Electric polarization free energy

To include the effect of solvent polarization in molecular mechanics, Still and co-workers turned to the generalized Born modelT i i", 194-203 this model, the electric polarization free energy is written in atomic units as... 

A enp is the change in the internal electronic kinetic and electronic and nuclear coulombic energy of the solute upon relaxation in solution, which is driven by the favorable electric polarization interaction with the solvent, while Cp is the electrostatic polarization free energy expressed in terms of the generalized Bom approximation (equation 40). 

The Self-Consistent Reaction Field (SCRF) model considers the solvent as a uniform polarizable medium with a dielectric constant of s, with the solute M placed in a suitable shaped hole in the medium. Creation of a cavity in the medium costs energy, i.e. this is a destabilization, while dispersion interactions between the solvent and solute add a stabilization (this is roughly the van der Waals energy between solvent and solute). The electric charge distribution of M will furthermore polarize the medium (induce charge moments), which in turn acts back on the molecule, thereby producing an electrostatic stabilization. The solvation (free) energy may thus be written as... 

The Electrical A nalogue of Magnetic Cooling. Three Processes bg Which Ions Are Introduced into Solution.. 1 Polar Dielectric in an Electrostatic Field. The Concepts of Faraday and Maxwell. The Electrostatic Energy in the Fields of Ions. The. Charging of a Condenser. The Amount of Free Energy Lost, by a Dielectric. The Behavior of Solvents in an Electrostatic Field. A Dielectric in the Field of a Charged Sphere. Two Types of Process Contrasted. 

From a comparison of Eqs. (9) and (22) we see that H = F(0 ). To elucidate the physical meaning of the exponent in Eq. (22), we consider first the case when 0 = 1 (barrierless reaction). In this case Eq. (20) determines the change of the free energy of the system F(l) when it is polarized by the electric field AEU = E -E (only the free energy related to the inertial polarization is considered). It may be easily seen that the absolute value of F(l) is equal to the energy of the reorganization of the medium Es (>0). 

Since P must remain normal to z and n, the polarization vector forms a helix, where P is everywhere normal to the helix axis. While locally a macroscopic dipole is present, globally this polarization averages to zero due to the presence of the SmC helix. Such a structure is sometimes termed a helical antiferroelectric. But, even with a helix of infinite pitch (i.e., no helix), which can happen in the SmC phase, bulk samples of SmC material still are not ferroelectric. A ferroelectric material must possess at least two degenerate states, or orientations of the polarization, which exist in distinct free-energy wells, and which can be interconverted by application of an electric field. In the case of a bulk SmC material with infinite pitch, all orientations of the director on the tilt cone are degenerate. In this case the polarization would simply line up parallel to an applied field oriented along any axis in the smectic layer plane, with no wells or barriers (and no hysteresis) associated with the reorientation of the polarization. While interesting, such behavior is not that of a true ferroelectric. 

As mentioned above, the PCM is based on representing the electric polarization of the dielectric medium surrounding the solute by a polarization charge density at the solute/solvent boundary. This solvent polarization charge polarizes the solute, and the solute and solvent polarizations are obtained self-consistently by numerical solution of the Poisson equation with boundary conditions on the solute-solvent interface. The free energy of solvation is obtained from the interaction between the polarized solute charge distribution and the self-... 

Several possible ferroic phenomena become evident from equation (6.60), depending upon the dominance of particular terms. In a material which has a large value of spontaneous polarization, other terms become unimportant and the free energy in an electric field is governed by the expression... 

The allowance for polarization in the DH model obviates the need for separation of long-range and short-range attractive forces and for inclusion of additional repulsive interactions. Belief in the necessity to include some kind of covolume term stems from the confused analysis of Onsager (13), and is compounded by a misunderstanding of the standard state concept. Reference to a solvated standard state in which there are no interionic effects can in principle be made at any arbitrary concentration, and the only repulsive or exclusion term required is that described by the DH theory which puts limits on the ionic atmosphere size and hence on the lowering of electrical free energy. The present work therefore supports the view of Stokes (34) that the covolume term should not be included in the comparison of statistical-mechanical results with experimental ones. 

Assuming further that linear response theory for the solute/solvent system applies, the dependence of the nonequilibrium free energies of the system (in the ground Fg and excited Fe states) are portrayed in Figure 1 as a function of the electrical polarization of the solvent (see below). In a transient fluores-... 

When a ferroelectric single crystal is cooled below the phase transition temperature the electrical stray field energy caused by the non-compensated polarization charges is reduced by the formation of ferroelectric domains, see Figure 1.19. The configuration of the domains follows a head-to-tail condition in order to avoid discontinuities in the polarization at the domain boundary, VP = a. The built-up of domain walls, elastical stress fields as well as free charge carriers counteract the process of domain formation. In addition, an influence of vacancies, dislocations and dopants exists. 

In the implicit approach, as in the SCRF (self-consistent field reaction) method,25 the solvent is treated as a continuum whose principal characteristic is its dielectric constant. The solute is placed in a cavity within the solvent, which becomes polarized by its presence. In turn, this creates an electric field within the cavity. Subsequently, the free energy of solvation is calculated by a multipolar development. This method does not require much computer time. It ignores, however, specific solvent-solute interactions such as hydrogen bonds. 

---