Dependence of the gel point on molecular structure and reaction conditions

Abstract

The interpretation of gelation in irreversible polymerisations is discussed in terms of a combination of the Frisch and Kilb theories. According to this a branching parameter, λ, is determined from the equation λ=(α_c(ƒ– 1)– 1)/((1 –α_c)α_c(ƒ– 1)), and is interpreted using the relationship λ=(πνb²)ϕ(1, )/Nc_ext. In these expressions α_c is the critical value of the branching coefficient, ƒ is the branch-point functionality, ν is the number of bonds in the smallest ring which can form, b is the effective bond length of these bonds, ϕ(1, ) is a constant, and c_ext is a measure of the average concentration of a reaction system.

The interpretation is applied to data from polyurethane and polyester forming systems in which ƒ= 3. Two expressions for c_ext are tried—the average initial and average gel-point concentration of reactive groups, (c_a0+c_b0)/2 and (c_ac+c_bc)/2, respectively. The polyester results in particular are satisfactorily interpreted in this way, and over-all the results indicate a preference for the use of (c_ac+c_bc)/2. With this expression the correct limiting behaviour of λ at small c^–1_ext is found, and the values of b derived from the preceding equations are in better accord with those expected from solution properties.