Reciprocal radius of ionic atmosphere

Ks for isentropic compressibility [-(l/y)(3W3P)s]). 3. Symbol for reciprocal radius of ionic atmosphere. 

R is the radius of the polyion sphere, Z is the charge number of the polyion, C, is the concentration of added salt (mol/1), and k is the reciprocal length of ionic atmosphere. If we calculate the free charge distribution around the polyion sphere, we have Figure 3, and the effective charge of the polyion sphere [ ] is [4]... 

For a single electrolyte a quantity k may be defined as the reciprocal of the radius of the ionic atmosphere and is proportional to the square root of the concentration. In other words, the charge in the ionic atmosphere may be visualized as being uniformly distributed over the surface of a sphere of radius 1/k. 

The quantity, has units m, i.e. has the units of a length and as such it is often stated that /c represents the extent of the ionic atmosphere around the central j cation. Such a description can only be given if the value of k is measured from r = a, since the ionic atmosphere must always lie at distances, r > a. Alternatively it has been stated that k represents the reciprocal of the effective radius of the ionic atmosphere, again with the proviso that this is measured from r = a. However, these could be misleading statements, as is shown by the diagrams below. 

A key quantity in the Debye-Huckel theory, leading to the values of the constants A and B, is the screening length, k, the average reciprocal of the radius of the ionic atmosphere surrounding an ion in the solution, made up essentially by ions of the opposite charge. The square of this quantity is proportional to the ionic strength of the solution and also to the reciprocal of the product w T ... 

K has the dimension of reciprocal length. This is the reason for referring to k as the Debye radius. As we shall soon see, this may be interpreted as the effective radius of the ionic atmosphere. 

The quantity p (r), the fraction of charge between the spherical shells of radius r and r + dr, is plotted against r in Fig. 7. We can see from this figure that a central ion is surrounded by an atmosphere of ions of opposite sign, and that the thickness of this ionic atmosphere is 1/K, the reciprocal of the Debye-Huckel parameter. 

T = Xc,zf being the ionic concentration and s, the viscosity and the dielectric constant of the solvent, respectively , the reciprocal average radius of the ionic atmosphere a, the mean distance of closest approach of ions

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