T. Keyes

The role of local fields and interparticle pair correlations in light scattering by dense fluids: I. Depolarized intensities due to orientational fluctuations† Supported in part by the National Science Foundation (NSF Grant CHE 76-07384).

The polarized scattering intensity is calculated, in the Einstein-Smoluchowski approximation, for four thermodynamic states of a model diatomic; these are the same states for which the depolarized intensity was calculated in the first article (I) of this series. The polarized intensity is discussed in terms of an ‘effective isotropic polarizability’ α 0 eff and the ratio (α 0 eff/α 0)2, where α 0 is the gas-phase isotropic polarizability, and is both expressed formally and tabulated for the four states. Similarly in (I), depolarized intensities were discussed in terms of the ratio, (γ/Δα)2, where γ is the ‘effective polarizability anisotropy’ and Δα the gas-phase anisotropy. We find that (α 0 eff/α 0)2 lies much closer to unity than does (γ/Δα)2, in agreement with existing experimental data, which indicates that the introduction of effective polarizabilities is relatively unimportant or important, respectively, as polarized or depolarized scattering is considered.

Singlet and triplet exciton percolation in benzene isotopic mixed crystals

New, closed form, approximate expressions are obtained for the calculation of ideal percolation thresholds which are determined by the migration topology. Excitation tunneling theory is briefly reviewed and extended for application to nonresonant, long range energy migration in mixed molecular crytals. These theories are applied to new singlet and triplet exciton percolation data for benzene isotopic mixed crytals. The differences between these results and the theoretical expectations are used to emphasize the importance of exciton lifetime and exciton trapping in determining the extent of long range energy transport in molecular crytals.

The role of local fields and interparticle pair correlations in light scattering by dense fluids: IV. Removal of the point-polarizability approximation

The Kirkwood-Yvon dielectric theory is generalized to the case of fluids consisting of molecules possessing arbitrary polarizability densities. The theory is used to find expressions for the equilibrium dielectric constant, the polarized scattering intensity, and the depolarized scattering intensity, which we have previously calculated under the approximation (PPA) that molecules have point polarizabilities. A simplified version of the general theory, in which each atom in a polyatomic is given a point polarizability (PAPA), is proposed, and worked out in detail for the case of homonuclear diatomics. A discussion is given of how we hope to obtain numerical results in the near future for liquids composed of model homonuclear diatomics considered by us previously.

The intensity of light scattered by liquid CS2

We apply our recent theory of light scattering from fluids of optically anisotropic molecules to the case of liquid carbon disulfide. We focus our attention on δ2, the experimentally measured ratio of depolarized to polarized light scattering intensities. With the pair distribution function obtained from the RISM equation, we calculate δ2 using two models for the optical response of the fluid. In the first one (PPA) a point anisotropic polarizability is assigned to each molecule: in the second one (PAPA), each atom is given a point isotropic polarizability. We find that the more realistic PAPA model results in reasonable agreement with measurements of Burnham, Alms, and Flygare.

Structure and equilibrium optical properties of liquid CS2

Equilibrium optical properties of liquid carbon disulphide (CS2), i.e. its refractive index, Kerr constant and depolarized light scattering intensity are calculated using two models of optical response of the fluid. The first one, the point polarizability approximation (PPA) assumes that a point dipole, proportional to the total polarizability, is induced in each molecule. The second one, the point atomic polarizability approximation (PAPA) assumes that point dipoles are induced in individual atomic sites. The symmetry components of the intermolecular pair distribution function needed to calculate optical properties of the fluid are obtained by Monte Carlo computer simulation on a hard triatomic model of CS2 as well as by two approximate approaches using this same model. The approximations are both based on the use of the site superposition approximation (SSA) for the intermolecular pair distribution function. In the first approach, the SSA pair distribution is obtained using the Monte Carlo site-site fun...

Dielectric fluctuations, orientational fluctuations, and depolarized scattering

Linear response theory and Kirkwood–Yvon theory are combined to calculate the dielectric tensor in the presence of a weak molecular orientational order. The results for the dielectric tensor are then used to calculate depolarized scattering intensities via the ’’phenomenological’’ theory.

Effect of internal fields on depolarized light scattering from n-alkane gases

In this paper we extend the interacting site theory of optical response proposed by Applequist, Karl and Fung to molecules with internal degrees of freedom. We apply the theory to chain alkanes and calculate their polarizabilities. We find that the interacting site model agrees well with the experimental data on depolarized light scattering from small normal alkanes in the gas phase. Unlike the bond additive model, our model predicts the observed behaviour of the depolarization of the scattered light with the number of carbon-carbon bonds. We also discuss asymptotic behaviour of isotropic and anisotropic polarizabilities for long chains.

The relation of percolation to energy migration dynamics

Abstract Numerical solutions are presented of a master equation for energy migration among conducting sites on a lattice, averaged over site configurations for a given concentration. The relation between static percolation phenomenon and the dynamics of energy migration is explored.

New method for the calculation of light-scattering intensities; application to depolarized scattering from simple fluids

A new method is developed for calculating light-scattering intensities. It is shown how the dielectric constant, and the concept of a ‘primary variable’, whose fluctuations cause the scattering of light, may be built into formal scattering theory. An approximation, the resumed fluctuation expansion, which has some extremely desirable and previously unattainable attributes, is proposed. Using this approximation, an integral equation is derived, through which the light-scattering source may be iterated in powers of a ‘generalized Einstein-Smoluchowski’ source, which is proportional to a non-equilibrium dielectric tensor. To linear order, the theory reproduces the theory of Keyes, Kivelson, and McTague. The theory is analysed to second order, and the intensity of depolarized light scattered from simple fluids, due to non-uniform density fluctuations, is calculated. The calculated intensity is a function of the true dielectric constant, and contains the effect of short-ranged fluid structure on closely spaced...

Is depolarized light scattered from simple liquids mainly double-scattered?

Abstract The multiple-scattering series for depolarized light scattering from simple liquids is investigated. It is found that the leading term in the series, due to double—double scattering, is probably not large compared to double—triple (DT) scattering contributions. Existing theories, which neglect DT scattering, have concluded that the experimental data cannot be explained using the dipole—induced dipole (DID) model for the pair polarizability. It is suggested that a theory which includes DT scattering will not lead to rejection of the DID model.