Numerical Simulations of the Polymerization Models

The simulations have been performed as follows. Each iGLE describes fhe evolution of one polymer, therefore, the number of equations modeling the whole system is the number of active monomers, A. In the case when an active monomer possesses two reaction sites, so that the chain grows in two directions, the number of iGLEs doubles. The initial length Ri for each polymer i is set to zero. The /th chain is considered to have n monomers if the coordinate Ri is located near nL, the potential minimum (n — 1)L - - Rm Rj nL + Rm- After crossing a barrier the number of free monomers, N, changes it becomes AI -I- 1 [AI — 1] if the barrier is 

FIGURE 10.1 The structures of the monomer and the corresponding polymer for Qf-methylstyrene (top) and 4-vinylbenzocyclobutene (bottom) are displayed. 

For simplicity, we invoke the assumption of self-similarity in the pgp to claim that when monomers add to the activated end of a chain during polymerization, the rates are independent of polymer length. If so, the pgp can be approximated as a series of self-similar harmonic barriers and well potentials matched to a specified barrier height and exothermicity at each step. Adjacent well frequencies, coq and coi, are chosen to be equal to each other and are defined through L, e and/b, Eq. (30). Their values are specified by the particular system, and are provided below in each case. 

When applying to polymerization processes, the length L and the timestep At were rescaled in the following way L = 5 A and At = 0.049 s for of-methylstyrene and L = 6.5 A and At = 0.064 s for 4-vinylbenzocyclobutene, so that every dimensionless time unit corresponds to 12.3 s in the fist case and 15.9 s in the second one. 

The polymerization of of-methylstyrene has been experimentally studied by Greer and coworkers [79]. Poly(of-methylstyrene) is a fully flexible linear polymer chain 

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