Applications of the theory of branching processes to polymer systems can be so formulated, that all statistical parameters emerge automatically in a form which applies to the soluble part of the system, i.e., to the whole system up to the gel point, and to the sol fraction beyond. In a self-contained presentation, previous work along these lines is here extended to computing configurational statistics of systems arising most directly by condensation processes. These statistics are the mean-square radii of the molecules in such systems, averaged in various ways and useful for theories of light scattering and viscosity. Numerical calculations for random f-functional polycondensation are presented as plots of configurational parameters against conversion for f=3, 4, and 6. The general equations given extend beyond the random case to condensations with ``first-shell'' substitution effect, i.e., in which the rates of making or breaking a given bond between two repeat units depends on how many other bonds these two units carry (to further units). In terms of current theories, the intrinsic viscosity of a system at its gel point is shown to be finite. The spatial averaging of molecular size is based on random flight statistics. The well-known theorem by Kramers used in this connection is rederived on a simple topological basis, and generalized to deal with copolymerization of units of different sizes.

No abstract

Recent efforts to reformulate statistical theories of polymeric systems in terms of the theory of branching (``cascade'') processes, are here extended to calculations of statistical parameters for the theory of rubber elasticity, viz., the number and mean length of various forms of active network chains. New simple results are given for random f-functional polycondensation; it is shown that such systems are of interest in rubber elasticity studies in the region just after the gel point, where the concentration of active network chains varies rapidly with conversion, while the mean length of these chains diverges at the gel point. General exact formulas are derived for the random cross linking of arbitrary primary distributions, without assuming that the mean primary chain length is necessarily large; examples are worked out for uniform (homodisperse) chains, random, self-convoluted random, or Poisson primary distributions. Calculations are extended also to the cross-polymerization type of vulcanization reaction attributed to the cure of polybutadiene with peroxides. The results suggest reasons for differences in technical performance observed with such rubbers.

The initial products in the ultraviolet-light irradiation of aqueous phenol and the cresols at pH) 7 are the hydrated electron and the corresponding phenoxyl radicals. The hydrated electron decays by a first-order process of rate constant 4.3 x 104 sec-1 which is taken to be an upper limit for its reaction with water. The p-methyl phenoxyl radical disappears by a second-order dimerization to give 2, 2'-dihydroxy-5, 5'-dimethyl-biphenyl as a major product with a rate constant of 6.5 x 109 1. mole-1 sec-1. The optical generation of the hydrated electron from the neutral molecules can be explained by a rapid proton transfer from the excited state to the solvent prior to release of the electron.

No abstract