Induced and Permanent Dipole Moments

Two types of polarization processes may contribute to the total macroscopic polarization  

According to Onsager the induced moment term M( ) is determined by the internal or local field whereas the permanent dipole term is related to the directing field E ,ij orienting the permanent dipoles p. The combination of Eqs. (3.10) and (3.2) requires that the two different field vectors must be expressed in terms of the measured Maxwell field. The calculations of the terms and M p as functions of Ej , and E jj usually are approximations. The final expressions may be written in terms of conversion factors (g factors ) which are a function of particle anisotropies as well as of the properties of the medium in which the particles are embedded (polar, nonpolar, gas phase, or fluid phase). 

In line with Eq. (3.10) the molecular dipole moments m may generally be expressed as 

In anisotropic molecules m represents the vector sum of all dipolar contributions. The calculations are readily performed for ellipsoidal molecules and for simple geometries like a sphere, long cylinder, or flat disks. The total moment of an ellipsoid where the main polarization axes are the (half-)axes q = a,b,c, is given by the vector sum 

The dipole moment component along the axis q is expressed analogously to Eq. (3.11) as 

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The change in permanent and induced dipole moments might induce an electrical signal for transfer in a given direction indicated by the change in the transition vector. 

The asymmetry of distributions of positive and negative charges in a molecule can have important effects on its physical properties as well as on its chemical reactivity. This asymmetry can have two quite different origins, illustrated by the permanent and induced dipole moments. A molecule such as HF has a permanent dipole moment which results from the electronegativities of the H and F atoms but even a symmetrical molecule such as H2C=CH2 can acquire an induced dipole moment in an external electric field. 

In condensed media consisting of molecules, the intermolecular forces such as permanent and induced dipole interactions are generally small compared to intramolecular chemical binding forces. Therefore, the molecular identities and properties are conserved to a certain extent. They nevertheless differ significantly from those of an isolated molecule in the gas phase. Therefore, both in linear and non-linear optics the question arises of how to relate molecular to macroscopic properties. More specifically, how do the individual permanent and induced dipole moments of the molecules translate into the macroscopic polarization of the medium The main problem is to determine the local electric field acting on a molecule in a medium which differs from the average macroscopic field E (Maxwell field) in this medium. 

This allows us to define an effective dipole moment jreff as the sum of the permanent and induced dipole moments... 

A proper solvated electron is a particle localized in the potential well of a polar medium, the well being created by the interaction of electron charge with the permanent and induced dipole moments of the nearest as well as remote neighbours. This notion of the nature of a solvated electron, based on the idea that the Landau-Pekar theory initially advanced for solid bodies can be applied also to liquid systems, was advanced in 1948 since then considerable efforts have been made to develop it and verify it experimentally. In most liquid systems, localization of an electron is followed by the formation of a cavity where most of the density of the solvated electrons is concentrated. The cavity is surrounded by the orientated dipoles of the solvent. Usually, the radius of this cavity equals about 3-3.5 A which conforms to a solvated-electron molar volume of 70-100 cm . This is the reason why solutions with large concentrations of solvated electrons have a lower density. 

Many groups have investigated the suitability of various solvents for use in LM systems and have attempted to describe the relationship between solvent characteristics and transport properties [93-96]. Of all solvent properties, dielectric constant seems to be most predictable in its effect on transport [92]. For solvents, such as the halocarbons, transport usually decreases with increasing dielectric constants [93]. Figure 2.10 shows this trend for alkali metals binding by dicyclohexano-18-crown-6 in a number of alcohols. This trend holds true for many simple systems, but it breaks down under more complex conditions. Solvent donor number, molecule size, solvent viscosity, carrier solubility in the solvent, permanent and induced dipole moments, and heats of vaporization are important [94]. 

Benoit (1) performed a calculation similar to that of O Konski at a somewhat earlier date and included equations for the rise and decay of the birefringence under the action of a rectangular voltage pulse. Since the rise time depends on both permanent and induced dipole moments, it is a complex function involving more than one time constant and rather difficult to deal with experimentally. The decay time of birefringence, however, depends only on the molecular dimensions and for a rigid rod Benoit obtained the simple formula... 

Several factors contribute to the field-induced structural anisotropy that leads to optical anisotropy and hence to birefringence. All involve the particles polarization by the field and the partial alignment of their resultant dipole moments parallel to E. The resultant dipole moment / of a particle is the vector sum of its permanent and induced dipole moments. At the molecular level, electronic and atomic polarization occurs, the extent of which depends on the nature and symmetry of the molecule and on its polarizabilities (a and ax) along the parallel and perpendicular directions relative to the electric field or, for cylindrical symmetry, along the molecular axes a and b (a and a ). Naturally, the concept of the polarizability tensor is applicable to an assembly of molecules as a whole, e.g., a colloidal particle, as well. For such systems, and also for macromolecules and polyelectrolytes in an insulating medium, interfacial polarization may also have a major or even dominant contribution to the resultant dipole moment. 

Examination of this equation shows that if the signs of P and Q are the same (i.e., if the permanent and induced dipole moments tend to orient the ellipsoid in the same direction), then the rate of reaching the steady state (An -> Awo) is determined by the magnitude of P/Q The larger P/Q, the slower the process. If there is no permanent dipole (i.e., P/Q = 0, as expected for microemulsions) then Eq. (12) reduces to a simple exponential function. 

Let s consider dipoles. There are two types permanent and induced. A permanent dipole occurs when a charge separation is always present in a molecule, even in the absence of an> external electric fields. An induced dipole is a charge separation that arises only in the presence of an applied electric field. Some molecules have both permanent and induced dipole moments. 

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]. 

At high energy, the interaction of the ion with the neutral is sufficiently short and the collision cross section, cths, can be described by the hard-sphere collision model and determined via the sum of the physical radii ri and Z2 of the collision partners, using the equation cths = ( "1 + As the energy is decreased, the ion interactions with permanent and induced dipole moments of the molecule start to define the interaction potential, and at some energy (generally... 

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