Effects of Geometrical Confinement on Depletion Force in Colloidal System

The depletion force on a large hard sphere in a solvent of small hard spheres under geometrical confinement is investigated by using local density integration method through Monte Carlo simulations. The model considered here is a rectangular box with two boundless hard plates placed in a direction. Small hard spheres are randomly distributed in the box to form a hard sphere fluid. The number of small spheres is determined by the given volume fraction. The size ratio of the large to small-sphere is 5. Three systems maintained at bulk volume fractions 0.116, 0.229, and 0.341 are studied. The effects of geometrical confinement are taken into account through changing the distance of the two plates. To get rid of the finite size effect, the sizes of the box in other two directions are enlarged in a way when the distance between the two plates is decreased. The configurations of the small spheres are sampled according to the Metropolis algorithm with the two large spheres fixed at a separation. Each small sphere is chosen and relocated using a trial displacement. The new position is accepted so long as it does not result in an overlap with the large hard spheres, the other small spheres or the plates. To take the geometrical confinements into account, the fixed boundary condition is used corresponding to the two plates. Meanwhile the magnitude of the maximum random displacement is adjusted so that the overall acceptance ratio is about 0.3-0.5. The numerical results show that the depletion force is affected by the geometrical confinements. Furthermore, the nearer the two plates are to each other, the larger the effects from the geometrical confinement will be.