Polymerization iGLE model

The iGLE also presents a novel approach for studying the reaction dynamics of polymers in which the chemistry is driven by a macroscopic force that is representative of the macroscopic polymerization process itself The model relies on a redefined potential of mean force depending on a coordinate R which corresponds locally to the reaction-path coordinate between an n-mer and an (n -t 1 )-mer for R = nl. The reaction is quenched not by a kinetic termination step, but through an (R(t))-dependent friction kernel which effects a turnover from energy-diffusion-limited to spatial-diffusion-Iimited dynamics. The iGLE model for polymerization has been shown to exhibit the anticipated qualitative dynamical behavior It is an activated process, it is autocatalytic, and it quenches... 

Thus far, we have described the time-dependent nature of polymerizing environments both through stochastic [49-51] and lattice [52,53] models capable of addressing this kind of dynamics in a complex environment. The current article focuses on the former approach, but now rephrases the earlier justification of the use of the irreversible Langevin equation, iGLE, to the polymerization problem in the context of kinetic models, and specifically the chemical stochastic equation. The nonstationarity in the solvent response due to the collective polymerization of the dense solvent now appears naturally. This leads to a clear recipe for the construction of the requisite terms in the iGLE. Namely the potential of mean force and the friction kernel as described in Section 3. With these tools in hand, the iGLE is used... 

In order to illustrate the use of the iGLE and WiGLE models for polymerization reactions, we have studied several phenomenological forms of the polymer PMF of Fig. 5. In the studies to date, the nonstationary frictions have always included the form of Eq. (28) and as such are apphcable only to dense polymerizations. This class would certainly include solid-state polymerization (SSP) as long as none of the other quenching mechanisms discussed above were also operative, and the assumptions of the separation of time scales in the environmental motion are satisfied. In SSP, the heterogeneity in the environment would further require the use of the WiGLE dynamics with the possible inclusion of a time dependence in the w parameter. 

---