We report measurements of the glass transition temperature, $T_g,$ in free standing polymer films in a low $M_n$ limit where chain confinement effects are not observed. The measured $T_g$ values are accurately described by a layer model incorporating a mobile surface layer with a size determined by the length scale of cooperative dynamics. The analysis leads to a surface $T_g$ value and length scale of cooperative motion near bulk $T_g$ which quantitatively agree with independently determined values. The model and parameters provide a framework within which all previous measurements of $T_g$ values in thin supported films may be understood and provides values for the length scale of cooperative motion over an extended range of temperatures below the bulk $T_g$ value.

• Received 23 February 1999

DOI:https://doi.org/10.1103/PhysRevE.61.R53