Bernoullian statistics configurational sequences

Let us assume that the probability of generating a meso sequence when a new monomer unit is added at the end of a growing chain can be denoted by a single parameter, which we shall call Pjn (and similarly Pr for a racemic sequence). This implies an assumption that the polymer obeys Bernoullian statistics, that is, the probability of forming an m or r sequence is independent of the stereochemical configuration of the chain already formed. It follows of course that Pm + Pr =1. because addition can be only m or r type. 

Analysis of the configurational sequence statistics of polymers showed that the polymer obeys Bernoullian type chain growth (22,23). 

The crystallization of racemic di-a-substituted poly(B-propiolactones) is not due to the formation of short isotactic sequences of R or S units since the polymer obeys Bernoullian statistics, as we have discussed above. Its crystallization necessarily involves the incorporation into the crystal of motifs of R and S configurations. 

Gerken and Ritchey [190] reported the C-NMR of series of acrylonitrile-methyl methacrylate (A/M) copolymers and determined the copolymer microstructure. They reported the configuration probabilities of A/M copolymers and Bernoullian statistics were found to describe the monomer configuration, a result in conflict with the conclusions of Pham [191]. Gerken and Ritchey [190] assigned the resonance lines of carbonyl and nitrile carbons to different triad cotactic sequences on the assumption that M and A monomer units have the same sensitivity to the tacticity of an adjacent A monomer unit. Also they did not calculate cotactic triad fractions from C-NMR spectra and did not compare experimental cotactic triad fractions with those expected from configurational probabilities have been made. 

NMR m and r dyad analysis of syndiotactic polystyrenes prepared with MAO activated CpTiCb or Cp TiCl3 systems was in agreement with the Bernoullian symmetric statistical model for stereoselective propagation. The polymer microstracture is a long sequence of syndiotactic dyads with only isolated m defects and no consecutive isotactic dyads (Figure 14.17), which is consistent with a chain-end control mechanism directed by the configuration of the tertiary carbon of the last inserted styrene unit (unlike 1,3-asymmetric induction). Thus, the syndiotactic preference exerted by the chain end arises from the phenyl-phenyl repulsive interaction between the last inserted... 

To prove the existence of a Bernoullian sequence, only triad information is needed, but tetrad information is required to verify a first-order Markov sequence. More complicated stereochemical mechanisms are possible of course (such as reactions controlled by penultimate configurations), and these would have to be fitted by more complex statistical analyses requiring knowledge of more than two probabilities. However, most detailed analyses to date on the tactleities of polymers obtained in homogeneous free radical or ionic polymerization reactions have been found to conform to either Bernoullian or first-order Markovian statistics. 

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