Z-Average of Cross-Linked Copolymers and Branched Polycondensates

The theory of Odle et al. for the z-average of branched polycondensates isextended to the general case of co-cross-linking of primary chains withdifferent functionalities. Examples are given for free radical and step growthpolymerization. For polycondensates, assuming surplus of one functionality and complete conversion, a simple formula for the degree of polymerization DPz for functional groups is derived: DPz=f(w)(3)(2g(z)-g(w)(3))+g(w)(3)(2f(z)-f(w)(3)) / f(w)g(w)(1-(f(w)-1)(g(w)-1))(2) (1) (f(w),f(z),g(w),g(z): weight and z-averages of the functionalities of the monomers).The formula is applied to the branched step growth polymerization of monomers A(2)+A(f)+B-2 with reactive groups A and B and functionalities 2 and f > 2. The functionality fhas practically no influence on the weight averages DPw and M-w if calculated as a function of the relative branching density rho(r) = rho/rho(c), where rho(c) = A(f,c)/(A(f,c) + A(2)) and A(f,c) is the critical value at the gel point. The z-averages become increasingly larger with increasing f and the ratio DPz (f)/DPz (f=3) is linear in rho(r) and f.