Lorentz-Lorenz Equation Research Articles

Local field in anodic oxide films on valve metals

In this paper, methods of calculation of electronic polarizability of ions in anodic oxide films on aluminium, niobium and tantalum are discussed. It is shown that if considerable covalency of the chemical bond is taken into account electronic polarizability of metal and oxygen ions differs noticeably from that of “free” ions, determined by Fajans and Joos, Pauling and others. The Lorentz-Lorenz type equation which was derived makes it possible to calculate the ionic polarizablity of metal ion. The results obtained are in good agreement with those of other authors. In case of amorphous materials with mixed ionic-covalent chemical bond a new method of local field calculation is proposed.

Vapour-liquid coexistence curve of some alternative refrigerants in the critical region

Measurements of the refractive index coexistance curve for HFC-143a have been carried out with special attention to the critical region. The values of the critical temperature and the critical refractive index are estimated. The density coexistence curve for HFC-143a in the critical region is calculated by using the Lorentz-Lorenz equation. The density coexistence curves of HFC-32 and HFC-125 are also calculated from the previously reported vaues of the refractive index and compared with the reported values of density

Excess molar volumes, excess viscosities and refractive indices of a quaternary liquid mixture at 298.15 K

Density, viscosity and refractive index values for the propan-2-ol + methylacetate + dichloromethane + n-pentane mixture have been measured at 298.15 K, over the whole concentration range. Excess molar volumes and viscosities have been calculated. Flory's statistical theory has been applied to predict the excess molar volumes and compare then to the experimental data. We have also applied Grunberg and Nissan's equation for calculating viscosities and Lorentz-Lorenz's equation for predicting refractive indices, by knowing the values of the pure components.

Measurements of the refractive index of alternative refrigerants

Measurements of coexistence curves of the refractive index of HCFC-22, HFC23, HFC-32, HFC-125, and HFC-152a have been carried out in the range from ambient to critical temperature. Near the critical temperature the refractive index has distribution in both the vapor and the liquid phases in the test cell. Thus the values at the boundary between vapor and liquid are selected at those of saturated vapor and liquid, respectively. The values of the critical temperature and critical refractive index for each substance are estimated. The refractive index is related to density by the Lorentz-Lorenz equation. In the case of HFC-32 the value of the LL function is assumed to be constant in the limited region near the critical point, and the values of density of saturated vapor and liquid are calculated and are compared with the experimental values of density obtained byPVT measurement.

Solid state photoelectron spectroscopy of carotenoids

The threshold energies of carotenoids were determined by solid state photoelectron spectroscopy and their polarization energies were calculated with the dielectrical constant obtained via Lorentz-Lorenz equation. The influences on the threshold energy exerted by the chain-length of the system, the acceptor-strength of the end group, the number and kind of alkyl groups attached to the system and the conformation, especially the dihedral angle between chain and end group were investigated.[1]

Refractive-index measurements in freezing sea-ice and sodium chloride brines

Sea ice contains numerous pockets of brine and precipitated salts whose size and number distributions change dramatically with temperature. Theoretical treatment of scattering produced by these inclusions requires information on refractive-index differences among the brine, salts, and surrounding ice. Lacking specific data on refractive-index variations in the brine, we carried out laboratory measurements in freezing-equilibrium solutions between -2 and -32 °C. Index values at 589 nm increased from 1.341 to 1.397 over this temperature range, corresponding to salinities of 35 and 240 parts per thousand (ppt). Spectral data were also taken at 50-nm intervals between 400 and 700 nm in nonequilibrium solutions with salinities ranging up to 300 ppt. Spectral gradients increased slightly with salinity but showed no measurable dependence on temperature between +12 and -16 °C. The Lorentz-Lorenz equation, combined with data on density, molar refractivities, and brine composition, yielded temperature-dependent index predictions in excellent agreement with the experimental data. Similar index and density measurements in freezing sodium chloride brines yielded values nearly identical to those in the sea-ice brines. The absence of mirabilite crystals in sodium chloride ice, however, will cause it to have higher transmissivity and lower reflectivity than sea ice above -22 °C.

Densities and Refractive Indices for 1-Hexene + o-Xylene, + m-Xylene, + p-Xylene, and + Ethylbenzene

Densities and refractive indices were measured at 298.15 K for binary mixtures of 1-hexene + o-xylene, + m-xylene, + p-xylene, and + ethylbenzene over the entire composition range. The results were fitted to a polynomial relation to obtain the coefficients and standard errors. Excess volumes and molar refraction deviations were derived. Also, the refractive indices were compared with the predictions of the Lorentz-Lorenz, Gladstone-Dale, and Arago-Biot equations

Indices of refraction for the hitran compilation

Indices of refraction of sulfuric acid solutions, water, and ice, which will become part of the HITRAN database, are discussed. Representative calculations are presented for the sulfate aerosol, to illustrate the broadband spectral features of i.r. aerosol extinction spectra. Values of the sulfuric acid mass density are used in an application of the Lorentz-Lorenz equation, which is used to estimate the sensitivity of extinction coefficients to temperature dependent refractive indices.

高圧流体物性 冷媒の屈折率

The refractive index is an important optical property, and it is closely related to density by the Lorentz-Lorenz equation. The present status of the measurements of the refractive index coexistence curve is described with a special attention to alternative refrigerants recently studied. The values of critical refractive index of refrigerants estimated in the various references are tabulated. In case of HFC-32, the density coexistence curve in the critical region calculated from refractive index data is compared with that directly obtained from PVT measurements.

Determination of the molecular parameters of 4-(2′-methylbutyl)-phenyl-4′-n-octylbiphenyl-4-carboxylate

Abstract Chiral 4-(2′-methylbutyl)-phenyl-4′-octylbiphenyl-4-carboxylate (CE8) has been studied by dielectric, densytometric, refractometric and X-ray measurements. Transverse and longitudinal molecular polarizabilities have been calculated from the ordinary and extraordinary refractive indices and the density of CE8 using Neugebauer', Vuks, Lorentz-Lorenz equations with both Haller and Subramhanyama extrapolation. Effective value of the molecular dipole moment and the angle between the vector of the molecular dipole moment and the long axis of molecule have been calculated from the values of parallel and perpendicular components of the dielectric permittivity in the Iso and N* phases of this compound using the Maier and Meier equation.

Determination of refractive properties of fluids for dual-wavelength interferometry

Methods to calculate the refractive properties of solutions at different wavelengths are described by using experimental data at just two wavelengths. The properties are the refractive index and its gradients with temperature and concentration. Cauchy's equation is used to determine the refractive indices. The gradients versus temperature and concentration are then determined by using the Murphy-Alpert and the Lorentz-Lorenz equation, respectively. Finally, the particular case of a triglycine sulfate aqueous solution is considered as an example. The approach should provide the desired information for fringe analysis when dual-wavelength holographic or other interferometry is used for solving heat and mass transfer problems in fluids during crystal-growth experiments.

Chain orientation and anisotropies in optical and dielectric properties in thin films of stiff polyimides

AbstractThin films of poly(p‐phenylene biphenyltetracarboximide) (BPDA‐PDA), prepared by thermal imidization of the precursor poly(amic acid) on substrates, have been investigated by optical waveguide, ultraviolet‐visible (UV‐VIS), infrared (IR), and dielectric spectroscopies. The polyimide films exhibit an extraordinarily large anisotropy in the refractive indices with the in‐plane index n∥ = 1.806 and the out‐of‐plane index n⊥ = 1.589 at 1064 nm wavelength. No discernible effect of the film thickness on this optical anisotropy is found between films of ca. 2.1 and ca. 7.8 μm thickness. This large birefringence is attributed to the preferential orientation of the biphenyltetracarboximide moieties with their planes parallel to the film surface, coupled with the strong preference of BPDA‐PDA chains to align along the film plane. The frequency dispersion of the in‐plane refractive index n∥ is consistent with the results calculated by the Lorentz–Lorenz equation from the UV‐visible spectrum exhibiting several absorption bands in the 170–500 nm region. The contribution from the IR absorption in the range 7000–400 cm,−1 computed by the Spitzer‐Kleinmann dispersion relations from the measured spectra, adds ca. 0.046 to the in‐plane refractive index n∥. Tilt‐angle–dependent polarized IR results indicate nearly the same increase for the out‐of‐plane index n⊥. Application of the Maxwell relation then leads to the out‐of‐plane dielectric constant ε⊥ ≃ 2.7 at 1.2 × 1013 Hz, as compared with the measured value of ca. 3.0 at 106 Hz. Assuming this small difference to remain the same for the in‐plane dielectric constants ε∥, we obtain a very large anisotropy in the dielectric properties of these polyimide films with the estimated in‐plane dielectric constant ε∥ ≃ 3.4 at 1.2 × 1013 Hz, and ε∥ ≃ 3.7 at 106 Hz. © 1992 John Wiley & Sons, Inc.

Light scattering method of determining the second virial coefficient for simple molecules and oligomers

A procedure of determining the molecular weight and second virial coefficient for simple molecules and oligomers from light-scattering measurements on a binary solution is presented on the basis of the well-established theory of fluctuations in multicomponent systems. It consists of determining first total isotropic scattering from the solution and then the composition scattering by subtracting from the former the density scattering (the Einstein-Smoluchowski term), where the values at finite concentrations should be used for the density scattering and also for the refractive index and its increment appearing in the optical constant. The required value of the density scattering is obtained by multiplying its observed value for the pure solvent by the concentration correction factor that is evaluated from a proper relationship between the refractive index and density of the solution. From experimental results obtained for a solution of toluene in cyclohexane at 25.0 {degrees}C as an example, the Lorentz-Lorenz equation is recommended as such a relationship. It is demonstrated that the multiple scattering theory by Bullough, which has often been used, is erroneous. 35 refs., 5 figs., 1 tab.

Refractive index and density variations in pure liquids: a new theoretical relation

A new theoretical expression of the density fluctuation of the refractive index (dn 2 /dd) p or DFRI has been deduced from a general expression of the Lorentz-Lorenz equation and from the calculation of the partial derivatives of n 2 . The square of the refractive index in each point of the liquid has been considered as a function of the number N of molecules per volume unit, of the temperature T and of the pressure P

Ellipsometric investigation of the adsorption of acetylenic alcohols on iron

The adsorption kinetics of nine alkynols and four other related compounds on iron in H 2SO 4 were examined by in situ time-resolved automatic ellipsometry. The time, concentration and potential dependences of the adsorption, the subsequent orientation transition and polymer growth of the adsorbed layers formed by these compounds were determined. A new method based upon the Lorentz-Lorenz equation is deduced for the calculation of surface packing density of an adsorbed organic compound with a certain orientation on an electrode surface from ellipsometric data. Using this method, useful correlation between the molecular structure and the saturated surface packing density is obtained. In addition, the polarizabilities of an organic compound with different orientations on the surface are also obtained.

Time-resolved determination of volume shrinkage and refractive index change of thin polymer films during photopolymerization

Polymerization shrinkage and change of refractive index have been studied on thin sample layers during photopolymerization. By using laser interferometry and special substrates it was possible to determine both parameters simultaneously. The monomer studied was bis(2-hydroxyethyl)bisphenol A dimethacrylate (HEBDM). Once the refractive index and the shrinkage were known, the double-bond conversion could be calculated using the Lorentz-Lorenz equation. It has been found that shrinkage proceeds linearly with conversion until vitrification of the system sets in. From that moment shrinkage cannot keep up with conversion and lags behind. The described model can also be used to predict changes of thickness and refractive index upon further relaxation.

What is the lowest refractive index of an organic polymer?

The theoretical lower limit of the refractive index of organic polymers was investigated using the Lorenz-Lorentz equation. Starting from an extended data base, optimized refractive and density increments for functional groups were evaluated.

Refractometric studies of mesogenic molecules in isotropic solutions

Abstract The Lorenz-Lorentz equation for binary isotropic mixtures, consisting of anisotropic molecules, has been derived using the point-dipole approximation taking into account only pair molecular correlations. This permits the calculation of the effect of molecular correlations on the refractive index. Special attention has been paid to the case of infinite dilution in the solvents consisting of isotropic molecules, where an experimental check of the equations is possible. The specific refraction of some solutes with different molecular polarizability anisotropy and polarity has been studied in various solvents. It has been shown, that the main theoretically predicted features are observed in these experiments, but for a quantitative comparison information on the two-particle distribution function is needed.

Structures and Optical Properties of Resins Containing Several Carboxylic Acids Neutralized with Barium Ion

Monomer composites containing an aromatic carbozylic acid and methacrylic acid (or acrylic acid) partially neutralized with a barium compound showed good solubility in chlorostyrene at high barium ion concentrations, unlike composites containing only one carboxylic acid. The improved solubility was due to the presence of an ionic crosslink composed of the aromatic carboxylate ion and methacrylate (acrylate) ion bridged with a barium ion, which provided an effective structure for depressing the growth of ionic associations. The bulky structure also enabled resins to maintain their transparency after being copolymerized with chlorostyrene. The refractive indices and Abbe numbers of the resins were measured and differences in optical properties between various carboxylic acids were evaluated according to (Ru)/Mu and the density in the Lorentz-Lorenz equation, where (Ru) and Mu are the unit molar refraction and residue molecular weight, respectively. The resins with acrylic acid had a higher refractive index without decrease of the Abbe number at the same barium content than those with methacrylic acid, due to the effect of the former on increased resin density. The introduction of an aromatic acid having a high molar refraction value led to increase of the refractive index, but its effect on the increase was small, because it caused a drop in resin density.

Properties and structure of silicon nitride films synthesized by ion-beam-enhanced deposition

Silicon nitride films with a stoichiometric ratio of Si 3N 4 were synthesized by ion-beam- enhanced deposition (IBED). It was observed that a silicon nitride film formed by IBED is composed of a thin silicon-enriched top layer, a stoichiometric Si 3N 4 layer and a smooth transition layer at the interface next to the substrate. By detailed theoretical analysis and computer simulation of IR reflection interference spectra, refractive index profiles of the films were obtained. Composition profiles and refractive index profiles were correlated using the Lorentz-Lorenz equation. The fatigue and high temperature oxidation behaviour of metals can be improved using Si 3N 4 coatings made by means of IBED, and the mechanisms of these are discussed.