Local regularity of chain substances. I

The local regularity of chain substances composed of N linked elements, of which each can be in either of two states, the L‐configuration and the H‐configuration, is examined by means of statistical‐mechanical calculations. Introducing a virtual boundary energy at every boundary between the L‐regions, consisting of elements of the L‐configuration only, and H‐regions of H‐configuration elements only, we can deduce any average property of the chain from the logarithmic differentiation of the largest eigen‐value of the transition matrix. The average numbers of L‐ and H‐elements are NL = NB/(B + 1) and NH = N/(B + 1), respectively; that of L‐ or H‐parts is n = NLNH/N, and those of elements per L‐part and per H‐part are 〈l〉 = N/NH and 〈h〉 = N/NL, respectively, where B = exp {J/kT}, k is the Boltzmann constant and T the temperature. We can show the usual combinatory method gives the same results. Application of these relationships to a discussion of the stereospecificity of vinyl polymerization is referred to.