Permittivity of Liquids

Figure 30. Imaginary (a) and real (b) parts of the complex permittivity of liquid water H20 at 22.2°C. Ordinary water is represented by solid lines, heavy water is represented by dashed lines. To the left from vertical lines (for v < 20 cm 1). calculation is performed using approximation [17] modified as described in Appendix 3.2 in the rest region, it is performed using the data 51 given in Table XII.

A. di Matteo and A. Ferrarini, A molecular based continuum approach for the dielectric permittivity of liquids and liquid crystals, J. Chem. Phys., 117 (2002) 2397-2414. 

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. 

The extended simple point charge (SPC/E) model [59] is used. This model is known to give reasonably accurate values of static dielectric permittivity of liquid water at ambient conditions [60]. The MD simulations were performed for both H2O and D2O with the system size of 1024 particles at 220 K, 240 K, 267 K, 273 K, 300 K, and 355 K. The parallel molecular dynamics code for arbitrary molecular mixtures (DynaMix) is implemented by Lyubartsev and Laaksonen [61]. The simulations have been carried out on a Linux cluster built on the Tyan/Opteron 64 platform, which enables calculations of relatively long trajectories for a system of 1024 water molecules. The simulation run lengths depend on temperature and are in the range between 1 ns and 4 ns for the warmest and coldest simulation, respectively. As the initial condition was a cubic lattice, the equilibration time was chosen to be temperature dependent in the range from 200 ps at 355 Ktol ns at 200K. 

The permittivity of liquid water in the radiofrequency and microwave regions can be represented by the Debye equation (References 1 and 2) ... 

Fig. 3.8-1 The dielectric constant (relative permittivity) of liquid water as a function of temperature at its vapor pressure [8].

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... 

The permittivity of liquids at very high fields is given by the nonlinear dielectric effect ... 

Pressure influences the dielectric permittivity of liquid crystalline phases considerably. For some LCs that form antiparallel dimers, the observation of a small maximum in s(T) at 1 atm above the clearing temperature is well established. In recent high-pressure investigations a similar effect was found, that is, a maximum in e(p) at T = const in the isotropic phase in the neighbourhood of the NI transition. 

In this section we wish to consider all the possible contributions to the electric permittivity of liquid crystals, regardless of the time-scale of the observation. Conventionally this permittivity is the static dielectric constant (i.e. it measures the response of a system to a d.c. electric field) in practice experiments are usually conducted with low frequency a.c. fields to avoid conduction and space charge effects. For isotropic dipolar fluids of small molecules, the permittivity is effectively independent of frequency below 100 MHz, but for liquid crystals it may be necessary to go below 1 kHz to measure the static permittivity polymer liquid crystals can have relaxation processes at very low frequencies. 

As was pointed out in Sec. 1 of this chapter the symmetry of the phases will determine the number of independent components of the second rank electric permittivity furthermore the point group symmetry of the phase and the constituent molecules will fix the orientational order parameters that contribute to a microscopic expression for the permittivity. In order to complete the description of the low frequency or static electric permittivity of liquid crystals, it is necessary to consider the additional effects of chirality, and the translational order associated with smectic phases. 

A full theory of the frequency dependence of the electric permittivity of liquid crystals cannot yet be given. It is a formidable problem since it requires proper account to be taken of the influence of orientational order on molecular motion, as well as the effects of macroscopic dielectric anisotropy. The dielectric response of a rigid dipolar molecule rotating in an isotropic fluid can be described in terms of a single relaxation time or rotational diffusion constant. In a liquid crystal phase, the rotational motion is no... 

Liquid-crystalline molecules possess anisotropy of the electric polarizability, and nearly always a significant permanent dipole moment resulting from contributions from different bond moments, see Table 4.1. Therefore, the dielectric permittivity of liquid crystals is also a tensor quantity. Because of the assumed uniaxiality of the system under consideration, there are again only two principal elements of the dielectric permittivity tensor Szz=H and Bxx= yy= l- Subscripts II and 1 denote respectively the principal geometries of dielectric measurements, i.e. the probing electric field parallel and perpendicular to the director. 

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