Atomistic and Flory−Stockmayer Analyses of Irradiated i-PP Gel Fractions and Comparison with Results from PE

Abstract

Atomistic computation and Flory−Stockmayer (F−S) theory have been successfully applied to the analysis of gel fraction data from a microporous isotactic poly(propylene) (i-PP), irradiated and annealed in the presence of acetylene. The presence of linearly propagating chain reactions is demonstrated by the computed maximum possible gel−radiation dose curves (in the absence of scissions and chain reactions), being initially much smaller than the experimental gel fraction curve. Both analyses are carried out in terms of the number of “gel-effective” chain steps (NCS,D) per initiating radical at a given dose (D). The results are in keeping with two similar previous studies by the authors, on data from two different linear low-density poly(ethylene)s (LLDPEs), one of which had been conducted both in vacuo and in acetylene. With the exception of one LLDPE, the maximum NCS,D values ((NCS,D)max), and nth order decreases of NCS,D with respect to dose, derived by the two methods for both polyalkenes in all three studies, are in close 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. (NCS,D)max decreases with increasing preirradiated molecular weight of the polyalkenes, under equivalent conditions, because a smaller NCS,D is required to produce a given gel fraction. Both analyses demonstrate that all the gel fraction vs number of “gel-effective” cross-links per preirradiated molecule ((NXeff,D/NM)gel) curves conform to a universal function, irrespective of the initial degree of polymerization, or the irradiation and annealing conditions used to produce them. The universalities of the gel fraction vs (NXeff,D/NM)gel curves, are demonstrated in terms of the number- and weight-average preirradiated molecular weights in the 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.