Published: July 18, 2011 r2011 American Chemical Society 9873 dx.doi.org/10.1021/la200646h | Langmuir 2011, 27, 9873–9879 ARTICLE pubs.acs.org/Langmuir High Frequency Rheometry of Viscoelastic Coatings with the Quartz Crystal Microbalance Garret C. DeNolf, † Larry Haack, ‡ Joe Holubka, ‡ Ann Straccia, ‡ Kay Blohowiak, § Chris Broadbent, § and Kenneth R. Shull* ,† † Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States ‡ Ford Motor Company, Dearborn, Michigan, United States § Boeing, Seattle, Washington, United States 1. INTRODUCTION Quartz crystal resonators have been used for many applica- tions, with the most common involving detection of very small mass changes. 1 The high sensitivity to changes in mass on the surface has been utilized to characterize thin film deposition processes, 2,3 DNA attachment, 4,5 and molecular adsorption. 68 These applications most commonly utilize the Sauerbrey equa- tion, which relates shifts in the resonant frequency to the physical properties of the quartz to the density and thickness of a layer that is deposited on its surface: 9 Δf ¼ Δf sn ¼ nΔf s1 , Δf s1  2f 1 2 Z q Fd ð1Þ Here Δf is the shift in resonant frequency, n is the order of the harmonic (n = 1, 3, 5, ...), f 1 is the fundamental frequency of the quartz crystal, Z q is the shear acoustic impedance of the quartz (8.84  10 6 kg m 2 s 1 ), F is coating density, and d is the coating thickness. Because most applications of quartz crystal resonators are based on eq 1, it is common to refer to these instruments as quartz crystal microbalances (QCMs). We use this convention in this paper, even though we are not using the resonators as straightforward mass sensors. Note that for the commonly used quartz crystals with a thickness of 330 μm and f 1 = 5 MHz, a 1 mg/m 2 increase in Fd (equating to a thickness increase of 1 nm for a material with F = 1 g/cm 3 ) corresponds to a change in Δf s1 of 5.6 Hz. The Sauerbrey equation is accurate for layers that are thin and rigid, but this relation breaks down if the layer is viscoelastic, 1012 too thick, 13,14 or nonuniform. 15 However, the deviation from the Sauerbrey equation for viscoelastic materials can be accurately modeled, 1621 enabling a wide variety of additional applications for these devices. 2123 In this paper, we apply a generalized model of the QCM response for a uniform viscoelastic layer to characterize the cure behavior of a model paint coating. By measuring information at the first and third harmonics (n = 1, 3), we demonstrate a procedure for extracting quantitative viscoe- lastic parameters from the late stages of cure, where the material is highly elastic but has physical properties that evolve with time. The ability to measure these viscoelastic parameters, which are closely coupled to relevant mechanical properties such as the toughness of the coating, is important in a wide range of coating applications. 2. QCM THEORY 2.1. General Relationships. The interpretation of data obtai- ned from the quartz crystal microbalance has been summarized in an excellent review article by Johannsmann. 15 Here we provide a brief review of the technique and refer readers to this previous reference for a more detailed summary. The quartz crystal micro- balance uses a quartz crystal disk with an oscillating voltage applied across its thickness. The piezoelectric nature of the quartz causes the disk to oscillate transversely and propagate a shear wave into the sample above. The setup is shown schema- tically in Figure 1a. Using a network analyzer, the complex admittance of the system is determined. We are interested in the conductance, which is the real component of the admittance, Received: February 18, 2011 Revised: May 16, 2011 ABSTRACT: We describe a quantitative method for using the quartz crystal microbalance (QCM) to characterize the high frequency viscoelastic response of glassy polymer coatings with thicknesses in the 510 μm regime. By measuring the frequency and dissipation at the fundamental resonant fre- quency (5 MHz) and at the third harmonic (15 MHz), we obtain three independent quantities. For coatings with a predominantly elastic response, characterized by relatively low phase angles, these quantities are the mass per unit area of the coating, the density-shear modulus product, and the phase angle itself. The approach was demonstrated with a model polyurethane coating, where the evolution of these properties as a function of cure time was investigated. For fully cured films, data obtained from the QCM are in good agreement with results obtained from traditional dynamic mechanical analysis.