Relative permittivity pressure dependence

Equation (7.47) has to be differentiated with respect to pressure at constant temperature. This requires a knowledge of the pressure dependence of the relative permittivity at constant temperature. 

The pressure dependence of the relative permittivity has been determined for relatively few solvents only, although it is an important quantity in theoretical... 

Marcus, Y. and Hefter, G. T. On the pressure and electric field dependencies of the relative permittivity of liquids. J. Solution Chem. 1999, 28, 575-592. 

When carbon dioxide is heated beyond its critical point, with a critical temperature of tc = 31.0 °C, a critical pressure of pc = 7.38 MPa, and a critical density of Pc = 0.47 g cm , the gaseous and the liquid phase merge into a single supercritical phase (SC-CO2) with particular new physical properties very low surface tension, low viscosity, high diffusion rates, pressure-dependent adjustable density and solvation capability ( solvation power ), and miscibility with many reaction gases (H2, O2, etc.). It can dissolve solids and liquids. The relative permittivity of an sc-fluid varies linearly with density, e.g. for SC-CO2 at 40 °C, r = 1.4 1.6 on going from 108 to 300 bar. This... 

The thermophysical and thermodynamic properties of liquid water as well as its chemical properties, all depend on the temperature and the pressure. The thermophysical and thermodynamic properties include the density p, the molar volume V = M/p, the isothermal compressibility/ct = P (dp/d P)t = —V (dV/dP)T, the isobaric expansibility ap = —p dp/dT)p = V dV/dT)p, the saturation vapour pressure p, the molar enthalpy of vapourization Ayf7, the isobaric molar heat capacity Cp, the Hildebrand solubility parameter 3h = [(Ay// —RT)/ the surface tension y, the dynamic viscosity rj, the relative permittivity Sr, the refractive index (at the sodium D-line) and the self-diffusion coefficient T>. These are shown... 

Marcus Y (2012a) The standard partial molar volumes of ions in solution. Part 5. Ionic volumes in water at 125-200 °C. J. Phys. Chem. B 117 http //dx.doi/10.1021/jp212518t Marcus Y (2012b) Are ionic Stokes radii of any use J. Solution Chem in the press Marcus Y, Hefter G (1999) On the pressure and electric field dependencies of the relative permittivity of liquids. J Sol Chem 28 575-591 Marcus Y, Hefter G (2006) Ion pairing. Chem Rev 106 4585-4621... 

Figure 26 presents, as an example, the pressure dependence of the static permittivity and relaxation time for 8CB showing stepwise changes at the phase transitions. The measurement runs were started from a well-oriented nematic phase, and the smectic phase was reached by slowly increasing the pressure at T = constant or by decreasing the temperature at p = constant. However, the permittivity always dropped to relatively... 

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