Lorentz-Lorenz Equation Research Articles

Conductometric investigation of ion–solvent interactions of an ionic liquid {[emim]CH3SO3} in pure n-alkanols

Qualitative and quantitative analyses of molecular interaction prevailing in ionic liquid and organic solvent media, probed by electrical conductance have been reported. Conductometric studies of an ionic liquid {1-ethyl-3-methylimidazolium methanesulfonate [emim]CH3SO3} in n-propanol, n-butanol, and n-pentanol at 298.15 K reveal high molecular interaction contributed mainly by ion–dipole interaction. Association constants (KA), limiting molar conductance (Λ0), and the distance of closest approach of ions (R) for ion-pair formation have been analyzed using Fuoss conductance equation (1978). The molar conductivities observed were explained by the formation of ion-pairs (M++X¯→MX). The Walden product is obtained and discussed. Molar refraction (RM) has been calculated using the Lorentz–Lorenz equation. The results show more association of the ions in n-pentanol than in n-propanol and results have been interpreted in terms of ion–solvent and solvent–solvent interaction. The extent of interaction has also been expressed in terms of the association constant (KA) and shows the ion–dipole interaction to be a function of viscosity.

The density, refractive index, and thermodynamic behaviour of binary mixtures of 1,3-Diethenyl-1,1,3,3-tetramethyldisiloxane with aromatic hydrocarbons

Density and refractive index were measured for the binary mixtures composed of 1,3-Diethenyl-1,1,3,3-tetramethyldisiloxane and aromatic hydrocarbons (methoxybenzene, ethylbenzene, chlorobenzene, fluorobenzene and nitrobenzene) at five temperatures (283.15, 288.15, 293.15, 298.15, and 303.15)K and atmospheric pressure by a DMA4500&RXA170 combined system. Excess molar volumes were calculated and correlated by the Legendre polynomials. The isobaric coefficients of thermal expansion and excess isobaric coefficients of thermal expansion of five binary solutions were estimated from temperature dependence of densities. Values of partial excess volumes at infinite dilution and excess refraction indices for these five binary systems at different temperature were calculated from the adjustable parameters of the Legendre polynomials. The molar refractions were calculated from the Lorentz–Lorenz equation. Factors affected these excess quantities were discussed.

Acoustic behaviour and equation of state of amorphous ethylene–vinyl acetate copolymer studied by means of high-pressure Brillouin scattering spectroscopy

The determination of the equation of state (EOS) of amorphous materials is very important for fundamental understanding of the glass transition and applications as well. Simultaneous observation of both longitudinal and transverse acoustic modes by Brillouin scattering spectroscopy has been one of the major methods to obtain EOS of amorphous materials. However, the transverse acoustic mode is hardly seen from some of the amorphous polymers, which makes it difficult to derive EOS. The temperature and pressure dependences of the acoustic properties of amorphous ethylene–vinyl acetate (EVA) copolymer were measured by using high-pressure Brillouin scattering spectroscopy. The temperature variation induced large changes in the frequency shift and linewidth of the longitudinal acoustic mode due to strong coupling between the structural relaxation process and the propagating density fluctuations. The residual linewidth in the glassy state was attributed to the remnant intramolecular motions of EVA, the activation energy of which was estimated to be ∼3.30 ± 0.27 kcal/mol. The pressure–density relationship of EVA could be obtained for the first time by measuring the refractive index and using the Lorentz–Lorenz equation. The density and the refractive index exhibited monotonic increase up to approximately 12 GPa. The strong reduction of the acoustic damping at low pressures below ∼3 GPa was attributed to the collapsing free volume in EVA. The present study clearly shows that measuring the refractive index by high-pressure Brillouin spectroscopy may be an alternative method to get the EOS of polymeric materials whose transverse acoustic mode is too weak to be observed.

High‐Temperature Elastic Moduli of Flux‐Grown α‐GeO2 Single Crystal

From high-precision Brillouin spectroscopy measurements, six elastic constants (C11, C33, C44, C66, C12, and C14) of a flux-grown GeO2 single crystal with the α-quartz-like structure are obtained in the 298-1273 K temperature range. High-temperature powder X-ray diffraction data is collected to determine the temperature dependence of the lattice parameters and the volume thermal expansion coefficients. The temperature dependence of the mass density, ρ, is evaluated and used to estimate the thermal dependence of its refractive indices (ordinary and extraordinary), according to the Lorentz-Lorenz equation. The extraction of the ambient piezoelectric stress contribution, e11, from the C'11-C11 difference gives, for the piezoelectric strain coefficient d11 , a value of 5.7(2) pC N(-1), which is more than twice that of α-quartz. As the quartz structure of α-GeO2 remains stable until melting, piezoelectric activity is observed until 1273 K.

Physico-chemical study of lithium perchlorate in alkanols (C3–C5) with the manifestation of solvation consequences

Electrical conductances of lithium perchlorate have been measured in pure n-Propanol, n-Butanol and n-Pentanol at 298.15K. Association constants (KA), limiting molar conductances (Λ0), and co-sphere diameter (R) for ion-pair formation have been analysed using Fuoss conductance equation (1978). Apparent molar volume (ϕV), viscosity B-coefficient and molar refraction (RM) have been determined from measurement of density (ρ), viscosity (η), refractive index (nD) and speed of sound (u) respectively. The limiting apparent molar volume (ϕV0) and experimental slope (SV⁎) obtained from the Masson equation have been interpreted in terms of ion–solvent and ion–ion interactions respectively. The derived parameters A and B obtained from Jones–Dole equation represent ion–ion and ion–solvent interactions respectively. Molar refraction (RM) has also been calculated using the Lorentz–Lorenz equation. The adiabatic compressibility (βS) and limiting apparent molar adiabatic compressibility (ϕK0) have been evaluated using the u values.

Pressure dependence of acoustic behaviors and refractive index of amorphous Kel F-800 copolymer studied by Brillouin spectroscopy

The pressure dependences of the longitudinal sound velocity and the refractive index of amorphous Kel F-800 copolymer were investigated for pressures up to 13 GPa using high-pressure Brillouin spectroscopy combined with a diamond-anvil-cell technique. The sound velocity increased rapidly with increasing pressure at pressures below ∼2 GPa, whereas it showed a mild change at higher pressure values. This was attributed to substantial collapse of effective free volume in this amorphous material. The refractive index could be measured by comparing the Brillouin spectra measured from backward and forward, symmetric scattering geometries. The pressure–density relationship could be obtained by using Lorentz–Lorenz equation based on an assumption of constant polarizability, which was consistent with that reported by previous study.

Hydration numbers of ions in aqueous solutions of KOH, KCl, KI, and KIO3 according to refractometric data

Ion hydration in aqueous solutions of KOH, KCl, KI, and KIO3 was studied by refractometry. The sum of the hydration numbers of the potassium ion and each anion in these compounds and the hydration numbers of OH−, Cl−, I−, and IO3− anions were determined by the Lorentz-Lorenz equation at different salt concentrations. The model suggests that the polarizability of the hydrated ion is proportional to the cube of the ion radius and the volume of the hydrated ion equals the sum of the nonhydated ion and hydration shell volumes. The hydration numbers of the anions calculated by the proposed procedure increase with their radii in the sequence: OH−, Cl−, I−, and IO3−.

Prediction of refractive index and density of deep eutectic solvents using atomic contributions

Deep eutectic solvents (DESs) are considered as potential alternatives for ionic liquids (ILs). The evaluation of DESs as new generation of solvents for various practical application requires enough knowledge about some main physical, chemical, and thermodynamic properties. In this study, due to lack of data for DESs’ refractive indices, the refractive indices of twenty four DESs based on ammonium and phosphonium salts were measured and predicted using atomic contribution method. The atomic contributions data for molar refraction proposed by Wildman and Crippen which was developed for neutral compounds were employed to calculate the molar refractions of DESs. Subsequently, the refractive indices of DESs were predicted using Lorentz–Lorenz equation through the calculated DESs’ molar refractions and experimental DESs’ densities values. The absolute relative percentage error (ARPE) value of 0.56% and a regression coefficient (R2) value of 0.9822 both confirmed the highly possible application of the proposed method for predicting the refractive indices. In addition, the effect of DESs’ composition on refractive index of DESs was investigated and it was found that the refractive index of the DESs lies between that of the salt and HBD. Moreover, the densities of DESs were also predicted using Lorentz–Lorenz equation employing the calculated molar refraction and values of experimental DESs’ refractive indices. The ARPE of 1.43% shows that this method for prediction of densities of the synthesized DESs is applicable as well.

Probing solute–solvent interactions of some bio-active solutes in aqueous barium nitrate solution on the basis of physicochemical contrivances

Apparent molar volume (ϕV), molar refraction (R), viscosity B-coefficient and adiabatic compressibility (ϕK) of some bio-active solutes such as glycine, l-alanine, and l-valine have been measured in 0.01, 0.03, 0.05moldm−3 aqueous barium nitrate solutions at 298.15K. Masson equation was employed for the limiting apparent molar volumes (ϕV0), experimental slopes (SV*) to interprete the solute–solvent and solute–solute interactions respectively. Molar refractions (R) have been calculated using the Lorentz–Lorenz equation. Jones–Dole equation was used to derive parameters A and B to interprete the interactions. Limiting apparent molar adiabatic compressibilities (ϕK0) at infinite dilution were examined from the sound speed values.

Study of solvation consequences of α-amino acids in aqueous ionic liquid solution probed by physicochemical approach

The apparent molar volume (ϕV), viscosity B-coefficient, molal refraction (R) and adiabatic compressibility (ϕK) of glycine, l-alanine, and l-valine have been studied in 0.001, 0.003, 0.005moldm−3 aqueous tetrabutylphosphonium Tetrafluoroborate (Bu4PBF4) solutions at 298.15K from the values of density (ρ), viscosity (η), refractive index (nD) and speed of sound (u) respectively. The limiting apparent molar volumes (ϕV0), experimental slopes (SV*) are obtained from the Masson equation and have been interpreted in terms of solute–solvent and solute–solute interactions respectively. Jones–Dole equation were employed to analyze the viscosity data and the interpretation of the derived parameters A and B have also been carried out in terms of solute-solute and solute–solvent interactions in the solutions respectively. Molal refractions (R) have been determined with the help of Lorentz–Lorenz equation. Limiting apparent molar adiabatic compressibilities (ϕK0) of three amino acids at infinite dilution were evaluated and discussed.

Study of Solvation Behavior of Some Biologically Active Compounds in Aqueous Barium Chloride Solution

The density (ρ), viscosity (η), refractive index (nD), and speed of sound (u) of glycine, l-alanine, and l-valine have been determined in different mass fractions (w1 = 0.01, 0.03, 0.05) aqueous barium chloride solutions at 298.15 K. The limiting apparent molar volumes (ϕV0), experimental slopes (SV*) have been found out from the Masson equation. A and B coefficients have been obtained from the Jones–Dole equation. The Lorentz–Lorenz equation has been employed to measure molar refractions (R). Limiting apparent molar adiabatic compressibilities (ϕK0) of the studied amino acids at infinite dilution have also been measured. These derived parameters have been used to explore solute–solute and solute–solvent interactions in the solutions.

Femtosecond laser induced structural changes in fluorozirconate glass

Fluorozirconate glasses, such as ZBLAN (ZrF4-BaF2-LaF3-AlF3-NaF), have a high infrared transparency and large rare-earth solubility, which makes them an attractive platform for highly efficient and compact mid-IR waveguide lasers. We investigate the structural changes within the glass network induced by high repetition rate femtosecond laser pulses and reveal the origin of the observed decrease in refractive index by using Raman microscopy. The high repetition rate pulse train causes local melting followed by rapid quenching of the glass network. This results in breaking of bridging bonds between neighboring zirconium fluoride polyhedra and as the glass resolidifies, a larger fraction of single bridging fluorine bonds relative to double bridging links are formed in comparison to the pristine glass. The distance between adjacent zirconium cations is larger for single bridging than double bridging links and consequently an expansion of the glass network occurs. The rarified glass network can be related to the experimentally observed decrease in refractive index via the Lorentz-Lorenz equation.

Refractive index and optical dispersion of In2O3, InBO3 and gahnite

Refractive indices of In2O3, In2−xSnxO3, InBO3 and 2 different gahnite crystals (Zn0.95Fe0.05Al2O4 and Zn0.91Mg0.04Mn0.03Fe0.03Al1.99Fe0.01O4) were measured at wavelengths of 435.8–643.8nm and were used to calculate n (nD) at λ=589.3nm and (n∞) at λ=∞ with the one-term Sellmeier equation 1/(n2−1)=−A/λ2+B. Total polarizabilities, αtotal, were calculated from n∞ and the Lorenz–Lorentz equation. Refractive indices, nD and dispersion values, A, are, respectively, 2.093 and 133×10−16m2 for In2O3; 2.0755 and 138×10−16m2 for In2−xSnxO3; 1.7995 and 56×10−16m2 for Zn0.95Fe0.05Al2O4; 1.7940 and 57×10−16m2 for Zn0.91Mg0.04Mn0.03Fe0.03Al1.99Fe0.01O4 and no=1.8782 and ne=1.7756 and 〈63〉×10−16m2 for InBO3. The lack of consistency of the polarizabilities of Zn2+ in ZnO and In3+ in In2O3 with the Zn2+ and In3+ polarizabilities in other Zn- and In-containing compounds is correlated with structural strain and very high dispersion of ZnO and In2O3.

Control of Refractive Index of Fluorinated Polyimide by Proton Beam Irradiation

To clarify the feasibility of controlling the refractive index of a polymer by proton beam irradiation, we irradiated 1.0 MeV protons to a fluorinated polyimide film. Before and after the proton irradiation at a fluence between 1×1014 and 7×1016 cm-2, the film surface was scanned by a profilometer. It was found that the depth of a dent, which increases with fluence, was induced by the irradiation. The refractive index of the ion-irradiated region was calculated using the Lorentz–Lorenz equation, substituting the depth of the dent and the projected range of the protons. When the fluorinated polyimide was irradiated at a fluence of 7×1016 cm-2, the refractive index increased by about 3.3%, which agrees with the increment in refractive index measured by spectroscopic ellipsometry. The increment in refractive index (0.21%) induced by the irradiation of protons at the fluence of 1×1015 cm-2 is comparable to the value (0.35%) observed when protons were irradiated to SiO2 glass at a similar fluence. Therefore, it is reasonable to assume that the ion irradiation to a polymer can be a good method for fabricating a high-performance polymer-based optical waveguide.

Densities, speeds of sound, and refractive indices for binary mixtures of 1-butyl-3-methylimidazolium methyl sulphate ionic liquid with alcohols at T = (298.15, 303.15, 308.15, and 313.15) K

Experimental densities, speeds of sound, and refractive indices of the binary mixtures {1-butyl-3-methylimidazolium methylsulphate ([BMIM]+[MeSO4]−)+methanol, or 1-propanol, or 2-propanol, or 1-butanol} were measured over the whole range of composition at T=(298.15, 303.15, 308.15, and 313.15)K. From the experimental data, excess molar volumes, excess isentropic compressibilities, deviation in refractive indices and molar refractions were calculated. The excess molar volumes, change in isentropic compressibilities, and deviation in refractive indices were fitted by the Redlich–Kister smoothing polynomial. The Lorentz–Lorenz equation was applied to correlate the volumetric properties and predict the density or the refractive index of the binary mixtures. Results for these quantities have been discussed in terms of intermolecular interactions between the components of the mixtures. For all the systems studied, the excess molar volume and excess isentropic compressibility are negative, while the change in refractive index on mixing is always positive over the entire composition range and at all temperatures.

Effect of temperature and composition on the density, refractive index, and excess quantities of binary mixtures of 2,4,6,8-tetramethyl-2,4,6,8-tetraethenylcyclotetrasiloxane with aromatic hydrocarbons

Density and refractive index were determined for the binary mixtures containing 2,4,6,8-tetramethyl-2,4,6,8-tetraethenylcyclotetrasiloxane (D4Vi) and aromatic hydrocarbons (ethylbenzene, o-xylene, m-xylene, and p-xylene) at five temperatures (288.15, 298.15, 308.15, 318.15, and 328.15)K and atmospheric pressure by a DMA4500&RXA170 combined system. The density and refractive index correlations for these systems were tested by an empirical second order polynomial and by the Lorentz–Lorenz equation. Excess molar volumes were calculated and correlated by the Redlich–Kister equation and the Legendre polynomials. The values of the volume expansivity (coefficient of thermal expansion) of pure chemicals and four binary solutions were estimated from temperature dependence of densities. Values of partial excess volumes at infinite dilution for these four binary systems at different temperatures were calculated either from the adjustable parameters of Redlich–Kister smoothing equation or the Legendre polynomials. The deviations in refractive index were calculated and correlated by the Redlich–Kister polynomial expansions. The molar refractions were calculated from the Lorentz–Lorenz equation. The deviations in molar refractions were calculated and correlated by the Redlich–Kister polynomial expansions. Factors affected these excess quantities were discussed. The results obtained indicate that the excess molar volumes, the deviations in refractive index and the deviations in molar reactions at each temperature are negative. The system {D4Vi(1)+o-xylene(2)} exhibits the maximum negative deviations from ideality among these four systems, which is the result of multiple factors such as the partial interstitial accommodation effect, the steric hindrance, the size of molecule and the instantaneous dipole-induced dipole interactions.

Modulation of Polymer Refractive Indices with Diamond Nanoparticles for Metal-Free Multilayer Film Mirrors

Modulation of the refractive index of a polymer was achieved by combining it with diamond nanoparticles (NDs). The increase in the refractive index was controlled by the amount of NDs added, according to the Lorentz-Lorenz equation. The refractive index of poly(vinyl alcohol) (PVA), which was used as the base polymer, increased from 1.52 to 1.88. A multilayer film consisting of alternating layers of ND-PVA composite and poly(methyl methacrylate) exhibited ca. 80% reflectance with 10 bilayers.

Molecular Orientation in Stable Glasses of Indomethacin.

Spectroscopic ellipsometry has been used to measure the properties of indomethacin prepared by physical vapor deposition at Tsubstrate/Tg = 0.78, 0.84, and 0.90. The as-deposited glasses exhibited high kinetic stability and had densities 0.8-1.2% higher than the ordinary glass prepared by cooling the liquid at 1 K/min. Deposition at the higher temperatures yielded glasses with positive birefringence (up to Δn = 0.028), while the lowest-temperature sample was negatively birefringent (Δn = -0.015). These results indicate that substrate temperature can be used to manipulate molecular orientation in high-density and high-stability glasses. The data for the supercooled liquid and the ordinary glass of indomethacin are reasonably consistent with the Lorentz-Lorenz equation, but significant deviations are noted with the as-deposited materials.

The critical behavior of the refractive index near liquid-liquid critical points

The nature of the critical behavior in the refractive index n is revisited in the framework of the complete scaling formulation. A comparison is made with the critical behavior of n as derived from the Lorentz-Lorenz equation. Analogue anomalies to those predicted for the dielectric constant ε, namely, a leading |t|(2β) singularity in the coexistence-curve diameter in the two-phase region and a |t|(1-α) along the critical isopleth in the one phase region, are expected in both cases. However, significant differences as regards the amplitudes of both singularities are obtained from the two approaches. Analysis of some literature data along coexistence in the two-phase region and along the critical isopleth in the one-phase region provide evidence of an intrinsic effect, independent of the density, in the critical anomalies of n. This effect is governed by the shift of the critical temperature with an electric field, which is supposed to take smaller values at optical frequencies than at low frequencies in the Hz to MHz range.

Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa

The refractive index of water is precisely determined in the visible light range as a function of the pressure until 250 MPa by means of a new measurement device that uses a special pipe tee included in an interferometer set. This technique allows revisiting the Bradley-Tait and Sellmeier equations to make them dependent on the wavelength and the pressure, respectively. The Bradley-Tait equation for the pressure dependence of the water refractive index is completed by a wavelength-dependent factor. Also, in the considered pressure and wavelength ranges, it is shown that the Sellmeier coefficients can be straightforwardly linked to the pressure, allowing the determination of the refractive index of water for either any wavelength or pressure. A new simple model allows the determination of the density of water as a function of the measured refractive index. Finally, the polarizability of water as function of pressure and wavelength is calculated by means of the Lorentz-Lorenz equation.