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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 …