| Using general scaling arguments combined with mean-field theory and exact solution for the spherical model, we investigate the critical and off-critical behavior of the Casimir forces in fluid films of thickness L governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of the temperature and of the chemical potential of the fluid. We find that the total force is attractive both below and above the bulk critical temperature. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point, where critical density fluctuations arise, or in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of L-d, in the capillary condensation regime the force is much stronger with maximal amplitude decaying as L-1. In the latter regime we observe that the long-ranged tails of the fluid-fluid and the substrate-fluid interactions further increase that amplitude in comparison with systems with short-range interactions only. Although in the critical region the system under consideration asymptotically belongs to the Ising universality class with short-ranged forces, we find deviations from the standard finite-size scaling. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region. Finally, we discuss possible practical implications of the theory presented concerning the work of grippers in nanotechnology. |
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