Evidence for several dipolar quasi-invariants in liquid crystals.

The quasi-equilibrium states of an observed quantum system involve as many constants of motion as the dimension of the operator basis which spans the blocks of all the degenerate eigenvalues of the Hamiltonian that drives the system dynamics, however, the possibility of observing such quasi-invariants in solid-like spin systems in Nuclear Magnetic Resonance (NMR) is not a strictly exact prediction. The aim of this work is to provide experimental evidence of several quasi-invariants, in the proton NMR of small spin clusters, like nematic liquid crystal molecules, in which the use of thermodynamic arguments is not justified. We explore the spin states prepared with the Jeener-Broekaert pulse sequence by analyzing the time-domain signals yielded by this sequence as a function of the preparation times, in a variety of dipolar networks, solids, and liquid crystals. We observe that the signals can be explained with two dipolar quasi-invariants only within a range of short preparation times, however at longer times liquid crystal signals show an echo-like behaviour whose description requires assuming more quasi-invariants. We study the multiple quantum coherence content of such signals on a basis orthogonal to the z-basis and see that such states involve a significant number of correlated spins. Therefore, we show that the NMR signals within the whole preparation time-scale can only be reconstructed by assuming the occurrence of multiple quasi-invariants which we experimentally isolate.

Quantum irreversible decoherence behaviour in open quantum systems with few degrees of freedom: application to 1H NMR reversion experiments in nematic liquid crystals.

An experimental study of NMR spin decoherence in nematic liquid crystals is presented. Decoherence dynamics can be put in evidence by means of refocusing experiments of the dipolar interactions. The experimental technique used in this work is based on the MREV8 pulse sequence. The aim of the work is to detect the main features of the irreversible quantum decoherence in liquid crystals, on the basis of the theory presented by the authors recently. The focus is laid on experimentally probing the eigen-selection process in the intermediate time scale, between quantum interference of a closed system and thermalization, as a signature of the quantum spin decoherence of the open quantum system, as well as on quantifying the effects of non-idealities as possible sources of signal decays which could mask the intrinsic decoherence. In order to contrast experiment and theory, the theory was adapted to obtain the decoherence function corresponding to the MREV8 reversion experiments. Non-idealities of the experimental setting, like external field inhomogeneity, pulse misadjustments, and the presence of non-reverted spin interaction terms are analysed in detail within this framework, and their effects on the observed signal decay are numerically estimated. It is found that though all these non-idealities could in principle affect the evolution of the spin dynamics, their influence can be mitigated and they do not present the characteristic behaviour of the irreversible spin decoherence. As unique characteristic of decoherence, the experimental results clearly show the occurrence of eigen-selectivity in the intermediate timescale, in complete agreement with the theoretical predictions. We conclude that the eigen-selection effect is the fingerprint of decoherence associated with a quantum open spin system in liquid crystals. Besides, these features of the results account for the quasi-equilibrium states of the spin system, which were observed previously in these mesophases, and lead to conclude that the quasi-equilibrium is a definite stage of the spin dynamics during its evolution towards equilibrium.

Decoherence of multiple quantum coherences generated from a dipolar ordered state.

Starting from the hypothesis that the decay of coherent signals observed in 1H NMR experiments is driven by quantum interference, irreversible decoherence, and nonidealities in the experiment, we design an experiment to isolate and identify the irreversible attenuation of multiple-quantum coherences toward quasiequilibrium states of dipolar order in nematic liquid crystals (LCs). The experiment combines the well-known "magic sandwich" pulse sequence with preparation of dipolar ordered states and encoding of multiple-quantum coherences. The spin system composed of the dipole-coupled protons of a LC molecule provides an example of a small cluster of strongly interacting spins. We study decoherence rates under a sequence that reverses time evolution with the secular dipolar Hamiltonian to compensate coherent evolution of a closed quantum system. In this way, the time scale is made evident where irreversible decoherence takes place, providing insight into the nature of the processes responsible for the attainment of quasiequilibrium. The behavior of single- and double-quantum-coherence amplitudes with reversal time is interpreted as evidence of the quantum character (as opposed to stochastic character) of the processes that drive irreversible decoherence. The experimental method proposed is useful for probing the action of the environment on materials with quantum information processing potential.

NMR dipolar constants of motion in liquid crystals: Jeener-Broekaert, double quantum coherence experiments and numerical calculation on a 10-spin cluster.

Two proton quasi-equilibrium states were previously observed in nematic liquid crystals, namely the S and W quasi-invariants. Even though the experimental evidence suggested that they originate in a partition of the spin dipolar energy into a strong and a weak part, respectively, from a theoretical viewpoint, the existence of an appropriate energy scale which allows such energy separation remains to be confirmed and a representation of the quasi-invariants is still to be given. We compare the dipolar NMR signals yielded both by the Jeener-Broekaert (JB) experiment as a function of the preparation time and the free evolution of the double quantum coherence (DQC) spectra excited from the S state, with numerical calculations carried out from first principles under different models for the dipolar quasi-invariants, in a 10-spin cluster which represents the 5CB (4(')-pentyl-4-biphenyl-carbonitrile) molecule. The calculated signals qualitatively agree with the experiments and the DQC spectra as a function of the single-quantum detection time are sensible enough to the different models to allow both to probe the physical nature of the initial dipolar-ordered state and to assign a subset of dipolar interactions to each constant of motion, which are compatible with the experiments. As a criterion for selecting a suitable quasi-equilibrium model of the 5CB molecule, we impose on the time evolution operator consistency with the occurrence of two dipolar quasi-invariants, that is, the calculated spectra must be unaffected by truncation of non-secular terms of the weaker dipolar energy. We find that defining the S quasi-invariant as the subset of the dipolar interactions of each proton with its two nearest neighbours yields a realistic characterization of the dipolar constants of motion in 5CB. We conclude that the proton-spin system of the 5CB molecule admits a partition of the dipolar energy into a bilinear strong and a multiple-spin weak contributions therefore providing two orthogonal constants of motion, which can be prepared and observed by means of the JB experiment. This feature, which implies the existence of two timescales of very different nature in the proton-spin dynamics, is ultimately dictated by the topology of the spin distribution in the dipole network and can be expected in other liquid crystals. Knowledge of the nature of the dipolar quasi-invariants will be useful in studies of dipolar-order relaxation, decoherence and multiple quantum NMR experiments where the initial state is a dipolar-ordered one.

Quasiequilibrium states in thermotropic liquid crystals studied by multiple-quantum NMR.

Previous work showed that by means of the Jeener-Broekaert (JB) experiment, two quasiequilibrium states can be selectively prepared in the proton spin system of thermotropic nematic liquid crystals (LCs) in a strong magnetic field. The similarity of the experimental results obtained in a variety of LC in a broad Larmor frequency range, with crystal hydrates, supports the assumption that also in LC the two spin reservoirs, into which the Zeeman order is transferred, originate in the dipolar energy and that they are associated with a separation in energy scales: A constant of motion related to the stronger dipolar interactions (S), and a second one (W) corresponding to the secular part of the weaker dipolar interactions with regard to the Zeeman and the strong dipolar part. We study the nature of these quasi-invariants in nematic 5CB (4(')-pentyl-4-biphenyl-carbonitrile) and measure their relaxation times by encoding the multiple-quantum coherences of the states following the JB pulse pair on two orthogonal bases, Z and X. The experiments were also performed in powder adamantane at 301 K which is used as a reference compound having only one dipolar quasi-invariant. We show that the evolution of the quantum states during the buildup of the quasiequilibrium state in 5CB prepared under the S condition is similar to the case of powder adamantane and that their quasiequilibrium density operators have the same tensor structure. In contrast, the second constant of motion, whose explicit operator form is not known, involves a richer composition of multiple-quantum coherences of even order on the X basis, in consistency with the truncation inherent in its definition. We exploited the exclusive presence of coherences of +/-4,+/-6,+/-8, besides 0 and +/-2 under the W condition to measure the spin-lattice relaxation time T(W) accurately, so avoiding experimental difficulties that usually impair dipolar order relaxation measurement such as Zeeman contamination at high fields and also superposition of the different quasi-invariants. This procedure opens the possibility of measuring the spin-lattice relaxation of a quasi-invariant independent of the Zeeman and S reservoirs, so incorporating a new relaxation parameter useful for studying the complex molecular dynamics in mesophases. In fact, we report the first measurement of T(W) in a LC at high magnetic fields. Comparison of the obtained value with the one corresponding to a lower field (16 MHz) points out that the relaxation of the W-order strongly depends on the intensity of the external magnetic field, similarly to the case of the S reservoir, indicating that the relaxation of the W-quasi-invariant is also governed by the cooperative molecular motions.

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.

NMR proton spin dynamics in thermotropic liquid crystals subject to multipulse excitation.

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( composite function )y-(tau-thetax-tau)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 T2e presents a minimum when the pulse width thetax and the offset of the radiofrequency are set to satisfy resonance conditions (spin-lock). When measured as a function of the pulse spacing tau in "on-resonance" experiments, T2e 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 tau comparable with T2, the relaxation rate follows a power law T2e proportional to tau(-2), in all the observed cases, for the resonance conditions thetax=pi/3 and equivalent frequency omegae=pi/3tau. When tau is similar to or greater than typical dipolar periods, the relaxation rate becomes constant and for tau 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.