Debye-Huckel equation electrostatic potential

Except at absolute zero, every molecule must have one or more sources of electrostatic potential. Even if a molecule bears no net electrostatic charge, atomic dipoles which result from the motion of electrons in their orbits around a nucleus will give rise to dispersive van der Waals or London interactions. These atomic dipoles insure that a solute molecule has a small but finite electrostatic interaction energy with the surrounding solution molecules. For example, in aqueous ethanol solutions, the dipole—dipole interaction between ethanol and water molecules becomes the primary interaction energy. Ethanol molecules are not ionic, so use of the Debye—Huckel equation (57), based on Coulombic interaction, carmotbe used to determine the activity coefficient of an aqueous ethanol solution. At sensible... 

In order to describe the effects of the double layer on the particle motion, the Poisson equation is used. The Poisson equation relates the electrostatic potential field to the charge density in the double layer, and this gives rise to the concepts of zeta-potential and surface of shear. Using extensions of the double-layer theory, Debye and Huckel, Smoluchowski,... 

Poisson-Boltzmann equation — The Poisson-Boltz-mann equation is a nonlinear, elliptic, second-order, partial differential equation which plays a central role, e.g., in the Gouy-Chapman (- Gouy, - Chapman) electrical -> double layer model and in the - Debye-Huckel theory of electrolyte solutions. It is derived from the classical -> Poisson equation for the electrostatic potential... 

Accordingly, the electrostatic potential will decrease when going away from the interface (Fig. 12.2b), according to the Debye-Huckel theory discussed in Section 6.3.2. We recall the equation... 

We will not discuss the details of the Debye-Huckel theory. The main idea of the theory was to pretend that the ions in a solution could have their charges varied reversibly from zero to their actual values. This charging process created an ion atmosphere around a given ion with an excess of ions of the opposite charge. The reversible net work of creating the ion atmosphere was calculated from electrostatic theory. According to Eq. (4.1-32) the reversible net work is equal to AG, which leads to equations for the electrostatic contribution to the chemical potential and the activity coefficient for the central ion. The principal result of the Debye-Hiickel theory is a formula for the activity coefficient of ions of type i ... 

In a continuum solution, the eleefrostatic potential, Py (r), surrounding each solute ion, must be a solution to the Poisson— Boltzmann equation. The Debye— Huckel solution to the linearized Poisson—Boltzmann equation [15,20,23] gives the electrostatic potential at a distanee, r, from a solute ion, Y of diameter, ay, and valence, Vy, in a solvent wifli dieleetric strengfli, e, as... 

The derivation of the Debye— Hiickel equation for the activity coefficient is based on the linearized Boltzmann equation for electrostatic charge distribution around an ion. This limits the applicability of Eq. (57) to solutes with low surface potentials, which occurs for solution concentrations of monovalent ions of < 0.01 M. However, it is important to note that die method used for deriving activity coefficient equation (25) is based on rigorous thermodynamics and is not limited by the Debye—Huckel theory. If, for example, the Gouy—Chapman equation [22] was... 

The real behavior of systems is described by the activity coefficient y,. Instead of the concentration C of a dissolved species, one uses the activity a, = c y,. In the light of the Debye-Hiickel theory, y takes care of the electrostatic interactions of the ions. This is the main interaction for charged species in comparison with the smaller dipole and Van der Waals forces, which may be important in the case of uncharged species, but which are not included in the Debye-Huckel theory. The chemical potential p depends on the concentration according to Equation 1.37. 

Fig. 4. Comparison between the electrostatic potentials around a rod-like polyion calculated with and without the Debye-Hiickel approximation. The broken lines denote the calculated values of Equation (7), while the solid lines denote the values calculated from the Poisson-Boltzmann equation without the Debye-Huckel approximation. (Reproduced from Reference [6].)...

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