A dual‐mode interpretation of nuclear spin relaxation for ¹³CO₂ sorbed in polystyrene

Abstract Recently we presented a dual‐mode interpretation of the nuclear spin relaxation for 13 CO 2 sorbed in polycarbonate [E. J. Cain, W.‐Y. Wen, A. A. Jones, P. T. Inglefield, B. J. Cauley, and J. T. Bendler, Journal of Polymer Science, Part B, Polymer Physics , Vol. 29, p. 1009 (1991)]. We have made similar investigation on spin relaxation for 13 CO 2 sorbed in polystyrene and are presenting the results in this report. 13 C spin‐lattice relaxation, spin‐spin relaxation, and nuclear Overhauser enhancements (NOE) are reported for 13 CO 2 sorbed in glassy polystyrene. These spin relaxation parameters were determined as a function of temperature and Larmor frequency. A quantitative interpretation is based on a two‐site, rapid exchange model, which is consistent with the NMR result. Gas molecules in the dissolved site have rotational, collisional, and translational dynamics typical of low molecular weight liquids. Sorbed molecules in the Langmuir site have much slower rotational and translational motions. The activation energy for motions in the dissolved site is about 7.5 KJ/mol, while that for the Langmuir site is about 15.5 KJ/mol. The translational diffusion constants derived from the NMR data range from 10 −7 to 10 −9 cm 2 /s and are consistent with the apparent diffusion constant from the permeability measurements of 4.9 × 10 −8 cm 2 /s at 35°C. A relation between the permeability value and the NMR values is available from a theoretical description of the dual‐mode model in terms of a random walk on a lattice containing two sites. As a modification of our previous lattice model (E. J. Cain et al., Journal of Polymer Science, Part B, Polymer Physics , Vol. 29, p. 1009 (1991)), the temperature dependence of the fraction of Langmuir sites in the lattice is taken into account. Parameter values characterizing the motion of CO 2 in polystyrene are found to be similar to the corresponding ones in polycarbonate. © 1993 John Wiley & Sons, Inc.