Liquid solvent permittivity

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

Some molecular properties of polar solvents are summarized in table 4.3. The dipole moment and molecular polarizability are the molecular parameters which lead to the solvent permittivity. The other parameters listed are the molecular diameter and the Lennard-Jones interaction energy, Elj. These are of interest in assessing the role of van der Waals forces in determining the properties of a polar liquid. 

Carbohydrate-based nanofoams - Aerogels or nanofoams can be made by replacing the liquid solvent in a gel by air with the objective to minimize the substantial alteration of the gel network structure and volume. Nanofoams have unique physical and thermal properties such as low density, high specific surface area, low thermal conductivity, and low dielectric permittivity. The replacement of the liquid in a gel with air can be done with supercritical drying, but also ambient-pressure drying is an option (23,28-32). There are three classes of... 

It is given that the Hamaker constant of both alumina (which has a relative permittivity equal to 9.3) and the various liquid solvents can be given (as fraction of ksT) by the following equation ... 

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. 

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. 

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 ... 

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.)... 

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. 

Relative Permittivities (Dielectric Constants) D and Normal Liquid Ranges of Common Solvents... 

Most solvents consist of molecules that are intrinsic dipoles and have permanent dipole moments (pi). If such molecules are placed between the two plates of a capacitor as a vapor (or as a dilute solution in a nonpolar liquid), they are oriented by the electric field. Then, the orientational polarization and the induced polarization occur simultaneously, as described above. If er is the relative permittivity of the vapor, there is a relationship ... 

Water has high permittivity and moderate acidity and basicity. Thus, in water, many cations and anions are easily solvated (hydrated) and many electrolytes are highly soluble and dissociate into ions. Water has fairly wide pH and potential ranges and a convenient liquid temperature range. Of course, water is an excellent solvent. However, as in Table 1.7, the reaction environment can be expanded much wider than in water by use of a solvent of weak acidity and/or basicity. This is the reason why dipolar aprotic solvents, which are either protophilic or protophobic, are used in a variety of ways in modern chemistry. 

There are several physical properties of a solvent that are of importance in determining its behavior. Two of the most important from a pragmatic point of view are the melting and boiling points. These determine the liquid range and hence the potential range of chemical operations. More fundamental is the permittivity (dielectric constant). A high permittivity is necessary if solutions of ionic substances are 10 form readily. Coulombic attractions between ions are inversely proportional to the permittivity of the medium ... 

The solvents used for electroanalytical determinations vary widely in their physical properties liquid ranges (e.g., acetamide, N-methyl-acetamide and sulfolane are liquid only above ambient temperatures), vapour pressures (Table 3.1), relative permittivities (Table 3.5), viscosities (Table 3.9), and chemical properties, such as electron pair and hydrogen bond donicities (Table 4.3), dissolving ability of the required supporting electrolyte to provide adequate conductivity, and electrochemical potential windows (Table 4.8). A suitable solvent can therefore generally be found among them that fits the electroanalytical problem to be solved. 

The origin of the effect here represented by x0) can be derived from modelistic considerations. Solvent molecules are mobile entities and their contribution to the dielectric response is a combination of different effects in particular the orientation of the molecule under the influence of the field, changes in its internal geometry and its vibrational response, and electronic polarization. With static fields of moderate intensity all the cited effects contribute to give a linear response, summarized by the constant value e of the permittivity. This molecular description of the dielectric response of a liquid is... 

This mention of a family of solvents with particular physical properties prompt us to remark that there are other solvents with special physical quantities requiring some modifications in the methodological formulation of basic PCM. We cite, among others, liquid crystals in which the electric permittivity has an intrinsic tensorial character, and ionic solutions. Both solvents are included in the IEF formulation of the continuum method [20] which is the standard PCM version. 

For a uniform liquid sample such as the pure solvent, (r, r to) = jj((r — r to). Since the solvent quantity accessible from experiment is the dielectric permittivity, s(co), a further step is to relate )t(r — r to) to this quantity. From a coarse-grained model of dielectric response, one obtains... 

The permanent dipole moment /r of a polar molecule, as a solute molecule in a liquid solution in a nonpolar solvent or as a molecule in a gas, can be determined experimentally from measurements of the dielectric constant k. This quantity is the ratio of the electric permittivity s of the solution or gas to the electric permittivity sq of a vacuum (8.854 X 10- Fm ) ... 

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