A simple method analyzing 2H nuclear magnetic resonance line shapes to determine the activation energy distribution of mobile guest molecules in disordered systems

Abstract

We investigated the 2H nuclear magnetic resonance (NMR) line shape of deuterated benzene and hexamethylbenzene as guest molecules in organic glasses in the temperature range of 10–150 K. A broad distribution G(ln τ) of correlation times determines the slowing down of the molecular reorientation around the sixfold symmetry axis of the guests. The line shape is described by a superposition of temperature-dependent fractions F(T) of only two subspectra corresponding to fast and slowly rotating molecules; no spectra characteristic for intermediate mobility as found in crystal matrices are observed. Assuming a thermally activated motional process, the temperature dependence of G(ln τ) comes from a temperature-independent distribution of activation energies g(E). In this case, the derivative of the fraction dF(T)/dT yields directly the distribution g(E). Using this method an asymmetric distribution g(E) with its maximum at the low energy side is found for the glasses. While the general shape of g(E) is similar for different matrices, the mean activation energy differs significantly. We used the same approach to discuss similar ‘‘two-phase’’ spectra for the isotropic reorientation of toluene in polystyrene below the glass transition of the mixed system. Here, an alternative explanation is offered considering a distribution of glass transition points Tg for the dynamics of toluene in the mixed system.