Translation-rotation Coupling Research Articles

Statics and dynamics at the incommensurate transition in NaNO2

Abstract A microscopic model based on translation-rotation coupling leads to an incommensurate phase transition. Precursor effects are studied in the paraelectric phase. The coupled dynamics of translations and rotations is discussed.

Orientational pair correlations in dilute solutions of rodlike molecules

The orientational correlation times for the first and second rank spherical harmonics of single particle and collective orientational variables are calculated assuming that the rotorlike molecules undergo correlated rotational and translational motion. Rotation–translation coupling arises through the Oseen tensor operating between the rotors and introduces a concentration dependence in the single particle and collective times. A linear concentration dependence stems from the averaged Liouville operator, as found previously, and through the memory function, whose direct calculation has been hitherto ignored. Even in the presence of the memory function, the Keyes–Kivelson ratio of the collective and single particle correlation times is unaffected to linear order in the concentration of the tagged molecules. However, the memory function and the associated torque correlation function incorporate a linearly increasing concentration dependence in the single particle times.

The translational motion of molecules at short times: a study using molecular dynamic simulations and the model of itinerant oscillation

Abstract A newly developed version of the itinerant oscillator model for molecular translation in fluids is evaluated by means of data obtained from a molecular dynamics simulation of the fluid using an atom-atom potential. The data consists of: 1. Velocity ( v ) and force ( F ) autocorrelation functions. 2. Mean square displacements of molecular centres of mass and even moments thereof. 3. Autocorrelation of v2n and F2n (as a means of investigating the deviation of v and F from Gaussian behaviour). 4. The van Hove function Gs(R,t). The latter is matched against incoherent neutron scattering data observed by Dasannacharya and Rao [13] for liquid argon. The theoretical picture is realistic except that the neglect of cross-correlations and rotation-translation coupling is clearly affecting the agreement between the simulated and calculated mean square displacements. The self van Hove function Gs( R ,t) exhibits complicated non-Gaussian behaviour which will be difficult to follow using the theory of Brownian motion.

Transport properties of compressed atomic and molecular liquids, and solids and the molar volume

A comprehensive study is made of the volume dependence of the shear viscosity, the self-diffusion coefficient and the thermal conductivity reported of compressed atomic and molecular liquids which are composed of linear, quasi-spherical and dipolar molecules, and some hydrocarbons. The fluidity, φ, and the thermal resistivity, 1/λ, of atomic and non- associated molecular liquids along isotherms increase linearly with the molar volume over a substantial fraction of the liquid range, and the slopes of the φ and 1/λ vs. V plots, respectively, have a constant value characteristic for each liquid that satisfies a square-root-mass relationship. The latter can be used to predict transport coefficients of liquids which have not yet been measured, e.g. η and λ of liquid radon at saturation have been estimated. In addition, η of compressed liquid N 2O and C 2H 4, and of saturated liquid CF 4, and λ of compressed liquid neon and C 2H 4, and of both saturated and compressed liquid neopentane have been predicted. Using the Stokes-Einstein relation, D values of compressed xenon gas and of liquid NH 3 and C 6H 5F under compression have been found. Besides, the diffusion parameter, representing the slope of the linear D vs. V plot along an isotherm, increases with temperature, and its value for various molecular liquids and dense gases at room temperature closely satisfies a M −1 2 dependence. On the base of the latter revised values of the self-diffusion coefficient of compressed CS 2 are proposed. In general the predicted transport coefficients are believed to be reliable to within 10%. It is also shown that the viscous behaviour of a compressed liquid methane-propane mixture in the entire composition range can be represented by a single diagram. The transport properties of compressed water at elevated temperature, ammonia and methanol strongly depart from the square-root-mass relationships observed, which has been attributed to association effects in these molecular liquids. Experimental viscosities and self-diffusion coefficients of atomic and molecular liquids at low temperature and high density provide evidence that a description of the transport behaviour by hard spheres should not be correct. From a comparison between the thermal transport behaviour of atomic and non- associated molecular liquids evidence for rotation-translation coupling can be obtained. The jump in thermal resistivity at the liquid-plastic phase transition can be accounted for by the change in volume. An estimate is made of the thermal conductivity of SF 6 in the orientationally disordered phase at the melting point.

Diffusion coefficients for rigid macromolecules with irregular shapes that allow rotational-translational coupling.

We consider six-dimensional diffusion and frictional tensors for a rigid macromolecule immersed in a viscous fluid at low Reynolds number. Our treatment allows for screwlike properties which couple rotational and translational movements. We show that the center of diffusion of a screwlike body can be distinct from its hydrodynamic center of reaction. Symmetry conditions which ensure coincidence are examined. The center of diffusion is found to be the point of a body with the slowest diffusive movements, while rotations about the center of reaction encounter the least average resistance. The macroscopic translational diffusion coefficient is evaluated from a perturbation analysis of the six-dimensional diffusion equation. We show that methodologies which ignore translational-rotational coupling will necessarily underestimate the diffusion rate of screwlike particles. A procedural framework is presented to calculate diffusion coefficients of complicated bodies. As an example we treat a long bent rod.

Phonon spectra of methane physisorbed on graphite

We have investigated certain aspects of the dynamics of methane monolayers physisorbed on graphite. In particular, phonon frequencies have been calculated by applying the self-consistent harmonic approximation to a two-dimensional array of methane molecules arranged as stable tripods on a triangular lattice. The methane–graphite interaction was not considered explicitly, and only three degrees of freedom per molecule were taken into account: two translations parallel to the surface and rotation about the axis normal to the surface. A new intermolecular potential proposed by Righini and present authors was employed. It was found that the translation–rotation coupling plays an important role in determining the anharmonic frequency shift. The results are in good agreement with a recent neutron incoherent inelastic scattering experiment in which the momentum transfer is parallel to the graphite surface. The two main peaks observed around 9 and 5 meV are assigned to librational and translational modes, respectively.

ChemInform Abstract: ON THE PHASE TRANSITION IN SYM‐TRIAZINE‐MEAN FIELD THEORY

A Landau mean field description of the nearly second order phase transition in sym‐triazine crystals at ∼200 K is presented. A model Hamiltonian is generated which consists of the appropriate symmetry elastic constant terms, molecular rotational energy, and rotation–translation coupling terms (to second order in both strains and rotations). Due to the symmetry of the crystal in the high (R3c) and low (C2/c) temperature phases, third order terms in the rotational order parameter are nonvanishing; the transition is thereby a first order one (although only weakly so). This Hamiltonian is then converted to a free energy by addition of an entropy term calculated for an orientation distribution (about the z axis) based on pocket state functions. The Landau mean field model is developed by choosing a set of order parameters Ry (molecular rotation about the y axis) and strains e5 and (e1‐e2). The free energy expression is used to calculate relations between order parameters by setting ∂F/∂Ry=∂F/e5=∂F/∂e7=0. Coup...

On the phase transition in s y m-triazine-mean field theory

A Landau mean field description of the nearly second order phase transition in sym-triazine crystals at ∼200 K is presented. A model Hamiltonian is generated which consists of the appropriate symmetry elastic constant terms, molecular rotational energy, and rotation–translation coupling terms (to second order in both strains and rotations). Due to the symmetry of the crystal in the high (R3̄c) and low (C2/c) temperature phases, third order terms in the rotational order parameter are nonvanishing; the transition is thereby a first order one (although only weakly so). This Hamiltonian is then converted to a free energy by addition of an entropy term calculated for an orientation distribution (about the z axis) based on pocket state functions. The Landau mean field model is developed by choosing a set of order parameters Ry (molecular rotation about the y axis) and strains e5 and (e1-e2). The free energy expression is used to calculate relations between order parameters by setting ∂F/∂Ry=∂F/e5=∂F/∂e7=0. Coupling terms including bilinear products of eρ’s and Ry are employed in this development. Renormalized temperature dependent elastic constants are derived. e5(T) is solved for and found to be in good agreement with observed temperature dependences. Librational frequencies are determined from (∂2H/∂RiRj)ep=Iω2iδij. It is found that in the low temperature phase Δω=‖ωy−ωx∝α e5 in lowest order. Observed power laws for frequencies, splittings and strains with respect to ε≡(T−Tc/T) are discussed in light of these new results. The role of third order terms in (Rx, Ry) is considered and found to be an important factor in apparent deviation from mean field exponents.

Rotational dynamics of rigid, symmetric top macromolecules. Application to circular cylinders

The formalism for the calculation of translational friction coefficients of symmetric top macromolecules presented in a previous paper [M. M. Tirado and J. García de la Torre, J. Chem. Phys. 71, 2585 (1979)] is here extended to the evaluation of rotational friction and diffusion coefficients. We show how the introduction of symmetry considerations leads to a great reduction of the computational requirements needed to solve the hydrodynamic interaction equations. We also obtain the translation–rotation coupling tensor from which the center of hydrodynamic stress can be obtained. For a rigid ring we have derived analytical solutions that reduce to those obtained by other authors when the unmodified interaction tensor is used. The general formalism is finally applied to the calculation of the rotational diffusion coefficients of circular cylinders modeled as stacks of rings and extrapolated to zero bead size. The resulting values are critically compared with those from earlier studies.

Experimental studies of acoustically induced birefringence

The theory of acoustically induced birefringence in liquids indicates that the birefringence should be proportional to the shear viscosity (η), the acoustic frequency (Ω/2π), and the square root of the acoustic intensity. Furthermore, the birefringence should be proportional to the square root of a dimensionless rotational translational coupling parameter (R0), a coupling parameter which also enters the theories of flow birefringence and of VH and HH depolarized light scattering. We have studied the acoustically induced birefringence of triphenylphosphite and have found the predicted dependence upon Ω,ℐ1/2 and η; in addition we find that R0 is independent of η and T, and that R0 has a value close to that obtained from flow birefringence and depolarized light scattering experiments. We have also studied the acoustically induced birefringence of solutions of large colloidal particles (gold sol); the existing theories predict that the birefringence should be linear in ℐ, and independent of Ω and η. Both previous work and ours indicate a strong Ω dependence; where previous work indicated linearly in ℐ, we find a dominant ℐ1/2 dependence together with a small term linear in ℐ; the dependence on η is still rather unclear. Our results on the gold sols are somewhat qualitative, in part because of insufficient characterization of the sols.

Lattice dynamics in RbCN

The dispersion of acoustic and optical phonons of rubidium cyanide has been measured at 300 K. The acoustic branches are affected by rotation-translation coupling in a way similar to the findings in KCN. The data are explained by a model which combines a shell model and rotation-translation coupling.

Transport properties and hydrodynamic centers of rigid macromolecules with arbitrary shapes

AbstractA general formalism, which includes translation–rotation coupling, is proposed for calculating translational and rotational transport properties, as well as intrinsic viscosities, of rigid macromolecules with an arbitrary shape. This formalism is based on Brenner's theory of translational–rotational dynamics and on methods for the calculation of hydrodynamic properties that have been already presented, and can be regarded as a generalization of the one proposed by Nakajima and Wada. The calculated transport properties depend on the origin as predicted by Brenner's theory, but in a disagreement with him, the center of resistance and the center of diffusion do not coincide. As one can define several hydrodynamic centers, which in practice turn out to be located at different points, the influence of the choice of the center on the calculated transport properties is discussed. An analysis of the translation–rotation coupling effects in translational diffusion reveals that they arise exclusively from hydrodynamic interactions and are rather small in some cases of interest. Finally, we present a study of the rotational diffusion of rigid bent rods with a fixed length‐to‐diameter ratio. The diffusion coefficients obtained can be useful to estimate changes with respect to a straight rod.

Studies of shear waves and translation–rotation coupling of liquid nitrobenzene in neat liquid and in carbon tetrachloride solution by depolarized Rayleigh scattering

High resolution depolarized Rayleigh spectra of nitrobenzene in CCl4 have been measured at several concentrations and temperatures. All spectra display a shear wave dip at the zero frequency. They are found to fit well to the form of a two-variable theory in the low frequency regions studied. The various parameters such as the collective molecular reorientation rate Γ, the shear wave relaxation rate q2νs, and the dynamic coupling coefficient R are obtained as a function of temperature and concentration. While the R value is found to be independent of temperature, it changes significantly with the nitrobenzene concentration. Moreover, the R value for pure nitrobenzene is found to be greater than 0.5, higher than any reported previously for a low viscosity liquid. The τRay values are found to follow the classical Stokes–Einstein relation, with zero intercept. The pair orientational correlation affects the Rayleigh relaxation time.

ChemInform Abstract: SELF‐DIFFUSION AND VISCOSITY OF METHYLCYCLOHEXANE IN THE DENSE LIQUID REGION

The self‐diffusion coefficients of liquid methylcyclohexane have been measured as a function of temperature and pressure over the density range 2.5⩽ρ/ρc⩽3.3 and temperature range 0.35⩽T/Tc⩽0.5 using the NMR spin echo technique with a fixed field gradient. Shear viscosities and densities have also been determined under the same experimental conditions. An approximate analysis of the experimental diffusion and viscosity data in terms of the rough sphere model of liquids yields effective hard core diameters and a parameter A that reflects the degree of coupling between the rotational and translational motion of methylcylohexane molecules. The strong temperature dependence of this coupling arises most likely from the nonspherical shape of the methylcyclohexane molecule. The behavior of the rotational–translational coupling and its possible connection to melting properties and to the experimental finding that methylcyclohexane does not form an orientationally disordered crystalline phase is discussed in a qual...

Role of rotational-translational coupling in vibrational relaxation of matrix-isolated diatomic molecules

Vibrational-rotational coupling, due to the fact that the center of interaction is displaced from the center of mass in a heteronuclear diatomic molecule, provides a mechanism for nonradiative vibrational relaxation of diatomic impurities in matrices. A theoretical expression for the rate constant in semiquantitative agreement with experiment is derived.

Computer simulations of dense molecular fluids

The effect of translation-rotation coupling on the displacements of molecules in dense fluids is discussed, first in connection with neutron scattering factors and then in connection with the distributions of atomic and centre of mass displacements of homonuclear diatomic molecules. Computer simulations of these properties are presented. In the simulations, the angledependent part of the interaction was changed by choosing different values for the molecular quadrupole moments while holding reduced density and temperature fixed. It was found that neither local anisotropy or coupling between centre of mass motion and reorientation was important in the systems studied. A rationale for this behaviour is suggested.

Orientational relaxation in molecular solids with translation rotation coupling

Starting from a Hamiltonian with bilinear coupling of translations and rotations and with single-particle orientational potential, we derive a closed transport equation for the dynamic displacement–displacement correlation function. The coupling to the rotation leads to a softening of the phonons and to an instability in the lattice at the orientational phase transition. The memory kernel which is due to the orientational velocity correlations is calculated in a systematic and consistent way. This leads to additional resonances in the displacement–displacement correlation function.

Rotational relaxation in sonic nozzle expansions

The thermal conduction model for cooling in sonic nozzle expansions is extended to rotational degrees of freedom. Unimolecular decomposition theory, as applied to collision complexes, provides a natural formalism for describing the rotational–translational coupling. Simple expressions are presented for the terminal ’’temperatures’’ as functions of the source parameters and the relevant long-range r−6 potential. Extensions to other potentials and to vibrational relaxation are indicated.

Static and dynamic aspects of order and disorder in CBr4

In the first part of this paper is presented a review of experimental work carried out on CBr4: X-ray and neutron diffraction, neutron diffuse scattering and neutron coherent inelastic scattering. Comparison is made with CD4, and it is deduced that translational and rotational motions are coupled in CBr4. Then in the second part, some consideration is given to the development of a model of translation–rotation coupling using the theoretical work of Yasuda on CD4.

Self-diffusion and viscosity of methylcyclohexane in the dense liquid region

The self-diffusion coefficients of liquid methylcyclohexane have been measured as a function of temperature and pressure over the density range 2.5⩽ρ/ρc⩽3.3 and temperature range 0.35⩽T/Tc⩽0.5 using the NMR spin echo technique with a fixed field gradient. Shear viscosities and densities have also been determined under the same experimental conditions. An approximate analysis of the experimental diffusion and viscosity data in terms of the rough sphere model of liquids yields effective hard core diameters and a parameter A that reflects the degree of coupling between the rotational and translational motion of methylcylohexane molecules. The strong temperature dependence of this coupling arises most likely from the nonspherical shape of the methylcyclohexane molecule. The behavior of the rotational–translational coupling and its possible connection to melting properties and to the experimental finding that methylcyclohexane does not form an orientationally disordered crystalline phase is discussed in a qualitative way.