Free energy electrical

The conformation of macro- or polyions has been defined and discussed briefly in Section 4.1.1. The conformation of a polyion is determined by a balance between contractile forces, which depend on conformation free energy, and extension forces, which arise from electrical free energy. The extent of conformational change is determined by several factors. Changes are facilitated by the degree of flexibility of the polyion, and conformational change is greatest at low concentration of polyions. 

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... 

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. 

Hesselink23) attempted to calculate adsorption isotherms for flexible polyelectrolytes. He assumed that, when adsorbed on a surface, a flexible polyelectrolyte takes a conformation consisting of one train and one tail. The theoretical treatment of Hoeve et al.4I) (cf. B.3.1) for non-ionic polymers was extended by taking into account the change in electrical free energy that occurs when the polyelectrolyte is brought from the solution onto the interface. The partition function Q for a system of N polyelectrolytes each consisting of n units, in which Na polyions are adsorbed on the surface of area S and Nf(Nf = N - N ) polyions remain in the bulk solution of volume V, is then represented by... 

The quantity AF is the electrical free energy of adsorption of Na polyions, o) and vn i are the partition functions for a tail of i units and that for a train of j( = n - i) units, n is the number of tails of i units, and d the first layer thickness. The partition function Wj is given by... 

Oosawa390 described a very simple theory based on the electric free energy to claculate the repulsive forces between parallel rod-like macoions in solution as a function of the charge density on the rods. The total extensive force... 

The volume change accompanying the charging process at constant pressure is negligible, and so W -- Wo may be identified with the difference between the electrical free energy of an ionic solution at a definite concentration and at infinite dilution. 

The electrical free energy of a pair of ions of charges +e and — at a distance y in a medium of dielectric constant e is given by G = e jer. The difference in value between the electrical free energy in water and that in ethyl alcohol as solvent is given by... 

It will be recalled that in 40b the solution under consideration was supposed to be so dilute that xd was negligible in comparison with unity. If, however, the term 1 -1- xd is retained in the denominator of the expression Cequation (40.3)] for the electrical potential, it will also appear in the equations for the electrical free energy and the activity coefficient. In this event, equation (40.14) becomes... 

If the cell is used as a source of electrical energy, (i.e. if it converts the free energy of a physical or chemical change into electrical free energy), it is called a Galvanic Cells. 

Thus, the electrical free energy of each sphere is equal to half its charge multiplied by its potential. 

When the electric field applied parallel to the hehcal axis is used to create the distortion, the electric free energy density is given by ... 

It is of interest to see how far these figures can be accounted for on a simple electrostatic basis. The electrical free energy of a pair of separated ions of charges + e and — e and radius r in a medium of dielectric constant 6 is given by and if we apply this to two media of dielectric constants 6 and 6" we have... 

The assumptions implied in this treatment are (a) that the system is mono-disperse, (b) that an abrupt change in the system occurs at the CMC, and (c) that there is a constant concentration of the monomer above the CMC. More refined calculation should take into account the micelle charge, counterion activity, and electrical free energy at the micelle surface (163). With these limitations in mind one can examine the values of JF , and TAS ... 

The situation, in fact, is that PA(ads) l C(ads) driving force for the charge separation in tne two layers that finite q g = -qg values represent, and charge separations involving any appreciable fraction of a monolayer require prohibitive amounts of electrical free energy. A complementary viewpoint is that Eq. 17 gives cs N=0.6 for the AgBr Pt system,... 

If we now ask what ratio of q g to minimizes AV and hence the interfacial electrical free energy, it is apparent by inspection that it is q s = - 2... 

Free energy of charging a sphere. A sphere with radius n in a medium with dielectric constant D is uniformly filled with a charge of volume density p. Derive the electrical free energy of this sphere in tw o different ways ... 

A simple eleetrostatie ealculaticm, considering the electrical free energy of the gjydne dipolar ion in water (dielectdc constant near 80) and in benzene (dielectric constant near 2) suggests that fg may be of the < der of 10 < (see Edsall, ret. 38, p. 108-110). 

The electrical free energy of interacting colloidal particles has been described by means of an approach using Hamiltonian methods in the calculus of variations. This approach gives results of great generality such as equation (11) in this article. 

The third electroviscous effect is due to the change of shape of suspending particles when their electrical free energy is modified by ionization and the presence of neutral salts. If a polymer molecule can undergo ionization, e.g. by reaction with a base or by reaction with some other ion-producing substance, electrostatic repulsion between the like charges introduced on the polymer chain modifies the partial molecular free energy of the polymer in the solution. With polymeric... 

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