Thickness Dependence of the Glass Transition Temperature in Thin Polymer Films

Abstract

In this paper the glass transition temperature (Tg) in thin polymer films has been studied. Ellipsometry
\nhas been used to measure Tg of poly(R-methylstyrene) (PAMS) thin films as a function of the film thickness
\nfor two molecular weights. When the films were thinner than a few hundred angstroms, substantial
\nreduction in Tg was apparent. The Tg depression pattern did not show the difference between molecular
\nweights. The Michaelis-Menten equation was adapted and used to fit the experimentally obtained Tg
\ndata. From this analogized Michaelis-Menten function fitting, the fitting parameters Tg,¥ and ê could be
\nobtained. The obtained Tg,¥ corresponded with the bulk Tg, and the parameter ê was correlated with the
\nstatistical segment length. A continuous multilayer model was proposed and derived to describe the effect
\nof surface on the observed Tg reduction in thin films, and the depth-dependent Tg profile was obtained.
\nThese results showed that Tg at the top surface was much lower than the bulk Tg and gradually approached
\nthe bulk Tg with increasing distance from the edge of the film. The model and equation were modified to
\napply for the polymer coated on the strongly favorable substrate and the freely standing film.