values of P12 and P13 are I-independent; by any particular choice of I, the other Pij's and hence a P set is fixed. For every P set there is a P″ set symmetrical with it, with I′ = 1 − I, which describes an identical chain formed in the opposite direction.