Self-atmosphere Potential of Ions

Equation (3.58) is a transcendental equation for jo- The solution of Eq. (3.58) can easily be obtained numerically for given values of cr, and n. Equation (3.58) is found to provide a quite accurate relationship between yo and cr for practical purposes. The reason for this is that the solution to Eq. (3.58) yields correct limiting forms both at Ka land at kckIC 1, that is, Eqs. (3.51) and (3.55). 

Finally, we give below an approximate explicit expression for i/cq applicable for small i/cq obtained by linearizing Eq. (3.58) with respect to i/cq, namely. 

We again see that in the limit of small Ka, the effective Debye-Hiickel parameter is given by Eq. (3.52) and that in the limit of large Ka, rod-like zwitterions behave like monovalent electrolytes of concentration nJ2 and the effective Debye-Hiickel parameter is given by Eq. (3.55). 

Another deficiency of the Poisson-Boltzmann equation is that as Kirkwood showed [8], it neglects the effects of the self-atmosphere (or fluctuation) potential. The 

We calculate the self-atmosphere potential of an ion near the planar surface. Imagine a planar uncharged plate in contact with a solution of general electrolytes composed of N ionic mobile species of valence z, and bulk concentration (number density) nf (i=l,2,. . . , N) (Fig. 3.10). Let and p, respectively, be the relative permittivities of the electrolyte solution and the plate. Consider the potential distribution around an ion. By symmetry, we use a cylindrical coordinate system r(s, x) with its origin 0 at the plate surface and the x-axis perpendicular to the surface. 

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To proceed further, one must separate the contribution to cp due to the ionic atmosphere from the contribution that the ion makes itself in the absence of other ions, that is, the so-called self-atmosphere potential. The latter quantity is given by... 

An important specialized type of voltammetric system is a self-contained cell for the determination of 02 in the gas or solution phases. This is the so-called Clark electrode,66,67 which consists of a platinum or gold electrode in the end of a support rod that is covered by an 02 permeable membrane (polyethylene or Teflon) such that a thin film of electrolyte is contained between the electrode surface and the membrane. A concentric tube provides the support for the membrane and the means to contain an electrolyte solution in contact with a silver-silver chloride reference electrode. The Clark device has found extensive application to monitor 02 partial pressure in blood, the atmosphere, and in sewage plants. By appropriate adjustment of the applied potential it gives a voltammetric current plateau that is directly proportional to the 02 partial pressure. The membrane material prevents interference from electroactive ions as well as from surface-contaminating biological materials. Figure 3.19 illustrates one configuration for this important device. 

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