Over the past 15 years, deviations in the glass transition temperature (Tg) of thin polymer films from bulk Tg have been characterized extensively. Considerably less work has been published concerning the elastic modulus of thin films, and there have been mixed results concerning the direction of deviations from bulk behavior. Film wrinkling and AFM based approaches have indicated a reduction in modulus with decreasing thickness while bubble inflation, nanoindentation, and tensile testing of nanofibers suggest an increase in modulus upon confinement. Brillouin light scattering (BLS) showed no change in modulus in one study, while a second BLS study reported a large increase in modulus for thin films. We have applied two new non-contact measurements to investigate the stiffness of thin and ultrathin polymer films. X-ray photon correlation spectroscopy (XPCS) studies have been performed on polystyrene (PS) and poly(2-vinyl pyridine) (P2VP) single layer films supported on silica. Polystyrene has also been studied in a bilayer geometry with three polymer underlayers, poly(4-vinyl pyridine) (P4VP), poly(isobutyl methacrylate) (PiBMA) and crosslinked poly(dimethyl siloxane) (PDMS). The XPCS technique probes the relaxation times of thermally induced capillary waves at the surface of a film, and the electric field of the x-rays decays evanescently in the top ~10 nm of the film due to the experimental geometry. Studies of PS single layer films on silica at 110 °C (Tg,bulk + 10 °C) show a stiffening behavior upon confinement in terms of the capillary wave relaxation times. For sufficiently large values of the in-plane scattering wavevector (q), the relaxation times of films ranging from 29-120 nm can be rescaled by monitoring τ/h as a function of qh, where τ is the measured capillary wave relaxation time and h is the film thickness. For qh > 1, all of the film relaxation times can be superposed, in accord with predictions from capillary wave theory. For qh < 1, stiffening behavior is observed where relaxation times are disproportionately longer in the thinner films, beyond what can be accounted for by capillary wave theory. Stiffening is not observed at 120 or 140 °C, where all of the film relaxation times superpose over the entire accessible range of qh. The same behavior is observed in P2VP supported on silica, a system which shows an increase in Tg upon confinement. Thus, this stiffening behavior appears uncorrelated with Tg-confinement effects.
Bilayers of thin and ultrathin PS on different bulk substrates were also studied, and revealed a connection between substrate modulus and PS surface relaxation times. The relaxation times of a 120 nm thick PS layer on the hardest substrate (silica) were roughly two orders of magnitude longer than for PS on the softest substrate (PiBMA). The order of relaxation times followed the order of substrate modulus: silica > P4VP > PDMS > PiBMA in order of decreasing modulus at 110 °C. The difference in relaxation times for PS on silica and PiBMA grew to roughly three orders of magnitude for 30 nm thick PS layers indicating a growth of this effect upon confinement. Interestingly, the effect of substrate modulus is not observed at 150 °C. The stiffening behavior observed for PS single layer films is also observed in the bilayer films, where a 30 nm PS layer on P4VP is stiffer than a 120 nm PS layer on P4VP. Thus, at temperatures near Tg we see that films stiffen upon confinement, and soften with decreasing substrate modulus. Confinement effects and substrate modulus effects are not observed at higher temperature. The XPCS measurements represent the first reported confinement effects by this technique and are the first experiments to indicate a pronounced dependence of thin film modulus on supporting material at thicknesses greater than 100 nm.
Fluorescence is also used to probe stiffness in confined polystyrene (PS) films through the intensity ratio (I3/I1) of the dye molecule pyrene. Pyrene fluorescence is sensitive to the polarity of its local environment because in a polar environment, excited state pyrene undergoes dipole-dipole coupling with the polar solvent molecules. These molecules then orient around the dye molecule which leads to a less mobile environment for pyrene and a lower I3/I1 value is measured. Recently, our research group has used I3/I1 to measure Tg in PS films, and I3/I1 decreases with decreasing temperature as the system becomes more dense. Thus, we hypothesize that lower I3/I1 values correspond to a stiffer environment. Films of PS were investigated on two substrates, glass and crosslinked PDMS, as well as in the free standing geometry. For all films exceeding ~400 nm, I3/I1 measured at 60 °C is independent of film thickness indicating a bulk response. With decreasing film thickness, free-standing PS shows softening (an increase in I3/I1) below ~400 nm. The I3/I1 value reaches a maximum at ~200 nm, at which point stiffening behavior (a decrease in I3/I1 with film thickness) is observed in films less than 200 nm thick. Silica- and PDMS-supported PS films show no softening, but report stiffening for films less than ~200 nm thick. For sufficiently thin films (less than 30 nm), I3/I1 is the same within experimental error for both supported and free standing PS. The stiffening behavior observed is not in accord with the Tg reductions seen for PS on silica; however, a stiffening in terms of elastic modulus and rubbery compliance has been reported by other research groups. Our XPCS results also suggest stiffening upon confinement in PS films or bilayers. This work represents the first use of I3/I1 to specifically monitor stiffness, and this technique can be extended to probe the distribution of stiffness within polymer films. By strategically placing labeled layers at different points (e.g. free surface or substrate) within an unlabeled film, it may be possible to quantify a gradient of stiffness within a polymer film.