We report a detailed study, using state-of-the-art simulation and theoreticalmethods, of the depletion potential between a pair of big hard spheres immersedin a reservoir of much smaller hard spheres, the size disparity being measuredby the ratio of diameters q=\sigma_s/\sigma_b. Small particles are treatedgrand canonically, their influence being parameterized in terms of theirpacking fraction in the reservoir, \eta_s^r. Two specialized Monte Carlosimulation schemes --the geometrical cluster algorithm, and staged particleinsertion-- are deployed to obtain accurate depletion potentials for a numberof combinations of q\leq 0.1 and \eta_s^r. After applying corrections forsimulation finite-size effects, the depletion potentials are compared with theprediction of new density functional theory (DFT) calculations based on theinsertion trick using the Rosenfeld functional and several subsequentmodifications. While agreement between the DFT and simulation is generallygood, significant discrepancies are evident at the largest reservoir packingfraction accessible to our simulation methods, namely \eta_s^r=0.35. Thesediscrepancies are, however, small compared to those between simulation and themuch poorer predictions of the Derjaguin approximation at this \eta_s^r. Therecently proposed morphometric approximation performs better than Derjaguin butis somewhat poorer than DFT for the size ratios and small sphere packingfractions that we consider. The effective potentials from simulation, DFT andthe morphometric approximation were used to compute the second virialcoefficient B_2 as a function of \eta_s^r. Comparison of the results enables anassessment of the extent to which DFT can be expected to correctly predict thepropensity towards fluid fluid phase separation in additive binary hard spheremixtures with q\leq 0.1.
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