Dielectric response permanent dipoles

The characterization of a solvent by means of its polarity is an unsolved problem since the polarity itself has, until now, not been precisely defined. Polarity can be understood to mean (a) the permanent dipole moment of a compound, (b) its dielectric constant, or (c) the sum of all those molecular properties responsible for all the interaction forces between solvent and solute molecules (e.g., Coulombic, directional, inductive, dispersion, hydrogen bonding, and EPD/EPA interaction forces) (Kovats, 1968). The important thing concerning the so-called polarity of a solvent is its overall solvation ability. This in turn depends on the sum of all-specific as well as nonspecific interactions between solvent and solute. 

The dielectric constant e of a gas sample depends on the total dipole moment induced in response to an applied electric field. The dipole moment is the vector sum of the partially oriented permanent dipoles pt which individual molecules i may possess, plus the field-induced dipoles a, E arising from the polarizability a of the molecules i, plus all interaction-induced dipoles fiik, plus the field-induced dipoles which arise from the interaction-induced polarizability ptk [93]. The dielectric constant e depends, therefore, on the density g of the gas, according to... 

The situation is very different for polar solvents, i.e., solvents that have a relevant permanent dipole moment. In such solvents the greatest part of the dielectric response originates from the slight reorientation of the applied external field, and only a small part from electronic polarization. For water, with s = 78.4 (at 25 °C), the electronic polarizability contribution is only... 

This extraction precisely reproduces the same London, Debye, and Keesom interactions, including all relativistic retardation terms that had been effortfully derived in earlier formulations. These interactions are distinguished by whether they involve the interaction of two permanent dipoles of moment //.uipoie, or involve an inducible polarizability aind. A water molecule, for example, has both a permanent dipole moment and inducible polarizability. The contribution of each water molecule to the total dielectric response is a sum of the form of Eqs. (L2.163) and (L2.173) in mks units,... 

Dielectric response of a gas For a gas of number density N of whose particles bear permanent dipole moments /xdipoie, for constant E... 

In this way, the relative dielectric response to static electric fields of a gas of polarizable molecules that also bear a permanent dipole moment is... 

P. J. W. Debye, Polar Molecules (Dover, New York, reprint of 1929 edition) presents the fundamental theory with stunning clarity. See also, e.g., H. Frohlich, "Theory of dielectrics Dielectric constant and dielectric loss," in Monographs on the Physics and Chemistry of Materials Series, 2nd ed. (Clarendon, Oxford University Press, Oxford, June 1987). Here I have taken the zero-frequency response and multiplied it by the frequency dependence of the simplest dipolar relaxation. I have also put a> = if and taken the sign to follow the convention for poles consistent with the form of derivation of the general Lifshitz formula. This last detail is of no practical importance because in the summation Jf over frequencies fn only the first, n = 0, term counts. The relaxation time r is such that permanent-dipole response is dead by fi anyway. The permanent-dipole response is derived in many standard texts. 

The expression given in Eq. (10) for the work assumes that p = 0, where p is the ionic strength of the medium. AG is the free-energy of the equilibrated excited-state (AG AE00), rD and rA are the molecular radii of the donor and acceptor molecules, e5 is the static dielectric constant or permittivity of the solvent, and z is the charge on each ion. ss is related to the response of the permanent dipoles of the surrounding solvent molecules to an external electrical field. Equation (9), the Bom equation, measures the difference in solvation energy between radical ions in vacuo and solution. 

Note first that in this older picture, for both the attractive (van der Waals) forces and for the repulsive double-layer forces, the water separating two surfaces is treated as a continuum (theme (i) again). Extensions of the theory within that restricted assumption are these van der Waals forces were presumed to be due solely to electronic correlations in the ultra-violet frequency range (dispersion forces). The later theory of Lifshitz [3-10] includes all frequencies, microwave, infra-red, ultra and far ultra-violet correlations accessible through dielectric data for the interacting materials. All many-body effects are included, as is the contribution of temperature-dependent forces (cooperative permanent dipole-dipole interactions) which are important or dominant in oil-water and biological systems. Further, the inclusion of so-called retardation effects, shows that different frequency responses lock in at different distances, already a clue to the specificity of interactions. The effects of different geometries of the particles, or multiple layered structures can all be taken care of in the complete theory [3-10]. 

Depending on the appearance of the spectrum when the angular frequency cu approaches zero, dielectric responses of materials are often classified as being either dipolar in nature or carrier dominated. In the first case, the polarization is attributed to the reorientation of permanent dipoles, and in the latter to the displacement of partially mobile charge carriers. These two behaviors may be interpreted as being manifestations of different values of the exponent a in a power law of the form oc at low frequencies when cu approaches zero, tends to zero whenever the exponent a > 1 but increases indefinitely when a < 1. Likewise, the real part / approaches a finite value when a > 1 but increases indefinitely in the same way as the imaginary part when a < 1. Since no finite value is approached when a < 1, this case usually is referred to as low-frequency dispersion (104,105). 

Ug expresses the electronic response (induced dipoles), oi is associated with the average orientation induced in the distribution of permanent molecular dipoles, and as denotes the total response. These contributions can in principle be monitored experimentally Immediately following a sudden switch-on of an external field T>, the instantaneous locally averaged induced dipole is zero, however after a time large relative to Xg but small with respect to Xn the polarization becomes Pg = ag D. Equation (1.237) is satisfied only after a time long relative to r . Similarly we can define two dielectric constants, Sg and Sg such that 5 = and Pg = [(sg —... 

This state describes (i) dielectric response arising from libration of a permanent dipole p in a hat-like potential well [the relevant librational band is located near the border of the infrared region (at 700 cm-1)] and (ii) the nonresonance relaxation band, whose loss peak is located at microwaves. The lifetime Tor of the LIB state is much less than a picosecond. 

In the first part of this work (Sections II through V) we have combined the formula for x given there without derivation, with the formulas for xq, and Xor> accounting for dielectric response, arising, respectively, from elastic harmonic vibration of charged molecules along the H-bond (HB), from elastic reorientation of HB permanent dipoles about this bond, and from a rather free libration of a permanent dipole in a defect of water/ice structure modeled by the hat well. The set of four frequency dependences, namely of Xor(v)> (v), X (v), and X (v), allows us to describe the water/ice wideband spectra. For these dependences and those similar to them—namely 0r(v), Asq(v), Ae/1(v), and Ae (v) for the partial23 complex permittivity—we refer to mechanisms a, b, c, and d. 

In addition to orientational polarization response, , may have translational contributions arising from solvent density fluctuations [226], As it was shown by Matyushov et al. [226, 227], molecular translation of the solvent permanent dipoles is the principal source of temperature dependence for both the solvent reorganization energy and the solvation energy. In fact, the standard dielectric continuum model does not predict the proper temperature dependence of E, in highly polar solvents It predicts an increase in contrast to the experimentally observed decrease in ,. with temperature. A molecular model of a polarizable, dipolar hard-sphere solvent with molecular translations remedies this deficiency of the continuum picture and predicts correct temperature dependence of ,., in excellent agreement with experiment [227a],... 

Coulomb forces are responsible for the stability of ionic crystals (e.g., NaCl). When such a compound is dissolved in a polar solvent (dipole moment //), dissociation and simultaneous solvation of the ions occur. The force of attraction between the ions is now inversely proportional to the dielectric constant of the solvent, and is thus reduced. New ion dipole forces are formed as a result of the attraction of the permanent dipoles of the solvent by the ions ... 

When discussing solvent effects, it is important to distinguish between the macroscopic effects of the solvent and effects that depend upon details of structure. Macroscopic properties refer to properties of the bulk solvent. An important example is the dielectric constant, which is a measure of the ability of the bulk material to increase the capacitance of a condenser. In terms of structure, the dielectric constant is a function of both the permanent dipole of the molecule and its polarizability. Polarizability refers to the ease of distortion of the molecule s electron density. Dielectric constants increase with dipole moment and with polarizability. An important property of solvent molecules with regard to reactions is the response of the solvent to changes in charge distribution as the reaction occurs. The dielectric... 

Because the high dielectric responses in the tetragonal phase of BaTiOs are caused by a deformation of the TiOe coordination polyhedron and consequently the creation of a permanent electric dipole, it is instmctive to consider from this viewpoint the dielectric properties in other ternary oxides. After the size effect in BaTiOa was clarified, works on the synthesis of materials with high e were focused on obtaining compounds with the maximum distortion in the crystal... 

Second, the polarizability of a medium can arise from the polarizabilities of the atoms or molecules composing it, even if they have no permanent dipole moment. Atoms or molecules that lack permanent dipoles have electronic polarizability, a tendency of nuclear or electronic charge distributions to shift slightly within the atom, in response to an electric field (see Chapter 24). The electronic polarizabilities of hydrocarbons and other nonpolar substances are the main contributors to their dielectric constants (D 2). 

Here ions themselves contribute to the dielectric response of the medium on account of their inherent dipole moment. This leads to dielectric increment of a solution medium. Typical ions such as Cl" and Na have spherical distributions and ions with permanent dipole moment are not too common, but can be encountered in ionic liquids, where ions tend to be larger molecular structures. 

Figure 5. Response of polar dielectrics (containing local permanent dipoles) to an applied electric field from top to bottom paraelectric, ferroelectric, ferrielectric, antiferroelectric, and helielectric (helical anti-ferroelectric). A pyroelectric in the strict sense hardly responds to a field at all. A paraelectric, antiferro-electric, or helieletric phase shows normal, i.e., linear dielectric behavior and has only one stable, i.e., equilibrium, state for E=0. A ferroelectric as well as a ferrielectric (a subclass of ferroelectric) phase shows the peculiarity of two stable states. These states are polarized in opposite directions ( P) in the absence of an applied field ( =0). The property in a material of having two stable states is called bistability. A single substance may exhibit several of these phases, and temperature changes will provoke observable phase transitions between phases with different polar characteristics.

Two kinds of dielectric responses due to the permanent and induced dipole moments are expected in the dilute solution of the conducting polymers. If carries move along a polymer chain even more slowly than the rotation of the chain, the inhomogeneous distribution of the carriers yields the permanent (or quasi-permanent) dipole moment on the polymer chain. Thus, the electric polarizability arises from the orientation of the permanent dipole moment towards the direction of the external field. On the other hand, if the carriers move much faster than the rotation, the external electric field induces the electric polarizability and exerts a different type of torque on the polymer chain. These two different responses can be clearly distinguished by FEBS [149]. 

The first is that of positively charged solutes. Here, the dominant cybotactic effects are those generally known as dielectric saturation. Near the positive charge the electric field E can be so large that the linearity in the dielectric response cannot be invoked any more. At the microscopic level this effect can be interpreted as due to a loss of thermal motion in the permanent dipoles of the. solute, thus reducing the local value of s. The use of higher powers of E in the Taylor... 

Polar materials, in which the molecules lack centosymmetric symmetry, can have permanent dipole moments and consequently would have quite large static dielectric constants. Water is an excellent example of a molecule with a permanent dipole moment. The bond angle of 107° between the two H ions places these virtually naked protons on one side of the doubly charged O ion, giving water a static relative dielectric constant of 80 and is responsible for the unusual properties of water and its frozen counterpart. The forces on a dipole are illustrated in Figure 23.5. 

---