Quartz Crystal Microbalance

A quartz crystal microbalance (QCM) is used throughout Chapter 5 and Chapter 6 of this thesis in order to monitor the progression of film growth on a substrate. The QCM is a gravimetric technique capable of monitoring the deposition of thin films with masses in the order of 10-9 g/m2 by sensing an addition of mass to a surface. The QCM KSV 500 quartz crystal microbalance used in this project is comprised of a closed chamber and quartz crystal resonator as shown in Figure 4.10. Solutions are introduced into the chamber through the top inlet valve, and adsorbates are allowed to adsorb onto the surface of a quartz crystal resonator. After a predetermined amount of time, the solution is extracted from the closed chamber using the outlet valve while the next solution is introduced into the chamber.

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(b)

Figure 4.10: (a) Schematic illustration and photograph of a QCM. Inset photograph shows a KSV QCM-500 used for the majority of QCM work in this thesis. (b) schematic illustration of a quartz crystal resonator showing the top (active) surface with desired surface coating, and the bottom surface with electrode coating.

The key component of a QCM is the quartz crystal resonator, which is used to sense the mass of the adsorbed species. Quartz crystal resonators are typically around 300 m

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thick160, and are sandwiched between two gold electrodes, which are used to apply an AC voltage across the quartz crystal resonator. As quartz is piezoelectric, oscillating deformation of the quartz crystal resonator occurs, with the piezoelectric properties and crystalline structure of the quartz crystal determining the mode of deformation and oscillation frequency. Overwhelmingly, quartz crystal resonators used in QCM apparatus are manufactured from AT-cut crystals, which yield oscillating transverse shear deformation at a frequency of 5 MHz. A standing shear wave is generated across the surface of the quartz crystal resonator when the appropriate excitation frequency is applied. The excitation frequency occurs when a crystal thickness is an odd multiple of half the acoustic wavelength and includes odd numbered harmonics such as the fundamental, third, fifth, seventh harmonic. Consequently, when a mass is adsorbed to the resonator surface, the frequency at which the resonator oscillates decreases proportionally to the adsorbed mass. In this manner, the adsorption of material to the quartz crystal surface can be monitored by the change in frequency.

Although a QCM is able to obtain signals from the lowest odd harmonic frequencies, a single harmonic frequency is typically chosen for subsequent analysis. Lower harmonic frequencies facilitate better energy trapping of the standing wave than higher harmonic frequencies.161 In this thesis, the third harmonic frequency was chosen for subsequent analysis, as the fundamental (resonant) frequency is responsible for driving the oscillation of the quartz crystal resonator. As such, the signal cannot be used for further analysis as it is typically influenced by a combination of effects arising from the noise inherent to the driving oscillation and the change in frequency due to adsorption.

81 4.4.2.1 Analysis of Adsorbed Mass

The addition of mass at a resonator surface can be analysed using a number of different modelling methods.160 Two of the most common methods however, are the Voigt model and the Sauerbrey equation. The Sauerbrey equation162 provides a simple method with which to calculate the theoretical mass of a rigid layer adsorbed to the surface of a QCM electrode based on the physical parameters of the quartz crystal resonator and the change in frequency experienced when a mass is adsorbed to the surface of the resonator. In contrast, the Voigt model assumes the oscillation of the adsorbed film is not coupled to that of the sensor and corrects for the deviation using the material and mechanical properties of the adsorbing species such as density, viscosity, elastic modulus. The Voigt model163 is typically suited to systems in which viscoelastic layers are present and generally requires computational analysis in order to model correctly. However, using the Voigt model for even the simplest systems can be computationally intensive, with most analyses delivering accurate results for systems up to only a few adsorbed layers. Consequently, the use of the Sauerbrey equation is favoured where appropriate due to its simplicity, while the Voigt model is generally only applied when conditions do not permit the use of the Sauerbrey equation, such as in the presence of viscous layers. For this reason, effort was directed towards the use of the Sauerbrey equation throughout the QCM analysis sections of this thesis.

The Sauerbrey equation provides a simple method with which to calculate the theoretical mass of a layer adsorbed to the surface of a QCM electrode. It relates the mass deposited on the electrode with the change in oscillation of the QCM resonator. This method assumes the adsorbed material forms a rigid layer on top of the quartz resonator and that the energy used to produce oscillation of the resonator is transferred through the layer without energy losses. In such a case, the system oscillates effectively

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as a resonator of mass equivalent to that of the quartz crystal resonator and the adsorbed film. As a result, the resonant frequency of the quartz crystal resonator is inversely proportional to the mass of the adsorbed layer, according to the Sauerbrey equation (Equation 4.4):

∆𝑓 =−2𝑓02∆𝑚 𝐴√𝜌𝑞𝜇𝑞

4.4

Where:

∆𝑓 = Measured frequency shift (Hz)

𝑓0 = Resonant frequency of quartz crystal resonator (Hz)

∆𝑚 = Mass change per unit area (g/cm2)

𝐴 = Piezoelectrically active area (i.e Area between electrodes, cm2) 𝜌𝑞 = Density of quartz, 2.648 g/cm3

𝜇_𝑞 = Shear modulus of quartz, 2.947 × 1011 g/cm s2

However, in order for the Sauerbrey equation to remain valid, the system under investigation must satisfy a series of conditions. Firstly, rigid layer deposition is required in order to ensure the layer fully couples to the oscillation of the quartz crystal resonator. Viscous layers do not fully couple to the oscillating QCM sensor. As a result, points within the layer that are further from the electrode surface will not oscillate with the same phase and frequency as that of the QCM crystal. In this case, applying the Sauerbrey equation to this system will result in an underestimation of the mass adsorbed. Consequently, the Sauerbrey mass is only applicable when the dissipation is low. In order to successfully apply the Sauerbrey equation, layers with a uniform thickness are also required. In order to ensure accurate results, the layers are

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also required to adsorb strongly enough to the crystal surface to prevent detachment. This again is necessary, in order to ensure complete coupling of the layer to the oscillating surface, with slippage between the adsorbed mass and the oscillating surface resulting in a lower sensed mass. In addition, it has been shown quantitatively that the Sauerbrey equation remains valid when the ∆𝑓 values of the different overtones are in agreement when scaled by the overtone, 𝑛.163 This condition was satisfied for all solution conditions trialled in this thesis, with the maximum average difference between overtones for each experiment being less than 12.99 Hz, approximately 1% of the overall frequency change experienced during the experiments. The dissipation parameter can also be used to assess whether the Sauerbrey equation may be applied to a specific system.

4.4.2.2 Dissipation

The dissipation is a parameter that quantifies the energy dampening of the system and is a key factor in determining which mode of analysis is appropriate for specific data sets obtained through QCM. Dissipation is a parameter that quantifies the sum of all energy losses in the QCM chamber per oscillation cycle and thus, provides an indication of the rigidity of an adsorbed multilayer film. A viscous layer is characteristic of a soft film and occurs when either the attractive intermolecular interactions between the adsorbed species within the layer are weak, or there is a greater amount of entrained water content within the layer. As a result, viscous layers absorb and dissipate kinetic energy from an adjacent resonator throughout the layer, thereby giving rise to high dissipation. Conversely, a system comprised of a rigid layer typically exhibits greater intermolecular interactions between the particles and chemical species within the layer, allowing the applied energy to transfer more efficiently through the layer. Consequently, dissipation values, ∆𝐷_𝑛, were used to characterise the rigidity of the prepared films in order to

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determine the validity of the Sauerbrey equation in this thesis. Although film rigidity is a continuum, a threshold for ∆𝐷𝑛/ (−∆𝑓_𝑛𝑛) of 4 × 10-7 Hz-1160 was defined as a guide in

order to distinguish between films that were more rigid and films that exhibit more viscoelastic behaviour.