Characterization of cross-linked rubber materials via proton rotating-frame relaxation measurements

Proton relaxation times in the rotating frame, as obtained from the decay of nuclear magnetization locked along a radio frequency field B-1, have been measured in a series of cross-linked natural rubber materials. These decays are monoexponential and the relevant time constants, T-1p, can be monitored as a function of the radio frequency field strength B-1. At any B-1 value, they appear to be correlated in a very sensitive way to the cross-link density. A novel interpretation of the T-1p dependence upon B-1 is presented. It is based on a theory describing the evolution of a two spin 1/2 system coupled by dipolar interaction in the presence of a spin-locking field. The measured rotating-frame relaxation rate is shown to be equal to the sum of the motionally related 1/T-1p and a term arising from the radio frequency field inhomogeneity. Both terms are proportional to the square of the dipolar interaction (the second moment in the present case where a distribution of dipolar interactions exists). Concerning changes of cross-link density, Tip measurements provide therefore a more direct information than transverse relaxation measurements (also performed in this study), the composite nature of the latter decay curves making their interpretation less straightforward. As a complement to the present relaxation study, we show the correlation of the self-diffusion coefficient of a solvent imbedded in the material with rubber T-1p values.