Resonance frequency measurement

Tg of blend was measured at the scan rate of 5°C/min by Dynamic Mechanical Analyzer (Du Pont DMA 981), which was a resonant frequency measuring type. Tgs were determined by the peaks of the loss modulus peaks. 

Polymer and resonance frequency Measure of crosslinking Ea/kJ mole 1 ... 

If the primary isotopic effect is neglected, very accurate values may be obtained for the gyromagnetic constant ratio y("7Sn)/y(119Sn) [equation (10)1 from the ratio of the tin resonance frequencies, vTMs(U7Sn)/vTMs(U9Sn)- The ratios of resonance frequencies measured for pairs of tin isotopes with different accuracies by various authors are compared in Table XIV. 

Fast detection of the electro-acoustic impedance is a condition for successful kinetic studies. Soares [64] introduced a circuit to measure both resonant frequency and damping resistance R, though not as fast as simple active oscillator methods mainly used for resonant frequency measurement. Most active circuits operate in the series frequency a>s although some oscillators are designed to operate in the parallel frequency wp , which is slightly higher and very susceptible to the value of Ca. 

The resonance frequency measured in NMR is normally expressed in terms of units independent of the spectrometer field strength and hence as a chemical shift (8) in parts per million with respect to a reference compound [i.e.,8 = (// ampic - f/rcfere,.ceVv,(10 ), where and are positions of the respective absorption lines (in Hz) and v is the spectrometer operating frequency]. 

A QCM uses an oscillating quartz crystal at its resonance frequency. Measuring the shift of the resonance frequency Af caused by a thin film deposited on the quartz surface allows to calculate the mass per unit area. Adding a dissipation monitoring to this concept (QCM-D), i.e., also monitoring the decay of the quartz osdllation when switching off the ac excitation, provides additional information on the viscoelastic properties of the thin film material, hi particular, the change of dissipation AD introduced by the thin film can be calculated. 

The sinc fiinction describes the best possible case, with often a much stronger frequency dependence of power output delivered at the probe-head. (It should be noted here that other excitation schemes are possible such as adiabatic passage [9] and stochastic excitation [fO] but these are only infrequently applied.) The excitation/recording of the NMR signal is further complicated as the pulse is then fed into the probe circuit which itself has a frequency response. As a result, a broad line will not only experience non-unifonn irradiation but also the intensity detected per spin at different frequency offsets will depend on this probe response, which depends on the quality factor (0. The quality factor is a measure of the sharpness of the resonance of the probe circuit and one definition is the resonance frequency/haltwidth of the resonance response of the circuit (also = a L/R where L is the inductance and R is the probe resistance). Flence, the width of the frequency response decreases as Q increases so that, typically, for a 2 of 100, the haltwidth of the frequency response at 100 MFIz is about 1 MFIz. Flence, direct FT-piilse observation of broad spectral lines becomes impractical with pulse teclmiques for linewidths greater than 200 kFIz. For a great majority of... 

The sharpness of the frequency response of a resonant system is conunonly described by a factor of merit, called the quality factor, Q=v/Av. It may be obtained from a measurement of the frill width at half maxuuum Av, of the resonator frequency response curve obtained from a frequency sweep covering the resonance. The sensitivity of a system (proportional to the inverse of tlie minimum detectable number of paramagnetic centres in an EPR cavity) critically depends on the quality factor... 

Ultrafast TRCD has also been measured in chemical systems by incoriDorating a PEM into the probe beam optics of a picosecond laser pump-probe absorjDtion apparatus [35]. The PEM resonant frequency is very low (1 kHz) in these experiments, compared with the characteristic frequencies of ultrafast processes and so does not interfere with the detection of ultrafast CD changes. 

Mass resonant analyzer. A mass analyzer for mass-dependent resonant-energy transfer and measurement of the resonance frequency, power, or ion current of the resonant ions. 

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. 

Bulk-wave piezoelectric quartz crystal sensors indirecdy measure mass changes of the coating on the surface of the sensing device. This change in mass causes changes in the resonant frequency of the device, and measurements ate based on frequency differences. 

Another resonant frequency instmment is the TA Instmments dynamic mechanical analy2er (DMA). A bar-like specimen is clamped between two pivoted arms and sinusoidally oscillated at its resonant frequency with an ampHtude selected by the operator. An amount of energy equal to that dissipated by the specimen is added on each cycle to maintain a constant ampHtude. The flexural modulus, E is calculated from the resonant frequency, and the makeup energy represents a damping function, which can be related to the loss modulus, E". A newer version of this instmment, the TA Instmments 983 DMA, can also make measurements at fixed frequencies as weU as creep and stress—relaxation measurements. 

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). 

The Weissenbetg Rheogoniometer is well suited to research on homogeneous viscoelastic fluids and elastic melts. For oscillatory shear a second motor-drive mechanism is added. This allows the use of 60 frequencies in the range of 7.6 x 10 to 40 Hz at ampHtudes between 2 x 10 and 3 X 10 rad. An electronic circuit improves the precision of oscillatory measurements, particularly at frequencies neat the natural resonance frequency of the instmment itself (298). 

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). 

Young s modulus can be deterrnined by measuring the stress—strain response (static modulus), by measuring the resonant frequency of the body... 

The Young s modulus of the specimen is determined by accurately measuring its resonant frequency while driving it in a standing longi-... 

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