The validity of the theory of gelation in vinyl‐divinyl copolymerization
Authors: Minnema L. , Staverman A. J. 
Published: April 2003

AbstractThe classical theory of gelation correctly described gelation as a result of molecular network formation. Generally in vinyl‐divinyl copolymerization two effects may give rise to deviations from the classical theory, viz., decreased reactivity of pendent vinyl groups as they are shielded by the rest of the molecule and internal cyclization reactions. In order to study these effects two kinds of measurements were carried out: (a) Measurement of the amount of crosslinking by determining the molecular weights of crosslinked, soluble polymers and of the “primary” molecules that result if all crosslinks in both gel structures and crosslinked, soluble molecules are served. In copolymers of methylmethacrylate (MM) and N,N′‐bis(β‐methacryloxyethyl)‐p‐xylylenediurethane (MXU) all crosslinks were readily broken by the reaction of hydrogen bromide with the xylylenediurethane groups of MXU, even if the polymerization had been carried out far beyond the gelpoint. (b) Determination of vinyl unsaturation in soluble polymers, either (for low degrees of unsaturation) by means of a kinetic analysis of the oxidation of KMnO4, or with pyridine sulfate dibromide. The actual crosslinking density (ρexp) is found from the well‐known relations ρc = 1/Yw (Flory) and ρ = 1/Yw − 1/Pw (Stockmayer). The ideal crosslinking density (ρid), that is, the crosslinking density calculated on the assumption that no shielding and no cyclization occur, is found from copolymerization data (r1 = 0.6; r2 = 1.1) and simple statistical reasoning. The ratio ρexp/ρid = A contains the effects of shielding and cyclization as a product of two factors, f and q. q denotes the extent of cyclization and is found directly from the measurement of vinyl unsaturation; f denotes the shielding effect and is found as a result of the measurement of both A and q. The results of the investigation may be summarized as follows: (1) In a copolymerization with a given fraction of the divinyl‐monomer in the monomer mixture, the effect of shielding is found to remain constant as the reaction proceeds. (2) The reactivity of unsaturated groups in a growing copolymer strongly decreases with increasing values of the ratio MXU/MM in the copolymer. (3) In copolymerizations without solvent, pendent vinyls are consumed in cyclization reactions to the extent of 20–25% regardless of the ratio of MM to MXU in the copolymer. The extent of ring formation increases slightly with increasing conversion. (4) Copolymerizations carried out in benzene solution show a rapid increase in the extent of cyclization with increasing dilution. The magnitude of the shielding effect is almost independent of dilution irrespective of the degree of conversion in the range investigated. Experimentally, a linear relationship is found between q and the dilution V/V0, whereas theoretically a linear relationship between 1/q and V/V0 is to be expected. The explanation of this discrepancy is that not only cyclizations occur predominantly within one chain, but also that a growing radical chain will only react with a pendent vinyl group which is nearest to its radical end on the polymer chain. (5) Diffusion control of the crosslinking reaction is found not to occur.