Subject: Re: CCL:Question about charged micellar spheres

From: [email-masked] (Eberhard von Kitzing)
Date: Mon, 24 Jul 95 15:12:26 +0200

Dear Dr. Shapiro,

>     Suppose there are two sets of positively-charged spherical micelles
>one "big" and one "small", and these micelles are capable of binding to a
>surface.  It stands to reason that when two such positively-charged micelles
>bind to a surface they will not come right up against one another because
>they will be repulsed by their mutual positively-charged surfaces.  Now, if
>the _density_ of charges on the surface of the spheres is the same (i.e.,
>both the big micelles and the small micelles have the same number of positive
>charges per unit surface area), will two small micelles be able to sit closer
>to one another than two large micelles, i.e., will there be greater repulsive
>forces between two large micelles resulting in their sitting further away
>from one another than between the two smaller micelles?

The interaction of the micelles with the wall depends on the charge density
of the wall, the diameter d of the micelles compared to the Debye-length
lDH of the system, i.e., the ionic strength of the surounding electrolytes.

As long as the Debye length lDH is small compared to the diameter d of the
micelles, the concentration of the micelles at the wall (before contact)
will be close to the bulk solution concentration. Any charge at the wall
will be screened by the ions in solution. If, however, lDH >> d, the
micelles and the ions will compete with each other in screening the wall
charges. 

On has to bear in mind that the binding of micelles to the wall may change
the charge density in the wall.

> If you could explain the answer to this problem in a
>straightforward mathematical way, I would be most grateful.

You may have a look at:

David C. Grahame (1947). "The Electrical Double Layer and the Theory of
Electrocapillarity." Chemical Reviews 41 441-501.

Robert U. Muller and Alan Finkelstein (1972). "The effect of surface charge
on th voltage-dependent conductance induced in thin lipid membranes by
Monazomycin." The Journal of General Physiology 60 285-306.

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Eberhard von Kitzing
Max-Planck-Institut fuer Medizinische Forschung
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