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

Abstract

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.

Continuous solution copolymerization of ethylene with propylene using a constrained geometry catalyst system

“…Methylene sequence distributions from one to six and longer consecutive methylene units were therefore used for the analysis. [10,[20][21][22] We calculated the methylene sequence distributions (x n,1 to x n,6+ ) as well as the total number fraction of even methylene sequences ( v i1 x nY2i ) using the equations published in our previous work. [10] The sequence distributions and average sequence lengths for the samples with F P higher than 0.14 are shown in Tab.…”

“…These different insertions made the copolymerization system behave like a terpolymerization. [20,22] We denoted 10 and 01 type propylene as 2 and 3, respectively. As the 10 and 01 types were not distinctive in the monomer, they had the same concentration of [M P ].…”

“…A unique b was unable to be obtained. [20][21][22] Mathot et al [22] proposed an approach to estimated maximum and minimum b values. The maximum b can be calculated at p 22 = 0 (indicating the maximum probability for 10 type propylene insertion) while the estimate of the minimum value is performed at p 33 = 0 (referring to the most probable for 01 type propylene insertion).…”

“…From the conditional probabilities, one may estimate five reactivity ratios (r ij ) in a terpolymerization using the following relationships (r 32 = v): [20,22] 10 01 and 01 00 10…”

“…These values were similar to those estimated without considering propylene inversion. A comparison with vanadium catalyst [22] is also given in Tab. 7.…”