We propose a theory for the structure of the interphase in polymeric nanocomposites based on the freely-jointed chain near an impermeable spherical inclusion. The theory considers only the entropic exclusion between a polymer and the inclusion. The radius of gyration of the polymer chain and its distortion from spherical symmetry are perturbed strongly when the chain end is closer than 3R(g0) from the surface of the sphere, where R-g0 is the unperturbed radius of gyration. Also, the maximum expansion of the chain is bounded by (4/3)(1/2), equal to a 15% increase. The shape of the polymer chain is elongated tangentially to the surface when the chain end originates in the interphase, but elongates radially due to entropic repulsion when the chain end is very close to the surface of the sphere. All the distortions of the polymer conformation from ideality, and hence the spatial extent of the interphase, occur within the depletion region associated with colloids. The model is used to explain recent experimental results showing that polymer chain dimensions increase in the presence of nanoparticles. The model quantitatively reproduces the observations at low filler loadings using no adjustable parameters, suggesting that entropic arguments can describe the majority of the effect there. (C) 2010 Elsevier Ltd. All rights reserved.