Sauerbrey Equation Research Articles

Transduction mechanism of acoustic-wave based chemical and biochemical sensors

Acoustic-wave-based sensors are commonly known as mass-sensitive devices. However,acoustic chemical and biochemical sensors also face so-called non-gravimetric effects,especially if they work in a liquid environment. The one-dimensional transmission-linemodel (TLM) is a powerful tool, which considers the influence of geometric and materialproperties on the sensor transduction mechanism, most importantly the influence ofviscoelastic phenomena. This paper demonstrates the concept of modelling acousticmicrosensors on quartz crystal resonators. Particular attention is paid to special caseswhich allow for simplifications or specific solutions of the TLM, like the acoustic loadconcept (ALC), the BVD model or the Sauerbrey equation. Deviations from theone-dimensional assumption of the TLM are suspected to significantly contribute to theacoustic sensor response in biosystems. We therefore introduce a generalization of the ALCto get access to two- or three-dimensional effects, which are up to now not considered in theTLM. As examples, signatures of interfacial phenomena or non-uniform films arediscussed.

Sauerbrey Equation of Quartz Crystal Microbalance in Liquid Medium

Sauerbrey Equation of Quartz Crystal Microbalance in Liquid Medium

Characterization of the Viscoelasticity and the Surface Roughness of Electrochemically Prepared Conducting Polymer Films by Impedance Measurements at Quartz Crystals

The electrical impedance of quartz crystals was measured during electropolymerization of poly (PBT) and poly-(3,4-ethylenedioxythiophene) (PEDT) from acetonitrile and propylene carbonate. Due to the viscoelastic behavior and the high surface roughness, application of the Sauerbrey equation to relate frequency shifts to mass changes leads to systematic errors. A novel procedure is presented to calculate the mass changes, the viscoelastic properties (complex shear modulus), and the surface roughness of the conducting polymer layers from the shift of the resonance curve of the quartz crystal. The dependence of the surface morphology of PEDT and PBT on the preparation conditions could be monitored in situ. The values of the complex shear moduli show that these polymers have rubber-like behavior. The damping increase of the quartz at the initial stages of the polymer deposition is mainly a surface roughness effect. As the polymer thickness increases, internal friction (viscoelasticity) also begins to contribute to the damping. © 2002 The Electrochemical Society. All rights reserved.

Study of the hydrogen/palladium system by fast quartz microbalance techniques

Electrogravimetric and coulometric measurements were performed on thin palladium film by means of a quartz crystal microbalance. According to the applied potential, two regions appear: the α-phase and the β-PdH phase. If in the first one microbalance and coulometric measurements gave compatible results in the latter phase large differences were observed. Various hypothesis can explain this dysfunction. On the one hand, the quartz microbalance would not only measure a mass change in the β-PdH phase but a frequency change related to the stress due to the insertion of hydrogen atoms in the palladium lattice as well. Therefore, the Sauerbrey equation would not be valid. On the other hand, the trapping of hydrogen in sites close to the electrode surface would change the rheology of this sublayer, which can change the value of the Sauerbrey coefficient. At least in the α-PdH phase, the model presented in this paper was in good agreement with the experimental results. In addition to the classical mechanism (Volmer, Heyrovski, Tafel reactions) the consideration of a trapping of hydrogen in a sublayer under the electrode surface and a direct desorption of the trapped hydrogen is validated.

An Electrode-Separated Piezoelectric Sensor as a Surface Monitoring Technique for Anionic Surfactant Adsorption on Quartz Surface

In the configuration of an electrode-separated piezoelectric sensor (ESPS), the quartz crystal surface is in a direct contact with the liquid phase. With the pre-adsorption of Ca2+ as the ionic bridge, anionic surfactant can adsorb on the negatively charged quartz surface (pH > 2.0). The adsorption process of sodium dodecyl benzenesulfonate (SDBS) was monitored in real time with the ESPS method. It was shown that the adsorption of SDBS on quartz surface by Ca2+ inducement was reversible with respective to the dilution of solution phase. The adsorption behavior can be analyzed using Langmuir model. The adsorption and desorption rate constants were estimated to be ka = (108.4 ± 6.4) mol−1L s−1 and kd = (2.57 ± 0.32) × 10−3 s−1, respectively. The observed adsorption densities in the ESPS method were significantly greater than the true ones. The influence on surface roughness of the quartz disc on adsorption densities should be corrected by adding a calibration coefficient in the Sauerbrey equation. The saturation adsorption density is 0.223 µg/cm2 for SDBS on quartz surface. Double layer occurs for the adsorption of SDBS on quartz surface.

An EQCM study of the oxidative deposition of alkylthiolates on gold

The oxidative deposition of alkylthiolates on a gold surface has been studied with the electrochemical quartz crystal microbalance (EQCM) method. The surface concentration of alkylthiolates calculated from the oxidative charge and from the EQCM signal using the Sauerbrey equation are in excellent agreement for depositions done in 0.1 M KOH and 0.1 M LiOH aqueous solutions. Potential step experiments allowed the measurement of the mass of alkylthiolates deposited versus time. These experiments show that the oxidative deposition of alkylthiolates occurs in two steps for slow deposition rates and in one step for fast deposition rates. The EQCM data of the oxidative deposition of alkylthiolates can be described by a combination of a potential dependent instantaneous nucleation-growth process and a potential independent Langmuir process. At faster deposition rates, the deposition occurs only by the nucleation and growth mechanism whereas at slower deposition rates up to one-third of a monolayer can be deposited via a Langmuir process.

Multistep Adsorption of Perfluoropolyether Hard-Disk Lubricants onto Amorphous Carbon Substrates from Solution

We have used a quartz crystal microbalance (QCM) to study the solution-phase adsorption of the perfluoropolyether lubricants Fomblin ZDOL and Demnum SA from perfluorohexane and perfluorobutylmethyl ether onto model carbon-coated hard-disk surfaces. The validity of the QCM results and the applicability of the well-known Sauerbrey equation have been verified through combined QCM and surface plasmon resonance experiments. The adsorption isotherms are relatively simple and exhibit a Langmuir-like behavior. However, the plateau region is sometimes ill-defined, and the adsorption process is strongly dependent on the history of the system. The adsorbed mass at a particular concentration shows a pronounced dependence on the equilibration time between successive concentration changes, even though the adsorption kinetics appears to have equilibrated. In the first few seconds, the adsorption process is diffusion limited, with the adsorbed mass quickly increasing to a maximum before decaying to the equilibrium value....

An extended Butterworth-Van Dyke model for quartz crystal microbalance applications in viscoelastic fluid media.

An extended Butterworth-Van Dyke (EBVD) model with frequency-independent parameters for the characterization of a resonant compound formed by a quartz crystal in contact with a finite viscoelastic layer contacting a semi-infinite viscoelastic medium is extracted by analysis of the lumped element model. The formulation of the EBVD model is compared with the complete expression of the electrical admittance of the loaded quartz derived from the transmission line model (TLM). Relative deviations between them do not exceed 3% around 1% bandwidth near resonance. An extended Martin & Granstaff's model and an explicit expression for the frequency shift that supposes an extension of Kanazawa's model for viscoelastic media are obtained. An analysis of the errors associated with the extraction of shear parameters of the coating for different materials prove that, to obtain an error less than 5% in the shear parameters determination, the viscoelastic contribution, defined as the relative error in the thickness computed from the frequency shift by Sauerbrey equation, must be greater than a limit that depends on Q, which is defined as the ratio of the shear storage modulus (G') to shear loss modulus (G"). In the materials studied, polymers in the transition range or in the rubbery state with Q = 1 and 10, the viscoelastic contribution must be higher than 15% and 50%, respectively, for a 5% limit error in the shear parameters extraction. A criterion for a practical determination of the appropriate viscoelastic regimes is indicated.

Response of a Thickness-Shear-Mode Acoustic Wave Sensor to the Adsorption of Lipoprotein Particles

The properties of three different lipoprotein films were investigated using a thickness-shear-mode acoustic wave sensor in conjunction with an oscillator circuit that provides an automatic gain control (AGC) output. The oscillator records a frequency shift that is dependent upon both the mass and dissipative properties of the film and associated overlayers, but the shift in AGC voltage (ΔAGC) depends only upon the dissipative properties of the film. The total recorded frequency shift (ΔFT) is treated as a sum of two terms: ΔFM, the mass contribution of the frequency shift, and ΔFD, the frequency shift attributed to energy dissipation. An empirical relationship between ΔFD and AGC is found by measuring both parameters in purely dissipative fluids, which were mixtures of glycerol and water in the experiments presented here, and establishing a calibration curve from the corresponding data. ΔFT and AGC changes were measured during the formation of lipoprotein films on the thickness shear mode (TSM) acoustic wave sensor. The AGC change measured for a lipoprotein film is converted to ΔFD. From this, the ΔFM for the film can then be determined by finding the difference between the total measured frequency shift for the film and ΔFD; the mass of the lipoprotein films is estimated using the Sauerbrey equation. The information provided by the AGC feature of the oscillator circuit reveals that films formed from the low-density lipoprotein fraction are rigid and dense as compared to films formed from the high and very-low-density lipoprotein fractions.

Adsorption of Lipid Vesicles on Hydrophobic Surface Investigated by Quartz Crystal Microbalance

The adsorption of lipid vesicles on a hydrophobic substrate has been investigated in aqueous buffer solution by means of the quartz crystal microbalance (QCM) and ellipsometry. As a hydrophobic substrate, 1-octadecanethiol (ODT) was self-assembled on a gold-coated AT-cut quartz, and lipid vesicles were prepared by the injection method using the synthetic phospholipid l-α-dipalmitoylphosphatidylcholine (DPPC). Although the in-situ ellipsometry thickness measurement dictated that only a monolayered DPPC was formed on the ODT-modified gold substrate, the frequency change measured by QCM was found to correspond to the formation of nearly 30 layers of DPPC on ODT when the usual Sauerbrey equation was assumed to hold in the present system as well. To interpret the nonideal QCM behavior, we have developed a modified four-layer model for QCM operating in a liquid medium. On the basis of the model, the physical characteristics of QCM were related to the electrical parameters of the equivalent QCM circuit. The prop...

Ion-selective piezoelectric sensor for niacinamide assay in serum and urine.

An ion-selective piezoelectric (ISP) sensor was successfully applied for the determination of niacinamide in serum and urine. By coating a polyvinylchloride membrane containing niacinamide-silicotungstate on one electrode of a thickness-shear mode piezoelectric quartz crystal, the ISP device can adsorb niacinamide selectively. The amount of coating applied to the crystal was calculated from the Sauerbrey equation by monitoring the frequency change. The logarithm of the frequency shift was linear with the logarithm of niacinamide concentration over the range from 1.0 x 10(-9) to 1.0 x 10(-3) M with a detection limit of 1.0 x 10(-9) M at pH 7.0. Influencing factors were investigated and optimized. The results for real samples obtained by the proposed method were in good agreement with those obtained by the conventional methods.

Evaluation of antibody immobilization methods for piezoelectric biosensor application

The immobilization of anti- Salmonella antibodies by two methods were studied and evaluated for their potential use in a piezoelectric biosensor. The optimum temperature–time combinations for the highest immobilization yields were determined for both methods. Protein A binding was found to be 67.4±3.8% on the gold surface which then allowed an immobilization of 42.1±2.09% antibody. The degree of antibody immobilization via surface aldehyde groups of glutaraldehyde (GA) on a precoated quartz crystal with polyethylenimine (PEI) was 31.6±0.3%. A piezoelectric probe was designed and used in dry assays to observe the frequency change due to addition of mass by the immobilization layers. The frequency changes recorded showed a better reproducibility and less added mass for the Protein A method. The frequency decrease due to μg of added antibodies was compared to frequency decrease calculated by the Sauerbrey equation. The experimental data was found to be only ∼8% of theoretical data. The functionality of the immobilized antibodies with the Protein A method was tested with S.typhimurium in a wet chamber and the frequency decrease was compared to results of a similar system activated with PEI–GA immobilization. The frequency decreases with S.typhimurium concentration of ∼1.5×10 9 CFU/ml were 50±2 Hz and 44±3 Hz for the Protein A method and PEI-GA method, respectively. It was concluded that although both methods resulted in comparable activities in terms of % immobilized protein and frequency decreases due to Salmonella binding, the Protein A method was favorable due to stability and better reproducibility of the immobilization layers.

Mixed Cation and Anion Transport during Redox Cycling of a Self‐Doped Polyaniline Derivative in Nonaqueous Media

This work describes a microgravimetric study of the charge compensation process in different supporting electrolyte solutions of propylene carbonate or acetonitrile for a polyaniline derivative, poly (aniline‐co‐N‐propane sulfonic acid aniline), PAPSAH. The viscoelastic properties of thin PAPSAH films were investigated using an electroacoustic impedance technique. These results demonstrate that the film behaves rigidly, validating the use of the Sauerbrey equation for mass measurements with the electrochemical quartz crystal microbalance (EQCM). Both cation and anion participation in the charge compensation process were studied using cyclic voltammetry and EQCM measurements. On a molar basis, the cation and anion contributions during the redox process for thin films of this material are roughly 50% each in supporting electrolytes. The cation and anion participation during the redox process increase in the following order: tetrabutylammonium and , respectively. The significance of these results for applications of self‐doped polyaniline derivatives in nonaqueous media is discussed. © 2000 The Electrochemical Society. All rights reserved.

Técnicas in situ de baixo custo em eletroquímica: a microbalança a cristal de quartzo

Among in situ techniques, the electrochemical quartz crystal microbalance (EQCM) is a powerful tool for the study of electrochemical reactions that produce mass changes in the electrode/solution interface. This review present some systems in which the EQCM combined with classical electrochemical techniques, gives relevant information for understanding the charge transport process at a molecular level. The aim of this review is to do a brief description of experimental arrangements, with emphasis on some special cares that must be considered by the users. Secondly, some chosen electrochemical systems where the technique was successfully applied are discussed. Finally, a brief analysis of electroacoustic impedance experiments was done in order to show when the Sauerbrey equation can be used.

Polyelectrolyte adsorption processes characterized in situ using the quartz crystal microbalance technique: alternate adsorption properties in ultrathin polymer films

The alternate adsorption processes of polyelectrolytes from solution have been investigated in situ using a functionalized (gold electrode) quartz substrate via the quartz crystal microbalance (QCM) technique. The deposition process involved the alternate layer by layer electrostatic (Coulombic) interaction between oppositely charged adsorbing polyelectrolytes resulting in ultrathin multilayer films. Three kinds of polyelectrolyte combinations were used: poly(diallyldimethylammonium chloride) (PDADMAC), poly(ethylenimine) (PEI) and poly(allylamine hydrochloride) (PAH) as the cationic polymers and poly(sodium-4-styrensulfonate) (PSS) as the anionic polymer for polycation/polyanion combinations. The electrical behavior of the piezoelectric ‘quartz crystal’ was sensitive to the adsorption properties of the polyelectrolytes, thus allowing close observation of the time-dependent adsorption processes. The adsorption relationship was explored for different polyelectrolyte pair-combinations, alternate solution concentration and the presence of rinsing and drying steps. The results showed that the amount of frequency change is mostly dependent on the immediate subphase environment of the crystal surface, i.e. aqueous environment versus air in relation to the classic Sauerbrey equation.

A Novel Ion-Selective Sensor for Procaine Hydrochloride Based on a Piezoelectric Quartz Crystal Coated with a Procaine Tetraphenylborate PVC Membrane

A novel ion-selective sensor for procaine hydrochloride has been proposed and applied successfully to analysis of pharmaceutical preparations. The sensor is based on modification of the Ag-electrode of an AT-cut piezoelectric quartz crystal with a PVC membrane containing procaine tetraphenylborate. A linear relation between the logarithm of the response frequency and the logarithm of the procaine hydrochloride concentration was found experimentally and could be explained by combination of a modified Sauerbrey equation and the Freundlich isotherm. The detection range was from 8.3 × 10−8 to 5.0 × 10−3 M with a detection limit of 8.3 × 10−8 M. The selectivity of the sensor and the influence of experimental parameters such as solution pH and detection time were investigated.

Characterization of Porous Thin Films Using Quartz Crystal Shear Resonators

A new model for the characterization of porous materials using quartz crystal impedance analysis is proposed. The model describes the equivalent electrical and/or mechanical impedance of the quartz crystal in contact with a finite layer of a rigid porous material which is immersed in a semi-infinite liquid. The characteristic porosity length (ξ), layer thickness (d), liquid density (ρ), and viscosity (η) are taken into account. For films thick compared with the characteristic porosity length (d ≫ ξ), the model predicts a net increase of the area which is translated into a linear relationship between the quartz equivalent impedance Z = R + XL (XL = iωL, ω = 2πf, f being the oscillation frequency of the quartz resonator) and the ratio d/ξ. For low-viscosity Newtonian liquids, for which the velocity decay length δ = (2ωη/ρ)1/2 is much smaller than ξ, Z corresponds to the impedance of a semi-infinite liquid in contact with an increased effective quartz area which scales with the ratio d/ξ. In this case, R = XL in agreement with Kanazawa equation. For liquids of higher viscosity, the effect of the fluid trapped by the porous matrix is apparent and is reflected in the impedance, which has an imaginary part (XL) higher than its real part (R). In the limit of a very viscous liquid, the movement of the porous film is completely transferred to the liquid and all the mass moves in-phase with the quartz crystal electrode. In this limiting case the model predicts a purely inductive impedance, which corresponds to a resonant frequency in agreement with the Sauerbrey equation. The model allows us, for the first time, to explain the almost linear behavior of R vs XL along the growth process of conducting polymers, which present a well-known open fibrous structure. Films of polyaniline−polystyrenesulfonate were deposited on the quartz crystal under several conditions to test the model, and a very good agreement was found.

Validation of the mass response of a quartz crystal microbalance coated with Prussian Blue film for ac electrogravimetry

Prussian Blue (PB) films have been considerably studied for many research applications such as electrochromic material development, new material for batteries, etc. Many analytical techniques were employed for examining PB electrochemical behaviour in solution and the quartz crystal microbalance (QCM) used in the alternative regime (ac electrogravimetry) appeared as an attractive in situ mass sensor due to its low cost and its high mass sensitivity. Unfortunately, the validity of the common Sauerbrey equation was questionable with these films or in other terms if the QCM was used as a pure mass sensor. In this work PB film is examined through acoustic measurements and the response can be interpreted as a pure mass change if the thickness is around 0.15 μm. Over this limit, film viscoelastic contributions can affect drastically the mass change estimation: if the thickness is two times larger, the mass error reaches 40%.

Investigation of the cathodic electropolymerization of acrylonitrile, ethylacrylate and methylmethacrylate by coupled quartz crystal microbalance analysis and cyclic voltammetry

Abstract The cathodic electropolymerization of acrylonitrile (AN), ethylacrylate (EA) and methylmethacrylate (MMA), has been monitored for the first time by coupled electrochemical quartz crystal microbalance (QCM) and cyclic voltammetry analyses. These data have been compared to the previously published analyses for methacrylonitrile (MAN). At the potential E p1 of the less cathodic of the two voltammetric peaks observed (peak I), the polymer formed is anchored firmly to the cathode even in a good solvent for it, and it remains adsorbed when the voltammetric scan is repeated up to E p1 . In parallel, a linear relationship is observed between the frequency change recorded in situ by the QCM up to E p1 and the PAN film thickness measured ex-situ by ellipsometry. However, when potentials more negative than peak I are scanned, the polymer desorption (degrafting) occurs as assessed by solubilization in a good solvent. Polymerization is also resumed but in solution and no longer as grafted chains. The major difference between the acrylic monomers (AN and EA) and the methacrylic ones (MMA and MAN) is that part of the methacrylic chains are not grafted at E p1 . This coexistence of adsorbed and desorbed chains is not observed for the polyacrylic chains in that potential range. The mass of PAN deposited onto the cathode has been approximated from the film thickness and the Sauerbrey equation, so allowing the M n of the grafted chains to be estimated.

EQCM and Quartz Crystal Impedance Measurements for the Characterization of Thiophene-Based Conducting Polymers

AbstractEQCM was extensively used to investigate ion-transport phenomena during dopingundoping processes of electronically conducting polymers. Several early studies assumed that the polymer films were rigidly coupled to the quartz crystal so as to relate the mass change to the quartz crystal resonant frequency change via the Sauerbrey equation. However, the rigidity of electronically conducting polymer films is doubtful and it has to be demonstrated. Quartz crystal impedance analysis near the resonance is of paramount importance to get insight into the viscoelastic properties of the film [1] and to avoid misleading in the interpretation of EQCM data.This contribution presents and discusses quartz crystal impedance measurements, performed with a Frequency Response Analyzer in the 9MHz region, and EQCM data collected for a dithienothiophene based polymer.