The surface segregation from free space polymer blends based on purely entropic effects is investigated using computer simulation and integral equation theory, Computer simulations are performed for tangent-hard-sphere chains of length ranging from short 10 bead chains to experimentally realistic 500 bead chains. The chain segments of one species experience a bending potential which is introduced between any two consecutive bonds and this serves to make this component stiffer than the other blend component. Computer simulations and numerical wall polymer reference interaction site model (wall-PRISM) integral equation calculations for finite hard core athermal chains demonstrate that at liquidlike densities the segments of the stiffer polymer always partition to a neutral surface, apparently independent of the length of the polymer chains in question. Although the primary factor affecting this segregation is the better local packing of the stiff chains at the surface, lattice mean-field calculations suggest that local conformational changes in the molecules also favor the stiff chains at the surface under these conditions. Further, nonlocal effects appear to be irrelevant in this context. Recently, field theoretic based models have suggested in the context of an incompressible approximation that stiffness disparity is the underlying cause for the experimentally observed surface segregation of branched molecules from blends of linear and branched hydrocarbon polymers (the branched molecules were considered more "flexible" or "conformationally smaller"). The segregation observed in the simulations, however, is both much smaller in magnitude and of the opposite sign to that seen in the field theoretic calculations. Coupled with results of independent work on the bulk behavior of these athermal mixtures, which do not capture the experimentally observed phase separation, we suggest that hydrocarbon blends, at least over the chain lengths examined, cannot be modeled in terms of purely entropic effects, but rather through the incorporation of energetics. Analytic wall-PRISM results for a thread like model of the polymer molecules are also presented, and show that the various approximations made in deriving analytical theories critically affect the magnitude and the sign of the predicted athermal segregation. The connections of our analytical work to recent field theoretic analyses is also discussed.