1H nuclear magnetic resonance and spin–lattice relaxation in solid, high-density polyethylene

Abstract

¹ H spin–lattice relaxation, in both laboratory and on-resonance rotating frames, are reported for five samples of a high-density, linear polyethylene prepared so as to produce a range of lamellar crystalline widths. The samples are also characterised by measurements of density, Raman longitudinal acoustic modes (LAM) crystallinity (DSC) and small-angle X-ray scattering (SAXS). The laboratory-frame spin–lattice relaxation (LFSLR) is well represented by a single process, and the relaxation rates are linearly related to the crystalline fraction (DSC), which is consistent with the prediction of the fast-diffusion limit of the two-region, spin-diffusion-coupled model of relaxation in these systems. The rotating-frame relaxation (RFSLR) is, as found in previous studies, a multi-exponential process. It is shown that a fit to four components is optimum in terms of quality of fit and signal-to-noise ratio and that this leads to accurate values for the amplitude and time constant of the dominant, longest relaxation-time component. It is also shown that the use of a solid-echo refocussing pulse, following the spin-locking substantially increases the total signal observed but has a much smaller effect on the amplitudes and time constants. The values of the relaxation times and amplitudes for the two longest relaxation time components for each sample are compared with the predictions of the slow-diffusion limit of the spin-diffusion model. The longest relaxation-time component is found to be proportional to the square of the lamellar thickness determined from Raman LAM, and this is used to deduce a value for the spin-diffusion coefficient in the crystalline region, D₂≈ 2 × 10¹⁶ m² s^–1. Assuming the slow-diffusion limit, the amplitudes of the long-time components in the RFSLR are used to derive values for the size of the disordered region, l₁, using both the Raman and NMR derived values of l₂, the size of the crystalline region. The l₁ and l₂ values obtained from the RFSLR are used to derive densities for regions 1 and 2 from the measured sample densities. The values of (l₁+l₂) from NMR are compared with those obtained from SAXS, and good agreement is found. The validity of the spin-diffusion model is further supported by the data reported here. The relaxation processes (both LF and RF) seem to imply a higher degree of ‘crystallinity’ than revealed by DSC or X-ray diffraction. The LFSLR and RFSLR are internally self-consistent, and this suggests that for SLR the crystalline component includes a fraction of the material characterised as non-crystalline by other methods (XRD, DSC).