Effect of Polyelectrolyte Multilayers on the Response of a Quartz Crystal Microbalance Mikko Saloma 1 ki, † Kari Loikas, ‡ and Jouko Kankare* ,‡ Department of Chemistry, University of Turku, FIN-20014 Turku, Finland, and Graduate School of Chemical Sensors and Microanalytical Systems The effect of a polyelectrolyte (PE) multilayers made by a layer-by-layer technique on the response of a quartz crystal microbalance (QCM) is studied by using novel mathemati- cal methods based on the Mo 1 bius transformations and their matrix representations in the complex plane. In the first method, the basic properties of the Mo 1 bius transfor- mation are used for obtaining the PE bilayer matrix from the QCM impedance measurements taken at four different numbers of layers. In the second method, nonlinear fitting with concomitant error estimation is used for obtaining the elements of the bilayer matrix. The methods are applied to a multilayer composed of 1 5 0 bilayers of poly- (sodium 4 -styrenesulfonate) and poly(diallyldimethylam- monium) chloride on a quartz crystal resonator. The structure of the system is discussed, and the bulk acoustic impedance and areal mass density of the bilayer are calculated from the layer matrix. A very versatile and facile technique for the preparation of thin organic films is the sequential layer-by-layer (LbL) deposition of oppositely charged polyelectrolytes, as initially reported by Decher et al. 1 A huge number of reports have been published on the use of these techniques for various kinds of polyelectrolytes from purely synthetic polymers to polymers of biological origin. The main advantage of polyelectrolyte multilayers (PEMs) is the possibility of tailoring the surface properties, such as functionality, charge, and wettability, by the choice of the outermost layer, keeping control at the same time over the layer thickness, lateral homogeneity, and low surface roughness, all this by using a very simple fabrication process. Naturally, there is a need to monitor these properties during or after the deposition process. Very often, the PEMs will be used in an aqueous environment, and conse- quently, the control of the properties should be done in situ. The number of techniques available for these purposes is rather limited. If the polyelectrolytes have spectral absorbance at some UV-vis-NIR wavelength, absorbance measurement is a viable method for estimating the amount of material on a transparent substrate. 2,3 In situ ellipsometry can be used for the measurement of the layer thickness in many cases. 4 One of the most powerful methods is the quartz crystal microbalance (QCM) which gives the areal mass density, that is, mass per unit area, of PEM. Additionally, QCM may give also information on the elastic properties of PEM if the electrical impedance measurement and subsequent data treatment are properly done. The experimental techniques presently available for the full characterization of the oscillating thickness-shear mode (TSM) resonator are based either on a freely oscillating quartz crystal, for which the oscillation frequency is determined by the resonant frequency of the crystal itself, or on an electrical impedance measurement in which the resonator is a passive element as the measurement frequency is swept across the resonant region of the crystal and its response is recorded. In the present study, we do not pay attention to the measurement technique because, anyway, the data from different methods can be brought to a common form. Instead, we are concentrating on using the collected data as efficiently as possible. The elastic properties of thin films can be described by the bulk acoustic impedance of the material. This is a complex-valued parameter that depends also on the vibrational frequency used for its measurement. An additional parameter is the areal mass density, that is, mass per unit area of the resonator coating. The primary parameter obtained from the QCM measurement used is the local acoustic impedance ( LAI) at the interface of the resonator surface and the film coated on it, also called surface mechanical impedance. This parameter is also complex-valued. Hence, there are three material parameters, that is, areal mass density and the real and imaginary components of bulk acoustic impedance, which characterize the thin film on the resonator surface. However, only two parameters, that is, the real and imaginary components of the local acoustic impedance, are obtained from a single measurement. Consequently, no unique solution is obtained for any of these three unknown parameters unless further measurements are done or new assumptions are made. 5 For a long time, areal mass density was the only parameter obtained from the QCM by using the celebrated Sauerbrey equation. 6 In this case, an implicit assumption was made that the film was made of fully elastic material without any energy losses. Later, it was realized that the viscoelasticity of the film may introduce errors to the mass determinations. Various models, * Corresponding author. E-mail: jouko.kankare@ utu.fi † Graduate School of Chemical Sensors and Microanalytical Systems. ‡ Department of Chemistry, University of Turku. (1) Decher, G.; Hong, J. D. Makromol. Chem. Macromol. Symp. 1991 , 46, 321. (2) McAloney, R. A.; Sinyor, M.; Dudnik, V.; Goh, M. C. Langmuir 2001 , 17, 6655-6663. (3) Lukkari, J.; Saloma ¨ki, M.; A ¨ a ¨ ritalo, T.; Loikas, K.; Laiho, T.; Kankare, J. Langmuir 2002 , 18, 8496-8502. (4) Harris, J. J.; Bruening, M. L. Langmuir 2000 , 16, 2006-2013. (5) Hillman, A. R.; Jackson, A.; Martin, S. J. Anal. Chem. 2001 , 73, 540-549. (6) Sauerbrey, G. Z. Phys. 1959 , 155, 206-222. Anal. Chem. 2003, 75, 5895-5904 10.1021/ac034509z CCC: $25.00 © 2003 American Chemical Society Analytical Chemistry, Vol. 75, No. 21, November 1, 2003 5895 Published on Web 10/04/2003