Debye-Huckel length

Equation (2.30) represents the potential produced by a charge Zt of ionic atmosphere at a distance 1/k. The quantity 1/k has the dimensions of length and is appropriately called the thickness (or radius) of the ionic atmosphere in a given solution. Also, k Ms called the Debye-Huckel length and is assigned symbol Erom Eq. (2.21)... 

The average thickness of the double layer, lk, that is, the Debye-Huckel length, is given as (Chattoraj and Birdi, 1984) ... 

University in Ithaca. Nobel Prize in 1936 for contributions to the knowledge of molecular structure based on his research on dipole moments, X-ray diffraction (Debye-Scherrer method), and electrons in gases. His investigations of the interaction between ions and electric fields resulted in the - Debye-Huckel theory. See also -> Debye-Falkenhagen effect, - Debye-Huckel limiting law, - Debye-Huckel length, - Debye relaxation time. 

Debye length — (also - Debye-Huckel length) In the formulation of the - Debye-Huckel theory the counter ions surrounding the sample ion under consideration are substituted in an attempt of simplification by an ionic cloud. The radius of this ionic cloud or atmosphere giving the distance between the ion under consideration and the location where dq/ (1/k) is at maximum (dq is the charge enclosed in a shell of dr thickness around the ion, and k is the - Debye-Huckel parameter). The Debye length rD (LD and other symbols are also used) also is given by... 

See also -> Huckel equation of electrophoretic mobility, -> Debye-Huckel approximation, -> Debye-Huckel length, -> Debye-Huckel limiting law, -> Debye-Huckel-Onsager theory, -> Debye-Huckel parameter. 

Hence, the maximum value of the charge contained in a spherical shell (of infinitesimal thickness dr) is attained when the spherical shell is at a distance r = rc from the reference ion (Fig. 3.15). For this reason (but see also Section 3.3.9), re" is known as the thickness, or radius, of the ionic cloud that surrounds a reference ion. An elementary dimensional analysis [e.g., of Eq. (3.43)] will indeed reveal that k has the dimensions of length. Consequently, k is sometimes referred to as the Debye-Huckel length. 

Debye-Huckel length k. Hence, if the ions diffuse to a distance k the central ion... 

A typical disjoining pressure variation with film thickness is shown in Figure 7a. At small thicknesses, a repulsive force is observed which can be fitted with an exponential form exp-(jch), as expected for screened electrostatic repulsion k is close to the calculated inverse Debye Huckel length in the solution ... 

Under the most physiological conditions, the Debye-Huckel length (1/k) is about 10 A. At distances greater than 2 to 3kR, the difference between and becomes negligibly small. 

Here I is the ion strength of the solution, and the factor is inversely related to the Debye-HUckel length, measuring how far the electrostatic effects extend into the solution. The sinh( 0(r)/kT) term only applies for the region corresponding to the solvent, i.e. for r outside the cavity. Since q kT is dimensionless, the PBE is often written in terms of a reduced potential u instead. 

The most important parameter in equations (7.37) to (7.39) is k, which has the dimension of the reciprocal of length. In water at 25 C, = 0.329 /7A". Distance is the Debye-Huckel length and represents the thickness of the diffuse layer. This happens to be a misnomer because, over distance /c , the potential decreases only by j/exp(l) = tpd/2.1, but, in the weak potential approximation, the diffuse layer [equation (7.38)] can be treated as a parallel-plate capacitor Q = 6K with plates separated by distance /c . The variation in the potential in the solution, as a function of the distance from the surface, depends on the concentration and the charge of the ions present in the electrolyte (Figure 7.6). 

Debye-Huckel length 239 Dehydration 32, 213 Diaspore, see Aluminum a-AlOOH Diffuse layer 216,237 Dissolution-crystallization 44. 54, 72. 83. 88. 108... 

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