Calculation of SANS intensity for polyethylene: effect of varying fold planes and fold plane roughening

Abstract

The intensity of the small angle neutron scattering (SANS) for polyethylene crystallized in the lamellar habit from the melt at large supercoolings is calculated for μ = 0.01 to μ = 0.14 [ μ = ( 4π λ ) sin ( θ 2 ) ]. Computations are made on models which allow various amounts and types of chain folding and varying degrees of ‘tight’ or ‘regular’ folds. The models that fit the SANS data best have folding along lattice planes in which the stem separation is larger than 0.5 nm (5 Å) or which allow for fold plane roughening on a variety of fold planes. the ‘leapfrog’ type folds mentioned by Sadler were also considered, and a possible cause for their existence suggested. As an example, the variable cluster model gives a good account of the SANS data with the surface roughening suggested by nucleation theory with fold planes [110], [200], and [310], or a mixture. Even though the conditions of crystallization used in preparing the SANS specimens (large supercoolings) were conducive to the maximum surface disorder, the probability of ‘tight’ or ‘regular’ folding, p tf , was found to be ∼0.7 for the best models. This corresponds closely to the theoretical lower bound p tf = 2 3 which is rigorous for the case of non-tiled stems. The probability of strictly adjacent re-entry in a single specified fold plane, p ar , was ∼0.4 to ∼0.7 depending on the particular model chosen. The best models fit not only the SANS data, but also the liquid and crystal density, degree of crystallinity, and characteristic ratio (or radius of gyration). None of the models show the density anomaly inherent in the switchboard or random re-entry models of Yoon and Flory.