Diffusion of Charged Colloidal Particles at Low Volume Fraction:
Theoretical Model and Light Scattering Experiments
DIMITER N. PETSEV 1 AND NIKOLAI D. DENKOV
Laboratory of Thermodynamics and Physico-chemical Hydrodynamics, Facultyof Chemistry,
Universityof Sofia, 1126 Sofia, Bulgaria
Received April 30, 1991; accepted August 21, 1991
An appropriate mean force potential was utilized in Felderhof's Theory to derive simple analytical
expressions for the concentration dependence of the collective and short time self diffusion coefficients,
as well as for the sedimentation velocity of charged spherical particles. It is demonstrated theoretically
that the osmotic viriat and the Oseen hydrodynamic terms play a dominant role. To check the theoretical
model, the dependence of the collective diffusion coefficient on the volume fraction of latex particles
was experimentally studied. Dynamic light scattering was used at several different concentrations of
electrolyte. It turns out that our experimental results, as well as the results of other authors, are in very
good agreement with the proposed theoretical model. The results show that the increase of the electrolyte
concentration leads to increase of the particle charge, but almost does not change the particle surface
potential. A minimum in the dependence of the diffusion coefficient of a single particle on the ionic
strength was also obtained. © 1992 Academic Press, Inc.
1. INTRODUCTION
The first step in the quantitative treatment
of the Brownian diffusion was made by Ein-
stein ( 1 ). He expressed the diffusion coefficient
of spherical particles through the well known
Stokes-Einstein relation,
KT
DSE - 6~r~a ' [ 1.1 ]
where DSE is the diffusion coefficient, KT is
the thermal energy, n is the solvent shear vis-
cosity, and a is the colloidal particle radius.
This formula is valid for a single sphere, sub-
jected to Brownian motion when no other
spheres are present. The latter is a severe re-
striction, especially when the suspension is not
infinitely diluted and/or long range interpar-
ticle forces are acting. Even the short range
hard sphere interactions may affect the value
of the diffusion coefficient, above a certain
1To whom correspondence should be addressed.
Journal ~2f Colloid and lnterface Science, Vol. 149, No. 2, March 15, 1992
concentration of colloidal particles. Further-
more, such situations lead to a distinction of
two types of diffusion coefficients: (i) self-dif-
fusion coefficient, given by (2)
f0 °
1 (V(0). V(t))dt, [1.21
Ds =3
where Ds is the self diffusion coefficient, V is
the velocity of a single particle, and t is time;
(ii) collective diffusion coefficient, which is the
quantity that multiplies the concentration
gradient in Fick's Law,
j = -Dc grad C. [1.31
In Eq. [1.3], j is the particle flux, Dc is the
collective diffusion coefficient, and C is the
particle concentration. When the suspension
is infinitely diluted, the two coefficients Ds and
Dc coincide. However, they may differ in the
ease of finite concentrations of Brownian par-
ticles. For example, if hard sphere interactions
are present, Ds decreases with the particle
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Copyright © 1992 by Academic Press, Inc.
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