The distribution of low moleculer ions and the electric potential around a much charged colloidal particle in solution are discussed. The Poisson-Boltzmanm equation is adopted, but both the Debye-Hückel and the Gronwall methods are not used. In is assumed that each colloidal particle (of the radius a and the charge Ne
0) has a spherical free volume (of the radius R), in which n+j gegenios and j neben-ions are distributed. Then the Poisson-Boltzmann equation can be written as follows:
e
0/kT[d
2ψ/dr
2+2/rdψ/dr]=Κ
2e
e0ψ/kT-j/n+j∫
Rae
e0ψ/kTr
2dr/∫
Rae
-e0ψ/kTr
2dre
-e0ψ/kT, Κ
2=(n+j)e
02/DkT∫
Rae
e0ψ/kTr
2dr,
Where ψ denotes the electric potential, D the dielectric constant, and the integrals are normalization factors. In the former paper, the solution of this equation was calculated in the case when Κa<<1. In this paper, the equation is approximately solved when Κa>>1, and the following results are obtained.
(1) The Debye-Hückel approximation may be used in the region R≥r≥r
1. Where r
1 satifies the relation e
0ψ(r
1)/kT=1/Κa. And r
1/a is nearly equal to unity, even when the colloidal charge becomes ∞.
(2) The region r
1≥r≥a is just the non Debye-Hückel region. The potential in this region may be obtained by neglecting the term of dψ/dr in the equation, that is, ψ can approximately be expressed by the solution of one dimensional Poisson-Boltzmann equation.
(3) Κ
2 is independent of the colloidal charge and is given by the following formula:
Κ
2=3je
02/(R
3-a
3)DkT.
These results mean the characteristic condensation of gegenions in the vicinity of the surface of the colloidal particle.
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