Molecular Distributions at Equilibrium. I. Theory of Equilibria in Scrambling Reactions and Interpretation of NMR Spectra

Abstract

Stochastic graph theory has been developed and applied to the interpretation of chemical equilibria resulting from scrambling reactions which lead to size distributions of molecules. By this means, deviations from random scrambling are treated in terms of the effect on any given site in a molecule of the environment of neighboring atoms within the molecule. This treatment is applied to molecular-distribution data on the glassy phosphates and to thermodynamic data on the aliphatic hydrocarbons. It is also shown to be the basis for interpretation of nuclear magnetic resonance data obtained on families of equilibrated compounds. A formal treatment of ring—chain equilibria is presented, and equilibrium constants for interactions between parts of molecules are related to the usual constants involving whole molecules. The concept of crowding of chain segments is employed in estimating the number of ring closures in infinite-network macromolecules (i.e., structures having as many branches as or more branches than correspond to the ``gel point'').