RESUMO
We investigate the role that local motions and slow cooperative fluctuations have on the relaxation of the intrapair dipolar order in the nematic 5CB. With this purpose we present a theoretical and experimental systematic study which allow us to quantify the contribution from each type of molecular fluctuation to the intrapair dipolar order relaxation time, T(1D). The experimental work includes measurements of Zeeman and intrapair dipolar order relaxation times (T(1Z) and T(1D)) as a function of temperature at conventional NMR frequencies, in three complementary samples: normal and chain deuterated 4-n-pentyl-4(')-cyanobiphenyl (5CB and 5CB(d11)) and a mixture of normal 5CB and fully deuterated 4-n-pentyl-4'-cyanobiphenyl (5CB(d19)), 50% in weight. Additionally we perform T(1Z) field-cycling Larmor frequency-dependent measurements to obtain the spectral density of the cooperative fluctuations. The obtained results are as follows. (a) The cooperative molecular fluctuations have a strong relative weight in the relaxation of the intrapair dipolar order state, even at Larmor frequencies in the range of conventional NMR. (b) Alkyl chain rotations are an important relaxation mechanism of the intrapair dipolar order at megahertz frequencies. (c) Intermolecular fluctuations mediated by translational self-diffusion of the molecules is not an efficient mechanism of relaxation of the intrapair dipolar order.
RESUMO
We analyze the experimental conditions needed for creating two kinds of dipolar order, namely, intrapair and interpair order in thermotropic liquid crystals. By adapting to the case of liquid crystals the model of weakly coupled spin pairs first developed for oriented hydrated salts, we obtain that the dipolar signal at every preparation time can be regarded as a weighted sum of the pure intra- and pure interpair signals; the weights being determined by the amount of each kind of order resulting from the preparation sequence. The dipolar signal predicted by the model is symmetric in the preparation and observation times and the intrapair component is, in a good approximation, proportional to the time derivative of the FID, regardless of the number of different dipolar couplings (inequivalent pairs) present in the molecule. From this model we obtain a prescription for preparing the different dipolar orders both when the pairs are strictly equivalent or when they are not. The applicability of the spin thermodynamics approach in liquid crystals is tested in two typical thermotropic nematic samples: PAA d(6) (methyl deuterated p -azoxyanisole) and 5CB ( 4(') -pentyl-4-biphenyl-carbonitrile).
RESUMO
By means of the Jeener-Broekaert nuclear magnetic resonance pulse sequence, the proton spin system of a liquid crystal can be prepared in quasiequilibrium states of high dipolar order, which relax to thermal equilibrium with the molecular environment with a characteristic time (T1D). Previous studies of the Larmor frequency and temperature dependence of T1D in thermotropic liquid crystals, that included field cycling and conventional high-field experiments, showed that the slow hydrodynamic modes dominate the behavior of T1D, even at high Larmor frequencies. This noticeable predominance of the cooperative fluctuations (known as order fluctuations of the director, OFD) could not be explained by standard models based on the spin-lattice relaxation theory in the limit of high temperature (weak order). This fact points out the necessity of investigating the role of the quantum terms neglected in the usual high temperature theory of dipolar order relaxation. In this work, we present a generalization of the proton dipolar order relaxation theory for highly correlated systems, which considers all the spins belonging to correlated domains as an open quantum system interacting with quantum bath. As starting point, we deduce a formulation of the Markovian master equation of relaxation for the statistical spin operator, valid for all temperatures, which is suitable for introducing a dipolar spin temperature in the quantum regime, without further assumptions about the form of the spin-lattice Hamiltonian. In order to reflect the slow dynamics occurring in correlated systems, we lift the usual short-correlation-time assumption by including the average over the motion of the dipolar Hamiltonian together with the Zeeman Hamiltonian into the time evolution operator. In this way, we calculate the time dependence of the spin operators in the interaction picture in a closed form, valid for high magnetic fields, bringing into play the spin-spin interactions within the microscopic time scale. Then, by adopting the spin-temperature density operator to represent the collective state of the spin system, and removing the traditional hypothesis of high temperature, we deduce an expression for the first order quantum contribution to T1D (-1), in terms of spectral densities, with coefficients in form of spin traces. The properties that distinguish our result from the high-temperature T1D (-1) are as follows. (a) It is exclusively associated to cooperative fluctuations. (b) Because of its quantum character, it relies on both considering the lattice degrees of freedom quantum mechanically and including the spin-spin interactions in the microscopic time scale. With regard to the average dipolar Hamiltonian, only the nonsecular part plays a relevant role. (c) Associated with the structure of the spin operator involved in the quantum contribution, a term arises which is proportional to the number of spins in the correlated molecular domains, showing that the quantum contribution may be of macroscopic size in highly correlated systems. When applied to nematic liquid crystals, the new term exhibits the typical nu(-1/2) Larmor frequency dependence through the spectral density of the OFD, in consistence with the experimental results.