Spheriodal multipolar expansions for intermolecular energy in crystal theory .: II. Lattice energy of the orthorhombic structure of actylene crystal

The spheroidal formalism for the interaction energy between two non-overlapping ellipsoidal charge distributions is applied to the determination of the lattice energy of the orthorhombic structure of the acetylene crystal. The molecules are assimilated to quadrupolar prolate ellipsoids and the pair potential is assumed to be a sum of two terms: a Kihara corepotential extended to prolate ellipsoids and the spheroidal quadrupolar interaction. The value so obtained for the lattice energy is ?25.01 kJ mole^? while an evaluation of the corresponding observed value is ?23.81 kJmole^?.     

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson-Boltzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle.     

Spheroidal multipolar expansions for intermolecular energy in crystal theory. Lattice energy and cell dimensions of the orthorhombic structure of benzene crystal

The oblate spheroidal formalism for the interaction energy between two non-overlapping ellipsoidal charge distributions is applied to the determination of the lattice energy and cell dimensions of the orthorhombic structure of benzene crystal. The molecules are assimilated to quadrupolar oblate ellipsoids and the pair potential is assumed to be a sum of two terms: a Kihara core-potential extended to oblate ellipsoids and the spheroidal quadrupolar interaction. The value so obtained for the lattice energy is -51.3 kJ mole^-1 at unit cell dimensions of 7.7, 8.1 and 7.4 A, while the observed heat of sublimation corrected for zero-point vibration is -52.3 kJ mole^-1 and the experimental cell dimensions are 7.39, 9.42 and 6.81 A at 138 K.     

Electrostatic potential for some non-spherical organic molecules: An oblate-spheroidal dipolar approximation

A spheroidal dipolar expansion is used for the determination of the electrostatic potential due to three non-spherical organic molecules: to-luene, phenol and cyclohexanone. The agreement of experimental facts with the prediction of the most probable reactive sites on each molecule deduced from calculated equipotential maps is discussed.     

The molecular orientation of para-sexiphenyl on Cu(110) and Cu(110) p(2x1)O.

Controlling the molecular growth of organic semiconductors is an important issue to optimize the performance of organic devices. Conjugated molecules, used as building blocks, have an anisotropic shape and also anisotropic physical properties like charge transport or luminescence. The main challenge is to grow highly crystalline layers with molecules of defined orientation. The higher the crystallinity, the closer these properties reach their full intrinsic potential, while the orientation determines the physical properties of the film. Herein we show that the molecular orientation and growth can be steered by the surface chemistry, which tunes the molecule-substrate interaction. In addition, the oxygen reconstruction of the surface, demonstrates the flexibility of the organic molecules to adopt a given surface corrugation and their unique possibility to release stress by tilting.     

Spatial Taming and Trapping of Molecules

Molecular beam techniques for study of collisional and spectroscopic processes have recently been enhanced by use of static electric or magnetic fields to orient or align molecules with permanent dipole moments. A more general method is now in prospect, applicable both to alignment and to spatial trapping of molecules. This exploits the anisotropic interaction of the electric field vector of intense laser radiation with the dipole moment induced in a polarizable molecule by the laser field. The interaction creates directional superpositions of field-free states that correspond to oblate spheroidal wavefunctions, with eigenenergies that decrease with increasing field strength. We suggest that this polarizability interaction produces the marked alignment found in laser-induced dissociative ionization of CO by the Saclay group. We also present calculations illustrating the feasibility of spattal trapping. In combination with supermirror focussing and buffer-gas cooling, an intense infrared laser can typically confine molecules for long-times (-hours) within a small (-picoliter) and cold (?1°K) “pocket of light.”     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 1. Approximate expression for the free energy of hydrophobic association based on a Gaussian-overlap model

A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers.     

Low-angle x-ray scattering from crazes and fracture surfaces in polystyrene

Both crazes and fracture surfaces in glassy polymers produce a low-angle scattering of x-rays. Scattering patterns are anisotropic and often show considerable streaking. In the one case (polystyrene) studied extensively so far, detalied analysis suggests that the craze is approximated as a collection of spheroidal or irregular-shaped voids surrounded by material with anisotropic density distribution arising from its orientation in the stress direction. The void dimension is about 90–115 Å and the specific internal surface area about 170 m²/cm³ of craze. These results and those from electron microscopic studies are reasonably consistent.     

Determination of polarity parameters for liquid crystals using solvatochromic method in anisotropic and isotropic phases

The use of liquid crystals (LCs) as anisotropic solvents is desired for various potential applications and usually for other organic and inorganic compounds. In this work, solvent polarity parameters are obtained using a spectroscopic method for four LCs with a range of high and low dielectric anisotropy (?ε). Solvatochromic polarity parameters for these LCs were defined via Kamlet–Abboud–Taft polarity functions characterizing different temperatures and phases, isotropic and anisotropic, and using the Reichardt’s dye and 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridinio) phenolate standard probe. The investigated polarity parameters reveal the effects of LC media on the photo-physical behaviour of solute molecules in isotropic and anisotropic media. Subsequently, a new LC polarity parameter (Z_o) is introduced as an overall matrix anisotropy polarity parameter to characterize variation between isotropic and anisotropic phases. The values of Z_o are sorted from higher to lower dielectric anisotropies (?ε).     

Approximate analytic expressions for the electrophoretic mobility of spheroidal particles

Approximate analytic expressions are derived for the electrophoretic mobility of spheroidal particles (prolate and oblate) carrying low zeta potential in an electrolyte solution under an applied tangential or transverse electric field. The present approximation method, which is based on the observation that the electrophoretic mobility of a particle is determined mainly by the distortion of the applied electric field by the presence of the particle. The exact expression for the equilibrium electric potential distribution around the particle, which can be expressed as an infinite sum of spheroidal wave functions, is not needed in the present approximation. The electrophoretic mobility values calculated with these approximate expressions for spheroidal particles with constant surface potential or constant surface charge density are in excellent agreement with the exact numerical results of previous reports with the relative errors less than about 4%.     

Molecular dynamics simulations for CO2 spectra. II. The far infrared collision-induced absorption band

Classical molecular dynamics simulations have been carried out for gaseous CO(2) starting from various anisotropic intermolecular potential energy surfaces. Through calculations for a large number of molecules treated as rigid rotors, the time evolution of the interaction-induced electric dipole vector is obtained and the Laplace transform of its autocorrelation function gives the collision-induced absorption rototranslational spectrum. The results are successfully compared with those of previous similar calculations before studies of the influences of the intermolecular potential and induced-dipole components are made. The calculated spectra show a significant sensitivity to anisotropic forces consistently with previous analyses limited to the spectral moments. The present results also demonstrate the importance of vibrational and back-induction contributions to the induced dipole. Comparisons between measured far infrared (0-250 cm(-1)) spectra at different temperatures and results calculated without the use of any adjustable parameter are made. When the best and more complete input data are used, the quality of our predictions is similar to that obtained by Gruszka et al. [Mol. Phys. 93, 1007 (1998)] after the introduction of ad hoc short-range overlap contributions. Our results thus largely obviate the need for such contributions the magnitudes of which remain questioned. Nevertheless, problems remain since, whereas good agreements with measurements are obtained above 50 cm(-1), the calculations significantly underestimate the absorption below, a problem which is discussed in terms of various possible error sources.     

Molecular dynamic simulation methods for anisotropic liquids

Methods of molecular dynamics simulations for anisotropic molecules are presented. The new methods, with an anisotropic factor in the cell dynamics, dramatically reduce the artifacts related to cell shapes and overcome the difficulties of simulating anisotropic molecules under constant hydrostatic pressure or constant volume. The methods are especially effective for anisotropic liquids, such as smectic liquid crystals and membranes, of which the stacks of layers are compressible (elastic in direction perpendicular to the layers) while the layer itself is liquid and only elastic under uniform compressive force. The methods can also be used for crystals and isotropic liquids as well.     

On the shape of the Q-branch of Raman scattering spectra in dense media. Anisotropic scattering

The Q-branch width of the anisotropic Raman spectrum for linear molecules has been shown to increase with density. Until the overlap of the O-, Q-, S-branches is small, the product of the half-widths of isotropic and anisotropic Q-branches, in units of mean frequency, is a constant characterizing the collision strength.     

The use of the finite element method for calculating the thermophoresis velocity of large aerosol particles

The finite element method has been employed to calculate the thermophoresis velocity of solid aerosol particles, the sizes of which are much larger than the mean free path of molecules in a gas. The thermophoretic velocities of axially symmetric particles moving along their rotation axes have been numerically calculated. Cylindrical particles, particles having a shape resulting from rhomb rotation around one of its diagonals, and spheroidal particles have been considered. The data obtained for spheroidal particles have been compared with the available results of analytical calculations.     

Carbon-13 spin–lattice relaxation of tropane alkaloids. Anisotropic rotational motion of tropine and pseudotropine

The ¹³C spin–lattice relaxation times of tropine and pseudotropine have been measured in CDCl₃ as a function of concentration. The same relative increase in concentration serves to increase the relaxation rates much less in the region 0.9–5.0 wt.% than in the region 5.0–14.3 wt.%. The rotational diffusion coefficients have been calculated from the relaxation data using Woessner's anisotropic rotational diffusion model. Reorientation of both molecules is shown to be moderately anisotropic. The principal axes of the rotational diffusion tensor in the symmetry plane of both molecules are rotationally shifted from the principal axes of the moment of inertia tensor of the free molecules, and the main rotational axis is parallel with a line passing through the centre of mass of the molecule and the nitrogen atom.     

Computer simulation studies of anisotropic systems. XI. Second- and fourth-rank molecular interactions

The Maier-Saupe theory for nematic liquid crystals provides a reasonable account of their orientational order and its temperature dependence. The theory is based on second-rank anisotropic interactions and its predictions can be improved by the introduction of higher-rank terms as in the Humphries-James-Luckhurst theory. However comparison with the properties of real nematogens does not allow an unambiguous test of the theory because the form of the pair potential is unknown. This is not the case for computer simulations where the intermolecular potential is defined. We have therefore undertaken a Monte Carlo study of the influence fourth-rank interactions on nematic behaviour and report the results of our simulations here. The model nematogen used as a reference is that developed by Lebwohl and Lasher in which the particles are confined to the sites of a simple cubic lattice and interact via a second-rank anisotropic potential. The simulation gives the internal energy, the heat capacity at constant volume and the second-rank order parameter as a function of temperature, as well as the nematic-isotropic transition temperature. These results are used to provide the first unambiguous test of the Humphries-James-Luckhurst theory. We also discuss the changes in the transition temperature which are caused by the introduction of the fourth-rank term in the pair potential using thermodynamic perturbation theory for the Helmoltz free energy.     

Equation of state based on the weeks-chandler-andersen perturbation theory

An equation of state based on the Weeks-Chandler-Andersen (WCA) perturbation theory utilizing the simplified random-phase approximation (RPA) term is p of state is applied successfully to calculate the P-V-T relationship for a spherical molecule, argon.For nonspherical molecules, the effects of anisotropic interactions are treated empirically. The calculated P-V-T relationships and saturated properties for nonspherical and nonpolar molecules agree well with experimental data. The potential parameters for nonpolar substances are well correlated with the acentric factors.     

Absorption anisotropy of cubic or randomly oriented chromophores in anisotropic solvents. Dispersion induced linear dichroism (DILD)

A new mechanism through which cubic or orientationally averaged solutes could gain absorption anisotropy (linear dichroism) in the presence of an anisotropic (oriented) solvent medium is proposed. Transitions of the unoriented species exhibit a dispersion induced linear dichroism (DILD) as a result of dispersive coupling to the transitions of the oriented system. The phenomenon depends on the nature of the angular distribution of solute molecules about a particular solvent species, being maximised for a cylindrical distribution around a polymer, but still yielding a measurable DILD for spherical distributions of the solute. It is also shown that the LD of non-cubic or oriented solutes in anisotropic media should be corrected for a significant DILD contribution.     

Anisotropic networks, elastomers and gels

Anisotropic networks, elastomers and gels exhibit piezoelectric, pyroelectric, ferroelectric and NLO properties of potential interest for use communication and processing technologies. The formation, properties and applications of such anisotropic, mainly liquid crystalline, networks are described. If some of the molecules in a liquid mixture contain at least two reactive groups which can be either photochemically or thermally polymerized, then crosslinked, anisotropic networks, elastomers and gels can be produced. Solid macroscopically aligned elastomers or networks can be formed as required beforehand or simultaneously by orientation of the sample. Anisotropic gels consist of a solid anisotropic network and non-covalently bonded, but strongly oriented domains of low molar mass liquid crystals. Anisotropic networks, elastomers preformed amorphous or liquid crystalline polymers incorporating additional reactive groups, which can be macroscopically oriented in the additional crosslinking reactions. Reversible networks, elastomers and gels can be prepared either non-covalently or covalently by thermally side group polymers and low molar mass molecules, liquid crystalline properties in the pure state. in many electro-optic devices for optical and gels can be prepared from liquid crystalline state and then fixed by reversible linkages between, for example, neither of which necessarily exhibit