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# Density Profiles and Thermodynamics of Rod-like Particles
between Parallel Walls

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

Cavendish Laboratory, Madingley Road,

Cambridge, CB3 OHE,
UK.

Department of Physics and Astronomy,

University of Edinburgh,
JCMB King's Buildings,

Mayfield Road, Edinburgh EH9 3JZ, UK.

Van't Hoff Laboratory, University of Utrecht,

Padualaan 8,
3584 Utrecht, The Netherlands.

### Abstract:

We study the density profile of mutually avoiding
rodlike particles in the space between two parallel plates, held in
equilibrium with a bulk phase of isotropic, semidilute rods. We
employ a self-consistent integral equation, which becomes exact as
the rod aspect ratio . We also use computer simulation
to study finite aspect ratio systems. We then use an ``extended Gibbs
adsorption isotherm" to express the free energy (as a function of
plate separation) in terms of an integral of the surface excess with
respect to chemical potential. This allows thermodynamic properties,
such as surface tension and the depletion force between plates,
to be found. For
, the results confirm both the thermodynamic
consistency of the integral equation, and the accuracy of our
previous work on the depletion force (which was based on calculating
only the contact density of rods at the walls). To extract
thermodynamic data from simulations, the same Gibbs isotherm
method is very efficient, as it utilizes the statistics of the full
density profile rather than just the contact density. This allows
precise thermodynamic results for confined rod systems to be
obtained from simulation for the first time. Those for
*L*/*D* = 10,20 are shown to be already quite close to the predictions
for infinite aspect ratio.

*Yong Mao *

Tue Apr 22 14:50:08 BST 1997