Z‐Average of Cross‐Linked Copolymers and Branched Polycondensates

The theory of Odle et al. for the z‐average of branched polycondensates is extended to the general case of co‐cross‐linking of primary chains with different functionalities. Examples are given for free radical and step growth polymerization. For polycondensates, assuming surplus of one functionality and complete conversion, a simple formula for the degree of polymerization DP z for functional groups is derived: ( 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 f has practically no influence on the weight averages DP w and M w if calculated as a function of the relative branching density ρ r = ρ/ρ c , where ρ 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 DP z ( f )/ DP z ( f = 3) is linear in ρ r and f .