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# Depletion Force In Colloidal Systems

**Y. Mao , M. E. Cates and H. N. W. Lekkerkerker **

Cavendish Laboratory, Madingley Road,

Cambridge, CB3 OHE, UK.

Department of Physics and Astronomy,

University of Edinburgh, King's Buildings,

Mayfield Road, Edinburgh EH9 3JZ, UK.

Van't Hoff Laboratory, University of Utrecht,

Padualaan 8, 3584 Utrecht, The Netherlands.

### Abstract:

The entropic depletion force, in colloids,
arises when large particles are placed in a solution of smaller
ones, and sterically constrained to avoid them. We calculate the
interaction between large spheres (of radius *R*) in a dilute solution of
mutually avoiding small spheres (of diameter and volume fraction
), to third order in . In addition to the well-known attractive
force for , we find a repulsive barrier at larger separations,
and beyond that a secondary minimum. Except for unusually large size ratios
(perhaps abetted by relatively high density ), these features
of the interaction potential are too small, compared to , for
kinetic stabilization (arising from the barrier) or flocculation into the secondary
minimum, to be widespread, although such effects are
possible in principle. For feasible size ratios,
the same features should have observable consequences
for the radial distribution function of the large spheres. Such effects can be viewed as
precursors, at low density, of liquidlike structuring
(solvation forces) expected at higher . Our third order calculation
gives satisfactory agreement with a recent computer simulation at moderate
density and size ratio ( ).

*Yong Mao *

Tue Apr 22 14:30:30 BST 1997