Stratified Layer Systems

Chapter

Abstract

Samples, which are homogeneous in the resonator plane, can be modeled as acoustic multilayers. The deformation pattern is a plane wave. Thin films exposed to air behave as predicted by Sauerbrey. For somewhat thicker films, there is a viscoelastic correction scaling as the square of the film’s mass. For films exposed to a liquid, the viscoelastic correction is independent of thickness. If the layer is soft, the correction can be substantial, even for molecularly thin films. Under certain conditions, the film’s elastic compliance, Jf′, can be calculation from the ratio of ΔΓ and (–Δf). Thick films display a film resonance.

References

  1. 1.
    Lu, C.S., Lewis, O.: Investigation of film-thickness determination by oscillating quartz resonators with large mass load. J. Appl. Phys. 43(11), 4385 (1972)Google Scholar
  2. 2.
    Crane, R.A., Fischer, G.: Analysis of a quartz crystal microbalance with coatings of finite viscosity. J. Phys. D-Appl. Phys. 12(12), 2019–2026 (1979)ADSCrossRefGoogle Scholar
  3. 3.
    Benes, E.: Improved quartz crystal microbalance technique. J. Appl. Phys. 56(3), 608–626 (1984)ADSCrossRefGoogle Scholar
  4. 4.
  5. 5.
    Johannsmann, D., Mathauer, K., Wegner, G., Knoll, W.: Viscoelastic properties of thin-films probed with a quartz-crystal resonator. Phys. Rev. B 46(12), 7808–7815 (1992)ADSCrossRefGoogle Scholar
  6. 6.
    Granstaff, V.E., Martin, S.J.: Characterization of a thickness-shear mode quartz resonator with multiple nonpiezoelectric layers. J. Appl. Phys. 75(3), 1319–1329 (1994)ADSCrossRefGoogle Scholar
  7. 7.
    Martin, S.J., Bandey, H.L., Cernosek, R.W., Hillman, A.R., Brown, M.J.: Equivalent-circuit model for the thickness-shear mode resonator with a viscoelastic film near film resonance. Anal. Chem. 72(1), 141–149 (2000)CrossRefGoogle Scholar
  8. 8.
    Wolff, O.: Private communicationGoogle Scholar
  9. 9.
    Salomaki, M., Kankare, J.: Modeling the growth processes of polyelectrolyte multilayers using a quartz crystal resonator. J. Phys. Chem. B 111(29), 8509–8519 (2007)CrossRefGoogle Scholar
  10. 10.
    Domack, A., Johannsmann, D.: Plastification during sorption of polymeric thin films: a quartz resonator study. J. Appl. Phys. 80(5), 2599–2604 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    Johannsmann, D.: Viscoelastic analysis of organic thin films on quartz resonators. Macromol. Chem. Phys. 200(3), 501–516 (1999)CrossRefGoogle Scholar
  12. 12.
    Domack, A., Prucker, O., Ruhe, J., Johannsmann, D.: Swelling of a polymer brush probed with a quartz crystal resonator. Phys. Rev. E 56(1), 680–689 (1997)ADSCrossRefGoogle Scholar
  13. 13.
    Johannsmann, D.: Viscoelastic, mechanical, and dielectric measurements on complex samples with the quartz crystal microbalance. Phys. Chem. Chem. Phys. 10(31), 4516–4534 (2008)CrossRefGoogle Scholar
  14. 14.
    Martin, S.J., Granstaff, V.E., Frye, G.C.: Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading. Anal. Chem. 63(20), 2272–2281 (1991)CrossRefGoogle Scholar
  15. 15.
    Voinova, M.V., Jonson, M., Kasemo, B.: ‘Missing mass’ effect in biosensor’s QCM applications. Biosens. Bioelectron. 17(10), 835–841 (2002)CrossRefGoogle Scholar
  16. 16.
    Kankare, J.: Sauerbrey equation of quartz crystal microbalance in liquid medium. Langmuir 18(18), 7092–7094 (2002)CrossRefGoogle Scholar
  17. 17.
    Du, B.Y., Johannsmann, D.: Operation of the quartz crystal microbalance in liquids: Derivation of the elastic compliance of a film from the ratio of bandwidth shift and frequency shift. Langmuir 20(7), 2809–2812 (2004)CrossRefGoogle Scholar
  18. 18.
    Voinova, M.V., Rodahl, M., Jonson, M., Kasemo, B.: Viscoelastic acoustic response of layered polymer films at fluid-solid interfaces: continuum mechanics approach. Phys. Scr. 59(5), 391–396 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    Rodahl, M., Kasemo, B.: On the measurement of thin liquid overlayers with the quartz-crystal microbalance. Sens. Actuators A-Phys. 54(1–3), 448–456 (1996)CrossRefGoogle Scholar
  20. 20.
    Craig, V.S.J., Plunkett, M.: Determination of coupled solvent mass in quartz crystal microbalance measurements using deuterated solvents. J. Colloid Interface Sci. 262(1), 126–129 (2003)CrossRefGoogle Scholar
  21. 21.
    Tsortos, A., Papadakis, G., Gizeli, E.: Shear acoustic wave biosensor for detecting DNA intrinsic viscosity and conformation: a study with QCM-D. Biosens. Bioelectron. 24(4), 836–841 (2008)CrossRefGoogle Scholar
  22. 22.
    Papadakis, G., Tsortos, A., Bender, F., Ferapontova, E.E., Gizeli, E.: Direct detection of DNA conformation in hybridization processes. Anal. Chem. 84(4), 1854–1861 (2012)CrossRefGoogle Scholar
  23. 23.
  24. 24.
    Lekner, J.: Theory of Reflection of Electromagnetic and Particle Waves. Springer, Berlin (1987)Google Scholar
  25. 25.
    Bernoulli, D.: Hydrodynamica (1738). http://en.wikipedia.org/wiki/Hydrodynamica. Accessed 15 June 2014
  26. 26.
    Larson, R.G.: The Structure and Rheology of Complex Fluids. Oxford University Press, New York (1998)Google Scholar
  27. 27.
    Vinogradova, O.I.: Slippage of water over hydrophobic surfaces. Int. J. Miner. Process. 56(1–4), 31–60 (1999)CrossRefGoogle Scholar
  28. 28.
    Thompson, P.A., Troian, S.M.: A general boundary condition for liquid flow at solid surfaces. Nature 389(6649), 360–362 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    Huang, D.M., Sendner, C., Horinek, D., Netz, R.R., Bocquet, L.: Water slippage versus contact angle: a quasiuniversal relationship. Phys. Rev. Lett. 101(22), 226101 (2008)Google Scholar
  30. 30.
    Barrat, J.L., Bocquet, L.: Large slip effect at a nonwetting fluid-solid interface. Phys. Rev. Lett. 82(23), 4671–4674 (1999)ADSCrossRefGoogle Scholar
  31. 31.
    Neto, C., Evans, D.R., Bonaccurso, E., Butt, H.J., Craig, V.S.J.: Boundary slip in Newtonian liquids: a review of experimental studies. Rep. Prog. Phys. 68(12), 2859–2897 (2005)Google Scholar
  32. 32.
    Bowden, F.P., Tabor, D.: Friction lubrication and wear—a survey of work during last decade. Br. J. Appl. Phys. 17(12), 1521–1524 (1966)ADSCrossRefGoogle Scholar
  33. 33.
    Tucker, C.L., Moldenaers, P.: Microstructural evolution in polymer blends. Annu. Rev. Fluid Mech. 34, 177–210 (2002)ADSCrossRefMathSciNetGoogle Scholar
  34. 34.
    Barnes, H.A.: A review of the slip (wall depletion) of polymer-solutions, emulsions and particle suspensions in viscometers—its cause, character, and cure. J. Nonnewton. Fluid Mech. 56(3), 221–251 (1995)CrossRefGoogle Scholar
  35. 35.
    Lefevre, B., Saugey, A., Barrat, J.L., Bocquet, L., Charlaix, E., Gobin, P.F., Vigier, G.: Intrusion and extrusion of water in highly hydrophobic mesoporous materials: effect of the pore texture. Colloids Surf. A-Physicochem. Eng. Aspects 241(1–3), 265–272 (2004)CrossRefGoogle Scholar
  36. 36.
    Boehnke, U.C., Remmler, T., Motschmann, H., Wurlitzer, S., Hauwede, J., Fischer, T.M.: Partial air wetting on solvophobic surfaces in polar liquids. J. Colloid Interface Sci. 211(2), 243–251 (1999)CrossRefGoogle Scholar
  37. 37.
    Al-Fetlawi, H., Shah, A.A., Walsh, F.C.: Modelling the effects of oxygen evolution in the all-vanadium redox flow battery. Electrochim. Acta 55(9), 3192–3205 (2009)CrossRefGoogle Scholar
  38. 38.
    Zhitomirsky, I.: Cathodic electrodeposition of ceramic and organoceramic materials. Fundamental aspects. Adv. Colloid Interface Sci. 97(1–3), 279–317 (2002)CrossRefGoogle Scholar
  39. 39.
    Ferrante, F., Kipling, A.L., Thompson, M.: Molecular slip at the solid-liquid interface of an acoustic-wave sensor. J. Appl. Phys. 76(6), 3448–3462 (1994)ADSCrossRefGoogle Scholar
  40. 40.
    McHale, G., Lucklum, R., Newton, M.I., Cowen, J.A.: Influence of viscoelasticity and interfacial slip on acoustic wave sensors. J. Appl. Phys. 88(12), 7304–7312 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    Ellis, J.S., Hayward, G.L.: Interfacial slip on a transverse-shear mode acoustic wave device. J. Appl. Phys. 94(12), 7856–7867 (2003)ADSCrossRefGoogle Scholar
  42. 42.
    Daikhin, L., Gileadi, E., Tsionsky, V., Urbakh, M., Zilberman, G.: Slippage at adsorbate-electrolyte interface. Response of electrochemical quartz crystal microbalance to adsorption. Electrochim. Acta 45(22–23), 3615–3621 (2000)CrossRefGoogle Scholar
  43. 43.
    Zhuang, H., Lu, P., Lim, S.P., Lee, H.P.: Effects of interface slip and viscoelasticity on the dynamic response of droplet quartz crystal microbalances. Anal. Chem. 80(19), 7347–7353 (2008)CrossRefGoogle Scholar
  44. 44.
    Tretheway, D.C., Meinhart, C.D.: Apparent fluid slip at hydrophobic microchannel walls. Phys. Fluids 14(3), L9–L12 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    Klein, J., Kumacheva, E., Perahia, D., Mahalu, D., Warburg, S.: Interfacial sliding of polymer-bearing surfaces. Faraday Discuss. 98, 173–188 (1994)ADSCrossRefGoogle Scholar
  46. 46.
    Urbakh, M., Tsionsky, V.; Gileadi, E.; Daikhin, L.: Probing the solid/liquid interface with the quartz crystal microbalance. In: Steinem, C., Janshoff, A. (eds.) Piezoeletric Sensors. Springer, Heidelberg (2006)Google Scholar
  47. 47.
    Du, B.Y., Goubaidoulline, E., Johannsmann, D.: Effects of laterally heterogeneous slip on the resonance properties of quartz crystals immersed in liquids. Langmuir 20, 10617–10624 (2004)CrossRefGoogle Scholar
  48. 48.
    Decher, G.: Fuzzy nanoassemblies: toward layered polymeric multicomposites. Science 277(5330), 1232–1237 (1997)CrossRefGoogle Scholar
  49. 49.
    Wolff, O., Seydel, E., Johannsmann, D.: Viscoelastic properties of thin films studied with quartz crystal resonators. Faraday Discuss. 107, 91–104 (1997)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institute of Physical ChemistryClausthal University of TechnologyClausthal-ZellerfeldGermany

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