Giorgio J. Moro

Calculation of ESR spectra and related Fokker–Planck forms by the use of the Lanczos algorithm

The applicability of the Lanczos algorithm in the general ESR (and NMR) line shape problem is investigated in detail. This algorithm is generalized to permit tridiagonalization of complex symmetric matrices characteristic of this problem. It is found to yield very accurate numerical solutions with at least order of magnitude reductions in computation time compared to previous methods. It is shown that this great efficiency is a function of the sparsity of the matrix structure in these problems as well as the efficiency of selecting an approximation to the optimal basis set for representing the line shape problem as distinct from actually solving for the eigenvalues. Furthermore, it is found to aid in the analysis of truncation to minimize the basis set (MTS), which becomes nontrivial in complex problems, although the efficiency of the method is not very strongly dependent upon the MTS. It is also found that typical Fokker–Planck equations arising from stochastic modeling of molecular dynamics have the pro...

Electron‐spin relaxation and ordering in smectic and supercooled nematic liquid crystals

We report on careful line shape studies of slow motional and orientation dependent ESR spectra of a deuterated liquid‐crystal‐like spin probe dissolved in a benzilidene‐derivative (40,6) and in cyanobiphenyl derivative (S2 and 5CB) liquid crystals. The simulation of the ESR spectra is based on the Lanczos algorithm recently applied by Moro and Freed in a general and efficient formulation of slow motional and ordering effects on ESR line shapes. With 40,6 which exhibits monolayer smectic phases, we find that the main change in the spin relaxation upon passing from the nematic to the smectic A phase consists of changes occuring in ordering attributable to packing forces on functional groups. Such ordering effects appear to be further enhanced in the SB phase with consequent alterations in dynamics. With S2, which exhibits an interpenetrating bilayer smectic A phase, we find unusual ESR spectra in that phase which may be simulated on the basis of a model of cooperative distortions static on the ESR time scal...

A shape model for molecular ordering in nematics

An explicit form for the orientating potential acting in uniaxial liquid crystal phases is derived, by analogy with the surface anchoring potential which determines the orientation of macroscopic anisometric particles. The surface of a molecule is determined by describing the molecule as an assembly of van der Waals spheres. The model is successfully applied to predict the ordering tensors for a variety of systems, namely, solutions in nematic solvents of small and rigid probes, or relatively long n-alkanes with many degrees of internal freedom, and pure nematogens formed by aromatic cores attached to flexible chains.

SHAPE MODEL FOR ORDERING PROPERTIES OF MOLECULAR DOPANTS INDUCING CHIRAL MESOPHASES

An extension to chiral phases of a model derived previously to interpret orientational properties in liquid crystal solvents of molecules with arbitrary shape leads, quite naturally, to the definition of a traceless chirality tensor, useful for predicting the structures of twisted nematics induced by chiral solutes. The magnitude and handedness of the helical pitch in the induced chiral phase depend on the interplay of the chirality tensor components and the ordering of the different axes of the chiral probe in a given nematic solvent. The effect of changing the molecular structure of the solute and the temperature is discussed for a number of typical dopants, including biphenyl, binaphthyl and heptalene derivatives. Although the model has been derived in a form suitable for application to induced cholesteric structures, it contains the basic ingredients to account for the physical behaviour of chiral smectic-C* mesophases.

Diffusive and jump description of hindered motions

Site jump models are often used to interpret spectroscopic effects of molecular motions occurring in the presence of potential wells. Continuous diffusion equations, albeit complex to handle, are expected to give a more detailed picture of the dynamics and to provide molecular interpretation of the kinetic parameters. In the paper we show how the results of random walk models can be recovered from the correct solutions of the diffusion equations. To this purpose, two routes are followed. First, a procedure is developed for the exact calculation of the time integral of pertinent correlation functions, to be compared with the time constant for the kinetic process of interest. Secondly, the asymptotic solutions of the diffusion equations, valid in the limit of high potential gradients, are used to derive ‘localized functions’, which lead quite naturally to master equations for jumps among discrete sites. Rotational diffusion in uniaxial liquid crystals, translational motions across smectic layers, hindered i...

ESR studies of 0−2 adsorbed on Ti supported surfaces: Analysis of motional dynamics

Temperature‐dependent ESR spectra of O−2 adsorbed on Ti ions supported on porous Vycor glass were observed over the range 4.2 to 400 °K. These spectra were obtained under normal high vacuum conditions as well as under UHV conditions (P⩽10−9 Torr) and are very well resolved. It was observed that the line position of the g tensor component that is perpendicular to the internuclear axis of O−2 remained constant with temperature, whereas the other two components of the g tensor shift in position with temperature, and are accompanied by drastic line shape changes. This observation indicates that the molecular motion of O−2 on the surface is highly anisotropic, consisting essentially of planar rotation about the axis perpendicular to the internuclear axis of O−2 and parallel to the normal to the surface. Furthermore, the observation of nonequivalent 17O hfs of O−2 suggests that the internuclear axis of O−2 might be tilted slightly from the surface and/or one oxygen is closer to the Ti4+. The ESR line shapes w...

A theoretical model of phospholipid dynamics in membranes

Static and dynamic properties related to the internal configurational motions have been calculated for the alkyl chains of phospholipid molecules in a membrane environment in the liquid crystal phase. The calculations have been performed for the chain 1 of 1,2‐dipalmitoyl 3‐sn‐phosphatidylcholine (DPPC), a typical constituent of phospholipid membranes. Under the assumption of fixed bond lengths and bond angles, the internal dynamics of the chain is described in terms of 15 dihedral angles. The time evolution of the angular variables is assumed to be diffusional in character, and a master equation for transitions among the stable conformers is constructed from the energetics and hydrodynamics of the chain. This method is an extension to the time domain of the rotational isomeric state (RIS) approximation, which has been widely used to compute static properties of the chains. After calculation of the suitable correlation functions, effective rate constants relevant for spectroscopic and kinetic observables ...

A modified wigner function set for the smoluchowski operator representation in anisotropic liquids

Abstract The set of non-orthogonal functions D j pq (Ω) P 1/2 (Ω), in which the Wigner rotation functions are multiplied by the equilibrium orientational distribution, is shown to provide a convenient basis for the solution of the rotational diffusion problem in anisotropic liquids,in the entire range of orientational ordering.

A shape model for the twisting power of chiral solutes in nematics

Abstract The twisting power of chiral probes in nematics is interpreted in terms of a shape model, in which the surface elements of the solute molecules tend to align with the local director. The theoretical treatment is based on a previous approach, suitable for relating order parameters in nematics to molecular shape, and leads to the definition of a molecular pseudo-tensor whose orientational average determines the pitch and handedness of the helical macrostructures. Results of numerical calculations performed for distorted biphenyl and binaphthyl molecules are in agreement with the experimental results.

Coupling of the overall molecular motion with the conformational transitions. II. The full rotational problem

Abstract The method proposed in the companion paper for analysing the coupling between overall and internal dynamics is applied to the study of the full rotational motion of a molecule with one internal degree of freedom. For systems characterized by a finite set of stable conformers determined by the minima of the intramolecular potential, a simplified time evolution operator of mixed type is derived, with the continuous diffusion equation and the generalized random walk operator representing the overall rotation and the internal dynamics, respectively. The dependence on the conformational state of the rotational diffusion tensor is one source of coupling between these two types of motion. Another source is represented by the recoil rotations acting on each subunit during a conformational transition. Both conformational-dependent rotational diffusion tensors and recoil rotations can be calculated from a model for the friction exerted by the solvent. Some applications of the theory are presented in relation to the butane molecule and the molecules having the structure of biphenyl, with particular emphasis on the calculation of the experimental observables in NMR and dielectric relaxation measurements.