Helmholtzs Theory

Another important and fundamental consequence of Figure 2.9 is that the Helmholtz theory cannot cope with a concentration dependence of the differential capacitance nor can it be modified in such a way as to incorporate a minimum in (derM/d V) at low concentrations of electrolyte. Instead, a second theory must be invoked, having a dependence on electrolyte concentration but in such a way that it is only important at low concentration. A first step... 

As regards the origin of the double layer the Helmholtz theory gives no information, but several other theories have been formulated. Modem electrical theories suppose every conducting substance to contain large numbers of negatively charged ions, called electrons, which are exactly alike no matter in what substance they are found. When two s.T. 5... 

As a result of these experiments Smith concludes that (a) the simple Helmholtz theory of the double layer is insufficient to account for all the observed facts. The potential difference mercury-electrolyte is not purely electrostatic, but depends on the nature of the ions, as, according to Nemst s theory, it should do. This theory, it will be remembered, involves the " solution pressure of the ions, which varies with their chemical nature. (6) The potential difference mercury-electrolyte is not necessarily zero when the interfacial tension is a maximum, although in the particular case of dilute KC1 this condition is very nearly fulfilled. 

Perrin-Helmholtz theory, 873 Phase angle, impedance, 1129 Phase difference, impedance, 1127 Phase formation, one dimensional, underpotential deposition, 1316 Phenyl compounds, 979 Phonon spectra, 1463 Phonon, 1517... 

The capacity provides a good test of theories of the constitution of the double layer on the simple diagrammatic theory (often called the Helmholtz theory) that positive and negative charges face each other in two plane parallel sheets at a fixed distance apart, it should remain constant on the various theories of the diffuse double layer, it should change in various ways. Philpot4 has measured the charge on a mercury surface,... 

We have now successfully reduced the vector Helmholtz equation to the scalar Helmholtz equation for transverse fields. Under the conditions derived in Section III, transverse fields are often an accurate description of a Gaussian beam. In order to study the effects of diffraction on transverse fields, we note that scalar diffraction theory is based on the scalar Helmholtz theory (Born and Wolf, 1980, pp. 370-386). Thus, we may use scalar diffraction theory with the function u to elucidate the effects of diffraction on Gaussian beams that are well approximated by transverse fields. 

The Gouy-Chapman theory provides a better approximation of reality than does the Helmholtz theory, but it still has limited quantitative application. It assumes that ions behave as point charges, which they cannot, and it assumes that there is no physical limit for the ions in their approach to the TPB, which is not true. Stem, therefore, modified the Gouy-Chapman diffuse double layer. His theory states that ions do have finite size, so they cannot approach the TPB closer than a few nm [54, 60], The first ions of the Gouy-Chapman diffuse double layer are in the gas phase but not at the TPB. They are at some distance 8 away from the zirconia-metal-gas interface. This distance will usually be taken as the radius of the ion. As a result, the potential and concentration of the diffuse part of the layer are low enough to justify treating the ions as point charges. Stem also assumed that it is possible that some of the ions are specifically adsorbed by the TPB in the plane 8, and this layer has become known as the Stem layer. Therefore, the potential will drop by T o - Pg over the molecular condenser (i.e., the Helmholtz plane) and by T g over the diffuse layer. Pg has become known as the zeta (Q potential. 

This simple idea of Helmholtz, that a layer of ions from the solution becomes attached to the surface, was modified in 1910 by the French physicist Georges Gouy (1854-1926) and in 1913 by the British chemist David Leonard Chapman (1869-1958). These workers pointed out that the Helmholtz theory is unsatisfactory in neglecting the Boltzmann distribution of the ions. They suggested that on the... 

A particular problem with the Helmholtz theory arises from the equation for the resonant frequency for a string under tension ... 

S. S. Yoon, R. A. Jepsen, S. C. James, J. Liu, G. Aguilar Are drop-impact phenomena described by Rayleigh-Taylor or Kelvin-Helmholtz theory . Drying Technol., 27, 316-321 (2009). 

The retinal rods are more sensitive in the ultraviolet, and there are specialized cones for the blue, green and red regions respectively. Since these sensitivities are slightly dilferent for each human being, the 1931 Commission Internationale de I Eclairage (CIE) defined the response curve for a standard observer in order to overcome this difficulty. This curve, which is illustrated in Fig. 2.9b is actually three curves, one for each response region of the spectrum, and it is based upon the Young-Helmholtz theory discussed above [18, 19]. 

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