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, E_a,η, were derived from the functions η'(T). E_a,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.

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.

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.

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, k_D, 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 |η_Sph|, where |η_Sph| must be less than ∼100 η_bulk with η_bulk 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)

A fast EQCM measures the kinetics of the viscosity changes inside the double layer following voltage jumps.

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.

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.

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.

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-T_g 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" ω_C = 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 (B_22,SIC) and static light scattering (B_22,SLS), and the diffusion interaction parameter as determined with dynamic light scattering (k_D). While B₂₂ and k_D describe protein-protein interactions in diluted samples, the QCM can be applied to concentrated solutions, thereby being sensitive to higher-order protein-protein interactions.

Lipid phase behavior studied with a quartz crystal microbalance: A technique for biophysical studies with applications in screening

Quartz crystal microbalance (QCM) is emerging as a versatile tool for studying lipid phase behavior. The technique is attractive for fundamental biophysical studies as well applications because of its simplicity, flexibility, and ability to work with very small amounts of material crucial for biomedical studies. Further progress hinges on the understanding of the mechanism, by which a surface-acoustic technique such as QCM, senses lipid phase changes. Here, we use a custom-built instrument with improved sensitivity to investigate phase behavior in solid-supported lipid systems of different geometries (adsorbed liposomes and bilayers). We show that we can detect a model anesthetic (ethanol) through its effect on the lipid phase behavior. Further, through the analysis of the overtone dependence of the phase transition parameters, we show that hydrodynamic effects are important in the case of adsorbed liposomes, and viscoelasticity is significant in supported bilayers, while layer thickness changes make up the strongest contribution in both systems.

Probing the electrical impedance of thin films on a quartz crystal microbalance (QCM), making use of frequency shifts and piezoelectric stiffening

Using a temperature-responsive polymer film as an example, it was shown that a conventional quartz crystal microbalance (QCM) can probe a sample's electrical properties in addition to its thickness and softness. The film's electrical impedance was accessed by alternating between the driving voltage being applied to the front electrode and the back electrode. The opposing electrode was grounded in both cases. In the first configuration, the electrical properties of the sample do have an influence on the resonance frequency because of piezoelectric stiffening. In the second, they do not. Using this scheme, it was monitored how the electrical impedance of a film composed of a mixture of poly-N-isopropylacrylamide and polyvinylalcohol changes when the film swells and deswells.

Coupled resonances allow studying the aging of adhesive contacts between a QCM surface and single, micrometer-sized particles

Interparticle contacts and contacts between particles and surfaces are known to change over time. The contact area, the contact stiffness, and the contact strength usually increase as the contact ages. Contact aging is mostly driven by capillary forces, but also by plastic deformation. Making use of acoustic resonators, we have studied the stiffness of contacts between the surface of a quartz crystal microbalance (QCM) and individual, micrometer-sized particles adsorbed to the resonator surface. Studying single particles avoids ensemble-averaging. Central to the analysis is the coupled resonance, occurring when a surface-attached particle together with the link forms a resonator of its own. If the frequency of this second resonator comes close to one of the crystal's overtones, plots of shifts in resonance bandwidth versus overtone order display a resonance curve. This secondary resonance is caused by the coupling between the particle's resonance and the main resonance. One can read the frequency of the coupled resonance from this plot. Similarly, resonance curves are observed in plots of frequency and bandwidth versus time, if the contact stiffness varies smoothly with time. Because the coupled resonance is a characteristic feature, it is easily identified even in cases where frequency shifts of some other origin are superimposed onto the data. For the cases studied here, the links stiffened while they dried. Interestingly, the efficiency of coupling between the particle resonance and the main resonance decreased at the same time. This can be explained with an increase in the link's bending stiffness. The analysis highlights that a QCM experiment amounts to vibrational spectroscopy on surface-attached particles. Among the application examples is the adsorption and drying of a lycopodium spore. Clearly, the technique is also applicable to problems of bioadhesion.

Colloidal Stability and Magnetic Field-Induced Ordering of Magnetorheological Fluids Studied with a Quartz Crystal Microbalance

This work proposes the use of quartz crystal microbalances (QCMs) as a method to analyze and characterize magnetorheological (MR) fluids. QCM devices are sensitive to changes in mass, surface interactions, and viscoelastic properties of the medium contacting its surface. These features make the QCM suitable to study MR fluids and their response to variable environmental conditions. MR fluids change their structure and viscoelastic properties under the action of an external magnetic field, this change being determined by the particle volume fraction, the magnetic field strength, and the presence of thixotropic agents among other factors. In this work, the measurement of the resonance parameters (resonance frequency and dissipation factor) of a QCM are used to analyze the behavior of MR fluids in static conditions (that is, in the absence of external mechanical stresses). The influence of sedimentation under gravity and the application of magnetic fields on the shifts of resonance frequency and dissipation factor were measured and discussed in the frame of the coupled resonance produced by particles touching the QCM surface. Furthermore, the MR-fluid/QCM system has a great potential for the study of high-frequency contact mechanics because the translational and rotational stiffness of the link between the surface and the particles can be tuned by the magnetic field.

Stiffness of sphere-plate contacts at MHz frequencies: dependence on normal load, oscillation amplitude, and ambient medium

The stiffness of micron-sized sphere-plate contacts was studied by employing high frequency, tangential excitation of variable amplitude (0-20 nm). The contacts were established between glass spheres and the surface of a quartz crystal microbalance (QCM), where the resonator surface had been coated with either sputtered SiO2 or a spin-cast layer of poly(methyl methacrylate) (PMMA). The results from experiments undertaken in the dry state and in water are compared. Building on the shifts in the resonance frequency and resonance bandwidth, the instrument determines the real and the imaginary part of the contact stiffness, where the imaginary part quantifies dissipative processes. The method is closely analogous to related procedures in AFM-based metrology. The real part of the contact stiffness as a function of normal load can be fitted with the Johnson-Kendall-Roberts (JKR) model. The contact stiffness was found to increase in the presence of liquid water. This finding is tentatively explained by the rocking motion of the spheres, which couples to a squeeze flow of the water close to the contact. The loss tangent of the contact stiffness is on the order of 0.1, where the energy losses are associated with interfacial processes. At high amplitudes partial slip was found to occur. The apparent contact stiffness at large amplitude depends linearly on the amplitude, as predicted by the Cattaneo-Mindlin model. This finding is remarkable insofar, as the Cattaneo-Mindlin model assumes Coulomb friction inside the sliding region. Coulomb friction is typically viewed as a macroscopic concept, related to surface roughness. An alternative model (formulated by Savkoor), which assumes a constant frictional stress in the sliding zone independent of the normal pressure, is inconsistent with the experimental data. The apparent friction coefficients slightly increase with normal force, which can be explained by nanoroughness. In other words, contact splitting (i.e., a transport of shear stress across many small contacts, rather than a few large ones) can be exploited to reduce partial slip.

Coarsening of the pore network in drying latex films upon interparticle aggregation

The lateral drying front observed during film formation from latex dispersions with a Tg of the polymer around room temperature is composed of three three distinct lines. The lines are characterized by a decrease in turbidity, a renewed sharp increase in turbidity, and a more gradual decrease in turbidity at the end of what can be called a "halo". Microcracks with herringbone morphology develop at the first line, where the turbidity decreases. If macrocracks are present, these nucleate close to the end of the halo. At the line, where the turbidity sharply increases, one also observes an increase in stress birefringence. The substructure of the drying front is characteristically different from the structures described previously for films drying from hard particles. In particular, the renewed increase in turbidity cannot be explained as pore-opening, but rather is the consequence of a coarsening of the pore network after the particles jump into contact. A capillary instability sets in, by which the small pores collapse under the polymer/water interfacial energy, while the larger pores expand correspondingly. The instability (related to the Rayleigh instability of liquid jets) makes the films appear turbid. Also, the induced mechanical heterogeneity prevents straight macrocracks from penetrating into the halo because crack deflection and crack branching would result, which is energetically unfavorable.

Steady flows above a quartz crystal resonator driven at elevated amplitude

A steady flow of liquid was observed above the surface of a quartz crystal microbalance under conditions where the oscillation amplitude exceeded 10 nm. The streaming flow occurs parallel to the displacement vector and is directed towards the center of the plate. It is expected to have applications in acoustic sensing, in microfluidics, and in micromechanics in a wider sense. The flow is caused by the nonlinear term in the Navier-Stokes equation, which can produce a nonzero time-averaged force from a periodic velocity field. Central to the explanation are the flexural admixtures to the resonator's mode of vibration. Unlike pressure-driven flows, the acoustically driven steady flow attains its maximum velocity at a distance of a few hundred nanometers from the surface. It is therefore efficient in breaking bonds between adsorbed particles and the resonator surface. As a side aspect, the flow pattern amounts to a diagnostic tool, which gives access to the pattern of vibration. In particular, it leads to an estimate of the magnitude of the flexural admixtures to the thickness-shear vibration.

Correlation between particle deformation kinetics and polymer interdiffusion kinetics in drying latex films

Using an experimental setup which determines the turbidity of the sample and the efficiency of Förster resonance energy transfer (FRET) at the same time, we have correlated the particle deformation kinetics in a drying latex film, quantified by light scattering with the kinetics of polymer interdiffusion. Interdiffusion was quantified making use of energy transfer (FRET) between donor molecules and acceptor molecules, bound to polymer chains on different particles. When the chains cross the interparticle boundaries, the rate of energy transfer increases. The latex was prepared by miniemulsion polymerization. The amount of emulsifier employed during polymerization had a pronounced effect on the relative timing of interdiffusion and particle deformation. Increasing the amount of emulsifier delayed the onset of interdiffusion relative to the time when the film became transparent. This is mostly the consequence of a size effect, as opposed to surfactant acting as a barrier for transport.

Partial slip in mesoscale contacts: dependence on contact size

Using acoustic resonators, we have studied the occurrence and the magnitude of partial slip between glass spheres and polymer surfaces. The measurement relies on the shifts of resonance frequency and bandwidth, Δf and ΔΓ, induced by the contact as well as the dependence of Δf and ΔΓ on the amplitude of oscillation. One often finds a decrease of Δf at elevated amplitudes, which goes back to partial slip (also "microslip"). Building on two different models of partial slip, we derive the frequency-amplitude relation from the force-displacement relation. In accordance with both models, the bandwidth is found to increase with amplitude in the partial slip regime. For the highest amplitudes and largest spheres investigated, one observes a decrease of bandwidth with amplitude, which is interpreted as a transition to gross slip. Deviating from both models of partial slip, Δf is sometimes found to be independent of amplitude in the low-amplitude range. Constant Δf implies linear force-displacement relations. The critical amplitude for the onset of partial slip depends on the contact radius, where partial slip is more pronounced for larger contacts. This finding can be explained by a smooth stress profile at the edge of the contact with no singularity. The stress at the edge might be lowered by nanoscale roughness, by capillary forces, or by the inability of the two surfaces to reestablish a sticking contact at the turning point of the oscillation.

Attractive forces on hard and soft colloidal objects located close to the surface of an acoustic-thickness shear resonator

Colloidal particles located close to the surface of an acoustic thickness shear resonator feel an attractive steady force, which is induced by the high-frequency tangential motion of the resonator surface. The range of the force is about half the penetration depth of the transverse viscous wave, that is, half of the thickness of the Stokes boundary layer. For an oscillation amplitude of 10 nm and a particle radius of 100 nm, the depth of attractive potential well corresponds to about 3 times the thermal energy, k(B)T. The force therefore suffices to overcome Brownian motion.

Addition of halloysite nanotubes prevents cracking in drying latex films

Investigating the process of film drying from aqueous dispersions containing a polymer latex as well as halloysite nanotubes (HNTs), we found that composite films could be formed without cracking under conditions where films of the pure polymer would always crack. Scanning electron micrographs showed that the HNTs were well dispersed and, further, that the distribution of fiber orientations was close to isotropic. The pendulum hardness of films formed from acrylate dispersions strongly increased upon addition of the inorganic phase. The pencil hardness, on the other hand, was poor, which presumably goes back to insufficient coupling between the organic and the inorganic phase. All films were white in appearance. For fiber concentrations higher than 10 vol %, the final films were porous.

On-line determination of Förster resonance energy transfer efficiency in drying latex films: correlation of interdiffusion and particle deformation

An instrument is described, which measures the efficiency of Förster resonance energy transfer (FRET) in parallel to the sample's turbidity. The instrument was used to study the film formation from polymer latex dispersions. In this context, the FRET efficiency reflects the diffusion of polymer chains across the interparticle boundaries, while the loss of turbidity reflects the progress of particle deformation. Particle deformation causes tensile in-plane stress, while polymer interdiffusion creates cohesion and thereby helps to prevent cracking. The relative timing between the two therefore is of fundamental importance for successful film formation. The on-line determination of FRET efficiency while the film dries is complicated by the fact that the fluorescence lifetime of the donor, τ(D), depends on the water content in the vicinity of the donor. In the established procedure for data analysis, drifts in τ(D) induce corresponding artifical drifts in the values of the FRET efficiency. A novel algorithm for the analysis of fluorescence decay profiles is proposed, which makes use of the method of moments. The FRET efficiency is quantified by the upward curvature of the fluorescence decay curve in log-linear display. In the application example, interdiffusion is delayed relative to particle deformation by about 10 min. For successful film formation, this delay should be as small as possible.

Hearing what you cannot see and visualizing what you hear: interpreting quartz crystal microbalance data from solvated interfaces

Over the last 2 decades, the quartz crystal microbalance (QCM or QCM-D) has emerged as a versatile tool for investigating soft and solvated interfaces between solid surfaces and bulk liquids because it can provide a wealth of information about key structural and functional parameters of these interfaces. In this Feature, we offer QCM users a set of guidelines for interpretation and quantitative analysis of QCM data based on a synthesis of well-established concepts rooted in rheological research of the last century and of new results obtained in the last several years.

Hemispherical nanobubbles reduce interfacial slippage in simple liquids

Using an electrochemical quartz crystal microbalance (EQCM), we have produced bubbles of nanoscopic size at the front electrode of an acoustic shear wave resonator. Nanobubbles are usually expected to increase the resonance frequency because they have a low density and, also, because a liquid slides easily at a liquid-air interface. However, the bubble-induced frequency shift in many cases was negative, which implies positive hydrodynamic thickness and reduced slippage. The explanation is based on Laplace pressure. Due to the bubbles' inherent stiffness, the space in-between neighboring bubbles may turn into an assembly of pockets which move with the underlying substrate in the same way as a solid film. If, first, the bubbles are so small that the Laplace pressure can overcome the viscous drag, and, second, the contact angle is in the range of 90°, the latter effect dominates. This interpretation was corroborated by a calculation using the finite element method (FEM). The argument as such is not limited to acoustic shear waves: hemispherical nanobubbles increase the surface drag in stationary flows in the same way.

Self-stratification during film formation from latex blends driven by differences in collective diffusivity

Coatings with vertical gradients in composition were produced by drying an aqueous polymer dispersion containing both charged and neutral particles. After drying, the neutral component was enriched at the film/air interface. The spontaneous vertical segregation between the two types of particles goes back to a difference in collective diffusivity. As the film dries, a layer enriched in polymer develops at the top. Due to their mutual repulsion, charged spheres escape from this layer more quickly than their neutral counterparts. Provided that the total time of drying is between the times of diffusion for the two types of particles (approximately H(0)(2)/D(c) with H(0) the initial film thickness and D(c) the collective diffusivity of the respective species), a concentration gradient persists after the film has turned dry. This effect can be used to create a functionally graded material (FGM) in a single coating step.

Stress fluctuations in drying polymer dispersions

Drying polymer dispersions usually experience tensile stress, induced by the reduction in volume and by the rigid substrate. Due to edge-in drying, the stress is usually heterogeneous over the film. Stress peaks play a decisive role in the formation of cracks. This work relies on membrane bending, a technique that provides spatially resolved stress maps. In the experiments reported here, stress fluctuations on the order of 10% on the time scale of a few seconds were found. The stress fluctuations occur coherently over the entire drying front. Fluctuations go back to slight fluctuations in humidity of the environment (as opposed to local stress relaxations due to reorganizations of the particle network). The stress fluctuations disappear when covering the sample with a lid. They can be enhanced by blowing humid or dry air across the sample surface. Modeling builds on the assumption that all stresses go back to capillary pressure created at the menisci in between different spheres at the film-air interface. The local radius of curvature changes in response to slight variations in ambient humidity according to the Kelvin equation. The fluctuations are observed under a wide variety of drying conditions and should be included in film formation models.