Atomistic and Flory-Stockmayer analyses of irradiated i-PP gel fractions and comparison with results from PE

Atomistic computation and Flory-Stockmayer (F-S) theory have been successfu lly applied to the analysis of gel fraction data from a microporous isotact ic poly(propylene) (i-PP), irradiated and annealed in the presence of acety lene. The presence of linearly propagating chain reactions is demonstrated by the computed maximum possible gel-radiation dose curves tin the absence of scissions and chain reactions), being initially much smaller than the ex perimental gel fraction curve. Both analyses are carried out in terms of th e number of "gel-effective" chain steps (N-CS,N-D) per initiating radical a t a given dose (D). The results are in keeping with two similar previous st udies by the authors, on data from two different linear low-density poly(et hylene)s (LLDPEs), one of which had been conducted both in vacuo and in ace tylene. With the exception of one LLDPE, the maximum N-CS,N-D values ((N-CS ,N-D)(max)). and nth order decreases of N-CS,N-D with respect to dose, deri ved by the two methods for both polyalkenes in all three studies, are in cl ose agreement. For reasons described, the nth order decrease rate constants from the two analyses differ by an order of magnitude, but follow the same trends. (N-CS,N-D)(max) decreases with increasing preirradiated molecular weight of the polyalkenes, under equivalent conditions, because a smaller N -CS,N-D is required to produce a given gel fraction. Both analyses demonstr ate that all the gel fraction vs number of "gel-effective" cross-links per preirradiated molecule ((N-Xeff,N-D/N-M)(gel)) curves conform to a universa l function, irrespective of the initial degree of polymerization, or the ir radiation and annealing conditions used to produce them. The universalities of the gel fraction vs (N-Xeff,N-D/N-M)(gel) curves, are demonstrated in t erms of the number- and weight-average preirradiated molecular weights in t he atomistic and F-S methods, respectively. This work paves the way to the simulation and characterization of gel fraction data to give the numbers of cross-links and scissions required to reproduce rheological data.