Mean‐Field Calculation ofM_Zfor Randomly Branched Condensation Polymers

Abstract

The mean‐field theory of Flory–Stockmayer for randomly branched polymers in the regime of strong chain overlap is extended to a calculation of MZ via the recursive method of Miller and Macosko. The formalism includes condensation polymers, copolymers, chain stoppers, bifunctional diluents to control the chain length between branch points, multiple branching agents, and arbitrary stoichiometries. MZ closely approximates the largest branched polymer in the system and is therefore a key parameter describing static scaling behavior near the gel point. Nonuniversal static scaling of MZ is illustrated with examples from the literature. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019, 57, 1415–1422

The z‐Average of Cross‐Linked Polymers

“…It is based on probability theory and does not require the molecular weight distribution and avoids the use of generating functions. The details of the theory are not repeated here and the reader is referred to the original publication [6] and for the extensions to Odle et al [22] The main extension is that we deal here with chains instead of monomers and the equations have to be modified accordingly.…”

“…[14][15][16] The MWD and M w for the general case A f and B g are known. [17][18][19][20][21] Odle et al [22] set up the general equations for the z-average and solved them for three examples:…”

“…[ 17–21 ] Odle et al. [ 22 ] set up the general equations for the z ‐average and solved them for three examples: A 2 + B 2 , A f , and A 2 + A 3 + B 2 .…”