AbstractA limited number of acrylamidomethyl ether groups can be introduced into cotton. We can assume that the reactive groups form a lattice and that when two or more adjacent sites are occupied, these neighboring vinyl groups will react with each other when a free radical catalyst is applied to them. A monomer group isolated from others by empty neighboring sites will remain unconverted. If each site has Z neighbors, Z being the coordination number, the conversion can be calculated as a function of the fractional site occupancy and of Z. The expression derived from the lattice model is mathematically equivalent to an expression which is based on an excluded volume model. In the latter, it is assumed that each reactive monomer has a reactive shell around it. If another monomer is placed within this shell, the two can react with each other. In terms of this model the parameter Z is defined as the ratio between the volume of the reactive shell and of the volume occupied by the monomer. The latter model offers some mathematical advantages and allows the calculation of both conversion and degree of polymerization from Z and the fractional site occupancy. It is shown that the ultimately achievable conversion and the degree of polymerization increases with Z and with site occupancy. Acrylamidomethylated cotton samples were treated with increasing amounts of ammonium persulfate and the conversion was determined. The data could be extrapolated to infinite initiator concentration and Z was found to have a value of 3.5–4. Since the reaction between double bonds on neighborings sites of a single cellulose chain would have a coordination number equal to 2, the fact that Z > 2 indicates that reaction between double bonds attached to different cellulose chains must occur. The fraction of links which are intermolecular is (Z‐2)/Z, being 43–50%. This result is an excellent agreement with previous data showing that only 42% of the crosslinks contribute to the increased resilience of cotton. It is likely that the termination of the polymerization reaction involves the combination of two radicals. Consequently, each polymeric or oligomeric chain contains two sulfate groups when ammonium persulfate is used as initiator. The molecular weight of these chains can be calculated from the mole ratio between the converted monomers and sulfur. The molecular weights determined this way agreed reasonably well with the molecular weight values calculated from the theory with Z = 4.
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