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Why, and why the effect depends on chain length in free-standing films, is debated.","posed_since":"","precise":"Free-standing polystyrene films thinner than about $8 \\times 10^{-6}$ cm (800 Angstrom) show $T_g$ reductions of tens of kelvin relative to bulk, with a dependence on molecular weight not seen in supported films. Determine whether the reduction arises from a mobile surface layer propagating into the film, from chain confinement or from another mechanism, and predict $T_g(h, M)$ for film thickness h and molecular weight $M$.","problem_ref":"74d4ea5b0c51fcaa9aae3890d7ae81ba62aae73a2fdb2d28e8033b4ef8808e08","references":"","settled_by":"A theory that predicts $T_{g}(h, M)$ for free-standing and supported films and agrees with measurements of local mobility profiles across the film.","status_note":"","title":"Why the glass transition temperature drops in thin polymer 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