Bulk dielectric constant

It has been shown that the polarizability of a substance containing no dipoles will indicate the strength o/any dispersive interactions that might take place with another molecule. In comparison, due to self-association or internal compensation that can take place with polar materials, the dipole moment determined from bulk dielectric constant measurements will often not give a true indication of the strength of any polar interaction that might take place with another molecule. An impression of a dipole-dipole interaction is depicted in Figure 11. 

If we now transfer our two interacting particles from the vacuum (whose dielectric constant is unity by definition) to a hypothetical continuous isotropic medium of dielectric constant e > 1, the electrostatic attractive forces will be attenuated because of the medium s capability of separating charge. Quantitative theories of this effect tend to be approximate, in part because the medium is not a structureless continuum and also because the bulk dielectric constant may be an inappropriate measure on the molecular scale. Eurther discussion of the influence of dielectric constant is given in Section 8.3. 

Manning s theory does not take the local effective dielectric constant into consideration, but simply uses the a value of bulk water for the calculation of E,. However, since counterion condensation is supposed to take place on the surface of polyions. Manning s 2, should be modified to E, by replacing a with aeff. The modified parameters E, is compared with E, in Table 1, which leads to the conclusion that the linear charge density parameter calculated with the bulk dielectric constant considerably underestimates the correct one corresponding to the interfacial dielectric constant. 

If the solute were simply a collection of point charges surrounded by a continuous dielectric medium with the bulk dielectric constant of the solvent, the self-energy and the strength of charge-charge interactions in the solute would be reduced by a factor of . This is called dielectric screening. However, the solute itself occupies a finite volume, and solvent is excluded from this volume. This reduces the dielectric screening and is called... 

A considerable volume of literature has accumulated on conductance measurements in mixtures of solvents. Ion mobilities and association constants have been measured over a range of bulk dielectric constants with the aim of correlating bulk solvent properties with mobilities, ion association, and ion size parameters. An example of a widely used solvent mixture is water and 1,4-dioxane, which are miscible over all concentrations, providing a dielectric constant range of 2 to 78. The data obtained in systems containing two or more solvents must be treated with circumspection, as one solvent may interact more strongly with a given species present in solution than the other, and the re-... 

A great variety of aqueous—organic mixtures can be used. Most of them are listed in Table I with their respective freezing point and the temperature at which their bulk dielectric constant (D) equals that of pure water. These mixtures have physicochemical properties differing from those of an aqueous solution at normal temperature, but some of these differences can be compensated for. For example, the dielectric constant varies upon addition of cosolvent and cooling of the mixture in such a way that cooled mixed solvents can be prepared which keep D at is original value in water and are isodielectric with water at any selected temperature (Travers and Douzou, 1970, 1974). 

Temperature (°C) at which bulk dielectric constant (D) equals that of water (80). 

It is well known that a solvent can canse dramatic changes in rates and even mechanisms of chemical reactions. Modem theoretical chemistry makes it possible to incorporate solvent effects into calcnlations of the potential energy surface in the framework of the continnnm and explicit solvent models. In the former, a solvent is represented by a homogeneous medium with a bulk dielectric constant. The second model reflects specific molecule-solvent interactions. Finally, calculations of the potential energy surface in the presence or absence of solvents can be performed at various theory levels that have been considered in detail by Zieger and Autschbach [10]. 

Most continuum models are properly referred to as equilibrium solvation models. This appellation emphasizes that the design of the model is predicated on equilibrium properties of the solvent, such as the bulk dielectric constant, for instance. The amount of time required for a solvent to equilibrate to the sudden introduction of a solute (i.e., the solvent relaxation time) varies from one solvent to another, but typically is in the range of molecular vibrational and rotational timescales, which is to say on the order of picoseconds. 

The effective bulk dielectric constant is determined by measuring the distance between a maximum and minimum value of amplitude. The bulk loss factor is determined by measuring the amplitude of the signal under the sample with the loop, as a function of plunger distance from the beginning of the sample. 

The bulk capacitance is (besides geometric parameters) determined by the bulk dielectric constant e, like the mobility, s is usually quite insensitive with respect to P, C, and—unlike the mobility—also to T. Only at high carrier concentrations (e.g., formation of polar associates) or in special compounds (e.g., ferroelectrica) strong variations are to be expected. 

Here, T is the absolute temperature, e is the bulk dielectric constant of the solvent, P is the number of phosphate charges, k is the inverse of the Debye screening length, kB is the Boltzmann constant, qna is the renormalized charge, the interaction between the charges is screened Debye-Hiickel potential, and — j b is the distance between a pair of charges labeled i and /... 

Here, 8 = (z/z ) l/d), / is the local dielectric constant, is the bulk dielectric constant, / is the distance between two charges on the polylectrolyte, and d is the length of the dipole that is formed between one condensed couterion and the closest charged monomer [48]. 

However, the dielectric constant of the interactions of the water molecule from the first layer with the nearest dipole of the surface, denoted ei, is expected to be much smaller than the bulk dielectric constant of water, e. Denoting as E ] the field generated (in a vacuum) by a surface dipole, the field generated by all the dipoles of the surface is... 

While the field produced by remote dipoles can be treated as screened by a medium with a large dielectric constant (e = 80), the screening of the neighboring dipoles is much weaker. In the present treatment, we will simply assume that Elocal is produced only by the dipoles located within a radius 21 from the given site and that the dielectric constant for them is a constant e". The electric field caused by a neighboring molecule is given by eq 17 (with e" replacing e ). It is important to emphasize that the local dielectric constant e" is smaller than e, the bulk dielectric constant of water. 

The region near the surface (region I), of thickness S, is considered to have a dielectric constant e1 different from that in the remaining region between the plates (region II) e11, due to the constraint on the water molecules induced by the hairy surface. For simplicity, the dielectric constants in both regions are assumed to be constant, with that in region II equal to the bulk dielectric constant. 

Current efforts in quantum-chemical modeling of the influence of solvents may be divided into two distinct approaches. The first, the supermolecular approximation, involves the explicit consideration of solvent molecules in quantum-chemical calculations. Another possibility for simulating solvent influence is to replace the explicit solvent molecules with a continuous medium having a bulk dielectric constant. Models of this type are usually referred to as polarized continuum models (PCMs). 

The reactivity ratios observed are markedly different in polar and nonpolar solvents. These differences appear to be determined mainly by the nature of the solvation at the active chain end. Most of the change occurs at quite low concentrations of polar solvent in a primarily hydrocarbon medium hence, the bulk dielectric constant of the solution is not an important factor under conditions where most of the reaction is carried by ion pairs. In solvents such as tetrahydrofuran it might be possible to detect changes in reactivity ratios at different concentrations of active polymer chains as the proportion of free anions increases with dilution. No experiments have been reported yet to check this point. 

From = iv/(l - 8aecos0/a3) with pv = 1.86 D, we obtain tv = 2.138 D for the effective dipole moment in liquid water from the 298 K bulk dielectric constant. When this is used to estimate the cohesive energy between water molecules in approximately tetrahedral superdipoles at dipole-dipole or O O distances of 2.9 A, the results are about a factor of three too small. The simple dipole-dipole model for water was therefore replaced by a DP multipole-multipole point charge model for hydrogen bonding (c.f., Lih173), and the interactions... 

Since ea is determined by the counterfields from the second and further shells, increasing incoherence with rising number of shells will tend to compensate for the increasing value ofthe summation as the number increases, so its effective value will be close to unity. An experimental value of COS0 derived from the bulk dielectric constant is used here, which will give an effective value. 

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