R. H. Acosta, R. C. Zamar, G. A. Monti
NMR proton spin dynamics in thermotropic liquid crystals subject to multipulse excitation.
Physical Review E.  68(4), 041705  (2003)
P-03-190

Previous experiments of NMR spin-lattice relaxation times as a function of the Larmor frequency, as measured with the field-cycling technique (FC), were shown to be very useful to disentangle the various molecular motions, both local and collective, that dominate the relaxation in different time scales in liquid crystals. However, there are many examples where the known theoretical models that represent the molecular relaxation mechanisms cannot be fitted to the experimental trend in the region of low fields, making it difficult to obtain reliable values for the spectral densities involved, especially for the cooperative motions which dominate at low frequencies. In some cases, these anomalies are loosely ascribed to "local-field" effects but, to our knowledge, there is not a detailed explanation about the origin of these problems nor the range of frequencies where they should be expected. With the aim of isolating the dipolar effects from the influence of molecular dynamics, and taking into account the previous results in solids, in this work we investigate the response of the proton spin system of thermotropic liquid crystals 4-pentyl-4(')-cyanobiphenyl (5CB) and 4-octyl-4(')-cyanobiphenyl (8CB) in nematic and smectic A phases, due to the NMR multipulse sequence 90_?°-(?-?_x-?)_N. The nuclear magnetization presents an early transient period characterized by strong oscillations, after which a quasistationary state is attained. Subsequently, this state relaxes towards internal equilibrium over a time much longer than the transverse relaxation time T₂. As occurs in solids, the decay time of the quasistationary state T_2e presents a minimum when the pulse width ?_x and the offset of the radiofrequency are set to satisfy resonance conditions (spin-lock). When measured as a function of the pulse spacing ? in "on-resonance" experiments, T_2e shows the behavior expected for cross relaxation between the effective Zeeman and dipolar reservoirs, in accordance with the thermodynamic theory previously developed for solids. Particularly, for values of ? comparable with T₂, the relaxation rate follows a power law T_2e ? ?^-2, in all the observed cases, for the resonance conditions ?_x=?/3 and equivalent frequency ?_e=?/3?. When ? is similar to or greater than typical dipolar periods, the relaxation rate becomes constant and for ? much shorter than T₂, the thermodynamic reservoirs get decoupled. These experiments confirm that the thermodynamic picture is valid also in liquid crystals and the cross relaxation between the reservoirs can be detected without interference with spin-lattice relaxation effects. Accordingly, this technique can be used to estimate the frequency range, where cross-relaxation effects can be expected when Zeeman and dipolar reservoirs are put in thermal contact with each other and with the lattice, as in FC experiments. In particular, the present results allow us to associate the anomalies observed in low-field spin-lattice relaxation with nonadiabatic energy exchange between the reservoirs.