Zero-THz spectroscopy of rotator phases

The molecular dynamical evolution from hertzian frequencies to the far infrared (THz) is reported for various kinds of rotator phase environment. The zero to THz frequency spectral profiles are analysed in terms of itinerant libration and developments on this theme. The systems analysed are (i) the plastic rotator phase of t-butyl chloride and solid solutions of this solute in tetramethylsilane; (ii) these results are compared with those from a spectral study in the range up to THz frequencies of t-butyl chloride in vitreous decalin solvent; (iii) single crystalline pentachloronitrobenzene and a pressed disc thereof. This solid is representative of a class of rotator phases where orientational disorder is gradually frozen in at low temperatures, unlike the plastic rotators; (iv) solid solutions of dipolar solute molecules in non-dipolar rotator phase benzene and tetramethylsilane. This is an attempt at evaluating the electrodynamics of dipole-dipole interaction.

The data over the complete range of frequency is rationalized in terms of the itinerant libration mean square torque and theoretical evaluations of the observable sub-THz Debye relaxation times. This is the first attempt at modelling the molecular dynamics of the various kinds of rotator phases over the complete range of frequency at which the kinematics and electrodynamics of the constituent molecules are observable, either as the complex dielectric permittivity or the optical power absorption coefficient. This methodology is named zero-THz spectroscopy. Used properly, it is one of the most incisive methods available for studies of molecular dynamics.     

Nuclear magnetic spin-rotational relaxation times for symmetric molecules

It is shown that the problem of calculating times related to nuclear magnetic spin-rotational interactions may be solved for the symmetric rotator model of a molecule by employing the method already proposed in a general manner for asymmetric molecules that undergo rotational thermal motion. Expressions are derived for the spin-rotational correlation time and for the contributions arising from spin-rotational interactions to the longitudinal and transverse relaxation times.     

Mechanistic models of the ion-solvation shell system

The eigenfrequencies of solvation shell oscillations with respect to the ion are estimated in various approximations describing the ion–solvation shell system. The results of comparisonwith experiments suggest that the most appropriate is the model in which the solvated ion is considered to be a spherical rotator formed either by the entire solvation shell or by a layer of solvent molecules adjacent to the outer boundary of the solvation shell.     

Crystalline phases of alkyl-thiol monolayers on liquid mercury

The structure of octadecanethiol monolyers on liquid Hg surfaces, measured with subangstrom resolution, evolves with increasing coverage from a laterally disordered phase of surface-parallel molecules to ordered rotator phases of surface-normal molecules. For the latter, an abrupt transition is found at 19 A(2)/molecule from a rectangular packing of molecules tilted by 27 degrees in the nearest-neighbor direction to a hexagonal unit cell of untilted molecules. The unit cell of the tilted phase is centered for the chains and noncentered for the headgroups. The thiol headgroups associate in pairs with a single Hg atom, and the bonds form long-range orientational order. The different order of thiols on Au(111) and on Hg highlights the subphase's role in determining the overlayer's structure.     

Thermodynamics and X-ray studies of 2-alcohol monolayers: Two-dimensional phase diagrams

Monolayers of short chiral alcohols at the water surface provide a simple model for chiral interactions between molecules. This paper is focused on alcohols with two particular chain lengths, 2-tridecanol (2C13) and 2-tetradecanol (2C14). Thermodynamic and structural parameters were measured, varying the ratio of left and right enantiomers within monolayers. The evolution of melting temperatures and entropies is not consistent with the formation of a racemate. Grazing X-ray diffraction, revealing the molecular stacking, shows clearly that there is no chiral separation. In these two compounds molecules spontaneously self-assemble at the water surface as a solid solution. The chiral polar head-group is partially screened by the chain thermal disorder of the rotator phase. 2-tridecanol exhibits a hexagonal rotator phase stable in time and independent of temperature. Experiments performed close to the melting point show pre-transitional effects for mixtures different from 50/50. This broadening of the peak can be related to defects in 2D crystals, phenomena already observed for the melting of some 3D systems. Received 13 October 1999 and Received in final form 20 March 2000     

Sequential contact transformation formulation of asymmetric-rotator vibration-rotation Hamiltonian

The sequential contact transformation technique recently described in this journal by Niroomand-Rad and Parker is applied to the Amat-Nielsen expansion of the Darling-Dennison Hamiltonian of asymmetric rotator type molecules. The resulting formalism for the calculation of fourth-order Hamiltonian coefficients is significantly simpler than the conventional Amat-Nielsen contact transformation formalism. Therefore the eventual development of detailed expressions for fourth-order vibration-rotation interaction coefficients in terms of fundamental molecular constants now appears much more feasible.     

A Simple Derivation of the Luminescence Anisotropy Decay from Randomly Distributed Cylinders Rotating About a Single Axis

A simple derivation is given of the expression describing the anisotropy decay of luminescence for a solution of molecules that can only undergo rotational diffusion about a single cylindrical axis. The usual derivations of the anisotropy decay for this cylindrical model have simply taken limiting cases of the equations resulting from the general treatment of the anisotropy decay of a completely anisotropic rotator or the rotation of an ellipsoid. The arguments presented here can be understood without the mathematical sophistication required to follow the general derivations for the rotational diffusion of a completely anisotropic rotator or ellipsoids. The underlying physical mechanisms leading to a multiple exponential decay of the fluorescence anisotropy signal from a single axis rotating cylinder are clearly shown by following this derivation. The resulting expression for the anisotropy decay is not new. However, the derivation is easily understood, and this article is meant as an introduction to the more advanced treatments of anisotropy decay by rotational diffusion. After presenting the derivation of the rotating cylinder, the corresponding steps of these general treatments and this simple model are indicated. The model is of special interest for describing the anisotropy decay resulting from rotations of proteins within membranes.     

Molecular dynamics in solid n-nonadecane: Experiments and computer simulations

We have undertaken a collaborative study on the molecular dynamics and the phase transition mechanisms in low-dimensional molecular crystals by combining incoherent quasielastic neutron scattering, deuterium NMR and computer simulation techniques. In this paper, we summarize the method used for deriving a dynamical model for the reorientations of n-nonadecane molecules in the rotator phase R _I of the crystal. This model has been applied successfully to interpret experimental and computational data.     

快速象旋转器

在对象旋转器的象旋转特性进行了分析和论证的基础上,提出了快速象旋转器,并进行了数学上的论证,说明此种快速象旋转器在不提高现有象旋转器的转速的情况下,提高了旋转体与本文所提出的快速象旋转器的转速比。为观察到更高速旋转的物体,提供了一个新的途径。     

Thef-sum rule for “rotator strengths”

The concept of oscillator strengthsf for the emission and absorption of radiation by the electrons of an atomic system which has lead to the familiar Kuhn-Thomas-Reichef-sum rule has been extended to that of “rotator strengths” for a molecule approximated by a freely rotating rigid asymmetric rotator with a permanent body fixed dipole moment. As a consequence of the different type of physical system the resulting “f-sum rule for rotator strengths” holds only for what may be termed average rotator strengths (averaged over theM-degenerate sublevels).     

Coherent rotational states: Their formation and detection

In this paper, we describe molecules and nuclei, with energy spectrum close to that of an ideal rotator, and therefore capable of being pushed into a coherent rotational state. The formation of a coherent rotational state is obtained by means of a strong electromagnetic pulse. In the case of a molecule, resort is made to a laser pulse, while for a nucleus use is made of the Coulomb excitation in a heavy-ion collision. The latter is a thought experiment in that the “coherence” period obtained in the evolution of typical observables is out of reach of experimental detection. For the molecular case, the experiment is feasible and has been done.     

正氢和仲氢分子的核间距

采用ＦＴ－拉曼光谱技术，测定正氢和仲氢的转动拉曼光谱，计算出正氢和仲氢分子的核间距分别是７５．０３和７４．９８ｐｍ（１ｐｍ＝１０＾－１２ｍ）。     

Translational-rotational interaction in dynamics and thermodynamics of a two-dimensional atomic crystal with molecular impurities

The interaction between the rotational degrees of freedom of a diatomic impurity molecule and phonon excitations of a two-dimensional atomic matrix commensurate to the substrate is investigated theoretically. It is shown that the translational-rotational interaction leads to renormalization of the crystal field constants and a change in the form of the operator for the rotational kinetic energy as compared to the corresponding expression for a free rotator. The contribution from the rotational degrees of freedom of impurities to the low-temperature heat capacity of a diluted solution of diatomic molecules in the two-dimensional atomic matrix is calculated. The possibility of experimentally observing the predicted effects is discussed.     

MRI-negative rotator cuff tears

We report two cases of rotator cuff tear in which the T(2)-weighted MRI signal was negative at the first examination, but positive by the second examination without any changes in symptoms. Many authors have reported on correlations between the MRI and operative findings of rotator cuff tears. However, MRI findings, history of symptoms and operative findings in our patients suggest that there was a discrepancy between symptoms and MRI findings dependent on the period from the injury. Operative findings also indicate that intratendinous tears might have occurred first in these patients then progressed to partial or full thickness tears over time. We concluded that physicians should keep rotator cuff pathology in mind even in patients whose MRI findings are negative but symptoms of rotator cuff tear persist.     

Modelling of dynamical processes in a molecular crystal by NMR

In this contribution we report on the plastic crystal 1-chloroadamantane dynamics via conventional frequency dependent (¹H and ¹³C) and field cycling NMR measurements. A suitable microscopic dynamical model, worked out from from X-ray analysis is developed and the molecular motions are interpreted in terms of: self diffusion and dipolar molecular axis combined with uniaxial rotation. In the rotator phase the molecules execute a bimodal reorientation process whereas the uniaxial rotation solely persists in the low temperature phase. In both phases, the residence times exhibit an Arrhenius temperature dependence. The results confirm the existence of a dynamic crossover transition predicted by molecular dynamics simulation.     

Analysis of an anisotropic plate Faraday rotator coated with multilayer dielectric plates

The analysis of an anisotropic plate Faraday rotator coated with multilayer dielectric plates is presented by means of the matrix methods in conjunction with Fourier transformation technigues. It provides a closed-form representation of the electromagnetic field over the whole multilayer regions. The treatment does not limit the direction of the biased magnetic field and the numbers of the coated dielectric plates. Numerical results are presented and compared with that calculated with the method in ref.[1], and full-waveguide-band bandwidth for 47.5°±1.5° rotation angle is obtained for transmission type rotator in W band. Calculation for reflection type rotator is also presented and compared with the experiments.     

Quasiclassical calculation of the levels in a weakly asymmetric potential well corresponding to arbitrary quantum numbers m andl » n

The levels in a three-dimensional potential well are calculated in the case of asymmetric perturbations corresponding to arbitrary quantum numbers m andl » n; the results transform to zero oscillations whenl is small, and are also a generalization of the rotational levels of a rigid rotator in an external field. The results are used for Stark-effect calculation in diatomic molecules.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 11–15, December, 1978.It remains to thank G. V. Dubrovskii for wide-ranging discussion and comments on the work.     

Nuclear spin conversion of methane in pure and rare-gas mixed crystals

Spin species conversion has been observed by means of neutron scattering. Methane, matrixisolated in rare-gas crystals has been investigated by measuring the time dependence of the detailed balance factor of inelastic neutron spectra. The temperature dependence of conversion rates in the interval between 2 and 5 K turns out to be stronger than predicted by a single phonon process. In general, conversion times are of the order of hours in this temperature region. The influence of the matrix is well described by a coupled phonon density of states. Crystals of pure and krypton doped methane have been examined by measuring the time dependence of the total neutron scattering cross section. For pure methane, the temperature dependence of the conversion rates shows two regimes for both free rotator and ordered molecules. Below 5 K, the behavior is described by a single phonon process and above by an Arrhenius law. Rates are enhanced by krypton dotation, which is explained by changed level spacings due to orientational disorder.     

Rotation von zweiatomigen Dipolmolekülen in starken elektrischen Feldern

The motion of a rigid rotator in an electrical field is well known for small fieldstrengths where it is identical with the second-order perturbation of the Stark effect. At large fieldstrengths, the rotator becomes almost fixed about the field direction and its levels coincide with those of an harmonic oscillator. In this paper the energy levels are calculated by diagonalization for the intermediate region and its deviation from the two limiting cases is briefly discussed.     

On the uniqueness of the equilibrium state for plane rotators

We study the classical statistical mechanics of the plane rotator, and show that there is a unique translation invariant equilibrium state in zero external field, if there is no spontaneous magnetization. Moreover, this state is then extremal in the equilibrium states. In particular there is a unique phase for the two dimensional rotator, and a unique phase for the three dimensional rotator above the critical temperature. It is also shown that in a sufficiently large external field the Lee-Yang theorem implies uniqueness of the equilibrium state.