The Debye Charging Process

In the next section we shall derive the same expression (6.12.94) by a different charging process, known as the Debye charging process. 

In section 6.12.5 we computed the activity coefficient by charging one ion a in a system in which all the other ions were fully charged. Here we compute the work of charging all ions simultaneously. We start with the system at 7, F, N with the charging 

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The electric part Eei of the free energy of double-layer interaction (Eq. (5.4)) can be expressed in a different way on the basis of the Debye charging process in which all the ions and the particles are charged simultaneously from zero to their full charge. Let /I be a parameter that expresses a stage of the charging process and varies from 0 to 1. Then F x can be expressed by... 

Now, the Guntelberg charging process was suggested several years after Debye and Htickel made their theoretical calculation of the activity coefficient. These authors... 

Describe the difference between the Guntelberg and Debye charging processes. Which process should be more effective in deriving an equation for the activity coefficient ... 

The primary particle involved in the screening process is the mobile electron. One has then the problem of a self-consistent calculation of the charge distribution in the neighborhood of a test charge. The Thomas-Fermi approach to this problem is the analog of the Debye-Huckel calculation wherein allowance has been made for the Pauli exclusion principle. From any standard text one can obtain the Poisson equation (19)... 

V is the speed of sound, 6 is the Debye temperature, tc is the total phonon-scattering rate, w is the phonon-scattering rate due to three phonon normal processes. In this model, two additional scattering mechanisms of phonon (by point defects and by charge carriers) are considered. 

Another and possibly more convincing charging process has been used by P. Debye. Physik. Z t 25, 97 (1924), and consists in charging all the tons simultaneously by a given fraction of their total charge. 

The water species involved in this reaction must be neutral (and not OH") because of the fact that the rate of uracil photohydrate formation is independent of NaCl concentration up to 1M, and is the same in unbuffered water as in 0.1M phosphate buffer. The rate constant for photohydrate formation in CU was also observed, in a series of runs all made in the same day with the same initial CU concentration, to be 0.0418 0.010 at NaCl concentrations of 0, 0.001M, 0.01M, 0.1 M, and 1M. The lack of salt effect is consonant, according to Debye-Huckel theory (3) with the reaction of a charged species (UH+) with an uncharged species, as written in Reaction f, and eliminates reaction between two charged species in the product-forming process. 

As, a rule this condition is approximately satisfied. In the absence of processes resulting in charge separation, a stream remains electrically neutral except for the areas adjoining the charged surfaces. These areas are known as double electric layers or Debye s layers. Their thickness is small (from 1 up to 10 nanometers). The account of these layers is important when interactions between the small particles, and processes in the immediate proximity of the charged surfaces are considered. 

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