Debye-Hiickel bulk model

Together these essentially replace the Poisson-Boltzmann cell model with the Debye-Hiickel bulk model, allowing many more systems to be treated analytically, although not necessarily accurately, and providing considerable insight into the physical characteristics of electrolyte solutions. 

It was shown in Chapter 2 that the theoretical models defined by Eqs. (3.1)-(3.10) can be used also to describe the behaviour of the solutions of ionic surfactant RX in absence and presence of inorganic electrolyte XY. In this case, the Frumkin constant, in addition to the Van der Waals interaction, involves also the inter-ion interaction in the surface layer. Now instead of the concentration c the corresponding adsorption isotherms should be a function of the mean ionic products c = f (Crx xy rx > where f is the average activity coefficient of ions in the solution bulk. An equation accurately representing measured values of f. is the Debye-Hiickel euqation corrected for short-range interactions... 

At low surface potentials this equation reduces to the Debye-Hiickel expression above. Second, an inner layer exists because ions are not really point charges and an ion can only approach a surface to the extent allowed by its hydration sphere. The Stern model incorporates a layer of specifically adsorbed ions bounded by a plane, the Stem plane. In this case, the potential changes from P° at the surface, to (5) at the Stern plane, to P = 0 in bulk solution. 

The basic idea of embedding a hard core into the traditional theories like the Debye-Hiickel theory, (bulk electrolytes or Gouy-Chapman theory, metal-electrolyte interfaces), leads to tractable, and in some cases (colloidal suspensions) good theories, provided that we can ignore the effect of the structure of the solvent by using a continuum dielectric model (primitive model). 

Bulk Model Apparent Debye-Hiickel Surface Charge Density... 

Bulk Model Nonlinearizing the Debye—Hiickel Solution... 

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