Macromol. Chem. Phys. 200, 501–516 (1999) 501 Feature Article Viscoelastic analysis of organic thin films on quartz resonators Diethelm Johannsmann Max-Planck-Institute for Polymer Research, PO Box 3148, 55021 Mainz, Germany [email protected] (Received: August 7, 1998; revised October 2, 1998) SUMMARY: By analyzing the frequency shifts and bandwidths of coated quartz resonators the viscoelastic coefficients of the coatings may be derived. The paper gives an overview of the experimental procedure and the data analysis. Some examples of the application of this technique in the range of soft condensed matter are described. The swelling and plastification of polymer films in solvent vapor was monitored in-situ. We reported on measurements of the acoustic thickness of polymer brushes, the thickness of which varies with the solvent quality. The acoustic thickness is significantly larger than the optical thickness because the dilute outer portions of the swollen layer affects the acoustic behavior of the brush much more than the optical behavior. Sandwiching polymer layers between quartz plates and rigid overlayers expands the range of the applicability of the technique at the end of low film thicknesses, because the rigid overlayer adds inertia to the composite film and therefore enhances the stress acting on the layer of interest. Finally, the combination with optical birefringence measurements in Fabry-Perot configuration gives access to the stress-birefringence inside the polymer film. Normal stress components proportional to the square of the oscillation amplitude have been measured for the first time. I. Introduction The structure and dynamics of polymers on the meso- scopic scale has increasingly come into the focus of scientific interest in the past years. This development has been partly stimulated by the widespread tendency towards miniaturization. There is also a genuine scientific interest in polymers at this length scale because the meso- scopic scale coincides with many intrinsic length scales of polymers such as the radius of gyration, the hydrody- namic screening length, the domain size in block copoly- mers, the persistence length of stiff main chains, and many others 1) . Mechanical dynamical studies on the mesoscopic scale, however, are difficult. The standard mechanical dynami- cal equipment does not achieve the required mechanical precision. To date, most investigations have been carried out with the surface forces apparatus (SFA) 2) where two crossed cylinders are approached to each other. The dyna- mical behavior of polymers confined to the space between the cylinders can be probed by either modulating their distance or by shearing them with respect to each other 3–7) . Although similar efforts are reported for atomic force microscopes 8) , this technique is still in its infancy, the most prominent problem being the ill-defined contact area. A somewhat complementary approach consists of ana- lyzing the resonance spectrum of quartz crystals. In the context of quartz crystal microbalances 9, 10) where fre- quency shifts are converted to deposited mass, viscoelas- tic effects were widely perceived as an impediment to accurate mass determination. When the viscoelastic con- stants of the coating are known, correction for the visco- elastic effects is possible 11, 12) . This correction is particu- larly important for thick films and for soft materials such as rubber polymers. If, on the other hand, sufficient information can be gathered from the spectrum of resonances, the viscoelas- tic constants may actually be derived from quartz mea- surements. This additional information becomes accessi- ble by (a) measurement of the resonance frequency as well as the resonance bandwidth and (b) comparison of the resonant behavior on several harmonics. The techni- que is particularly suited for the investigation of fast dynamics in the MHz range. The fundamental laws governing the behavior of quartz crystals in contact with viscoelastic media have been described as early as 1948 by Mason in his book “Piezo- electric Crystals and their Applications to Ultrasonics” 13) . Mason does not, however, make reference to the study of thin films. The interest in quartz resonators was for a long time (and still is in terms of commercial application) gov- erned by frequency control. The effects of temperature, pressure, aging, external and internal stresses, mounting, and driving voltage were analyzed in great detail 14, 15) . Full three-dimensional modeling was undertaken 16) . In particular, it was recognized that the oscillation can be confined to the central portion of the quartz by using key- hole-shaped electrodes, edge profiling, or the use of Macromol. Chem. Phys. 200, No. 3 i WILEY-VCH Verlag GmbH,D-69451 Weinheim 1999 1022-1352/99/0303–0501$17.50+.50/0
Viscoelastic analysis of organic thin films on quartz resonators
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