Analyzing the Surface Temperature Depression in Hot Stage Atomic Force Microscopy with Unheated Cantilevers: Application to the Crystallization of Poly(ethylene oxide)

Abstract

The in situ study of phase transitions in polymers by real-time atomic force microscopy (AFM) has received much attention recently. In this paper we report on the accuracy of surface temperatures measured during variable-temperature AFM experiments. In AFM studies on organic and polymeric samples at elevated temperatures, the presence of an unheated AFM cantilever and tip close to the sample surface can result in a significant depression of the surface temperature. This effect was estimated by measuring the temperature depression quantitatively for a series of n-alkanoic acids in different gases, i.e., argon, air, and helium. We developed an analytical expression by modeling the observed surface temperatures and their distance dependence using heat transfer theory, which allows us to predict the temperature effects in different experiments. For poly(ethylene oxide) (PEO) we predict that no temperature correction is necessary for films thinner than 500 nm. To test the temperature calibration, we have acquired quantitative data on the crystallization of individual PEO lamellae in thin films on silicon surfaces. The lamellar growth rates, lamellar thicknesses, and melting ranges obey the typical dependencies on crystallization temperature and supercooling known from bulk polymer crystallization. The values for equilibrium melting temperatures, as well as surface free energies of the fold surfaces, determined by Hoffman−Weeks extrapolation, the Gibbs−Thompson equation, and the Hoffman−Lauritzen theory, compare favorably with values published in the literature and hence validate our model calculations.