An electrochemical quartz crystal microbalance (EQCM) based on microelectrode arrays allows to distinguish between adsorption and electrodeposition.

Using a precise electrochemical quartz crystal microbalance (EQCM), it was shown that electrogravimetry can be carried out with microelectrode arrays (MEAs). MEAs were prepared on the resonator surface by coating it with a thin polymer layer containing holes, where the holes constitute the microelectrodes. The preparation procedures, their benefits, and their limitations are discussed. Microelectrode-based electrogravimetry is challenging because the reduced active area reduces the QCM signal. It is still feasible. This work is limited to linear voltage ramps (as opposed to steps). The processes chosen for demonstration were the electrodeposition/stripping of copper and the redox cycling of methyl viologen dichloride (MVC). The current trace often showed microelectrodic behavior, depending on the sweep rate. For the case of copper deposition, the mass transfer rate was proportional to the electric current. For the case of MVC, the electric current showed a plateau at the ends of the current-voltage diagram, but the mass transfer rate did not change. The difference can be explained by adsorption and desorption going into saturation at the two ends of the voltage range. Based on whether or not a microelectrodic gravimetric signal is seen, it can be stated whether the mass transfer is closely linked to the current. Further advantages of the microelectrode-based EQCM are an improved access to fast processes, reduced effects of double layer recharging, and the possibility to work at a low electrolyte support.

Protein-protein interactions in solutions of monoclonal antibodies probed by the dependence of the high-frequency viscosity on temperature and concentration.

Using a quartz crystal microbalance with dissipation monitoring (QCM-D), the complex high-frequency viscosity,  = η' - iη'', of concentrated solutions of a monoclonal antibody (mAb) was studied with respect to its dependence on temperature, T, and concentration, c. Lysozyme and bovine serum albumin (BSA) served as reference materials. Viscoelasticity was found for the mAb solution, while the reference materials behaved like Newtonian liquids. The QCM-D probes the solution's dynamics on the time scale of a few tens of nanoseconds. The processes of relaxation accessed with the QCM-D are not amenable to standard viscometry. The inverse loss tangent at 15 MHz (equal to η''/η' at 15 MHz, quantifying the elastic contribution to the oscillatory stress) was between 0.1 and 0.5 for the concentrated mAb solutions. It decreased with increasing temperature and decreasing pH. Activation energies of viscous flow, Ea,η, were derived from the functions η'(T). Ea,η was found to be higher for the mAb solutions than for water. No such increase was found for the reference materials. This difference evidences protein-protein interactions (PPIs) between the mAb molecules, which do not exist in the same way for lysozyme and BSA. The excipients citrate and arginine did not noticeably affect the mAb's high-frequency viscosity as determined with the QCM-D.

Effect of Noise on Determining Ultrathin-Film Parameters from QCM-D Data with the Viscoelastic Model.

Quartz crystal microbalance with dissipation monitoring (QCM-D) is a well-established technique for studying soft films. It can provide gravimetric as well as nongravimetric information about a film, such as its thickness and mechanical properties. The interpretation of sets of overtone-normalized frequency shifts, ∆f/n, and overtone-normalized shifts in half-bandwidth, ΔΓ/n, provided by QCM-D relies on a model that, in general, contains five independent parameters that are needed to describe film thickness and frequency-dependent viscoelastic properties. Here, we examine how noise inherent in experimental data affects the determination of these parameters. There are certain conditions where noise prevents the reliable determination of film thickness and the loss tangent. On the other hand, we show that there are conditions where it is possible to determine all five parameters. We relate these conditions to the mathematical properties of the model in terms of simple conceptual diagrams that can help users understand the model's behavior. Finally, we present new open source software for QCM-D data analysis written in Python, PyQTM.

Square-Wave Electrogravimetry Combined with Voltammetry Reveals Reversible Submonolayer Adsorption of Redox-Active Ions.

Square-wave voltammetry on electrolytes containing reversible redox pairs in solution was complemented by acoustic microgravimetry, where multifrequency lock-in amplification provides for a time resolution of 2.5 ms and a frequency resolution after accumulation of 12 mHz. The instrument operates similar to a quartz crystal microbalance with dissipation monitoring (QCM-D). The use of square-waves rather than linear ramps makes the analysis more transparent because it reduces the contribution of non-Faraday currents. Also, square-wave electrogravimetry determines the rates of mass transfer with much better sensitivity than its counterpart based on linear voltage ramps. The shifts of frequency and bandwidth are in agreement with the Sauerbrey prediction, meaning that the overtone-normalized frequency shifts, Δf/n, are similar on the different overtones and that the shifts in half bandwidth, ΔΓ, are smaller than the shifts in frequency. Small deviations from the Sauerbrey prediction presumably result from the softness of the adsorbed layer. Because the response time of the QCM signals is much longer than the RC time of double layer recharging as determined with electrochemical impedance spectroscopy (EIS), interpretation in terms of adsorption and desorption is more plausible than interpretation in terms of changed viscosity in the diffuse double layer. Ions of methyl viologen (MV) were found to adsorb to the electrode surface more strongly in the state with a single charge than in the fully oxidized state carrying two charges. The difference in apparent thickness between the oxidized and the reduced state was up to 2 nm, depending on concentration. The gravimetric results obtained on flavin adenine dinucleotide (FAD) depended on pH. At neutral pH, adsorption was largest close to the redox potential. Presumably, the adsorbed molecules are semiquinones, that is, are the intermediates of the underlying two-electron process.

An Analysis of the Thermal Behavior and Effects of Circular Quartz Crystal Resonators for Microbalance Applications.

The accurate calculation of vibration frequency is essential in design of circular quartz crystal resonators which are the core elements of high-precision microbalances used for testing and measurement. Currently, the prediction of thermal effects on frequency through an analytical analysis is still in its developmental stage, mainly due to the complexity of solving the 3-D equations with the consideration of asymmetric structure of resonators and electrodes along with material anisotropy. By using a scalar differential equation for vibrations with the eigen-displacement of thickness mode, the eigen-frequency of a plano-convex AT-cut circular quartz crystal plate with asymmetric electrodes is determined. Furthermore, the temperature effect in the scalar differential equation is successfully obtained by incorporating the incremental thermal field theory into the 1-D analysis. The theoretical results agree well with the experimental data. The combination of the thermal field and the thickness model for circular quartz crystal resonators can realize a full analysis of thermal properties in vital applications such as high-sensitivity microbalance sensors.

Dipolar Interactions and Protein Hydration in Highly Concentrated Antibody Formulations.

Molecular interaction mechanisms in high-concentrated protein systems are of fundamental importance for the rational development of biopharmaceuticals such as monoclonal antibody (mAb) formulations. In such high-concentrated protein systems, the intermolecular distances between mAb molecules are reduced to the size of the protein diameter (approx. 10 nm). Thus, protein-protein interactions are more pronounced at high concentrations; so a direct extrapolation of physicochemical properties obtained from measurements at a low protein concentration of the corresponding properties at a high protein concentration is highly questionable. Besides the charge-charge interaction, the effects of molecular crowding, dipolar interaction, changes in protein hydration, and self-assembling tendency become more relevant. Here, protein hydration, protein dipole moment, and protein-protein interactions were studied in protein concentrations up to 200 mg/mL (= 1.3 mM) in different formulations for selected mAbs using dielectric relaxation spectroscopy (DRS). These data are correlated with the second virial coefficient, A2, the diffusion interaction parameter, kD, the elastic shear modulus, G', and the dynamic viscosity, η. When large contributions of dipolar protein-protein interactions were observed, the tendency of self-assembling and an increase in solution viscosity were detected. These effects were examined using specific buffer conditions. Furthermore, different types of protein-water interactions were identified via DRS, whereby the effect of high protein concentration on protein hydration was investigated for different high-concentrated liquid formulations (HCLFs).

Fast and slow EQCM response of zwitterionic weak electrolytes to changes in the electrode potential: a pH-mediated mechanism.

Using a fast electrochemical quartz crystal microbalance (EQCM), zwitterionic electrolytes were studied with regard to changes of resonance frequency and resonance bandwidth after the electrode potential was switched. In addition to a fast change of frequency (within milliseconds), a further, slower process with opposite direction is observed. Both the fast and the slow process change sign when the pH is varied across the isoelectric point (pI). The fast process can be attributed to double layer recharging. Its characteristic time is slightly larger than the charge response time (the RC-time) as inferred from electrochemical impedance spectroscopy (EIS). With regard to the slow process, amino acids with moderate concentration behave markedly different from concentrated solutions of proteins. For amino acids, the slow process is larger in amplitude than the fast process and the QCM response is Sauerbrey-like. The shift in half bandwidth is smaller than the shift in frequency and the overtone-normalized frequency shifts agree between overtones (-Δf/n ≈ const. with n the overtone order). This can be explained with a viscosity change in the diffuse double layer. Independent measurements show that the viscosities of these electrolytes are higher than the average in a pH range around the pI. Presumably, the slow process reflects a rearrangement of molecules after the net charge on the molecule has increased or decreased, changing the degree of dipolar coupling and, in consequence, the viscosity. For concentrated solutions of bovine serum albumin (BSA), the QCM response does not follow Sauerbrey behaviour, which can be explained with viscoelasticity and viscoelastic dispersion. The slow process lets the frequency and the bandwidth relax towards a baseline, which is the same for jumps to more positive and to more negative potentials. Presumably, the slow process in this case is caused by a reorientation of molecules inside the Helmholtz layer, such that they screen the electric field more efficiently than immediately after the voltage jump.

Soft Viscoelastic Particles in Contact with a Quartz Crystal Microbalance (QCM): A Frequency-Domain Lattice Boltzmann Simulation.

Shifts of frequency and bandwidth of a quartz crystal microbalance (QCM) in contact with a structured, viscoelastic sample have been computed with a linearized version of the lattice Boltzmann method (LBM). The algorithm operates in the frequency domain and covers viscoelasticity. The different domains are characterized by different values of the complex viscosity, η, equivalent to different values of the shear modulus, G. Stiff particles are given large |ηSph|, where |ηSph| must be less than ∼100 ηbulk with ηbulk the viscosity of the ambient liquid. Critical to the computational efficiency is a match of the LBM populations at the upper boundary of the simulation box to an analytical solution of the Stokes equation in the bulk above the box. The application example is a test of the ΔΓ/(-Δf)-extrapolation scheme, where Δf and ΔΓ are the shifts in resonance frequency and half bandwidth, respectively. For adsorbed particles, plots of ΔΓ/(-Δf) versus - Δf/n (with n the overtone order) show almost straight lines. The extrapolation of these lines to zero yields a frequency shift, which, after conversion to a thickness with the Sauerbrey equation, closely agrees with the height of the particles. Plots of Δf/n and ΔΓ/n versus n look similar to the corresponding plots obtained for viscoelastic films, where the parameters, which would usually be extracted from those plots (apparent mass and apparent compliance), depend on the geometry and the sample's viscoelasticity in a nontrivial way.

Studying Soft Interfaces with Shear Waves: Principles and Applications of the Quartz Crystal Microbalance (QCM).

The response of the quartz crystal microbalance (QCM, also: QCM-D for "QCM with Dissipation monitoring") to loading with a diverse set of samples is reviewed in a consistent frame. After a brief introduction to the advanced QCMs, the governing equation (the small-load approximation) is derived. Planar films and adsorbates are modeled based on the acoustic multilayer formalism. In liquid environments, viscoelastic spectroscopy and high-frequency rheology are possible, even on layers with a thickness in the monolayer range. For particulate samples, the contact stiffness can be derived. Because the stress at the contact is large, the force is not always proportional to the displacement. Nonlinear effects are observed, leading to a dependence of the resonance frequency and the resonance bandwidth on the amplitude of oscillation. Partial slip, in particular, can be studied in detail. Advanced topics include structured samples and the extension of the small-load approximation to its tensorial version.

Kinetics of viscoelasticity in the electric double layer following steps in the electrode potential studied by a fast electrochemical quartz crystal microbalance (EQCM).

Changes in the viscoelasticity of the electric double layer following steps in electrode potential were studied with an electrochemical quartz crystal microbalance (EQCM). The overtone scaling was the same as in gravimetry (-Δf/n≈ const with Δf the frequency shift and n the overtone order). Changes in half-bandwidth were smaller than changes in frequency. This Sauerbrey-type behaviour can be explained with either adsorption/desorption or with changes of the (Newtonian) viscosity of the diffuse double layer. While the QCM data alone cannot distinguish between these two processes, independent information supports the explanation in terms of double layer viscosity. Firstly, the magnitudes of the frequency response correlated with the expected changes of the viscosity-density product in the diffuse double layer. With regard to viscosity, these expectations are based on the viscosity B-coefficients as employed in the Jones-Dole equation. Expected changes in density were estimated from the densities of the respective salts. Secondly, the explanation in terms of liquid-like response matches the kinetic data. The response times of frequency and bandwidth were similar to the response times of the charge as determined with electrochemical impedance spectroscopy (EIS). Rearrangements in the Helmholtz layer should have been slower, given this layer's rigidity. Kinetic information obtained with a QCM can aid the understanding of processes at the electrode-electrolyte interface.

A Quartz Crystal Microbalance, Which Tracks Four Overtones in Parallel with a Time Resolution of 10 Milliseconds: Application to Inkjet Printing.

A quartz crystal microbalance (QCM) is described, which simultaneously determines resonance frequency and bandwidth on four different overtones. The time resolution is 10 milliseconds. This fast, multi-overtone QCM is based on multi-frequency lockin amplification. Synchronous interrogation of overtones is needed, when the sample changes quickly and when information on the sample is to be extracted from the comparison between overtones. The application example is thermal inkjet-printing. At impact, the resonance frequencies change over a time shorter than 10 milliseconds. There is a further increase in the contact area, evidenced by an increasing common prefactor to the shifts in frequency, Δf, and half-bandwidth, ΔΓ. The ratio ΔΓ/(-Δf), which quantifies the energy dissipated per time and unit area, decreases with time. Often, there is a fast initial decrease, lasting for about 100 milliseconds, followed by a slower decrease, persisting over the entire drying time (a few seconds). Fitting the overtone dependence of Δf(n) and ΔΓ(n) with power laws, one finds power-law exponents of about 1/2, characteristic of semi-infinite Newtonian liquids. The power-law exponents corresponding to Δf(n) slightly increase with time. The decrease of ΔΓ/(-Δf) and the increase of the exponents are explained by evaporation and formation of a solid film at the resonator surface.

Compressional-Wave Effects in the Operation of a Quartz Crystal Microbalance in Liquids:Dependence on Overtone Order.

The operation of the quartz crystal microbalance (QCM) in liquids is plagued by small flexural admixtures to the thickness-shear deformation. The resonator surface moves not only in the transverse direction, but also along the surface normal, thereby emitting compressional waves into the liquid. Using a simple analytical model and laser Doppler vibrometry, we show that the flexural admixtures are stronger on the fundamental mode than on the overtones. The normal amplitude of motion amounts to about 1% of the transverse motion on the fundamental mode. This ratio drops by a factor of two on the overtones. A similar dependence on overtone order is observed in experiments, where the resonator is immersed in a liquid and faces an opposite planar wall, the distance of which varies. Standing compressional waves occur at certain distances. The amplitudes of these are smaller on the overtones than on the fundamental mode. The findings can be rationalized with the tensor form of the small-load approximation.

Fast pH-mediated changes of the viscosity of protein solutions studied with a voltage-modulated quartz crystal microbalance.

An electrochemical quartz crystal microbalance is described, which achieves a time resolution down to 100 µs. Accumulation and averaging over a few hours bring the noise down to about 30 mHz. The application examples are pH-driven viscosity changes in albumin solutions. The pH was switched with the electrode potential. The characteristic response time is in the millisecond range. The focus is on experimental aspects as well as advantages and limitations of the technique.

An ultrafast quartz crystal microbalance based on a frequency comb approach delivers sub-millisecond time resolution.

Quartz crystal microbalance with dissipation monitoring (QCMD) is a simple and versatile sensing technique with applications in a wide variety of academic and industrial fields, most notably electrochemistry, biophysics, quality control, and environmental monitoring. QCMD is limited by a relatively poor time resolution, which is of the order of seconds with conventional instrument designs at the noise level usually required. In this work, we present a design of an ultrafast QCMD with submillisecond time resolution. It is based on a frequency comb approach applied to a high-fundamental-frequency (HFF) resonator through a multifrequency lock-in amplifier. The combination allows us to reach data acquisition rates >10 kHz. We illustrate the method using a toy model of a glass sphere dropped on the resonator surfaces, bare or coated with liposomes, in liquid. We discuss some interesting features of the results obtained with the dropped spheres, such as bending of the HFF resonators due to the impact, sphere bouncing (or the absence of it), and contact aging.

Gaseous "nanoprobes" for detecting gas-trapping environments in macroscopic films of vapor-deposited amorphous ice.

Vapor-deposited amorphous ice, traditionally called amorphous solid water (ASW), is one of the most abundant materials in the universe and a prototypical material for studying physical vapor-deposition processes. Its complex nature arises from a strong tendency to form porous structures combined with complicated glass transition, relaxation, and desorption behavior. To gain further insights into the various gas-trapping environments that exist in ASW and hence its morphology, films in the 25-100 µm thickness range were codeposited with small amounts of gaseous "nanoprobes" including argon, methane, helium, and carbon dioxide. Upon heating in the 95-185 K temperature range, three distinct desorption processes are observed which we attribute to the gas desorption out of open cracks above 100 K, from internal voids that collapse due to the glass transition at ∼125 K and finally from fully matrix-isolated gas induced by the irreversible crystallization to stacking disordered ice (ice Isd) at ∼155 K. Nanoscale films of ASW have only displayed the latter desorption process which means that the first two desorption processes arise from the macroscopic dimensions of our ASW films. Baffling the flow of water vapor toward the deposition plate greatly reduces the first desorption feature, and hence the formation of cracks, but it significantly increases the amount of matrix-isolated gas. The complex nature in which ASW can trap gaseous species is thought to be relevant for a range of cosmological processes.

Environmental-Stress-Induced Increased Softness of Electroactive Biofilms, Determined with a Torsional Quartz Crystal Microbalance.

Electroactive biofilms are intensely studied not only for energy conversion and electrosynthesis, but also as sensing systems. The electrical current produced by the layer is largely proportional to the rate of metabolism and therefore decreases when the biofilm experiences adverse environmental conditions. Acoustic measurements may complement this approach. The layer's softness can be inferred from shifts of resonance frequency and resonance bandwidth of a quartz crystal microbalance (QCM) contacting these layers. The layer's softness responds to the environment. Both negative potentials of the electrode (the equivalent of "suffocation") and lack of nutrient supply (the equivalent of "starvation") were studied. For comprehensive analysis, torsional resonators operating on three different modes of vibration are suited best. Such data can be fitted with a viscoelastic model, leading to a quantitative estimate of the shear modulus. On a more empirical level, one might also use the ratio of the shift in bandwidth to the negative shift in frequency as an indicator of stress. For ease of operation, one might even replace the torsional resonators with thickness-shear resonators.

Latex films with gradients in crosslink density created by small-molecule-based auto-stratification.

A suitable balance of convective and diffusive transport of small molecules contained in the liquid phase of a drying latex film leads to auto-stratification and to functionally graded films. Differing from blends of latex particles, which may also experience drying-induced segregation, small molecules retain their mobility after the particles have touched and have formed an elastically coupled network. The use of a thickener, which turns the dispersion into a weak gel and prevents the free flow of particles, is compatible with this approach (and even advantageous). A problem with small molecules is fast diffusive equilibration of concentration differences. For this reason, composition gradients along the lateral direction, where the characteristic length scale is centimeters, are more easily achieved than gradients along the vertical. Addition of a thickener slows down the diffusion, which aids the development of gradients along the vertical. The application example chosen was the crosslinking agent adipic dihydrazide, ADH, which takes part in keto-hydrazide coupling. Its heterogeneous distribution produces a spatially variable crosslink-density in the dry film as evidenced by Raman microscopy. A side aspect of the work is an inward flow of serum, which is observed for high-Tg films. An explanation for this "anti-coffee-ring effect" --based on pore collapse driven by the polymer-water interfacial energy combined with finite polymer elasticity-- is proposed.

Determination of the Shear Modulus of Thin Polymer Films with a Quartz Crystal Microbalance: Application to UV-Curing.

The photoinduced curing of a light-sensitive varnish was followed, based on a change of the film's shear modulus, G, as determined with a quartz crystal microbalance (QCM). The film thickness was in the range of a few hundred nanometers. Both the storage modulus, G', and the loss modulus, G″, were obtained. The analysis is based on a perturbation calculation. The equations differ from the more commonly used set of equations derived from the small-load approximation and the acoustic multilayer formalism (sometimes termed Voigt-model). The discussion revisits assumptions, accuracy, and limits of the technique. Critical to the analysis is a knowledge of the thickness of the electrode underneath the film.

Use of torsional resonators to monitor electroactive biofilms.

Whereas the study of interfaces and thin films with the quartz crystal microbalance (QCM) is well established, biofilms have proven to be a difficult subject for the QCM. The main problem is that the shear wave emanating from the resonator surface does not usually reach to the top of the sample. This problem can be solved with torsional resonators. These have a resonance frequency in the range of tens of kHz, which is much below the frequency of the thickness-shear QCMs. The depth of penetration of the shear wave is correspondingly larger. Data acquisition and data analysis can proceed in analogy to the conventional thickness-shear QCM. Torsional resonators may also be operated as electrochemical QCMs (EQCMs), meaning that a DC electrical potential may be applied to the active electrode and that shifts of frequency and bandwidth may be acquired in parallel to the electrical current. Here we report on the formation of mixed-culture biofilms dominated by the microorganism Geobacter anodireducens. The viscoelastic analysis evidences an increase in rigidity as the films grows. Potential sweeps on electroactive biofilms reveal a softening under negative potentials, that is, under conditions, where the layer's metabolism was slowed down by insufficient oxidative activity of the substrate. For comparison, biofilms were monitored in parallel with a conventional thickness-shear QCM.

Characterizing protein-protein-interaction in high-concentration monoclonal antibody systems with the quartz crystal microbalance.

Making use of a quartz crystal microbalance (QCM), concentrated solutions of therapeutic antibodies were studied with respect to their behavior under shear excitation with frequencies in the MHz range. At high protein concentration and neutral pH, viscoelastic behavior was found in the sense that the storage modulus, G', was nonzero. Fits of the frequency dependence of G'(ω) and G''(ω) (G'' being the loss modulus) using the Maxwell-model produced good agreement with the experimental data. The fit parameters were the relaxation time, τ, and the shear modulus at the inverse relaxation time, G* (at the "cross-over frequency" ωC = 1/τ). The influence of two different pharmaceutical excipients (histidine and citrate) was studied at variable concentrations of the antibody and variable pH. In cases, where viscoelasticity was observed, G* was in the range of a few kPa, consistent with entropy-driven interactions. τ was small at low pH, where the antibody carries a positive charge. τ increased with increasing pH. The relaxation time τ was found to be correlated with other parameters quantifying protein-protein interactions, namely the steady shear viscosity (η), the second osmotic virial coefficient as determined with both self-interaction chromatography (B22,SIC) and static light scattering (B22,SLS), and the diffusion interaction parameter as determined with dynamic light scattering (kD). While B22 and kD describe protein-protein interactions in diluted samples, the QCM can be applied to concentrated solutions, thereby being sensitive to higher-order protein-protein interactions.