| Abstract: | When, in a poly-α-olefin, the probability that a given placement be isotactic depends upon the tacticity of only a finite number of immediate predecessors, the resulting diastereosequence distribution obeys the theory of Markoff chains. When this is not the case, one says that the resulting diastereosequence distribution is non-Markoffian. A special case of a Markoffian distribution is given by a simple Markof chain in which the tacticity of a given placement is assumed to be affected by only the tacticity of the immediately preceding placement. Another special case is, of course, the Bernoulli trial distribution in which the probability that a given placement be isotactic is independent of the tacticity of all other placements. A high resolution NMR spectrum can sometimes yield a quantitative determination of the concentrations of isotactic and syndiotactic placements and the concentrations of the three types of possible adjacent pairs of such placements (i.e., isotactic, syndiotactic, and heterotactic pairs). When this is the case, the spectrum can be used to determine whether or not a given diastereosequence distribution is Bernoullian. However, because the longest diastereosequences whose concentration can be measured by NMR spectroscopy involve only two placements, an NMR spectrum cannot check whether a given non-Bernoullian distribution be simple Markoffian or Markoffian in general. In fact, non-Markoffian distributions are compatible with existing NMR spectra on polymers prepared by anionic polymerizations. In this paper we work within the framework of Kac's theory of stationary statistical processes and point out some general results which are valid for both Markoffian and non-Markoffian processes. The results are applied to NMR spectroscopy and it is pointed out which calculations used to check the self-consistency of NMR data and to obtain the mean length of closed diastereosequences are valid for both Markoffian and non-Markoffian distributions. |
