Static and Dynamic Scaling Close to Gelation in Chain‐Polymerization: Effect of Reactor Type

Abstract

Because of the familiarity of gelation theories in polycondensation reaction of multifunctional groups, often the gel‐point is defined as the point of diverging weight averaged molar mass. The authors present an industrially relevant counter‐example to this common perception. Chain‐growth polymerization in realistic reactors introduces history dependent crosslinking probability. For copolymerization of a two functional monomer (ethylene) with a four functional comonomer (nonconjugated diene), the authors show from a Monte Carlo scheme that standard gelation scaling exponents remain valid for a semibatch reactor. However, for syntheses in a continuous stirred tank reactor (CSTR), all commonly measured molar mass moments (number, weight and “z”‐averaged moment) remain finite at the gel‐point; the first moment to diverge is the fourth moment. Hence, identification of the gel point from experimental observations is difficult, and cannot be achieved through monitoring of the weight averaged molar mass. The authors use a numerical scheme based on the tube model of polymer melts to predict the rheology of the generated molecules. Stress relaxation follows a power‐law decay, but due to dynamic dilution effects the CSTR resins exhibit much slower increase in the zero shear viscosity as the gel point is approached as compared to the semibatch reactor resins.

A comparative study of thermodynamic, conformational, and structural properties of bottlebrush with star and ring polymer melts

“…For example, common commodity polymers in the melt state, such as alkanes, often involve randomly branching of the molecules in their synthesis. [124][125][126][127] We also note that the supercoiled DNA in the chromosomes of bacteria and other organisms has been observed to have a randomly branched polymer structure [128][129][130] so that the emergence of chromosome territories separating DNA molecules under crowed conditions of the cell under interphase conditions (non-replicating genetic conditions) could be a natural consequence of the randomly branched polymer structure of these macromolecules. In summary, we may expect numerous practical consequences arising from the alteration of molecular packing from the presence of molecular branching in polymer materials.…”

Predicting Average Molecular Weights and Branching Level for Self‐Condensing Vinyl Copolymerization in a CSTR

“…CSTR models have been developed for many other types of highly branched polymers . For example, Smagala and McCoy used material balances and method of moments to simulate controlled radical polymerization with chain transfer to polymer .…”

“…However, hyperbranching (i.e., the behavior of branches on branches) is “distinctly different” in CSTR and batch. Formation of highly branched polymers via regular (uncontrolled) free radical polymerization in CSTRs have also been modeled . A major challenge in modeling these systems is the sudden increase in to infinity at the gelation point, which occurs in some free radical polymerizations (e.g., systems with chain transfer to polymer and termination by combination, leading to H‐shaped branches).…”

Controlled Synthesis, Characterization, and Flow Properties of Ethylene–Diene Copolymers

“…In contrast, molecules that exit the reactor immediately after being synthesized will have all the pendant dienes unreacted. This dependence of reaction probability on the residence time of a particular molecule leads to different molar mass distributions in continuous stirred tank reactors (CSTR) and in semibatch reactors . The gelation transition in semibatch reactor follows classical mean‐field behavior.…”

“…Many of the subsequent theoretical studies retained the closure approximation, while introducing more complexity in the description of the reaction steps. In a recent publication, we used Monte Carlo simulations to show that the exponential distribution of residence times of the molecules synthesized in a CSTR and the residence time dependence of the probability for branch formation at the pendant dienes lead to molar mass distributions with power‐law tails with the power‐law exponent demanding finite values of the first three moments of the molar mass at gelation. Since the commonly measured number, weight, and z ‐averaged molar masses are predicted to be finite at the gel point, a direct experimental determination of gelation is quite difficult, if not impossible.…”