Chain configuration and statistics of stereochemical propagation

Let us consider a vinyl polymer from an unsymmetrically substituted monomer in the planar conformation. The neighbouring C—C bonds can form one of the two possible diads, meso (m) and racemic (r), 

In sterically random propagation, the probability of meso diad generation Pm in each addition is equal to 0.5, and the ratio of triads in the chain is i h s = = 1 2 1. In an atactic polymer, the diads m and r are statistically distributed in the chain. Natta [81] called the simplest stereoregular chains isotactic —mmmm— and syndiotactic —rrrr—. Monomers with both a and / carbons unsymmetrically substituted can form diisotactic polymers 

In the simplest case, when the structure of the propagating chain does not affect the configuration of the generated diad, the formation probabilities of meso and racemic diads, Pm and Pr, are related as Pr = (1 — Pm). Chain structure obeys Bernoulli statistics as if the added units were selected at random from a reservoir in which the fraction Pm of the total amount is m, and the fraction (1-Pm) is r. An isotactic polymer will be formed for Pm - 1, and a syndiotactic polymer for Pm - 0. Within these limits the chains will consists of randomly ordered m and r structures. 

Coleman and Fox published an alternative mechanism [82], According to these authors, the propagating centres exist in two forms, each of which favours the generation of either the m or r configuration. When both centres are in equilibrium, and when this equilibrium is rapidly established, the chain structure can be described by a modified Bernoulli statistics [83, 84]. The configurations of some polymers agrees better with this model than with first-or even second-order Markov models [84, 85]. 

When the manner of addition is affected by the growing chain end, the configurations of the added units will not obey Bernoulli statistics. In the simplest case, first-order Markov statistics will operate. Addition will be characterized by two parameters because the probability of r diad generation by monomer addition to an m end unit, will not be identical with monomer addition to an r end unit, P . The probabilities of m or r diad generation by addition to m or r chain ends will be bound by the relations P = (1 — Pmr) rm 0 rr) According to first-order Markov 

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