Lorenz Equation

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 2829 Experts worldwide ranked by ideXlab platform

Donald R Paul - One of the best experts on this subject based on the ideXlab platform.

  • physical aging of thin glassy polymer films free volume interpretation
    Journal of Membrane Science, 2006
    Co-Authors: Yongjiang Huang, Xiaoyan Wang, Donald R Paul
    Abstract:

    Abstract Previous studies have documented the dramatic effects of film thickness, at least compared to the bulk state, and the more modest effects of aging temperature and polymer structure on physical aging of thin glassy polymer films. In this paper, these results are interpreted in terms of the free volume calculated from the refractive index, determined by ellipsometry, using the Lorentz–Lorenz Equation. The relative progress of aging towards the final equilibrium state was determined using this approach. The free volume data were fitted to the Struik model for the self-retarding volume contraction on aging to obtain the thickness and temperature dependent parameters. The gas permeability versus aging time is related to the free volume computed from the refractive index. The effect of prior history on the aging of thin glassy polymer films was briefly explored.

  • physical aging of thin glassy polymer films monitored by optical properties
    Macromolecules, 2006
    Co-Authors: Yongjiang Huang, Donald R Paul
    Abstract:

    The change in refractive index of thin films formed from three glassy polymers, polysulfone, a polyimide, and poly(2,6-dimethyl-1,4-phenylene oxide), measured by ellipsometry was used to track their physical aging. These thin films with thicknesses less than 1 μm were aged for up to 6000 h at 35 °C. A pronounced aging response via refractive index change, attributed to the densification of the glassy polymers, was observed for each film. The Lorentz−Lorenz Equation was used to relate changes in refractive index to densification, or volume relaxation, with aging time. The volumetric aging rate was shown to be dependent on the polymer structure and the film thickness. These thin films age at rates orders of magnitude more rapid than expected for bulk or thick films.

  • effect of temperature on physical aging of thin glassy polymer films
    Macromolecules, 2005
    Co-Authors: Yanbin Huang, Donald R Paul
    Abstract:

    The effect of temperature on the kinetics of physical aging of thin films formed from two amorphous glassy polymers, polysulfone based on bisphenol A and poly(2,6-dimethyl-1,4-phenylene oxide), was investigated by monitoring the changes in gas permeability and refractive index. Films with different thicknesses were subjected to isothermal aging at three temperatures, ranging from 35 to 55 °C, for a period of aging of more than 200 days. The rate of permeability loss and the rate of densification determined from the refractive index change by using the Lorentz−Lorenz Equation were found to increase with aging temperature. Similar qualitative trends of aging rate were noted by the two measurements. The combination of effects of aging temperature and film thickness on aging behavior were studied and compared with previous research.

Yongjiang Huang - One of the best experts on this subject based on the ideXlab platform.

  • physical aging of thin glassy polymer films free volume interpretation
    Journal of Membrane Science, 2006
    Co-Authors: Yongjiang Huang, Xiaoyan Wang, Donald R Paul
    Abstract:

    Abstract Previous studies have documented the dramatic effects of film thickness, at least compared to the bulk state, and the more modest effects of aging temperature and polymer structure on physical aging of thin glassy polymer films. In this paper, these results are interpreted in terms of the free volume calculated from the refractive index, determined by ellipsometry, using the Lorentz–Lorenz Equation. The relative progress of aging towards the final equilibrium state was determined using this approach. The free volume data were fitted to the Struik model for the self-retarding volume contraction on aging to obtain the thickness and temperature dependent parameters. The gas permeability versus aging time is related to the free volume computed from the refractive index. The effect of prior history on the aging of thin glassy polymer films was briefly explored.

  • physical aging of thin glassy polymer films monitored by optical properties
    Macromolecules, 2006
    Co-Authors: Yongjiang Huang, Donald R Paul
    Abstract:

    The change in refractive index of thin films formed from three glassy polymers, polysulfone, a polyimide, and poly(2,6-dimethyl-1,4-phenylene oxide), measured by ellipsometry was used to track their physical aging. These thin films with thicknesses less than 1 μm were aged for up to 6000 h at 35 °C. A pronounced aging response via refractive index change, attributed to the densification of the glassy polymers, was observed for each film. The Lorentz−Lorenz Equation was used to relate changes in refractive index to densification, or volume relaxation, with aging time. The volumetric aging rate was shown to be dependent on the polymer structure and the film thickness. These thin films age at rates orders of magnitude more rapid than expected for bulk or thick films.

Jose Carlos Cobos - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamics of mixtures with strong negative deviations from raoult s law xiv density permittivity refractive index and viscosity data for the methanol cyclohexylamine mixture at 293 15 303 15 k
    Thermochimica Acta, 2016
    Co-Authors: L F Sanz, J A Gonzalez, Isasias Garcia De La Fuente, Jose Carlos Cobos
    Abstract:

    Abstract Densities, kinematic viscosities, refractive indices and dielectric permittivities have been measured over the whole concentration range for the methanol + cyclohexylamine mixture at (293.15–303.15) K and 0.1 MPa. Dynamic viscosities, η , were obtained from densities and kinematic viscosities. This set of experimental values has been used to determine, excess functions for volume, V m E , refractive index, n D E , and permittivity, e r E , as well as deviations of η from the linear dependence on mole fraction, Δ η . Viscosity data were correlated by the following semi-empirical Equations: Grunberg-Nissan, Hind, Frenkel, Katti-Chaudhri, Teja-Ric e, McAllister, and Heric. The large and negative V m E values and the positive Δ η values obtained reveal the existence of strong interactions between unlike molecules in the studied mixture. Such interactions become weaker in cyclohexylamine systems when the size of the alcohol increases. Values of the molar refraction determined from the Lorentz-Lorenz Equation show that dispersive interactions become more relevant for the mixtures including the longer 1-alkanols. The positive e r E values indicate that dielectric polarization is strengthened along the mixing process. It has been ascribed to the mixture compounds form multimers of larger effective dipole moment than those which come from the alcohol dissociation upon mixing. The experimental data have been also used to calculate the Kirkwood’s correlation factor, g K , the orientational polarization, P m , and the corresponding excess magnitudes. From these calculations, it is concluded that the methanol mixture is more structured than those with longer 1-alkanols due to a strengthening of orientational polarization in comparison to that of the ideal solution.

  • Thermodynamics of mixtures with strong negative deviations from raoult’s law. XIV. density, permittivity, refractive index and viscosity data for the methanol + cyclohexylamine mixture at (293.15–303.15) K
    Thermochimica Acta, 2016
    Co-Authors: L F Sanz, J A Gonzalez, Isasias Garcia De La Fuente, Jose Carlos Cobos
    Abstract:

    Abstract Densities, kinematic viscosities, refractive indices and dielectric permittivities have been measured over the whole concentration range for the methanol + cyclohexylamine mixture at (293.15–303.15) K and 0.1 MPa. Dynamic viscosities, η , were obtained from densities and kinematic viscosities. This set of experimental values has been used to determine, excess functions for volume, V m E , refractive index, n D E , and permittivity, e r E , as well as deviations of η from the linear dependence on mole fraction, Δ η . Viscosity data were correlated by the following semi-empirical Equations: Grunberg-Nissan, Hind, Frenkel, Katti-Chaudhri, Teja-Ric e, McAllister, and Heric. The large and negative V m E values and the positive Δ η values obtained reveal the existence of strong interactions between unlike molecules in the studied mixture. Such interactions become weaker in cyclohexylamine systems when the size of the alcohol increases. Values of the molar refraction determined from the Lorentz-Lorenz Equation show that dispersive interactions become more relevant for the mixtures including the longer 1-alkanols. The positive e r E values indicate that dielectric polarization is strengthened along the mixing process. It has been ascribed to the mixture compounds form multimers of larger effective dipole moment than those which come from the alcohol dissociation upon mixing. The experimental data have been also used to calculate the Kirkwood’s correlation factor, g K , the orientational polarization, P m , and the corresponding excess magnitudes. From these calculations, it is concluded that the methanol mixture is more structured than those with longer 1-alkanols due to a strengthening of orientational polarization in comparison to that of the ideal solution.

L F Sanz - One of the best experts on this subject based on the ideXlab platform.

  • thermodynamics of mixtures with strong negative deviations from raoult s law xiv density permittivity refractive index and viscosity data for the methanol cyclohexylamine mixture at 293 15 303 15 k
    Thermochimica Acta, 2016
    Co-Authors: L F Sanz, J A Gonzalez, Isasias Garcia De La Fuente, Jose Carlos Cobos
    Abstract:

    Abstract Densities, kinematic viscosities, refractive indices and dielectric permittivities have been measured over the whole concentration range for the methanol + cyclohexylamine mixture at (293.15–303.15) K and 0.1 MPa. Dynamic viscosities, η , were obtained from densities and kinematic viscosities. This set of experimental values has been used to determine, excess functions for volume, V m E , refractive index, n D E , and permittivity, e r E , as well as deviations of η from the linear dependence on mole fraction, Δ η . Viscosity data were correlated by the following semi-empirical Equations: Grunberg-Nissan, Hind, Frenkel, Katti-Chaudhri, Teja-Ric e, McAllister, and Heric. The large and negative V m E values and the positive Δ η values obtained reveal the existence of strong interactions between unlike molecules in the studied mixture. Such interactions become weaker in cyclohexylamine systems when the size of the alcohol increases. Values of the molar refraction determined from the Lorentz-Lorenz Equation show that dispersive interactions become more relevant for the mixtures including the longer 1-alkanols. The positive e r E values indicate that dielectric polarization is strengthened along the mixing process. It has been ascribed to the mixture compounds form multimers of larger effective dipole moment than those which come from the alcohol dissociation upon mixing. The experimental data have been also used to calculate the Kirkwood’s correlation factor, g K , the orientational polarization, P m , and the corresponding excess magnitudes. From these calculations, it is concluded that the methanol mixture is more structured than those with longer 1-alkanols due to a strengthening of orientational polarization in comparison to that of the ideal solution.

  • Thermodynamics of mixtures with strong negative deviations from raoult’s law. XIV. density, permittivity, refractive index and viscosity data for the methanol + cyclohexylamine mixture at (293.15–303.15) K
    Thermochimica Acta, 2016
    Co-Authors: L F Sanz, J A Gonzalez, Isasias Garcia De La Fuente, Jose Carlos Cobos
    Abstract:

    Abstract Densities, kinematic viscosities, refractive indices and dielectric permittivities have been measured over the whole concentration range for the methanol + cyclohexylamine mixture at (293.15–303.15) K and 0.1 MPa. Dynamic viscosities, η , were obtained from densities and kinematic viscosities. This set of experimental values has been used to determine, excess functions for volume, V m E , refractive index, n D E , and permittivity, e r E , as well as deviations of η from the linear dependence on mole fraction, Δ η . Viscosity data were correlated by the following semi-empirical Equations: Grunberg-Nissan, Hind, Frenkel, Katti-Chaudhri, Teja-Ric e, McAllister, and Heric. The large and negative V m E values and the positive Δ η values obtained reveal the existence of strong interactions between unlike molecules in the studied mixture. Such interactions become weaker in cyclohexylamine systems when the size of the alcohol increases. Values of the molar refraction determined from the Lorentz-Lorenz Equation show that dispersive interactions become more relevant for the mixtures including the longer 1-alkanols. The positive e r E values indicate that dielectric polarization is strengthened along the mixing process. It has been ascribed to the mixture compounds form multimers of larger effective dipole moment than those which come from the alcohol dissociation upon mixing. The experimental data have been also used to calculate the Kirkwood’s correlation factor, g K , the orientational polarization, P m , and the corresponding excess magnitudes. From these calculations, it is concluded that the methanol mixture is more structured than those with longer 1-alkanols due to a strengthening of orientational polarization in comparison to that of the ideal solution.

Michel Aillerie - One of the best experts on this subject based on the ideXlab platform.

  • Water density and polarizability deduced from the refractive index determined by interferometric measurements up to 250 MPa
    Journal of Chemical Physics, 2012
    Co-Authors: Laurent Weiss, Abdel Tazibt, Albert Tidu, Michel Aillerie
    Abstract:

    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.