The average degree of polymerization i?,, depends on the average degree of hydrolysis f,, as I/@, = a + bR,, over a large range of x:, for all metal oxide alkoxides and oxide trialkylsilyloxides that have been formed by hydrolysis and examined in solution. A number of general theoretical models are developed which permit quantitative interpretation of the parameters a and b. Mixtures of linear or branched chains in proportions governed wholly or partly by the degree of polymerization of the unhydrolyzed alkoxide can explain all the data on oxide alkoxides in solution in their corresponding alcohol, and the model leads to a plausible mechanism for disproportionation. Similar models with more complex structure can be involved in the metal oxide trialkylsilyloxides. Heterogeneity in the composition of the repeating units or in the number of metal-oxygen-metal bridges between successive repeating units can also be significant for both oxide alkoxides and oxide trialkylsilyloxides. Models involving cyclic chains are possible, but steric effects make them improbable in many cases. Mixtures of chains with equal average degrees of hydrolysis for each type of chain have been assumed in previous analyses, but are shown to be special cases of the more general model.
IntroductionBradley and co-workers have examined a large number of the polymeric hydrolysis products of metal alkoxides (1-7) and of metal trialkylsilyloxides (8-1 1). Hydrolysis of metal alkoxides gives metal oxide alkoxides, or polyalkylmetalloxanes, e.g.