Correlation NMR and Inversion of the Laplace Transform

NMR spectroscopy can provide element specific information on ion motion in solid polymer electrolytes via relaxation rate studies. Local motions can be inferred from measurements of longitudinal, T₁, and spin-spin, T₂, relaxation mechanisms, however extraction of correlation times can be challenging due to the distributions of dynamics present in these systems. The inversion of the Laplace transform can extract relaxation rate distributions in a decay process. When used with T₁-T₂ correlation NMR experiments, the dynamic environments can be observed and aspects of the distributions dissected in terms of correlation time, electric field gradient, and dipolar coupling to hydrogen in the polymer. This approach has been applied to the study of a single-ion conductor made from blends of linear poly(ethyleneimine)-graft-poly(ethylene glycol) with linear poly(ethyleneimine) bearing lithium N-propylsulfonate groups. While conductivities of 10^-3 S/cm are observed, the amount of free lithium ion participating in conductivity is not obvious and data on lithium ion dissociation from the N-propylsulfonate group is needed. Using correlation spectroscopy, the varying lithium populations as a function of temperature and Li:O ratio will be presented and the utility of this method described.