Electrical contribution, free energy

Atoms of elements that are characterized by a valence greater than four, eg, phosphoms or arsenic (valence = 5), are one type of dopant. These high valence dopants contribute free electrons to the crystal and are cabed donor dopants. If one donor atom is incorporated in the lattice, four of the five valence electrons of donor dopants are covalentiy bonded, but the fifth electron is very weakly bound and can be detached by only ca 0.03 eV of energy. Once it is detached, it is available as a free electron, ie, a carrier of electric current. A sibcon crystal with added donor dopants has excess electron carriers and is cabed n-ty e (negative) sibcon (Fig. Ic). 

The first integral in Equation 17 is identified as the electrical contribution to the change in free energy in forming the charged interface (3) and may be evaluated using Equation 12... 

We recall that the first integral in Equation 23a represents the change in electrical free energy in forming the diffuse double layer. This contribution to f, the free energy of formation of the charged interface, is positive and hence represents an unfavourable component which opposes the formation of the charged interface. 

On the other hand, the electrical free energy per unit area of double layer (second term) is high and positive even for relatively low surface potential. The contribution of this term could be tens of m Nm. This requires to have a... 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

In order to evaluate the potential dependence of the free energy of activation, without knowledge of the structure of the activated complex, it is assumed that the electrical contribution to the standard free energy of the transition state lies between that to the standard free energy of P and that to the standard free energy of R in the rds. The symmetry factor or transfer coefficient, a, for the rds has the same properties as outlined in Sect. 3.1. 

From the solution of the Poisson-Boltzmann equation one can calculate the electrostatic contribution to the free energy. It is illustrative to divide G into two parts302. The first is concerned with the free energy of the electric field and is given by ... 

Recently, Attard [30] proposed a different approach which provides a variational formulation of the electrostatic potential in dielectric continua. His formulation of the free energy functional starts from Equation (1.77), which he justifies using a maximum entropy argument. He defines a fictitious surface charge, s, located on the cavity boundary. The charge s, which produces an electric field /, contributes together with the solute... 

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