Proton and carbon-13 relaxation and molecular motion in glassy bisphenol-A polycarbonate

Abstract

An interpretation of proton and carbon-13 spin–lattice relaxation in glassy polycarbonate is developed which is consistent with the geometry, time scale, and amplitude determined from chemical shift anisotropy line shape collapse. The line shape data indicate π flips and libration about the same axis as the predominant motions. A correlation function incorporating these motions is developed to quantitatively interpret the proton spin–lattice relaxation data and the line shape collapse. The π flip process is described as an inhomogeneous distribution of correlation times using the Williams–Watts fractional exponential. An apparent activation energy of 46 kJ/mol is determined with the fractional exponent remaining constant at 0.15. The librational motion is described by the Gronski formalism where the amplitude increases with the square root of temperature; and the rotational diffusion constant, linearly with temperature. Rotational diffusion constants fall in the range of 108 to 109 s−1 which is comparable to those observed in solution in sterically hindered polycarbonates. The librational motion only contributes to spin–lattice relaxation at the higher temperatures so that only an order of magnitude estimate of the restricted rotational diffusion constant results. This correlation function is then applied to carbon-13 T1 data taken at various positions across the chemical shift anisotropy line shape on an isotopically enriched system. Little change in spin–lattice relaxation with position is observed which is consistent with the broad distribution of π flip correlation times. The rate of carbon-13 spin–lattice relaxation is also fairly well predicted. Comparisons are made with magic angle sample spinning spin–lattice relaxation both in the laboratory and rotating frame. The former is fairly well approximated by the correlation function while the latter requires a significant spin–spin contribution to be reconciled with the rest of the interpretation.