Intramolecular character of the intrapair dipolar order relaxation in the methyl deuterated nematic para -azoxyanisole

MRI assessment of multiple dipolar relaxation time (T1D) components in biological tissues interpreted with a generalized inhomogeneous magnetization transfer (ihMT) model

T_1D, the relaxation time of dipolar order, is sensitive to slow motional processes. Thus T_1D is a probe for membrane dynamics and organization that could be used to characterize myelin, the lipid-rich membrane of axonal fibers. A mono-component T_1D model associated with a modified ihMT sequence was previously proposed for in vivo evaluation of T_1D with MRI. However, experiments have suggested that myelinated tissues exhibit multiple T_1D components probably due to a heterogeneous molecular mobility. A bi-component T_1D model is proposed and implemented. ihMT images of ex-vivo, fixed rat spinal cord were acquired with multiple frequency alternation rate. Fits to data yielded two T_1Ds of about 500 μs and 10 ms. The proposed model seems to further explore the complexity of myelin organization compared to the previously reported mono-component T_1D model.

Proton NMR relaxation of the dipolar quasi-invariants of nematic methyl deuterated para-azoxyanisole within the high-temperature Redfield relaxation theory

The high-temperature Redfield spin-lattice relaxation theory is used for calculating the relaxation times of the different dipolar quasi-invariants in an eight-spin system which represents methyl deuterated para-azoxyanisole (PAAd6) in the nematic phase. According to previous experiments, this system can be considered as composed of weakly coupled pairs of strongly interacting spins, the ortho protons of the aromatic rings, thus, it possesses four quasi-invariants of the motion: Zeeman, dipolar intrapair and interpair, and singlet orders. We write the set of coupled differential equations which describe the relaxation of the generalized inverse spin temperatures of the four quasi-invariants. The relaxation constants are then calculated in terms of experimental two-spin spectral densities of the lattice motions. The relation between the multispin and the two-spin spectral densities is also deduced. Calculation shows that the Zeeman and singlet quasi-invariants are uncoupled from the dipolar ones, and that the relaxation time of the singlet order is much longer than those of the Zeeman and dipolar orders. The calculated cross relaxation rate between the dipolar orders through the lattice is small enough to be observable in the experiment. We also show that the nonsecular term associated with the collective motions dominates relaxation of the intrapair and interpair energies in PAAd6, while the local motions do not play a significant role, in qualitative agreement with the reported experimental behavior. The dipolar relaxation times predicted by the theory are significantly larger than the experimental ones, the difference being even more pronounced for the interpair quasi-invariant. We show that the discrepancy cannot be overcome neither by resorting to a realistic model for the spin system nor considering the various possible cross-relaxation pathways among the quasi-invariants. This feature points out the high- temperature approximation as a source of the discrepancy. We discuss the effect that slow and ultraslow molecular modes could have on the relaxation of the dipolar order.

On the role of collective and local molecular fluctuations in the relaxation of proton intrapair dipolar order in nematic 5CB

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.

Dipolar quasi-invariants in 1H NMR of nematic thermotropic liquid crystals

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).

Nuclear magnetic resonance proton dipolar order relaxation in thermotropic liquid crystals: A quantum theoretical approach

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.