Effect of polyfunctional chain transfer agents on molecular weight distribution in free‐radical polymerization, 1. The ideal case: C equals one

Abstract

The theoretical approach to free-radical polymerization in the presence of polyfunctional transfer agents can be derived in a simple way if the effects of primary chains and termination reactions are neglected. Under these conditions, and for values of the chain transfer constant C = 1, the analytical expressions for the number-and weight-average degree of polymerization, dispersion index and weight distribution function were derived through the elementary probability theory and generating functions. Numerical examples are reported on the relationship between distribution parameters, functionality and monomer conversion.

Size exclusion chromatography of branched polymers: Star and comb polymers

“…The DP distribution obtained from the random sampling technique, by generating 2610 4 polymer molecules, is shown by the circular symbols in Fig. 7, which agrees well with the theoretical distribution 12,17,18) . The weight-average DP of the theoretical distribution is P w;theory = 500, while the simulated absolute value was P abs w;sim = 501.1.…”

“…In practice, not all functional groups would react, and we assumed that the probability that a functional group is reacted is equal to p = 0.5. This type of star polymers could be synthesized by employing an ideal tetrafunctional chain transfer agent in free-radical polymerization 12,18) . In this case, linear polymer molecules (polymers with 1 and 2 arms) coexist with branched polymers (polymers with 3 and 4 arms).…”

Molecular Weight Development in Free-Radical Polymerization with Polyfunctional Chain-Transfer Agents, 2. Substitution Effects

“…The probability for this event to happen is p (3) s,i , given by Equation (23). A chain belonging to the jth fraction (i a j) can be connected to this P-CTA molecule when the P-CTA possesses 2 or 1 unreacted functional groups, namely, b ij (3,2) or P jÀ1 k¼iþ1 b ð3;2Þ ik b ð2;1Þ kj .…”

“…Yuan et al [2] reported that the equal reactivity model can be applied for the methyl methacrylate polymerization in the presence of the polyfunctional thiols, in which the number of functional groups, f was changed from 1 to 4. However, they neglected the effect of bimolecular terminations in analyzing the data, [3,4] and the average molecular weights were determined from the size-exclusion chromatography calibrated by linear polymers that would yield smaller molecular weights for branched polymers. On the other hand, Ullisch and Burchard [5] speculated the substitution effects, a theory that after some of the functional groups in a polyfunctional chain-transfer agent (P-CTA) have reacted, the reactivity of the rest of the functional groups changes due to both chemical and physical effects, based on their experimental results for the styrene polymerization using polyfunctional thiols.…”

Molecular Weight Development in Free-Radical Polymerization with Polyfunctional Chain-Transfer Agents, 1. Equal Reactivity Model

“…Strictly, their approach is valid only for an equilibrium system, i. e., they assume an imaginary polymer structure that would be formed when all links are cut at a given conversion level and then all molecules are rebuilt based on the average link probabilities. [4] Yuan et al [5,6] considered the limited cases in which star polymers are formed exclusively in the absence of combination termination. They obtained a full molecular Full Paper: The analytic expression for the weight-average molecular weight development in free-radical polymerization that involves a polyfunctional chain-transfer agent is proposed.…”