Electrically free

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. 

One of the most exciting properties of some materials is superconductivity. Some complex metal oxides have the ability to conduct electricity free of any resistance, and thus free of power loss. Many materials are superconducting at very low temperatures (close to absolute zero), but recent work has moved the so-called transition temperature (where superconducting properties appear) to higher and higher values. There are still no superconductors that can operate at room temperature, but this goal is actively pursued. As more current is passed through... 

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... 

The end point of the titration may be determined either colorimet-rically (free iodine present) or electrically (free water increases the conductivity of the solution). 

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 ... 

In Chap. 3 the corresponding relation between elastic stifiFnesses and compliances sxfx determining also inverse effects was derived yielding (3.55 ). This relation has to be specified in similar manner by stating the pertinent constraints. It must be clarified if these are to be interpreted as isothermal ( = const) or adiabatic (a = const) and as electrically free (E = const) or clamped (D = const). These distinctions are indicated by the symbols A and + in Table 4.3. 

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... 

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