Effect of dielectric properties of solvents on the quality factor for a beyond 900Â MHz cryogenic probe model

A previous report by Kelly et al. [J. Am. Chem. Soc. 124 (2002) 12013] indicated that the ionic conductivity of aqueous solution produces a significant contribution to the sensitivity loss in high-resolution NMR equipped with a cryogenically cooled probe. The loss in a sample solution contains two contributions: one from the ionic conductivity and the other from the dielectric loss; the latter is especially important at high frequencies such as above 900 MHz. Here, we investigated the effect of the dielectric conductivity on the quality factor of a 930 MHz cryogenic probe model; in particular, it deals with the ionic aqueous solutions and organic solvents commonly used for NMR in biological research and the chemistry of natural compounds. The sample quality factor, Qs, at first increases with the real part of the relative dielectric permittivity ε′ and then saturates. In the case of polar organic solvents, the transverse electric field on the sample decreases with ε′, resulting in an increase of Qs. In the case of non-polar organic solvents, the dielectric conductivity is so small that the gradient of the increase is steep, resulting in much larger Qs though the ε′ is small. The effect of the transverse electric field is negligible if the ε′ becomes large, thus the loss for ionic aqueous solution is mainly governed by a loop current induced in the sample solution. As the induced electromotive force is independent of the ε′, the Qs is saturated at high values of ε′. Based on the Qs obtained with the cryogenic probe model, the sensitivity for the cryogenic probe is expected to be as follows: the loss in sensitivity by loading water is more than 66%, i.e., the effect of the dielectric conductivity of water is remarkable at high frequencies; polar organic solvent suffers much larger losses, which is due to the enhancement of the effective sample resistance by the effect of ε′; a non-polar organic solvent is nearly free of the sensitivity loss as the dielectric conductivity is negligible; the reverse micelle behaves similarly.