Equilibrium ring concentrations and the statistical conformations of polymer chains: Part 8. Calculation of small ring concentrations in polydihydrogensiloxane and polydimethylsiloxane equilibrates

Abstract

Theoretical molar cyclization equilibrium constants K x for small, unstrained cyclics [H 2SiO] x ( x=4−8) and [(CH 3) 2SiO] x ( x=4−9) in undiluted polydihydrogensiloxane and polydimethylsiloxane equilibrates are calculated using the Jacobson and Stockmayer theory, without assuming that the corresponding chain molecules obey Gaussian statistics. The statistical conformations of dihydrogensiloxane chains are described by a simple rotational isomeric state model with skeletal bonds assigned to trans ( ø=0°) and gauche ( ø= ±120°) states with equal probability; and the statistical conformations of dimethylsiloxane chains are described by Flory, Crescenzi and Mark's (FCM) rotational isomeric state model. Dihydrogensiloxane and dimethylsiloxane chains in undiluted equilibrates are assumed to be unperturbed by excluded volume effects, and the probabilities of intramolecular cyclization are calculated by simply computing the statistically weighted fractions of the total number of conformations defined by the rotational isomeric state models that have terminal atoms in juxtaposition for ring closure. The calculated K x values for cyclic dihydrogensiloxanes are compared with the published experimental K x values for the homologous cyclic hydrogenmethylsiloxanes and dimethylsiloxanes. The FCM rotational isomeric state model of polydimethylsiloxane gives theoretical molar cyclization equilibrium constants for the cyclics [(CH 3) 2SiO] 8 and [(CH 3) 2SiO] 9 in excellent agreement with the experimental values. However, it is shown that before the FCM model can be used to calculate the molar cyclization equilibrium constants for smaller dimethylsiloxane rings, it must be modified so that it takes into account the mutual interdependence of sequencies of bond rotational states.