Liquids, 266 permittivity

The task of statistical thermodynamics in describing the dielectric properties of a liquid is to develop a model for the liquid permittivity in terms of the dipole moment and polarizability of the component molecules. The usual approach has been to assume that the liquid molecule can be represented as a polarizable hard... 

The critical voltage Vc required for stable electrospraying can be estimated through a balance between the capfllary stress, of order y// , where/ lO -lO m is the principal curvature of the meniscus, of the same order as the radial capillary dimension, and the electric stress where is the liquid permittivity, V the applied voltage, and d the electrode separation ... 

Because of the presence of the lone pairs of electrons, the molecule has a dipole moment (and the liquid a high permittivity or dielectric constant). 

Liquids The rate of dissipation of charges in a liquid, assuming that its conductivity and dielectric permittivity are constant, can be expressed as ... 

The refractive index of a medium is the ratio of the speed of light in a vacuum to its speed in the medium, and is the square root of the relative permittivity of the medium at that frequency. When measured with visible light, the refractive index is related to the electronic polarizability of the medium. Solvents with high refractive indexes, such as aromatic solvents, should be capable of strong dispersion interactions. Unlike the other measures described here, the refractive index is a property of the pure liquid without the perturbation generated by the addition of a probe species. 

Table 1 shows various solvents (in alphabetical order) used in lithium batteries. The table contains the names of the solvents, their acronyms, the liquid range represented by melting (0m,°C) and boiling points (0m,°C), and the physical properties at 25 °C unless otherwise noted, permittivity s, viscosity rjl cP), and density >o/( kg L 1). The data are taken from Ref. [15], where the original literature is cited, or from more recent references given in the table. 

E7.6 Given the following permittivities (dielectric constants) for several liquid solvents at 293.15 K. 

The low permittivity of these liquids compared with water inhibits dissociation of the acids so that cement formation demands much more reactive basic oxides. Oxides and hydroxides that are capable of cement formation are ZnO, CuO, MgO, CaO, Ca(OH)2, BaO, CdO, HgO, PbO and BiaOj (Brauer, White Moshonas, 1958 Nielsen, 1963). In practice these are confined to two calcium hydroxide and special reactive forms of zinc oxide. 

An interface between two immiscible electrolyte solutions (ITIES) is formed between two liqnid solvents of a low mutual miscibility (typically, <1% by weight), each containing an electrolyte. One of these solvents is usually water and the other one is a polar organic solvent of a moderate or high relative dielectric constant (permittivity). The latter requirement is a condition for at least partial dissociation of dissolved electrolyte(s) into ions, which thus can ensure the electric conductivity of the liquid phase. A list of the solvents commonly used in electrochemical measurements at ITIES is given in Table 32.1. 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

With a liquid flowing across the plane of the material, as in a geotextile filter, the permeability perpendicular to the plane can be divided by the thickness, T, to obtain a new value, permittivity (see Figure 26.23). In crossplane flow, T is in the denominator for planar flow, it is in the numerator. Crossplane flow is expressed as... 

Hydrated ions are formed by introducing gaseous ions into aqueous solutions, i.e. the hydration of gaseous ions. Since liquid water is a polar solvent of large permittivity, hydration reduces the energy level of ions. We consider the hydration of gaseous ions at the standard state as shown in Eqn. 3-27 ... 

Paddison et al. performed high frequency (4 dielectric relaxation studies, in the Gig ertz range, of hydrated Nafion 117 for the purpose of understanding fundamental mechanisms, for example, water molecule rotation and other possible processes that are involved in charge transport. Pure, bulk, liquid water is known to exhibit a distinct dielectric relaxation in the range 10—100 GHz in the form of an e" versus /peak and a sharp drop in the real part of the dielectric permittivity at high / A network analyzer was used for data acquisition, and measurements were taken in reflection mode. 

In contrast to liquid water, a detailed mechanistic understanding of the physical and chemical processes occurring in the evolution of the radiation chemical track in hydrocarbons is not available except on the most empirical level. Stochastic diffusion-kinetic calculations for low permittivity media have been limited to simple studies of cation-electron recombination in aliphatic hydrocarbons employing idealized track structures [56-58], and simplistic deterministic calculations have been used to model the radical and excited state chemistry [102]. While these calculations have been able to reproduce measured free ion yields and end product yields, respectively, the lack of a detailed mechanistic model makes it very difficult... 

Liquid polyols are interesting among nonaqueous solvents because, like water and monoalcohols, they are hydrogen-bonded liquids with a high value of relative permittivity (Table 9.2.1), and therefore they are able to dissolve to some extent ionic inorganic compounds. Moreover, reactions can be carried out in such solvents under atmospheric pressure up to 250°C, i.e., at a temperature range higher than in water or monoalcohols such as methanol or ethanol. 

Physical properties of the solvent are used to describe polarity scales. These include both bulk properties, such as dielectric constant (relative permittivity), refractive index, latent heat of fusion, and vaporization, and molecular properties, such as dipole moment. A second set of polarity assessments has used measures of the chemical interactions between solvents and convenient reference solutes (see table 3.2). Polarity is a subjective phenomenon. (To a synthetic organic chemist, dichloromethane may be a polar solvent, whereas to an inorganic chemist, who is used to water, liquid ammonia, and concentrated sulfuric acid, dichloromethane has low polarity.)... 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

That liquid water possesses a high relative permittivity which is associated with its property as a good solvent for polar molecules and ionic compounds... 

When the same procedure takes place in a medium such as liquid water, the vacuum permittivity in equation (1.2) is replaced by the permittivity of the medium. Normally the permittivities for a variety of solvents are expressed as relative permittivities, r, at given temperatures. Some typical values of relative permittivites are given in Table 1.4. 

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