Shear oscillations

In the series branch of the equivalent electrical circuit, Lq is proportional to the quartz inertial mass displaced by the shear oscillation, Cq is proportional to the energy stored in the quartz crystal during oscillation and Rq describes the energy frictional loses of the quartz crystal. 

Hook, F., Rodahl, M., Brzezinski, P., and Kasemo, B. (1998). Energy dissipation kinetics for protein and antibody-antigen adsorption under shear oscillation on a quartz crystal microbalance. Langmuir 14, 729-734. 

Gramespacher H and Meissner J (1992) Interfacial tension between polymer melts measured by shear oscillations of their blends. J Rheol 36 1127-41. 

Liquid loading of a device performing a shear oscillation leads to an entrainment of a thin liquid film with exponential decay of the entrained shear movement (Fig. 7.18.6), in which the decay length 3 is given by [12]... 

For a homogeneous thin film with a thickness smaller than the wavelength of the shear oscillations, the shift of the resonance frequency can be expressed in terms of the change in surface mass density of the film, Anzf, (in units g cm ). This was given by Sauerbrey [8] as ... 

Evidently, there are two distinct frequencies, where either the numerator or the denominator of the complex impedance becomes zero. However, the case of zero impedance is determined exclusively by the serial capacity, whereas the parallel determines the frequency of infinite impedance. These two frequencies thus correspond to the resonance frequencies of the two part circuits mentioned above and are also correctly reproduced in the frequency spectrum of the QCM. Observable side resonances (as shown especially in the insert with lower span) can be traced back to mechanical oscillations that differ from the main one one is the result of antisymmetric thickness shear oscillation, the other of a twist oscillation. The ratio of intensity between the desired thickness shear wave and the side resonances is mainly defined by the ratio between electrode diameter and quartz substrate thickness. This is illustrated in Fig. 4, where the damping spectra for both a 10 MHz and a 5 MHz device are given. In both cases the electrode diameter here is 8 mm (the spectra in Fig. 3 were recorded with 4 mm electrode diameter). Evidently, the 5 MHz QCM shows the desired response pattern, where the shear resonance by far dominates the electrical behaviour. The 10 MHz QCM, however, shows very pronounced side resonances. The rather large electrode diameter (compared to the thickness) very strongly favours the occurrence of torsional motions within the substrate, thus reasonable amplitudes are generated for this mode. 

According to Eq. 2 the shift AD mirrors changes in energy dissipation of the shear oscillation. Measuring the change in energy dissipation becomes im-... 

Fig. 8 a Experimental setup to perform impedance analysis of the shear oscillation. Quartz resonators are used as the bottom plate of a measuring chamber that is mounted in a temperature-controlled Faraday cage. Impedance data is recorded with a gain/phase analyzer in the vicinity of the fundamental resonance of 5 MHz (typically from 4.97 MHz to 5.04 MHz). b Butterworth-Van Dyke equivalent circuit to analyze the impedance raw data of the loaded resonator. All parameters except Zl are assigned to the unperturbed resonator whereas Zl denotes the impedance of the load material (cell layer) on the resonator surface... 

Fig. 9 Experimental raw data of the shear oscillation as recorded by impedance spectroscopy. a Impedance magnitude of a cell-covered and a cell-free resonator as a fimction of frequency, b Phase spectra of a cell-covered (filled circles) and a cell-free (open circles) resonator in comparison...

Taken together, these studies revealed that confluent cell layers in contact to the resonator lead to a significant increase of energy dissipation from the shear oscillation [33] as we had learned already from the QCM-D experiments presented in Sect. 2.4. The impact of the cells on energy dissipation is individual and dependent on the cell type. It is important to mention in this context that different batches of a certain cell line may also cause a different QCM response within certain limits. This is not surprising for cell biologists since cells of the same kind but taken from different batches may show a certain variance in their behavior and it underlines that the QCM is capable of picking up these subtle differences. 

Fig. 14 Schematic of the combined QCM-ECIS setup. In order to perform electrochemical impedance analysis of the adherent cell layer on the substrate electrode, an additional low impedance platinum dipping electrode is introduced into the measurement chamber. Impedance analysis of the cell layer (ECIS mode) is performed in the frequency range between 1 Hz and 1 MHz, whereas the shear oscillation is analyzed close to its fundamental resonance between 4.97 MHz and 5.04 MHz. A computer-controlled relay allows switching between both modes automatically...

When the resonant condition of a thickness-shear oscillation is satisfied for AT-cut piezoelectric crystals, a shear wave propagates through the bulk of the material, perpendicular to the faces of the crystals. The fundamental resonance frequency, fo is given by ... 

Since the mid 1980s and the advent of rehable second generation controlled-stress rheometers, the controlled-stress technique has become widely established. The facility which most of this type of instrument offers, i.e. of performing three different types of test (steady shear, oscillation and creep), makes them particularly cost effective. 

Pre-strain was included in modulated stress testing of rubber and the dimensions of the pre-strained specimens used in calculation of the loss modulus. The loss modulus was independent of pre-strain for filled and unfilled rubbers. A test specimen geometry was chosen where pure shear could be superimposed with a small strain imparted with a shear oscillation. Again, loss modulus was mostly independent of pre-strain for filled and unfilled rubbers, including those filled with carbon black. The results enable understanding of energy dissipation mechanisms in rubber composites. ... 

The polymer is a branched polyethylene melt with = 1.55 x 10 and Mw/M = 11.9, flowing at 170 °C in a 3.3 1 planar contraction. The hnear viscoelastic properties and the nonlinear parameters for a four-mode PTT equation are shown in Table 10.1. Different values of e were used for each mode, but with a constant value of f = 0.08. These parameters provide a reasonable fit to the transient and steady-state shear and extensional data, although the nonlinear parameters for the two longest relaxation times cause small oscillations in startup of simple shear that are not observed experimentally using parameters that ehmi-nate the shear oscillations causes the calculated extensional stresses to be too low, and the contraction flow results are sensitive to the extensional stresses. The mean relaxation time was 1.74 s, the average velocity in the downstream channel was 7.47 mm/s, and the downstream channel half-width (the characteristic length) was 0.775 mm. The Weissenberg number based on downstream channel properties was therefore 16.8. 

When a gel is subjected to sinusoidal shear oscillation with an angular frequency ca and amplitude yo, the real G and imaginary part G of complex shear modulus, G (G = (G + iG ) - known as storage shear modulus and loss modulus respectively- may be obtained. The storage modulus (G ) is proportional to the elastic energy that is stored in... 

Figure 9.7 Working principle of the quartz crystal microbalance. The quartz crystal is excited to shear oscillate at its resonance frequency. Changes in adsorbed mass or viscous coupling of adsorbed layers lead to changes in resonance frequency and width of the resonance peak.

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