Rotational diffusion of biaxial probes in biaxial liquid crystal phases

Modeling of motional EPR spectra using hindered Brownian rotational diffusion and the stochastic Liouville equation

Electron paramagnetic resonance (EPR) spectra of molecular spin centers undergoing reorientational motion are commonly simulated using the stochastic Liouville equation (SLE) with a rigid-body hindered Brownian diffusion model. Current SLE theory applies to specific spin systems such as nitroxides and to high-symmetry orientational potentials. In this work, we extend the SLE theory to arbitrary spin systems with any number of spins and any type of spin Hamiltonian interaction term, as well as to arbitrarily complex orientational potentials. We also examine the limited accuracy of the frequency-to-field conversion used to obtain field-swept EPR spectra and present a more accurate approach. The extensions allow for the simulation of EPR spectra of all types of spin labels (nitroxides, copper²⁺, and gadolinium³⁺) attached to proteins in low-symmetry environments.

Rotational diffusion of shape switching particles in nematic liquid crystals

The theory of rotational diffusion of particles of various symmetry embedded in a liquid crystal host, essential to interpret a variety of spectroscopic observables, has been available for some time, but only for the case of rigid molecules. Here we generalize the treatment and present a theory to describe the rotational diffusion of shape-changing particles dispersed in nematic liquid crystals. The interaction of the particles with the environment is modeled by an effective field potential, while the particles are allowed to assume an arbitrary discrete number of shapes. The transition between shapes is modeled by a Markovian process which is combined with rotational diffusion. Our model is applied to the simple case of a particle that can exchange between three shapes: a rod, a disk, and a sphere. We consider in detail the effect of shape transitions in some selected correlation functions which are relevant for experiments.

Shear-induced mesostructures in biaxial liquid crystals

We study nematodynamics of a mesoscopic system consisting of sheared biaxial liquid crystalline polymers using a hydrodynamical kinetic theory. We solve the governing Smoluchowski equation using the Galerkin method in selected regions of the material parameter space and a range of accessible shear rates to investigate stable mesoscopic states and robust structures. The imposed shear flow breaks the rotational symmetry in the quiescent state to induce truly biaxial flow-aligning steady states, logrolling states, out-of-plane steady states, exotic time-periodic motions, and chaotic motions in different regimes of material parameters and shear rates.

Computer simulations of biaxial nematics

Biaxial nematic (N(b)) liquid crystals are a fascinating condensed matter phase that has baffled, for more than thirty years, scientists engaged in the challenge of demonstrating its actual existence, and which has only recently been experimentally found. During this period computer simulations of model N(b) have played an important role, both in providing the basic physical properties to be expected from these systems, and in giving clues about the molecular features essential for the thermodynamic stability of N(b) phases. However, simulation studies are expected to be even more crucial in the future for unravelling the structural features of biaxial mesogens at the molecular level, and for helping in the design and optimization of devices towards the technological deployment of N(b) materials. This review article gives an overview of the simulation work performed so far, and relying on the recent experimental findings, focuses on the still unanswered questions which will determine the future challenges in the field.

Molecular Dynamics in the Smectic A and C* Phases in a Long-Chain Ferroelectric Liquid Crystal: 2H NMR, Dielectric Properties, and a Theoretical Treatment

In this work, the rotational-diffusion coefficients D(parallel) and D(perpendicular) for the ferroelectric smectogen (+)-(S)-4-[4'-(1-methylheptyloxy)] biphenyl 4-(10-undecenyloxy)benzoate have been studied by means of 2H NMR spectroscopy in the smectic C phase, using a new theoretical approach (Domenici,V.; Geppi, M.; Veracini, C. A. Chem. Phys. Lett. 2003, 382, 518). The analysis of spin-lattice relaxation times has been performed in terms of the diffusional constant and the activation energy of the internal and overall molecular-reorientational motions, and the results are compared to the smectic A (SmA) phase. Moreover, from the 2H NMR data in the SmA phase, the dielectric permittivity and the dielectric relaxation time functions are investigated using a theoretical approach. The longitudinal and transverse components of the real Rchigammaomega and imaginary chigammaomega (gamma = parallel, perpendicular) parts of the complex susceptibility tensor and the nematic-like rotational-viscosity coefficients, lambda2 and lambda5, are calculated.

Chain dynamics in a chiral C phase by deuteron spin relaxation study

Molecular reorientations and internal conformational transitions of an aligned chiral liquid crystal (LC) 10B1M7 are studied by means of deuterium spin-lattice relaxation in its smectic A (SmA) and smectic C* (SmC*) phase. The motional model which is applicable to uniaxial phases of many LCs is found to be adequate even when the phase is a tilted SmC* phase. The deuterium NMR spectrum in this phase cannot discern rotations of the molecular director about the pitch axis. The basic assumption is that the phase biaxiality is practically unobservable. However, the relaxation rates can be accounted for by the tilt angle between the molecular director and the layer normal in the SmC* phase. The tumbling motion appears to show a higher activation energy upon entering from the uniaxial SmA into the SmC* phase.

Deuteron NMR study of molecular dynamics in a compound exhibiting a reentrant nematic phase

A deuteron NMR study of molecular dynamics in the partial bilayer smectic A(d) and reentrant nematic phases of a pure chain-deuterated compound is presented. The deuteron spin-lattice relaxation times T(1Z) and T(1Q) were measured as a function of temperature for two different frequencies (15 and 46 MHz). The experimental results were interpreted in terms of the internal conformational motions of a chain decoupled from the molecular small-step rotational diffusion and the order director fluctuations. The latter motion was found to be essential to the fit of experimental results in the reentrant nematic phase. The fitting parameters obtained by using a global target fitting method are acceptable when compared with those obtained from other deuteron and proton NMR studies of the same mesophases.

Conformational dynamics of a metallomesogen studied by 2H-NMR spectroscopy

In this work we present a quantitative analysis of both quadrupolar splittings and deuterium Zeeman and quadrupolar spin-lattice relaxation times reported in the literature for two isotopomers of Azpac, an acetylacetonate derivative of the cyclopalladated 4, 4'-bis(hexyloxy) azoxybenzene. Azpac-d(4) is deuterated at the aromatic rings and Azpac-d(26) is deuterated on the alkoxy chains. The additive potential method is used to model the splittings, while the derived spectral densities are interpreted using the decoupled model in conjunction with the Nordio model. The two side chains are assumed to be noninteracting and identical in their conformations in order to limit the size of the transition rate matrix needed to describe correlated internal bond rotations in the chains. Rotational diffusion constants and internal jump rate constants are derived for this metallomesogen.

Deuteron NMR study of a long-chain smectic liquid crystal: molecular order and dynamics

Deuteron Zeeman (T(1Z)) and quadrupolar (T(1Q)) spin-lattice relaxation times and quadrupolar splittings were measured in the nematic and smectic A phases of a chain-deuterated 4-n-octyloxy-4'-cyanobiphenyl (8OCB-d17) at 15.1 and 46 MHz. To model the NMR observables, the so-called pentane effect is used to limit the number of possible conformations in the chain, and is found to be a good approximation. The additive potential method is employed to construct the potential of mean torque using the quadrupolar splittings. A decoupled model is used to describe correlated internal motions in the chain, which are independent of the molecular reorientation. The latter motion is treated using the small-step rotational diffusion model of Nordio (Tarroni and Zannoni), while the former motion is described using a master rate equation. In the nematic phase, order director fluctuations are found to be necessary. The relaxation data in both mesophases were treated using a global target method, and the derived motional parameters are acceptable in comparison with those found for 6OCB.

Dynamics and ordering in mixed model membranes of dimyristoylphosphatidylcholine and dimyristoylphosphatidylserine: a 250-GHz electron spin resonance study using cholestane

We report here on a 250-GHz electron spin resonance (ESR) study of macroscopically aligned model membranes composed of mixtures of dimyristoylphosphatidylcholine (DMPC) and dimyristoylphosphatidylserine (DMPS), utilizing the nixtroxide-labeled cholesterol analog cholestane (CSL). Two clearly resolved spectral components, distinct in both their ordering and dynamics, are resolved. The major component in membranes composed mostly of DMPC shows typical characteristics, with the long axis of CSL parallel to the bilayer normal with slow (10(6) </= R </= 10(7) s-1) rotational diffusion rates, as expected for cholesterol. The second component grows in as the mole fraction of DMPS increases. A detailed analysis shows that CSL senses a local, strongly biaxial environment. Our results imply that the inefficient packing between cholesterol and DMPS occurs probably because of the strong interactions between the PS headgroups, which provide the local biaxiality. Such a packing of the headgroups has been predicted by molecular dynamics simulations but had not been observed experimentally. The analysis of these spectral components was greatly aided by the excellent orientational resolution provided by the 250-GHz spectra. This enabled the key qualitative features of this interpretation to be "read" off the spectra before the detailed analysis.