Lorentz-Lorenz Equation Research Articles

Temperature dependence of thermodynamic properties of leucyl–glycine aqueous solutions from 15 to 45 °C

Densities, ultrasonic speeds and refractive index of leucyl–glycine aqueous solutions were determined from 15 to 45 °C, at 5 °C intervals, for the molality range 0–0.3. Apparent molar volumes, V ϕ ,2, and apparent molar isentropic compressions, K S , ϕ,2 , of the solute have been derived from density and ultrasonic speed data. Limiting values of partial molar volumes, V 2 ∞, partial molar isentropic compressions, K S,2 ∞, and partial molar isobaric expansions, E P,2 ∞, have been obtained. Molar refractivities, R m, have been derived from the refractive index using the Lorentz–Lorenz equation. The molar refractivities of the solute, R m,2 ∗ , were calculated by a least squares fitting method. Interesting correlations between the temperature dependence of the different thermodynamic properties studied were found and interpreted in terms of molecular interactions in solution and configurations of the dipeptide skeleton.

LANDAU GHOSTS AND ANTI-GHOSTS IN CONDENSED MATTER AND HIGH DENSITY HADRONIC MATTER

It is observed that the "ghost" (originally discovered by Landau in quantum electro-dynamics) and its counterparts in other theories are indeed ubiquitous as they occur in a one-loop approximation to any conventional (unbroken) gauge theory. The mechanism is first exposed in its generality via the Dyson equation and a simple but explicit example in condensed matter is provided through the static Clausius–Mossotti equation and its dynamic counterpart, the Lorenz–Lorentz equation. The physical phase transition phenomenon associated with it is found to be super-radiance. We verify quantitatively that water (and many other polar liquids) are indeed super-radiant at room temperature. In quantum chromo-dynamics on the other hand, we encounter, thanks to asymptotic freedom, an "anti-ghost" which is closely associated with color confinement. Thus, in QCD, free quarks and glue exist in a super-radiant phase and hadronic matter exists in the normal one.

Refractive Index and Dispersion of Fluorides and Oxides

The refractive indices of 509 oxides and 55 fluorides were analyzed using two forms of a one-term Sellmeier equation: (1) 1/(n2−1)=−A/λ2+B, where A, the slope of the plot of (n2−1)−1 versus λ−2 in units of 10−16 m2, gives a measure of dispersion and B, the intercept of the plot at λ=∞, gives n∞=(1+1/B)1/2 and (2) n2−1=EdEo/(Eo2−(ℏω)2), where ℏω=the photon energy, Eo=the average single oscillator (Sellmeier) energy gap, and Ed=the average oscillator strength, which measures the strength of interband optical transitions. Form (1) was used to calculate n at λ=589.3 nm (nD) and n at λ=∞ (n∞), and the dispersion constant A. The total mean polarizabilility for each compound was calculated using the Lorenz–Lorentz equation: αe=3/4π [(Vm) (n∞2−1)/(n∞2+2)], where Vm is the molar volume in Å3. Provided for each compound are: nD, n∞, Vm, 〈αe〉, 〈A〉, 〈B〉, 〈Ed〉, 〈Eo〉, the literature reference, the method of measurement of n and estimated errors in n. Results obtained by prism, infrared reflectivity, ellipsometry, and interference methods are compared. Consistency of dispersion values among like compounds and structural families is used to evaluate the accuracy of refractive index data. Dispersion values range from 40 to 260×10−16 m2 with the majority of values in the range of 60–100×10−16 m2. High dispersion is associated with s2, p6, d10, and transition metal ions, H2O, and crystalline hydrates, whereas normal dispersion values are found in borates, aluminates, gallates, silicates, germanates, phosphates, and sulfates not containing H2O or any of the above ions. Exceptionally high dispersion is observed in liquid H2O, Fe2O3, Y3Fe5O12, FeOOH, Fe2(SO4)3, UO2, Cu2O, V2O5, MgCrO4⋅7H2O, and Cs2Mg(CrO4)2⋅6H2O.

Gasochromic switching of tungsten oxide films: a correlation between film properties and coloration kinetics

Optically switchable coatings based on tungsten oxide offer a wide variety of promising applications, such as the dynamic variation of transmission in smart windows. Our research focuses on the gasochromic switching of amorphous tungsten oxide (WO x ) films with a palladium catalyst cap-layer, where coloration takes place in a gas atmosphere with diluted hydrogen and bleaching can be achieved by an oxygen containing gas. The samples are produced by DC-magnetron-sputtering and show a laterally inhomogeneous switching behaviour where the coloration speed varies over more than one order of magnitude. To understand this phenomenon, the films were analyzed by optical spectroscopy with spatial resolution and subsequent simulation of their dielectric function. The switching kinetics of the films could be correlated to the index of refraction n: regions with high n did not switch, whereas regions with lower n showed fast switching behaviour. Since n is linked to the film density via the Lorenz–Lorentz equation, this implies that films with a low-density switch much faster than high-density films. Finally, a model to explain the observed lateral inhomogeneous deposition and coloration velocity is presented.

Determination of refractive index and electronic polarisability of oxygen for lithium-silicate melts using ellipsometry

The refractive index of Li 2O–SiO 2 melts has been measured using the ellipsometer constructed for high-temperature use. Measurements were carried out on four samples having different compositions over a wide temperature range (1300–1800 K). The standard deviation for the values measured was within ±0.0005. Additions of Li 2O were found to cause increases of refractive index in the temperature range investigated. At Li 2O concentrations <25 mol% the refractive indices of the melts increased with increasing temperature, similar to SiO 2. However, this temperature dependence became smaller with additions of Li 2O and at Li 2O concentrations more than 30 mol% the refractive indices of the melts decreased with increasing temperature. The temperature dependence of the refractive indices has been discussed from those of the density and the molar electronic polarisability on the basis of the Lorentz–Lorenz equation. In addition, the electronic polarisability of oxygen derived from the molar electronic polarisability increased with increasing temperature in each melt, suggesting that the ionicity of oxygen increases as temperature increases. Furthermore, additions of Li 2O were found to cause increases in the electronic polarisability of oxygen, due to the formation of non-bridging oxygen ions.

Electronic polarizability, optical basicity, and interaction parameter of La2O3 and related glasses

The electronic polarizability and optical basicity of La2O3 and related glasses have been determined from ultraviolet absorption spectra and calculations based on the Lorentz–Lorenz equation. The optical basicity for La2O3 oxide is found to be 1.07, being much larger compared with typical glass-forming oxides such as B2O3 (0.42) and SiO2 (0.48) but being similar to heavy element oxides such as TeO2 (0.93). The Yamashita and Kurosawa’s interaction parameter of La2O3 is 0.03 Å−3, indicating that La2O3 is classified as a normal ionic (basic) oxide, i.e., an ionic bonding character in the La3+–O bond is proposed. Close correlations are confirmed among optical basicity, interaction parameter, and oxygen 1s binding energy in x-ray photoelectron (XPS) spectra for La2O3–P2O5 and other La2O3-containing glasses. It is found from XPS and Raman spectra that La3+ ions in La2O3–P2O5 glasses act as network modifiers, supporting an ionic bonding character in the La3+–O bond. The parameters related to electronic polarizability in La2O3 determined in the present study would be useful for the design of rare-earth containing optical functional glasses.

Compositional Parameters of Segmented Poly(ester-siloxane)-Urethanes and Limitations in the Study of Dilute Solution Properties

This article discusses the syntheses, compositional parameters, and behavior of poly(ester-siloxane)-urethanes in dilute solution by GPC, refractometry, light scattering, and viscosity, as induced by chemical structure. From the theoretical point of view and experimental data, modified composition of the soft and hard segments yields different chain dimensions. Specific refractive index increments of these segmented copolymers in N, N-dimethylformamide and dimethylsulfoxide have been determined by the Lorenz-Lorentz equation and the corresponding group contributions to the molar refraction and to the molar volume. The results are in good agreement with the experimental values. It was observed that the light scattering studies are affected by the existence of the multicomponent systems, the compositional heterogeneity, and the possibility of structural formation of chains in solution, which cannot be destroyed by filtration.

Relationship between composition, density and refractive index for heavy metal fluoride glasses

The density and the refractive index for various compositions of heavy metal fluoride (HMF) glasses, used to make low-loss optical wave-guides, have been measured by standard archimedes method and by using as Pulfrich refractometer respectively. The density as a function of composition is calculated considering the effective volume of the ions contained in the glass to be invariant. The refractive index as a function of composition is also calculated, based on the Lorenz-Lorentz equation, by computing the electronic polarizability of HMF glasses. All calculated results are in good agreement with the observed data.

Interferometric Determination of Orientation and Some Optical Parameters of annealed Polyester Fibres

Multiple-beam Fizeau fringes in transmission have been applied to annealed PET fibres, to determine the refractive indices of their skin and core layers for plane polarized monochromatic light at λ =546.1 nm, vibrating parallel and perpendicular to the fibre axis. We obtained the optical orientation parameters by applying the equations used by Hermans and Ward. Some structural parameters such as electric polarizability were determined. The density of the samples studied was measured by a system based on the theory of vibrating strings. The density and optical results were used to calculate the degree of crystallinity, the mean square density fluctuation, the form birefringence, the number of monomeric units per unit volume, the harmonic mean polarizability of the dielectric, and the harmonic mean specific refractive index. The generalized Lorentz-Lorenz equation given by de Vries was used to determine the structural parameters of annealed PET fibres. Comparisons between the experimental results and those obtained by using the Lorentz-Lorenz and Hermans equations are given. Refractive index profiles are also given. The results show the new reorientation and layer changes accompanying annealing under different conditions. Illustrations are given of multiple-beam microinterferograms in transmission.

Refractive index and optical dispersion of rare earth oxides using a small-prism technique

Crystals of cubic Sc2O3, Lu2O3, Yb2O3 and Dy2O3 were grown as single-crystal fibres of dimensions of ~0.5?mm?15?mm using the laser-heated pedestal growth technique. Refractive indices of prisms prepared from these fibres were measured at wavelengths of 435.8-643.8?nm and were used to calculate n at ? = 589.3?nm (nD) and at ? = ? (n?) using the one-term Sellmeier equation 1/(n2-1) = -A/?2 + B. In addition, using the dispersion of two refractive indices of a larger crystal of monoclinic Gd2O3:Nd, we have estimated mean values of n? and nD. Total polarizabilities, ?total, were calculated from n? and the Lorenz-Lorentz equation. Refractive indices, nD, and dispersion values, A, were, respectively, 1.9943 and 66 for Sc2O3, 1.9349 and 66 for Lu2O3, 1.9470 and 68 for Yb2O3, 1.9757 and 73 for Dy2O3 and 2.086 and 62?10-16?m2 for Gd2O3:Nd. These data were used to estimate the refractive indices and total polarizabilities of cubic Tm2O3, Er2O3, Ho2O3, Tb2O3, Gd2O3 and Eu2O3, monoclinic Sm2O3 and hexagonal Nd2O3 from plots of the type ?total = a (atomic number) + ?b.

Intrinsic Birefringence of γ-Form Crystal of Nylon 6: Application to Orientation Development in High-Speed Spun Fibers of Nylon 6

The intrinsic birefringences of the α- and the γ-form crystals of nylon 6 were calculated from the atomic coordinates and the bond polarizabilities using the Lorentz-Lorenz equation. The intrinsic birefringence of the γ-form crystal was found to be significantly smaller than that of the α-form crystal. Those values were applied to the evaluation of the orientation function of the amorphous phase of the nylon 6 fibers produced by the high-speed spinning process. The molecular orientation in the amorphous phase increased to the maximum point and then decreased with the spinning speed. These results suggested that an inhomogeneous structure in the fiber was formed for the higher take-up speed.

Intrinsic Birefringence of γ-Form Crystal of Nylon 6: Application to Orientation Development in High-Speed Spun Fibers of Nylon 6

The intrinsic birefringences of the α- and the γ-form crystals of nylon 6 were calculated from the atomic coordinates and the bond polarizabilities using the Lorentz-Lorenz equation. The intrinsic birefringence of the γ-form crystal was found to be significantly smaller than that of the α-form crystal. Those values were applied to the evaluation of the orientation function of the amorphous phase of the nylon 6 fibers produced by the high-speed spinning process. The molecular orientation in the amorphous phase increased to the maximum point and then decreased with the spinning speed. These results suggested that an inhomogeneous structure in the fiber was formed for the higher take-up speed.

Opto-thermal properties of fibers XVIII?Skin-core structures variations in nylon 6 fibers due to different annealing conditions

Nylon 6 fibers (Amilan) were annealed at constant temperature 140 ± 1°C for different time durations (1–10 h). Refractive indices have been previously measured interferometerically. Two independent techniques were used to study the optical anisotropy and density in these fibers. The first was the application of a multiple-beam to determine the skin and core “mean” refractive indices and birefringence of the samples. The technique used multiple-beam Fizeau fringes in transmission. The second technique was an acoustic method for measuring the density of the investigated fibers. The optical results were used to calculate the optical orientation factors for skin and core. The values of (Δα/3α0), which depend upon the molecular structure of the polymer, remain constant and in agreement with the previous published data. The density results were used to calculate the degree of crystallinity of nylon 6 fibers. In addition, the results were used to calculate the mean square density fluctuation, the harmonic mean polarizability of the dielectric, specific refractivity of the isotropic dielectric and the virtual refractive index. Also, the number of monomer units per unit volume, and n1 and n2, which are the refractive indices of fully oriented fiber, were calculated and found to be (1.606 and 1.534). Hermans optical orientation functions have been compared with the generalized Lorentz-Lorenz equation given by de Vries. Microinterferograms and curves are given for illustration. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 3349–3360, 2001

SPECIFIC REFRACTIVE INDEX INCREMENTS OF POLYURETHANE/POLYDIMETHYLSILOXANE SEGMENTED COPOLYMERS

New polydimethylsiloxane-containing segmented block copolyure-thanes were obtained from aromatic or aliphatic diisocyanates, 1,4-butanediol and poly(ethylene glycol)adipate using a multistep polyaddition process. Specific refractive index increments of these segmented copolymers in N,N-dimethyl-formamide have been determined by the Lorenz-Lorentz equation and the corresponding group contributions to the molar refraction and to the molar volume. The results are in good agreement with the experimental values. Also, from the dependence between the specific refractive index increments and the weight fraction of 4,4′-methylene diphenylene diisocyanate units, w d , the ν0 and dν/dw d coefficients have been evaluated and the results are situated between the values reported in literature.

Coexistence curve of HFC-134a and thermal conductivity of HFC-245fa

The present paper deals with the experimental results for the refractive index of the saturated vapor and liquid of HFC-134a and the thermal conductivity of HFC-245fa in the liquid phase.The coexistence curve of the refractive index of HFC-134a up to the critical temperature has been measured. The density coexistence curve of HFC-134a in the critical region is calculated from the refractive index data by using the Lorentz–Lorenz equation. Assuming as the critical density ρC=511.0kgm−3, the critical temperature TC=374.107±0.020K and the critical index β=0.348±0.001 are obtained. The calculated density coexistence curve proved to be reasonable from the agreement with the directly measured values of density and the equation of state recently reported.The thermal conductivity of HFC-245fa in the liquid phase has been measured by using a transient hot-wire method. The nominal diameter of the long and short wires is 20μm and the effective length of them is around 60mm. Measurements are carried out in the range from 253 to 315K and up to 15MPa. The results for the thermal conductivity are correlated by the equation of temperature and pressure. The present results of HFC-245fa are compared with the predicted values of HFC-245fa as well as the experimental values of some propane series refrigerants.

Shrinkage and mechanical structural variations in cold drawn perlon fibers

In the present work nylon 6 (perlon) fibers were stretched at room temperature. The Pluta polarizing interference microscope with a micro-strain device was used for measuring some optical and mechanical parameters of the fibers. The values of the fully oriented refractive indices n 1 and n 2 were found to be 1.630 and 1.561. The generalized Lorentz–Lorenz equation given by de Vries was used to determine structural parameters of the fibers. Comparison between Herman's optical orientation function formula and the corrected formula by de Vries are given. The changes in the molecular orientation were evaluated to obtain the values of orientation functions f 2( θ), f 4( θ), f 6( θ), < P 2 (cos θ)> and < P 4 (cos θ)>. In addition, the shrinkage stress was found to increase with increase of the draw ratio. The dielectric constant, the dielectric susceptibility and the number of moles of network chains per unit volume were also calculated. Microinterferograms and curves are given for illustration.

Quasi-elastic Raman scattering and free volume in isotropic pressure-densified atactic poly(methyl methacrylate) glasses

We have made a series of isotropic pressure-densified atactic poly(methyl methacrylate) (PMMA) glasses with densities ranging from 1.1823 g/cm3 to 1.1963 g/cm3, in order to investigate how the glassy dynamics, measured by Raman scattering in the frequency range of 0.1–10 THz, depends on the thermomechanical history of the glasses. In particular, we investigate whether there is a correlation between the strength of the fast relaxation dynamics and the free-volume characteristics, such as the average free-volume size and the free-volume fraction. The fast relaxation strength is deduced from the quasielastic light scattering (QES) intensity; the free-volume size is measured with positron annihilation lifetime spectroscopy (PALS); and the free-volume fraction is determined from pressure–volume–temperature (PVT) data and the Simha–Somcynsky equation-of-state (EOS) theory. Our temperature-dependent Raman and PALS measurements show that both the QES intensity and the ortho-positronium (o-Ps) lifetime increase smoothly with the temperature. On the other hand, the relaxation strength of the densified glasses at room temperature is, within experimental error, independent of the density, whereas both the o-Ps lifetime from PALS and the free volume fraction from the PVT data decrease significantly with pressure densification. We therefore conclude that the fast relaxation intensity cannot be explained on the basis of free-volume quantities, contrary to a recently suggested correlation between the QES intensity and the free volume [V. N. Novikov et al., J. Chem. Phys. 107, 1057 (1997)]. On the other hand, the observed behavior is consistent with another recently suggested model [V. N. Novikov, Phys. Rev. B 58, 8367 (1998)] which attributes the fast relaxations to vibration anharmonicity. Moreover, we show that the measured increase in the refractive index of the pressure-densified glasses fits the Lorentz–Lorenz equation and compares well to predictions of the relative change in refractive index with formation pressure from our own as well as published PVT data.

Opto-thermal properties of fibers: 8. Optical and mechanical parameters variations on cold drawn thermally treated nylon 6-6 fibers

Refractive indices and birefringence changes with strain produced by different stresses in annealed and unannealed nylon 6-6 fibers (Promilan, Toray Industries Inc. Japan) were measured interferometrically. Calculations were carried out to determine the strain optical coefficient, the orientation factor, the orientation angle, the number of molecules per unit volume, the isotropic refractive index and the virtual refractive index. The effect of the draw ratio on the refractive index profile was studied. The generalized Lorentz–Lorenz equation given by de Vries has been used to compare the results obtained by Hermans' optical orientation function.

Electric potential energy of the incident light and the Hamiltonian of the induced oscillators in non-absorbing isotropic dielectrics

By considering an energy balance between the electric potential energy of the incident light and the Hamiltonian of the induced oscillators in a non-absorbing isotropic medium, the Newton–Drude equation, the Sellmeier dispersion formula, and the wavelength-dependent mean polarizability were derived. The Newton–Drude formula and the Lorentz–Lorenz equation were used to calculate the density-dependent mean polarizability of the densified silica glasses. The evaluated mean polarizability was compared with the band shifts in the UV- and IR-spectra with the density of glasses, and the validity of the Newton–Drude formula was discussed.

A Hybrid Film Thickness Evaluation Scheme Based on Multi-Channel Interferometry and Contact Mechanics

A hybrid evaluation scheme for EHL film thickness determination is proposed and discussed. The film thickness profile in the contact region is measured using interferograms produced with a novel multi channel interferometry method. Since the refractive index distribution in the contact is pressure-dependent, and the initial film thickness profile will be evaluated assuming atmospheric pressure, a refractive index correction scheme is employed. The correction scheme is based on the Lorenz-Lorentz equation and a pressure-density relation together with a numerical pressure solver taking the initial film thickness measurement as input. The film thickness determination scheme is applied to an interesting phenomenon that can be observed at sliding conditions when the discrepancy occurred in the form of a deep and large dimple in the conjunction. Such a dimple appeared instead of the conventional plateau. The phenomenon was studied under different degrees of sliding. The detailed film thickness maps and pressure distributions for highly loaded EHL conjunctions at high degrees of sliding are produced using a hybrid evaluation scheme. The results are analyzed and discussed. [S0742-4787(00)00301-5]