Bernouillian statistics

Moreover it has been shown that PV0CC1 prepared by free-radical polymerization of vinyl chloroformate (V0CC1) is an atactic polymer having a Bernouillian statistical distribution as expected (J[9). In order to extend our studies on the chemical modification of PV0CC1, the stereoselective character of the nucleophilic substitution of the chloroformate units with phenol has been examined by the study of the 13c-NMR spectra of partly modified polymers in the region of the aliphatic methine carbon atoms. The results obtained in this field are presented here. 

From these expressions it follows that the instantaneous distribution of the M units along the backbone (and consequently that of the grafts) formed instanteneously follows the Bernouillian statistics, provided the molar amount of the macromonomer in the reaction mixture is small enough. Fluctuations in composition generally remain within rather narrow limits, provided the conversion is not too high consequently, the content of grafts in a graft copolymer sample remains within narrow limits, too. 

The microstructure of acrylamide-sodium acrylate copolymers was determined by NMR (36). The monomer sequence distribution was found to conform to Bernouillian statistics and the reactivity ratios of both monomers were close to unity. These results which differ from those obtained for copolymers prepared in solution or emulsion (37) confirmed a polymerization process by nucleation and interparticular collisions. 

Figure 9.2 Lactide diastereoisomers and derived homo- and stereocopolymers obtained via ring-opening polymerisation, i predominantly isotactic, s predominantly syndiotactic, c stereocomplex, and lactic acid enantiomers and homo- and stereocopolymers obtained by polycondensation (ran randomly distributed L and D lactyl units according to Bernouillian statistics)...

The conditional probability of placement of the next A unit on a growing radical end — A i M depends on the cotacticity of the last diad, the propagation of the radical copolymerization does not follow the Bernouillian statistics. 

As for polyelectrolytes the Bernouillian statistics should not be suitable to represent the distribution of ionized and non-ionized units, since the influence of charges in place probably orients the addition of new charges during neutralization. On the contrary. Equation (4) should be valuable for rigid and helical copolymers since the main chain conformation would not change with the composition. The non-linearity would be only due to variations in the monomeric unit interactions according to the composition and the monomeric unit distribution along the macromolecule. 

In addition to the determination of the relative reactivities of both the comonomers and the growing free radicals, the knowledge of ri and rz can also serve to predict the frequency of AB or BA alternations in a statistical copolymer for a given composition of the feed. In the case of a Bernouillian statistics of distribution of monomeric units—that is, when the type of dyad formed is only determined by the nature of the growing chain end (which is the case in radical copolymerization)—it is relatively easy to predict the structure of the sequences appearing in a copolymer as a function of the composition of the feed and the reactivity ratios. 

The tacticity of anionically prepared polystyrenes has been the subject of extensive study by a number of groups of workers, mostly by means of 13C-NMR spectroscopy. From a study of the aromatic Cl resonances, Matsuzaki and coworkers found 234) that there is a tendency towards syndiotacticity when using -butyl-Iithium in toluene as initiator. From the sensitivity of the CMR spectrum to the nature of the solvent employed it was concluded that the polymerization did not conform to Bernoullian statistics. Randall examined the methylene resonances in the CMR spectrum and concluded that butyllithium initiated polystyrene is essentially atactic 235) and that propagation is Bernouillian. Uryu et al.236) examined polystyrene... 

A study of the NMR spectra of (acrylonitrile-methyl methacrylate) copolymers (PAM), with very low percentages in M monomer, allows a quantitative determination of AMA and MMA or AMM triad sequences from the methoxy resonances. The resolution of the complex pattern of the a-methyl resonances of isolated M units has been attempted. If our assignments are correct, the analysis of the cotactic pentad sequences (with a central M unit) has revealed that the configurations of the copolymer chain do not follow the Bernouillian or the first order Markoffian statistics. 

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