Density profiles and thermodynamics of rod-like particles between parallel walls

A study has been made of the density profile of mutually avoiding rod-like particles in the space between two parallel plates, held in equilibrium with a bulk phase of isotropic, semidilute rods, using a self-consistent integral equation which becomes exact as the rod aspect radio L/D --> infinity. Computer simulation investigations of finite aspect ratio systems also have been undertaken, and the extended Gibbs adsorption isotherm used 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 L/D --> infinity, the results confirm both the thermodynamic consistency of the integral equation, and the accuracy of previous work on the depletion force (based on calculating only the contact density of rods at the walls). To extract thermodynamic data from the 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. Precise thermodynamic results for confined rod systems have been obtained from simulation for the first time. Those for L/D = 10 and 20 are shown to be quite close to the predictions for infinite aspect ratio.