From: Helmut =?iso-8859-1?Q?C=F6lfen?= <coelfen@MPIKG-GOLM.MPG.DE>
  To  : rasmb@bbri.harvard.edu
  Date: Tue, 09 Oct 2001 11:15:36 +0200

Sedimentation of charged spheres / Compilation

Hello everybody,

This is a compilation of the answers I've received on my question if any 
theories or treatments of the
sedimentation of charged spheres are known. Thanks to all who have promptly 
responded for their
valuable hints.

Helmut


1) Jose Garcia de la Torre pointed me towards a reference:

"Perhaps the following reference can be useful for you
OHSHIMA,H.HEALY,T.W.;WHITE,L.R.;O'BRIEN,R.W.
JOURNAL OF THE CHEMICAL SOCIETY FARADAY TRANSACTIONS II, 80 (10), 1299
(1984).
SEDIMENTATION VELOCITY AND POTENTIAL IN A DILUTE SUSPENSION OF CHARGED
SPHERICAL COLLOIDAL PARTICLES"


2) Jo Butler gave the hint, that it is important to consider VBAR for the 
calculations

"You say that you know the v-bar for these charged spheres. While this may 
be true in vacuo, do you actually know the apparent v-bar which will be 
relevant when they have bound counterions/solvent due to their charge?
This could have a significant effect on the precision of your calculations."

This VBAR with bound counterions can be measured with the Anton Paar 
densitometer:

"Yes, if one measures the density increment under constant chemical 
potential of all diffusible components, one gets an apparent v-bar which 
does allow for the binding of solvent components.
(See Casassa, E. F., and Eisenberg, H. (1964). Thermodynamic analysis of 
multicomponent solutions, Adv Prot Chem 19, 287-395.)"



3) Arthur Rowe also gave references and pointed out the primary and secondary
charge effect

"When charged particles sediment, their differential migration with respect
to small ions present gives rise to an electric field, which retards
particle motion. That is classically known as the 'primary charge effect',
and is what you will have with your charged spheres. A so-called 'secondary
charge effect' can also arise, but only if co-/counter- ions with a
significant sedimentation rate are present - not the case I presume with
your spheres.
Migration of charged particles producing an electric field is related to the
electrophoretic retardation phenomenon, in which charged particles moving in
an electrical field are retarded as the result of a similarly induced field.
This phenomenon has long been known, numerical solutions which are probably
adequate have been computed and they fit experimental data:
Wiersema, P.H., Loeb, A.L. & Overbeek, J.Th.G. J Colloid Interface Sci. 22,
78 (1966)
Alas, as you have found, we hydrodynamics people have been less active than
our colloid science brethren - so far as I know, Pedersen's work probably
*is* the 'state of the art' ! It would of course be really nice if a quick
s upon (c, ionic strength, whatever) gave one serious charge information,
but I don't think it can be done, and I fear that the Zeta-Sizer still has
some mileage left in it.
But - guess what ? I see that next week, at the American Association for
Aerosol Research 20th Annual Conference October 15-19, 2001,in Portland,
Oregon (and we'll all be there . . . ) there is a paper being presented:
Effect of Charge on the Mobility of Singly and Multiply Charged Clusters and
Macromolecules, SVEN UDE, Yale Univ, Manuel Gamero-Castano, Yale University,
Juan Fernandez de la Mora, Yale University
A renaissance, perhaps ?"


4) Tom Laue contributed references:

"You will find a discussion of the primary and secondary charge effects in:
J. W. Williams, K. E. Van Holde, R. L. Baldwin, and H. Fujita. The Theory of
Sedimentation Analysis. Chem.Rev. 58:715-806, 1958.
and a discussion of theory in:
D. Stigter. Sedimentation of Highly Charged Colloidal Spheres. J.Phys.Chem.
84:2758-2762, 1980.
and some recent modeling in:
S. A. Allison. The Primary Electroviscous Effect of Rigid Polyions of
Arbitrary Shape and Charge Distribution. - Biophys. J. (or it may be
Biopolymers) 1998"


5) Marc Lewis had no direct reference but poined me towards the work of Fujita,
Eisenberg & Minton

Thanks again for all your help

Helmut