Resonance frequency viscosity

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Acoustic Wave Sensors. Another emerging physical transduction technique involves the use of acoustic waves to detect the accumulation of species in or on a chemically sensitive film. This technique originated with the use of quartz resonators excited into thickness-shear resonance to monitor vacuum deposition of metals (11). The device is operated in an oscillator configuration. Changes in resonant frequency are simply related to the areal mass density accumulated on the crystal face. These sensors, often referred to as quartz crystal microbalances (QCMs), have been coated with chemically sensitive films to produce gas and vapor detectors (12), and have been operated in solution as Hquid-phase microbalances (13). A dual QCM that has one smooth surface and one textured surface can be used to measure both the density and viscosity of many Hquids in real time (14). 

The shear-mode acoustic wave sensor, when operated in liquids, measures mass accumulation in the form of a resonant frequency shift, and it measures viscous perturbations as shifts in both frequency and dissipation. The limits of device operation are purely rigid (elastic) or purely viscous interfaces. The addition of a purely rigid layer at the solid-liquid interface will result a frequency shift with no dissipation. The addition of a purely viscous layer will result in frequency and dissipation shifts, in opposite directions, where both of these shifts will be proportional to the square root of the liquid density-viscosity product v Pifti-... 

In order that the programme can be used to calculate both the resonance frequency (RF) and angular resonance frequency (WR) for a chosen bubble (radius, br) it will be necessary to input the solvent density (d), the surface tension of the solvent (a), the solvent viscosity (q) and the solvent vapour pressure (pv). The programme can correct the data to the appropriate SI unit. For example, if a bubble radius of 10 cm was entered the correct response to the question Type in the initial (equilibrium) bubble radius in cm - line 280 - would be either 0.01 or lE-2 followed by return. The programme will convert the value to metres - (i.e. BR=.01 br). 

Schafer and coworkers [23] developed a QCM-IL sensor for use as an artificial nose using the ubiquitous [C4Cilm][PFg]. The IL was spin coated onto the surface of a 10 MHz AT-cut quartz crystal with gold electrodes. The work specifically studied the response of the sensor to ethyl acetate. The deposition of the IL on the surface of the electrode decreased the resonance frequency of the QCM by 2017 Hz. Exposure to increasing amounts of ethyl acetate vapor produced a linear increase in frequency, which was attributed to a progressive decrease in viscosity of the IL upon adsorption of the analyte. The response time, given as the time to full saturation of the... 

Fig. 4.9 Effect of kinematic viscosity on resonant frequency (adapted from Kanazawa et al., 1985)...

Piezoelectric acoustic wave devices also respond to small changes in mass at surfaces immersed in (viscous) liquids [9]. The resonance frequency of AT-cut quartz resonators immersed in liquids depends on the liquid density and viscosity. The transverse shear wave which penetrates into the viscoelastic deposit and into the liquid is damped due to energy dissipation associated with the viscosity of the medium (film or liquid) at the acoustic frequencies. 

In addition to mass changes at the quartz crystal surface and, liquid density and viscosity the resonant frequency can be affected by several other factors such as the liquid conductivity [10], the hydrostatic pressure... 

Mason [46] first observed that the viscoelastic properties of a fluid in contact with quartz crystals can affect the resonant properties. However, Mason s work had been forgotten and for a long time there have not been studies of piezoelectric acoustic wave devices in contact with liquids until Nomura and Okuhara [15] found an empirical expression that described the changes in the quartz resonant frequency as a function of the liquid density, its viscosity and the conductivity in which the crystal was immersed. Shortly after the empirical observations of Nomura were described in terms of physical models by Kanazawa [1] and Bruckenstein [2] who derived the equation that describes the changes in resonant frequency of a loss-less quartz crystal in contact with an infinite, non conductive and perfectly Newtonian fluid ... 

The resonant frequency also depends on the density and the viscosity of the contacting media. The frequency shift for measurement in air vs. vacuum is smaller than 10 Hz. However, the frequency shift from air to water or aqueous solution, for a 10 MHz crystal is about 4-12 kHz. The magnitude of this shift can be calculated by using the following relationship ... 

The sensitivity of the TSM resonant frequency to liquid properties, illustrated in the previous example, necessitates close control of liquid properties when hying to measure mass accumulation from solution [24]. Liquid viscosity, in particular, varies exponentially with absolute temperature and must be closely controlled to avoid spurious TSM resonator responses. 

Upon addition of an enzyme solution, a rapid decrease of resonator frequency is observed followed by a long period of the slower decrease (Fig. la). The adsorption of HRP on a PSS layer is essentially completed after 5-10 min. At the same time, the changes in series resonance resistance, which are proportional to the square root of density and viscosity of the media near the resonance surface [5], do not exceed 2 Ohm. It allows to consider the formed enzyme layers as a rigid and use the Sauerbrey equation to calculate the mass of the adsorbed HRP. 

Under extreme narrowing conditions the molecular correlation time, rc is related to the nuclear resonance frequency by equation (23). These conditions are usually found in low viscosity solutions and within their... 

The far-infrared (FIR) absorption spectrum of low-viscosity liquids contains a broad peak of resonant character with a resonant frequency and intensity which decreases with increasing temperature [14,15]. Phis phenomenon is known as the Poley absorption. It takes its name from the work of Poley [16], who observed that the difference between the high-frequency dielectric permittivity... 

Obviously a small wave velocity in the crystal improves the mass sensitivity of the sensor for a given mechanical resonance frequency/), whereas a large wave velocity increases the mass sensitivity if thickness of the crystal must not fall below a specific value. Table 1 illustrates these basic findings for AT-cut (exemplarily for a small Vq) and BT-cut quartz (exemplarily for a high Vq) for two cases a lOOnm rigid film (Sauerbrey case) and a semi-infinite hquid with a viscosity of 1 cP (Kanazawa case). 

Temperature dependence is a second major issue. It is small for AT-cut crystals however, temperature fluctuations cause fluctuations in Rq inversely proportional to Q [7]. This effect is small compared to temperature effects having their origin in properties of the measurand. In liquid apph-cations, the most temperature-sensitive value is the liquid viscosity. Here, temperature-induced variations in frequency increase with whereas mass sensitivity increases with m. Therefore, an elevated resonance frequency is helpful. 

Table 2 Definition of characteristic resonant frequencies and example data of frequency shifts generated from a rigid coating (density 1 gcm , thickness 100 nm) alone and with an additional semi-infinite Newtonian liquid (density Igcm, viscosity 1 cP) on top. Furthermore the effect of an external capacitance is considered (values in brackets) ...

This approach is dedicated to the measurement of hquid viscosity by determining the real part of the sensor admittance at series resonance frequency. According to this concept, one terminal of the sensor is fed with the (constant-level) output of a VCO. The resonator current I is measured by connecting a transimpedance amphfier at the second terminal. Due to the low input impedance of the transimpedance amphfier, the entire VCO output voltage is apphed to the sensor. Parasitic capacitances from the sensor terminals to ground (e.g., due the shielding of the connection cables) are on one side... 

In nematic liquid crystals, the viscosity depends on the relative orientation between the shear gradient and the orientation of the nematic phase. Close to a surface, the orientation is usually governed by surface orientational anchoring [77]. Anchoring transitions, for instance induced by the adsorption of an analyte molecule to the surface [78], can therefore be easily detected with the QCM [79,80]. This reorientation induced by adsorption amounts to an amplification scheme the expected shift in the resonance frequency and bandwidth... 

The quartz crystal resonator is a useful device for the study of thin-layer and interfacial phenomena. The crystals commonly employed have a fundamental resonance frequency of 5 -10 MHz and a resolution of the order of 0.1 -0.5 Hz. This high resolution makes the device sensitive to a myriad of physical phenomena, some of which are interrelated and some quite independent of each other. It cannot be overemphasized that the quartz crystal resonator acts as a true microbalance (more appropriately a nanobalance) only if in the course of the process being studied, the nature of the interface (its roughness, sHp-page, the density and viscosity of the solution adjacent to it, and the structure of the solvent in contact with it) is maintained constant. 

When placed in an electronic oscillator circuit, the portion of the quartz wafer located between the electrodes vibrates at its fundamental frequency. The frequency output from the oscillator, which is identical to the resonant frequency of the crystal, can be measured by a frequency counter. Several oscillator circuits are commercially available and they are generally similar to the circuit described in figure 19.3. The choice of the oscillator circuit is essentially influenced by the potential applications. Recent advances in piezoelectric research have shown that quartz crystals can oscillate in solution and several pioneering studies have been reported addressing the theoretical aspects of the oscillating frequency of piezoelectric crystals in solution. Several recently published circuits were briefly evaluated by Barnes [12] and some suggestions were made for improvements. In addition, the author described two new circuits which allow total immersion of the crystal in different media, viscous liquids of viscosity up to 40 cP and buffer and electrolytes of several millimolar ionic strength. 

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