Density-viscosity Product Research Articles

Kinetics of Charge Reversal in the Double Layer Studied with an Electrochemical Quartz Crystal Microbalance (EQCM-D)

Normal pulse voltammetry on inert electrolytes was combined with a new electrochemical quartz crystal microbalance (EQCM) with millisecond time resolution, which allows to probe the kinetics of charge reversal in the diffuse double layer (DL) after a step in electrode potential. The QCM responds to the charge reversal because the local viscosity-density product depends on the type and the concentration of the ions. The time resolution was improved to 1 ms using multifrequency lockin amplification, which allows to study kinetic effects in dynamic electrochemistry, which were previously not accessible with gravimetry. The noise was lowered to less than 10 mHz by modulating the electrode potential and averaging Δf and ΔΓ over many modulation cycles.The overtone scaling was found to be the same as in gravimetry (-Δf/n » const. and ΔΓ/n < -Δf/n with n the overtone order), which, however, is not caused by a deposition of a rigid film in the Sauerbrey sense. A Sauerbrey-type QCM response is also caused by changes in Newtonian viscosity inside a layer with a thickness far below the penetration depth of the shear wave (such as the double layer).The frequency response in the electrolytes studied correlated well with the viscosity B-coefficients of the respective ions as employed in the Dole-Jones equation. The time constants inferred from gravimetry were similar to the time constants (the RC-times) from electrochemical impedance spectroscopy (EIS). There were small differences, which presumably go back to slow rearrangements inside the Helmholtz layer, which are not seen in EIS.The QCM response to double layer recharging in inert electrolytes is of great importance for the interpretation of QCM results on processes involving Faradayic charge transfer. Such a response is omnipresent as a background and might be misinterpreted as a gravimetric signal.[1] References[1] Leppin, C.; Peschel, A.; Meyer, F. S.; Langhoff, A.; Johannsmann, D. Kinetics of Viscoelasticity in the Electric Double Layer Following Steps in the Electrode Potential Studied by a Fast Electrochemical Quartz Crystal Microbalance (EQCM). Analyst 2021, 146 (7), 2160–2171. Caption: Shifts in frequency and bandwidth in response to potential steps (left). The gravimetric signal followed the steps with a delay of a few milliseconds. The amplitude and the response time depend on cation type (right). The counter ion was NO3 -. Both the amplitude and the response time correlate well with the viscosity B-coefficient. Figure 1

A responsive viscosity sensing system with a flow channel based on a one-port resonator

Recently, more and more SAW sensors have been developed for viscosity sensing, bringing different ways of contacting the liquid with the device. It is important to choose a contact method that maximizes the performance of the device. Therefore, this paper describes the development of devices for detecting the viscosity of liquids and the evolution of fluid-device contact methods. And a responsive viscosity sensing system with a flow channel for real-time monitoring is developed in our work. The channel, made of polycarbonate, is responsible for regulating the flow direction and ensures that the sensing area covered by the liquid, the mass, and the morphology of the liquid load on the sensor are the same for each detection. Based on a one-port resonator, the sensor offers a faster response time, lower attenuation, and higher sensitivity of 38.6 kHz/ kg m−2 s−0.5. The real-time detection results also show that changes in flow rate do not affect resonant frequency. In addition, the sensor's frequency response to viscosity-density product has been conducted using glycerol solution to get a standard curve. Then the viscosity of the rinse water can be accessible by the frequency response. For the first time, the rinse solution directly from the washing machine is used to measure the residual detergent concentration. The residual concentrations of detergent in the first and second rinse solutions are 23 ppm and 6 ppm, respectively. The system is more convenient, more responsive, and more accurate.

Accuracy and precision of resonant piezoelectric MEMS viscosity sensors in highly viscous bituminous materials

This paper reports on the dynamic viscosity analysis of bituminous materials with piezoelectric MEMS plate-type resonators. To enable measurements even under such strong damping conditions in this high viscous environment, the 10th order roof-tile shaped vibrational mode is exploited. For actuation and sensing, a piezoelectric aluminium nitride (AlN) thin film is used in combination with a tailored electrode design. The resonator is calibrated by measuring its conductance frequency spectrum when immersed in six high viscosity (range: 150–45.000 mPa s) test liquids at temperatures from 30 °C to 100 °C. The determination of dynamic viscosity values of bituminous materials is done using the calibration function from the linear relationship between the quality factor Q and the inverse square root of the density-viscosity product ρμ−1/2 of the test liquids. Next, Q is mapped to ρμ−1/2 for bituminous materials measured at operating temperatures from 70 °C to 150 °C. Within the measurement accuracy a very good agreement of dynamic viscosity values determined by both the MEMS resonator and a rotational viscometer is demonstrated up to a maximum dynamic viscosity of about 60.000 mPa·s. Despite this limitation these results show the outstanding potential of piezoelectric MEMS sensors for the monitoring of even super high-viscous liquid properties.

Implementation and calibration of a phase detector circuit as a QCM sensor to characterize fluid properties

In this work, a quartz resonator or QCM sensor system based on a phase detector circuit is implemented. Until now, the phase detection method in QCM sensors has been used for mass measurement applications. In this work, the system is characterized for its use in applications to measure the properties of a liquid (density and viscosity). In a first part, the implementation of the system is described. Once implemented, it is calibrated with solutions of increasing viscosities, obtaining the sensitivity equation and the resolution of the output voltage to changes over the square root of the density-viscosity product. Finally, the results are compared with those obtained by the authors in previous works using oscillator circuits and a network analyzer as electronic measurement interfaces.

Implementation of a Density Sensitive Structure in the Torsionally Oscillating Resonant Pipe Viscosity Sensor

We present an improved version of a torsionally oscillating resonant pipe viscosity sensor. The new design offers the possibility to sense both, viscosity and density independently and at the same time. The first version of the sensor allowed only sensing the viscosity-density product, where the two values were not separable without additional knowledge or measurements. For the new design, density sensitive structures were additionally implemented into the pipe system. These structures force the fluid to follow the torsional oscillation of the pipe, therefore, in this region the fluid influences the behavior of the resonant structure like an additional mass. This leads to a frequency shift which is mainly density dependent. Due to this behavior it is now possible to use a higher order model to extract both viscosity and density out of one single measurement. We present the newly introduced sensor design, compare it to the first sensor design, describe the additional density sensitive structures and explain how the sensor was designed and evaluated using the Finite Element Method (FEM). We show how different values of viscosity and density influence the resonance frequency and the damping characteristics of the sensor. To prove the concept, we apply a calibrated higher order model to the simulation results and provide a first accuracy estimation.

Viscosity measurements of high-pressure liquids via a quartz crystal fundamental resonance

The pressure dependence of liquid viscosity for several liquids was obtained from the ΔΓ method using the bandwidth of the fundamental resonance peak of a quartz crystal resonator. The fundamental mode and the third overtone of the resonator in methyl laurate were determined and then compared to the square root of the viscosity–density product (ηρ) from the resonance frequency and bandwidth. The ηρ values obtained from the bandwidth of the fundamental mode were consistent with those obtained from other methods. The ΔΓ method could be applied to high-viscosity regions of bis(2-ethylhexyl) sebacate, using the relationship between ηρ and ΔΓ obtained from reference liquids at atmospheric pressure. The pressure dependence was obtained for methyl oleate viscosity up to 320 MPa; it is the major component of biodiesel fuel. In addition, the viscosity pressure dependence was obtained by the ΔΓ method from the fundamental mode in methanol and 1-pentanol that was previously measured up to 700 MPa with a smaller resonator.

Responsivity and sensitivity of piezoelectric MEMS resonators at higher order modes in liquids

Micromachined resonators completely submerged in liquids suffer from high viscous damping and low measurement signals compared to the operation in gaseous environment or in vacuum, which drastically decreases the sensing performance. A promising approach to decrease damping is the utilization of higher order modes. However, with the increase in mode order also the fluid-structure interaction decreases. In this context, it is unclear how the use of higher order modes helps, when targeting the characterization of fluid properties such as density and viscosity. In this paper, we demonstrate how the use of higher order modes affects both the responsivity and sensitivity of resonantly excited MEMS sensors when operated in liquids. The latter two key device parameters are experimentally investigated with respect to the inverse viscosity-density product (ρfluid·μfluid)-0.5 for the quality factor Q, the electrical conductance peak height ΔG and for the resonance frequency fres in standardized liquids with dynamic viscosity values ranging from 5 to 700 mPa∙s. It is observed, that an increase in mode order significantly increases the quality factor by a factor of 7, when comparing 1st to 10th order mode in a sample fluid with a dynamic viscosity of 5 mPa∙s), allowing the characterization of high viscous liquid with a dynamic viscosity up to 700 mPa∙s. Even so, no influence on the relative responsivity of Q and ΔG is observed. In fact, a decrease in the relative responsivity of fres is observed, so that no gain in response is achieved for all three parameters when the mode order is increased. However, higher order modes show significantly improved strain profiles on the surface of the resonating structure, resulting in increased ΔG values for the piezoelectric readout mechanism. Therefore, the sensitivity is substantially increased resulting in an improvement by a factor of ˜30, when comparing the 1st and 10th order mode. Even higher factors of ˜50 are obtained for Q and ΔG, what enables a minimal detectable (ρ·μ)−0.5 value of 0.000998 (mPa·s·kg/l)−0.5in a high viscous sample fluid with (ρ·μ)−0.5 = 0.040 (mPa·s·kg/l)−0.5 (for comparison: a common engine oil such as SAE 5W-40 has (ρ·μ)−0.5 = 0.039 (mPa·s·kg/l)−0.5at 0 °C).

Temperature decoupled viscosity-density product measurement in liquid by utilizing a dual-mode AlN-based acoustic wave resonator

In this letter, we report a two-in-one acoustic wave resonator with Rayleigh and Lamb modes for temperature decoupled viscosity-density product sensing. The Lamb mode of the resonator is sensitive to both the viscosity-density product and the ambient temperature, while the Rayleigh mode only responds to the ambient temperature and is not affected by liquid properties. These unique characteristics of the two modes are due to the different spatial distributions of the acoustic energy. Taking advantage of the aforementioned features, a beat frequency strategy is proposed to decouple the temperature influence from the viscosity-density product measurement, thus realizing temperature independent viscosity-density product sensing in a single acoustic wave resonator chip. Experimental results show that the accurate measurement of the viscosity-density product can be achieved in Newtonian liquids with a sensitivity of −0.36 MHz/kg m−2 s−0.5 within a wide temperature range from 20 °C to 80 °C. Our work holds great promise for liquid property measurement occasions with large fluctuations in ambient temperature, such as oil and gas exploration, automobile, and aeronautic applications.

Measurement of speed of sound, density compressibility and viscosity in liquid methyl laurate and ethyl laurate up to 200 MPa by using acoustic wave sensors

This paper presents measurements of speed of sound, density, viscosity and compressibility in liquid ethyl laurate and methyl laurate along isotherms ranging from (293.15 to 353.15) K at pressures that cover the pressure range of common rail direct fuel injection systems (up to 200 MPa). Measurements have been carried out by two different acoustic wave sensors assembled within a single device. The former works in the longitudinal mode to determine speed of sound whereas the latter acts in the thickness shear mode in order to measure the density viscosity product. The measurement principle of sound speed is based on pulse-echo technique whereas density is evaluated by integration of speed of sound measurement using Newton Laplace equation. Viscosity is determined from measurement of the resonance behavior of the thickness shear wave sensor. Finally both isothermal and isentropic compressibilities are obtained from density and speed of sound data.

Frequency Dependence of Dynamic Properties of Polyethylene Glycol Molecules on Oscillating Solid–Liquid Interface

Frequency dependence of the resonant length of polyethylene glycol (PEG) on a solid–liquid interface oscillating at megahertz was studied by a quartz crystal microbalance (QCM). A QCM frequency and a number-average molecular weight (Mn) of PEG were changed systematically. This attempt revealed that, in all of the frequencies used, the series-resonant frequency shift, ΔF, of the QCM against the square root of the density-viscosity product of the PEG solutions was linear and had intercept. In addition, the systematical analysis made it clear that the ΔF slope was explainable by the Debye process, and the ΔF intercept became constant above the resonant length. These results led to the novel findings that the resonant length of the PEG molecules formed by physisorption was equal to that in the region of the viscous penetration depth and that the relationship between resonant length and QCM frequency was able to be explained by τ ∝ Mnν, where τ is a relaxation time of molecule and ν is a constant. In particula...

Responses of a Quartz Crystal Resonator Against Viscosity of Liquid up to 700 MPa

Conductance spectra of a quartz crystal resonator against sweep frequency were obtained in methanol and 1-pentanol up to 700 MPa using a piston-cylinder type cell. A resonance peak around a nominal frequency was observed on the conductance spectra. The frequency shift of the resonance peak increased linearly with pressure. The frequency shift against pressure was represented as the sum of the parts attributed to the viscosity of the liquid and that on the pressure effect of the resonator. The measurements for the resonator immersed in methanol and 1-propanol showed that the part attributed to the compression of the resonator on the frequency shift was similar for the two liquids. An empirical relation was developed on the electrical response of the resonance against the viscosity of the surrounding liquid up to 700 MPa based on these results. It may become possible to estimate the viscosity-density product of various liquids up to this pressure from the frequency shift.

Screen Printed Electromechanical Micro-total Analysis System (μtas) for Sensitive and Rapid Detection of Infectious Diseases

The main objective of this article is to demonstrate by performing simulation measurements of biosensor that can detect the presence of pathogens through simultaneous mass and impedance techniques. This biosensor merges two biosensing techniques namely resonant frequency measurements and electrochemical impedance spectroscopy (EIS) on a single biosensor. Parallel measurements provide better sensitivities, have higher diagnostics accuracy and reduce the risk of false positives. Low cost, high resolution screen printing technology was used to fabricate the microelectromechanical array of μTAS on flexible piezoelectric substrates. The basic biosensor framework includes a substrate that highly sensitive sensor like thickness shear mode and immunosensor can be fabricated using quartz crystal lattice that integrated with electrochemical sensor [1]. The quartz crystal microbalance is a label free technique, which minimizes interference with the interaction being studied. A piezoelectric device is portable, simple and cost effective, and is suitable for real-time monitoring of biospecific interactions such as antigen-antibody, receptor ligand, and enzymes-substrate interactions with high sensitivity and specificity. For instance, the biological mixtures such as antibodies are capable of binding to terminal active functional groups (i.e., COOH, OH and NH2) of self-assembled monolayers (SAM) and immunocapture antigens such as glycoproptien or other targets[2]. The QCM can consequently detect mass changes due to these molecular interactions on the surface of the QCM. The top and bottom circular excitation electrodes with 150um diameter were modeled as gold (Au) films of 16 μm thickness. A sinusoidal voltage with amplitude of 5 mV was applied across the quartz crystal. Figure 1 shows the principle of integrated biosensors which gold electrodes were printed on both sides of a thin 500um quartz layer to form the quartz crystal microbalance (QCM)-impedance device. The silver (Ag) semicircular counter electrode was modeled around the top working electrode on the same area of the quartz crystal for performing the electrochemical impedance spectroscopy (EIS) experiments for detection of bacteria (E-Coli) and the results were compared to quartz crystal microbalance measurements. Furthermore, the use of gold surface can be incorporated into the transducer compatible with the biological samples such as use of highly specific monoclonal antibodies, and incorporation of amplification step to maximize the signal detection. In general, the quartz crystal is traditionally considered to be a mass sensitive sensor that produces response which it changes its resonance frequency to different thin film samples or liquids in contact with it surface. For a straight relationship between a thin film mass of the order of nanograms, the quartz crystal response will be of of the order of Hertz according to Eq. 1, Sauerbrey Equation [3]. ρq and μq are the specific density and the shear modulus in quartz, respectively. ϝ0 is the fundamental resonance frequency in quartz, related to its thickness, nq. Δm is the thin film mass deposited A, is the piezoelectrically active crystal area and n is the overtone number. Based on Eq. 1, it can be found that if the density of QCM changes, the resonant frequency of the device also changes, making the QCM suitable for monitoring changes in mass. [Display omitted] In contact with liquids, the crystal is capable of giving information about the density-viscosity product (√ρn) of the fluid by changing its resonance frequency and quality Q-factor according with Eq.3, Kanazawa equation[3]: [Display omitted] Where ρL and ηL are the density and viscosity in fluid respectively. Whilst, Eq. 4 indicates the decay characteristic length (δ) as linear relationship to the ratio viscosity to density of the liquid and inversely proportional the angular frequency (ω).Prior to device fabrication, 3D electric field analysis, resonant frequency simulations and thickness shear deformation were performed using automatic meshers by COMSOL Multiphysics. The resonator was modeled in three dimensions (3D), as an AT-cut quartz substrate of 500 μm thickness. The eigenfrequency analysis was performed to produce the quartz surface displacement and thickness shear deformation. The frequency domain analysis was conducted to obtain the resonant frequency of the resonator. Here we have tested the performance of the application of biosensors mainly in the detection of E-coli bacteria using QCM-impedance device using Escherichia coli cells as model of detection. Both frequency and impedance measurements were successfully obtained using cells both in media and in distilled water. We believe than this work offers a promising solution for the next generation of healthcare devices where high accuracy results are provided by low cost sensors.

Symmetric mechanical plate resonators for fluid sensing

In this contribution, we present a symmetric arrangement of electromagnetically actuated, resonating plates for viscosity and density measurement. Regarding the oscillation mode, the design resembles a tuning fork and is based on previously introduced resonating plate designs. It exhibits similar sensitivity to viscosity as previously characterized single plate resonators, while having two shear modes at different frequencies, that can be both actuated with the same setup allowing a multi-frequency analysis of viscoelastic liquids. We introduce the new design and present the results of FE simulations in order to determine the associated eigenmodes. We investigate the effects of the actuation method on the sensors performance by actuating with two different magnetic field configurations and by trying different configurations of the actuation and readout circuit, from which we show that with a particular configuration, Q-factors of up to 5000 can be reached for the symmetric shear mode. From these results we then proceed to suggesting a simplified lumped mechanical oscillator model explaining the dependence of the resonator’s Q-factor while operated in air on induced eddy currents damping. Measurement results are presented which show the general dependence of the new design’s actuated modes, the anti-symmetric and symmetric mode, on viscosity and density. We apply two different models to our data: a newly developed generalized model and a simplified version of that model which better describes the observed relation of our measurements to the square root of the product viscosity density. We then proceed to perform an estimated error analysis on viscosity, density, and the square root of their products based on the above mentioned applied models. From this error analysis several conclusions are drawn, mainly that the symmetric mode is more accurate than the anti-symmetric one, the sensor is generally more accurate for lower viscosity liquids, and lastly that the square root of the viscosity density product is a more suited value for the description of the sensor's behavior than the viscosity or the density alone.

Influence of liquid properties on the performance of S0-mode Lamb wave sensors: A theoretical analysis

Sensors based on thin film electroacoustic (TEA) devices have emerged as a promising alternative to quartz crystal microbalance and surface acoustic wave devices, in view of sensibility, miniaturization and easy integration. TEA devices include quasi-shear film bulk acoustic resonators (QS-FBAR) and S0 mode Lamb wave resonators (S0-LWR) based on AlN films. Despite the work done on the application of TEA devices as in-liquid biological and chemical sensors, a theoretical framework for S0-LWRs properly describing their sensing mechanisms is still needed. Here we validate a finite element analysis model on QS-FBARs and study the sensing mechanisms of S0-LWRs in liquid media. We show that S0-LWRs can sense changes in the dielectric permittivity of the liquid and demonstrate different sensitivities to viscosity and density. A complementary assessment of the S0-LWRs losses, dependent in a non-specific manner on the square root of the density viscosity product, provides the ability to discriminate density from viscosity changes on the entire device surface. Finally, with an S0-LWR optimization study we show that resolution improves with the decrease of the membrane thickness; however, a trade-off between sensitivity, quality factor and membrane fragility has to be considered.

A novel approach for differentiation of liquid samples with surface acoustic wave transducers and embedded microcavities

We discuss a novel method for sensing and differentiation of analytes trapped in a microcavity with an emphasis on liquids. The proposed sensing mechanism relies on capturing the analyte of interest in a microcavity etched on the delay line in contrast to the conventional mass loading method. The structure mainly consists of input and output interdigitated transducer (IDT) electrodes in an otherwise standard delay line configuration operated in Rayleigh mode along with a microcavity etched between the IDTs to trap minute amounts of liquids. Firstly, the responses of the system with the microcavity are explored using finite element method (FEM) analysis. Then, experimental results from delay lines on two different substrates, namely, Y-Z lithium niobate and ST-X quartz are analyzed. The system can distinguish between liquids with glycerin concentrations ranging from 60% to 90% in water and less than 5pL in volume in the high frequency range of 197MHz and 213MHz based on frequency and phase shift readings. Lithium niobate samples with 1.2μm deep microcavities provide an overall frequency sensitivity of −7.7kHz/(% glycerin). Quartz samples with 8.5μm deep microcavities have a sensitivity of −0.13°/(% glycerin). The minimum density–viscosity product experimentally differentiated using embedded microcavities is 1.9kg/m2√s. It is concluded that this method can be used to trap and interrogate minute amounts of liquids with different properties. Experimental results demonstrate that our approach can possibly be extended to certain solids, and to more complex structures like single biological cells.

Behavior of Polyethylene Glycol Molecules at an Oscillating Solid-Liquid Interface

The behavior of polyethylene glycol (PEG) molecules at an oscillating solid-liquid interface was examined using a quartz crystal microbalance (QCM). The number-average molecular weights (Mn) of PEG molecules were systematically varied. This study revealed that the shift in the energy dissipation factor, ΔD, of the QCM against square root of the density-viscosity product of the PEG solution is linear and has an intercept. Moreover, the systematical analysis revealed that the ΔD slope rapidly decreases with Mn, and the ΔD intercept becomes constant above 1.1×10(4) g/mol. Those results indicated that the resonant length of PEG molecules moving with the oscillating plate at 9 MHz is 97.6 Å. We also found that the difference between the resonant lengths calculated from ΔD and series resonance-frequency shift, ΔF, is related to the density of the thin PEG layer formed on the gold electrode.

Ferroelectric film bulk acoustic wave resonators for liquid viscosity sensing

A concept of accurate liquid viscosity sensing, using bulk acoustic wave (BAW) resonators, is proposed. The proposed BAW resonators use thin ferroelectric films with the dc field induced piezoelectric effect allowing for generation of pure longitudinal acoustic waves in the thickness excitation mode. This makes it possible to utilize exclusively shear liquid particle displacement at the resonator side walls and, therefore, accurate viscosity evaluation. The BAW resonators with the dc field induced piezoelectric effect in 0.67BiFeO3–0.33BaTiO3 ferroelectric films are fabricated and their liquid viscosity sensing properties are characterized. The resonator response is analyzed using simple model of a harmonic oscillator damped by a viscous force. It is shown that the resonator Q-factor is inversely proportional to the square root of the viscosity-density product. The viscosity measurement resolution is estimated to be as high as 0.005 mPa·s, which is 0.5% of the water viscosity.

Acoustic wave liquid sensors enhanced with glancing angle-deposited thin films

The application of nanostructured thin films grown by glancing angle deposition (GLAD) to enhance the sensitivity of Love wave liquid sensors was investigated. The effect of high-angle GLAD films, with and without nanostructure modification by ion milling and clustering, on device response was studied. Ion milling was used to prevent clustering of individual nanostructured posts, and was compared to films that were intentionally clustered. Both sets of modified films were shown to eliminate signal losses due to damping from the non-rigid, as-deposited posts. Sensitivity enhancement was tested by viscous loading with varying mixtures of glycerol and de-ionized water. Frequency shifts were found to be non-linear with the square root of the density–viscosity product, (ρη)1/2, and were modeled with exponentials. The sensitivity was shown to increase with film thickness, but decreased with increasing values of (ρη)1/2. There was also an increase in signal loss with film thickness under a liquid environment. The balance between sensitivity enhancement and signal loss must be carefully optimized with consideration for the intended application.

Resolution in QCM Sensors for the Viscosity and Density of Liquids: Application to Lead Acid Batteries

In battery applications, particularly in automobiles, submarines and remote communications, the state of charge (SoC) is needed in order to manage batteries efficiently. The most widely used physical parameter for this is electrolyte density. However, there is greater dependency between electrolyte viscosity and SoC than that seen for density and SoC. This paper presents a Quartz Crystal Microbalance (QCM) sensor for electrolyte density-viscosity product measurements in lead acid batteries. The sensor is calibrated in H2SO4 solutions in the battery electrolyte range to obtain sensitivity, noise and resolution. Also, real-time tests of charge and discharge are conducted placing the quartz crystal inside the battery. At the same time, the present theoretical “resolution limit” to measure the square root of the density-viscosity product of a liquid medium or best resolution achievable with a QCM oscillator is determined. Findings show that the resolution limit only depends on the characteristics of the liquid to be studied and not on frequency. The QCM resolution limit for measurements worsens when the density-viscosity product of the liquid is increased, but it cannot be improved by elevating the work frequency.

Dynamic properties of the polyethylene glycol molecules on the oscillating solid–liquid interface

The dynamic properties of polyethylene glycol (PEG) molecules on the solid–liquid interface oscillating at MHz were investigated using the quartz crystal microbalance (QCM). The number-average molecular weights (Mn) of the PEG molecules were systematically varied over 4 orders of magnitude. This study makes it clear that the series-resonant frequency shift, ΔF, of the QCM against the square root of the density–viscosity product of the PEG solution is linear and has the intercept. Moreover, systematical analysis reveals that the ΔF slope rapidly decreases with Mn and that the ΔF intercept becomes constant above 4.0×103gmol−1. As a result, those reveal that the resonant length of the PEG molecule moving with the oscillating plate of 9MHz is 54.2Å. We also find that the behaviors of ΔF due to Mn are mainly caused by the length of the PEG molecule.