Polymer properties, such as their mechanical strength, barrier properties, and dielectric response, can be dramatically improved by the addition of nanoparticles. This improvement is thought to be because the surface area per unit mass of particles increases with decreasing particle size, R, as 1/R. This favorable effect has to be reconciled with the expectation that at small enough R the nanoparticles must behave akin to a solvent and cause a deterioration of properties. How does this transition in behavior from large solutes to the solvent limit occur? We conjecture that for small enough particles the layer of polymer affected by the particles ("bound" polymer layer) must be much smaller than that for large particles: the favorable effect of increasing particle surface area can thus be overcome and lead to the small solvent limit with unfavorable mechanical properties, for example. To substantiate this picture requires that we measure and compare the "bound polymer layer" formed on nanoparticles with those near large particles with equivalent chemistry. We have implemented a novel strategy to obtain uniform nanoparticle dispersion in polymers, a problem for many previous works. Then, by combining theory and a suite of experimental techniques, including differential scanning calorimetry and positron annihilation lifetime spectroscopy, we show that the immobilized poly(2-vinylpyridine) layer near 15 nm diameter silica particles (similar to 1 nm) is considerably thinner than that at flat silica surfaces (similar to 4 to 5 nm), which is the limit of an infinitely large particle. We have also determined that the changes in the polymer's glass-transition temperature due to the presence of this strongly interacting surface are very small in both well-dispersed nanocomposites and thin films ( < 100 nm). Similarly, the polymer's fragility, as determined by dielectric spectroscopy, is also found to be little affected in the nanocomposites relative to the pure polymer. While a systematic study of the dependence of the bound polymer layer thickness on particle size remains an outstanding challenge, this first study provides conclusive evidence for the hypothesis that the bound polymer layer can be significantly smaller around nanoparticles than at chemically similar flat surfaces.