Errors induced in quartz crystal mass uptake measurements by nongravimetric effects: Considerations beyond the EerNisse caution

Abstract

We report frequency changes in AT‐cut quartz crystals for glassy polymers subsequent to temperature and carbon dioxide pressure changes. Anomalous frequency shifts are observed for the crystal subsequent to such changes. Since, the Sauerbrey equation has been applied routinely for mass uptake measurements in glassy polymers, using the quartz crystal microbalance fitted with AT‐cut quartz crystals, it is important that nongravimetric effects that impact the frequency change be well understood. In the present work, we provide a quantitative analysis of the breakdown of the Sauerbrey equation for viscoelastic materials by using the Johannsmann (Macromol Chem Phys 1999, 200, 501) treatment of the response of AT‐cut crystals. Clearly, there exist significant errors in mass uptake measurements for materials deposited on AT‐cut quartz crystals when precautions pertaining to film thickness and viscoelastic compliance are ignored. We show that while the early caution of EerNisse on stress effects in AT‐cut quartz crystals can be important in mass uptake measurements, for polymers, the major source of error arises from viscoelastic effects in the coating. We conclude that mass uptake measurements for films of compliant materials and polymers above their glass transition cannot be performed with accuracy, using AT‐cut quartz crystals if the results are not corrected for frequency shifts due to viscoelastic effects of the overlayer unless the films are extremely thin, that is, less than 100 nm. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 801–814, 2006

Gas permeation properties of poly(lactic acid) revisited

“…However, at this thickness, the deviation of the Sauerbrey equation will occur [13]. Also the significance of the viscoelastic effects on frequency shifts in the quartz crystal should be considered [14].…”

Effect of vapor phase ethylenediamine crosslinking of matrimid on alcohol vapor sorption and diffusion

“…40 The essence of the technique relies on applying an alternating electric field to electrodes on the faces of the cut crystal, which induces a directional mechanical deformation, or shear oscillation, in the crystal matrix. 41 Although the frequency of oscillation in the crystal depends on crystal cut and thickness, each individual crystal has a unique fundamental frequency. When a thin film is deposited onto the electrodes of the crystal and is mechanically adhered, the frequency decreases in direct proportion to the deposited mass.…”

“…Our previous work further discusses this technique and its potential limits and measurement errors. 39 Other literature describes limitations and errors associated with QCM measurements due to material viscoelastic properties, film thickness, crystal imperfections, temperature, and pressure effects, [24][25][26]41,42 however, most agree that glassy polymeric films with thicknesses less than 5.0 mm produce acceptable mass uptake measurements when conducted at near ambient temperature and pressure. 40 The coated crystals were placed in a vacuum oven at 60 8C for 24 h to ensure complete removal of solvent.…”

“…The technique of utilizing the piezoelectric property of appropriately cut quartz crystal to measure thin film deposition thickness was originally described and developed by Sauerbrey . The essence of the technique relies on applying an alternating electric field to electrodes on the faces of the cut crystal, which induces a directional mechanical deformation, or shear oscillation, in the crystal matrix . Although the frequency of oscillation in the crystal depends on crystal cut and thickness, each individual crystal has a unique fundamental frequency.…”

Supramolecular interactions between β-cyclodextrin and hydrophobically end-capped poly(ethylene glycol)s: A quartz crystal microbalance study

“…Concerning the validity of the Sauerbrey equation, viscoelastic effects were neglected in our experiments as the thickness of the polymer was considered acoustically thin enough [15] and surface concentration Γ (mol cm −2 ) can be calculated as follows: (…”