Viscoelastic properties of thin films studied with quartz crystal resonators

Abstract

We discuss the possibility of determining shear moduli for thin polymeric films coated on quartz resonators by analysing the variation of normalized frequency shift δf/f with different harmonics. For sufficiently thick films, the elastic compliance can be deduced from the increase in δf/f with overtone order. However, a correction must be applied to account for a frequency dependence of the Sauerbrey factor relating frequency shift to film mass. Since the elastic effect scales with the square of the film mass, the correction is most important for thin films. Possible sources of frequency dependence of the Sauerbrey factor are the finite thickness of the electrodes, lateral stress components, and insufficient control of the electrical boundary conditions. In order to obtain the shear compliance, the frequency dependence of the Sauerbrey factor was measured and subtracted from the data on polymeric thin films. The correction procedure can be avoided by using electrodeless quartzes and exciting the vibration with external electrodes across an air gap. Since, in this case, the Sauerbrey factor is approximately constant, the shear compliance can be obtained directly from the variation of δf/f with overtone order.

References

1. P. G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.
2. G. Reiter, Europhys. Lett., 1993, 23, 579.
3. J. L. Keddie, R. A. Jones and R. A. Cory, Europhys. Lett., 1994, 27, 59.
4. C. L. Jackson and G. B. McKenna, J. Chem. Phys., 1990, 93, 9002.
5. J. N. Israelachvili, Intermolecular and Surface Forcs, Academic Press, London, 2nd edn., 1991.
6. J. Klein, Annu. Rev. Mater. Sci., 1996, 26, 581.
7. J. Klein and E. Kumacheva, Science, 1995, 269, 816.
8. J. Klein, E. Kumacheva, D. Perahia, D. Mahalu and S. Warburg, Faraday Discuss., 1994, 98, 173.
9. J. Van Alsten and S. Granick, Phys. Rev. Lett., 1988, 61, 2570.
10. G. Hadzioannou, S. Patel, S. Granick and M. Tirell, J. Am. Chem. Soc., 1986, 108, 2869.
11. G. Sauerbrey, Arch. Elektrotech. Übertragung, 1964, 18, 617.
12. Applications of Piezoelectric Quartz Crystal Microbalances, ed. C. Lu and A. W. Czanderna, Elsevier, Amsterdam, 1984.
13. R. N. Thurston, in Mechanics of Solids, ed. C. Truesdell, Springer-Verlag, Heidelberg, 1984, vol. 4, ch. 36, p. 257.
14. W. P. Mason, Piezoelectric Crystals and their Applications to Ultrasonics, Van Nostrand, Princeton, NJ, 1948.
15. C. E. Reed, K. K. Kanazawa and J. H. Kaufman, J. Appl. Phys., 1990, 68, 1993.
16. V. E. Granstaff and S. J. Martin, J. Appl. Phys., 1994, 75, 1319.
17. D. Johannsmann, PhD thesis, Universität Mainz, 1990.
18. T. Nakamoto and T. Moriizumi, Jpn. J. Appl. Phys., 1990, 29, 963.
19. H. F. Tiersten, J. Acoust. Soc. Am., 1963, 35, 234.
20. F. Eggers and Th. Funck, J. Phys. E, 1987, 20, 523.
21. A. Domack and D. Johannsmann, J. Appl. Phys., 1996, 80, 2599.
22. A. Katz and M. D. Ward, J. Appl. Phys., 1996, 80, 4153.
23. A. Domack, O. Prucker, J. Rühe and D. Johannsmann, Phys. Rev. A, 1997, 56, 680.
24. P. G. deGennes, J. Phys. (Paris), 1976, 37, 1443.
25. G. J. Fleer, M. A. Cohen Stuart, J. M. H. M. Scheutjens, T. Cosgrove and B. Vincent, Polymers at Interfaces, Chapman and Hall, London, 1993.
26. J. Rühe, Habil.-thesis, Universität Bayreuth, 1995.
27. A. Halperin, J. Phys. (Paris), 1988, 49, 547.
28. E. B. Zhulina, O. V. Borisov, V. A. Pryamitsyn and T. M. Birshtein, Macromolecules, 1991, 24, 140.
29. D. Johannsmann, K. Mathauer, G. Wegner and W. Knoll, Phys. Rev. B, 1992, 46, 7808.
30. J. Krim, D. H. Solina and R. Chiarello, Phys. Rev. Lett., 1991, 66, 181.
31. G. Duda, A. J. Schouten, T. Arndt, G. Lieser, G. F. Schmidt, C. Bubeck and G. Wegner, Thin Solid Films, 1988, 159, 221.
32. O. Wolff, T. Jaworek, G. Wegner and D. Johannsmann, in preparation.
33. V. E. Bottom, Introduction to Quartz Crystal Unit Design, Van Nostrand Reinhold, New York, 1982.
34. J. D. Ferry, Viscoelastic Properties of Polymers, Wiley, New York, 1980.
35. C. Lu and O. Lewis, J. Appl. Phys., 1972, 43, 4385.
36. S. D. Stevens and H. F. Tiersten, J. Acoust. Soc. Am., 1986, 79, 1811.
37. E. Benes, K.-C. Harms and G. Thorn, Proceedings of the 39th Annual Frequency Control Symposium, 1985, p. 556.