The angular dependence of the intensity of neutron scattering by deuterated polymers dispersed in the protonated host in the semicrvstalline state has been computed over the scattering range 0~ <0.2 A,-~, where ,a =(4g/2)sin (0/2), for various morphologies that differ according to the mode of chain re-entry into the crystalline lamellae. Calculations have been carried out for melt-crystallized polyethylene and solution-grown polyethylene crystals of varying crystallite sizes and degrees of crystallinity. The scattering functions in the range 0"03 1 < 0"15 A-] are little affected by changes in crystallite sizes and crystallinities, but vary strongly with the tendency for adjacent re-entry and differ in magnitude and profile for the regularly folded morphology and the "switchboard' model. It was found that only the latter approximates the available experimental results. For melt-crystallized polyethylene optimum agreement with available experimental results is achieved by a statistical model in which the chain preferentially re-enters the crystalline layer at sites well removed from the site of emergence with a probability of about 0-7. For solution-grown polyethylene crystals, the model of nearby (but not regularly folded) re-entry gives good agreement with the results of Sadler & Keller [Macromolecules (1977), 10, 1128-1140.
IntroductionRecently Schelten, Ballard, Wignall, Longman & Schmatz (1976) conducted an experimental investigation of smallangle neutron scattering (SANS) by melt-crystallized polyethylene samples in which deuterated polyethylene chains (PED) were molecularly dispersed in the protonated host (PEH) matrix. Detailed analysis of the scattering functions by the present author in collaboration with Flory (Yoon & Flory, 1977) confirmed the conclusions reached by Schelten et al. (1976) that their results are incompatible with the regularly folded morphology that has gained widespread acceptance, according to which a chain molecule after traversing a crystalline iamella is assumed to re-enter the same lamella at the adjacent site and this process is repeated for the full length of the molecule. Rather, our analysis (Yoon & Flory, 1977) led to the conclusion that the predominant mode whereby a chain molecule successively traverses lamellae consists of re-entry of the same crystalline layer at a site well removed from its previous passage [-reminiscent of the 'switchboard' model (Fischer & Schmidt, 1962;Flory, 1962)] or penetration of the amorphous interlayer and entry of the neighboring iamella. Subsequent SANS investigation that followed (Schelten, Ballard & WignaII, 1978) showed that the major results of Schelten et ah (1976) are little changed when the lamellar repeat distance of thepolyethylene samples is decreased to ca 160 ,~ from ca 250 A. King et ah (1978) obtained similar scattering functions in the region #<0.04 A -1 for meltcrystallized polyethylene, where the lamellar repeat distance is ca 130 A. Sadler & Keller (1977) also obtained scattering functions which are in close agreem...