Frequency change

Direct Mass Measurement One type of densitometer measures the natural vibration frequency and relates the amplitude to changes in density. The density sensor is a U-shaped tube held stationaiy at its node points and allowed to vibrate at its natural frequency. At the curved end of the U is an electrochemical device that periodically strikes the tube. At the other end of the U, the fluid is continuously passed through the tube. Between strikes, the tube vibrates at its natural frequency. The frequency changes directly in proportion to changes in density. A pickup device at the cui ved end of the U measures the frequency and electronically determines the fluid density. This technique is usefiil because it is not affec ted by the optical properties of the fluid. However, particulate matter in the process fluid can affect the accuracy. 

The next task is to determine the plaeement of the eompensating zero and pole within the error amplifier. The zero is plaeed at the lowest frequency manifestation of the filter pole. Since for the voltage-mode controlled flyback converter, and the current-mode controlled flyback and forward converters, this pole s frequency changes in response to the equivalent load resistance. The lightest expected load results in the lowest output filter pole frequency. The error amplifier s high frequency compensating pole is placed at the lowest anticipated zero frequency in the control-to-output curve cause by the ESR of the capacitor. In short ... 

Such approximation is valid when the thickness of the polymeric layer is small compared to die thickness of die crystal, and the measured frequency change is small with respect to the resonant frequency of the unloaded crystal. Mass changes up to 0.05% of die crystal mass commonly meet this approximation. In die absence of molecular specificity, EQCM cannot be used for molecular-level characterization of surfaces. Electrochemical quartz crystal microbalance devices also hold promise for the task of affinity-based chemical sensing, as they allow simultaneous measurements of both tile mass and die current. The principles and capabilities of EQCM have been reviewed (67,68). The combination of EQCM widi scanning electrochemical microscopy has also been reported recently for studying die dissolution and etching of various thin films (69). The recent development of a multichannel quartz crystal microbalance (70), based on arrays of resonators, should further enhance die scope and power of EQCM. 

Example 2-3 The electropolymeric growth of 2 ng polyphenol onto a gold QCM crystal A = 1 cm2 /0 = 5 MHz) resulted in a frequency change of 12 Hz. Calculate the frequency change associated with the deposition of 4ng polyphenol onto a 0.5 cm2 crystal (/0 = 8 MHz). 

Figure 3a shows the spectra of CO adsorbed at room temperature on a typical Cr(II)/Si02 sample. At low equilibrium pressure (bold black curve), the spectrum shows two bands at 2180 and 2191 cm Upon increasing the CO pressure, the 2191 cm component grows up to saturation without frequency change. Conversely, the 2180 cm component evolves into an intense band at 2184 cm and a shoulder at 2179 cm The bands at 2191, 2184, and 2179 cm which are the only present at room temperature for pressures lower than 40 Torr, are commonly termed the room temperature triplet and are considered the finger print of the Cr(ll)/Si02 system (grey curve in Fig. 3). A new weak band at around 2100 cm appears at room temperature only at higher CO pressure. As this peak gains intensity at lower temperature, it will be discussed later. The relative intensity of the three components change as a function of the OH content (i.e., with the activation temperature and/or the activation time) [17].

Arai et al. (1997) used EQCM to study iodide absorption on polycrystalline gold in IM NaC104 containing different concentrations of Nal. Eigure 27.21 shows dynamic frequency change-potential A/-i curves for 0.1M NaC104 containing different concentrations of Nal. The frequency at potentials more positive than -0.8 V was less than that found without Nal. The frequency increased with... 

FIGURE 27.21 Frequency change-potential curves for 0.1 M NaC104 containing Nal. Concentration (1) OM, (2) 5.0X10- M, (3) S.OXIQ- M, (4) I.OXIO- M. Scan rate 0.1 V/s. (From Aral et al., 1997, with permission from Elsevier.)... 

In order to simplify the expression for G, one has to employ a sufficiently simple model for the vibrational modes of the system. In the present case, the solvent contribution to the rate constant is expressed by a single parameter E, the solvent reorganization energy. In addition, frequency changes between the initial and final states are neglected and it is assumed that only a single internal mode with frequency co and with the displacement Ar is contributing to G. Thus the expression for G reduces to [124] ... 

Schmickler W. 1996. Interfacial Electrochemistry. New York Oxford University Press. Schmickler W, Koper MTM. 1999. Adiabahc electrochemical electron-transfer reactions involving frequency changes of iimer-sphete modes. Electrochem Comm 1 402-405. Schmickler W, Mohr J. 2002. The rate of electrochemical electron-transfer reachons. J Chem Phys 117 2867-2872. 

The first application of the quartz crystal microbalance in electrochemistry came with the work of Bruckenstein and Shay (1985) who proved that the Sauerbrey equation could still be applied to a quartz wafer one side of which was covered with electrolyte. Although they were able to establish that an electrolyte layer several hundred angstroms thick moved essentially with the quartz surface, they also showed that the thickness of this layer remained constant with potential so any change in frequency could be attributed to surface film formation. The authors showed that it was possible to take simultaneous measurements of the in situ frequency change accompanying electrolysis at a working electrode (comprising one of the electrical contacts to the crystal) as a function of the applied potential or current. They coined the acronym EQCM (electrochemical quartz crystal microbalance) for the technique. 

Av reports the frequency change with respect to the gas phase frequency (experimental value, 2143 cm"1). The fflco/rco correlation method employed includes anharmonicity (see Ref. l for details). 

Some features of static NMR are illustrated in Fig. 3 (top), which depicts schematically the spectra for the quadrupolar nuclei in GaN, the two isotopes 69Ga and 71Ga with spin 7 = 3/2, and the 14N isotope with 7=1. The actual experimental spectra are shown for 71Ga in Fig. 3 (bottom left) and for 14N in Fig. 3 (bottom right). For the case of a single-crystal, Fig. 3 (top) shows that there is a 1/2 —1/2 CT about 4 kHz broad whose frequency changes only slightly with... 

The frequency change is small when compared to the difference between C = O (1700 cm-1) and C-O (1100 cm-1) stretches in line with the prevailing view that in planar amides relatively little charge is transferred to oxygen. The changes in frequency represent a small stiffening of the carbonyl bond at best. 

Figure 15.14 Cyclic voltammogram (top) and accompanying frequency change (bottom) for a poly(xylylviologen) film. Data taken from Ref. 15.

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