Fixed frequency system

Dynamic Mechanical Analysis (DMA) is a technique in which the elastic and viscous response of a sample under oscillating load, are monitored against temperature, time or frequency. This technique became well known by the impressive amount of information about the structure of polymers obtained with the torsion pendulum apparatus. The torsion pendulum DMA apparatus is a so-called resonant system i.e. the measuring frequency is not constant. The modern DMA systems are nearly always fixed frequency systems operating at frequencies between about 0.01 and 100 Hz. and in a temperature region ranging from about -150°C to 300°C. A survey of the DMA technique and the available commercial equipment was given by Wunderlich [1]. 

Medium to high equipment cost Uneven heating and hot spots (in case of fixed frequency system) Specific tooling material is mandatory... 

Microwaves have wavelengths between 1 mm and 1 m and hence have similar frequencies to radar and telecommunication devices. So as not to cause interference with these systems the frequency of radiation that can be emitted by household and industrial appliances is strictly regulated, with most appliances operating at a fixed frequency of 2.45 GHz. To some extent this reduces the flexibility of such equipment. 

Although the use of a probe provides several advantages over the use of baths (vide supra), they do suffer from a common disadvantage - they are only capable of operating at single fixed frequency. There are however two additional problems peculiar to probe systems ... 

Dynamic mechanical analyzers can further be divided into free resonance analyzers and forced resonance analyzers. In the case of free resonance analyzers, samples are allowed to oscillate freely (e.g., at their natural frequency) until oscillations cease. Forced resonance analyzers are nevertheless more frequently used. They are designed to apply oscillating stress at a fixed frequency and are ideal for scanning material performance over a wide temperature range (Menard, 1999). Sample preparation includes selection of an appropriate clamp system, which is a function of... 

Passing over to a space-fixed coordinate system with z J (Fig. 1.5(d)) and expanding the unit vector dJ over cyclic unit vectors, we obtain three components. Two of these, namely d 1 and d+1, similarly to (1.7) and (1.8), correspond to P- and i -types of transitions, with frequencies wo— and (jJo + Q. respectively. In addition, a new component d° appears which corresponds to Unear osciUations along the 2-axis with frequency cjo. This component of the vector d is connected with a Q-type transition, as a result of which we obtain a change in the electronic state of the molecule, but no change in its rotational quantum number A = J — J" = 0. 

The first level to be studied in detail by Tichten [35] was the N = 2 level of both para-Hi and ortho-H2. He measured a series of fixed-frequency magnetic resonance transitions, determining effective g- values and proving the identification of the c3nu state in the process. An effective Zeeman Hamiltonian may be written, in the space-fixed axis system,... 

Other groups have built tunable far-inffared spectrometers which do not involve high-frequency backward-wave oscillators. Verhoeve, Zwart, Versluis, Drabbels, ter Meulen, Meerts, Dymanus and McLay [61] have described a system in which fixed frequency far-inffared radiation is mixed with tunable microwave radiation in Schottky barrier diodes. This instrument has been operated up to 2.7 THz, and used to study OD and N2H+. A similar system, combined with a continuous supersonic jet, has been described by Cohen, Busarow, Laughlin, Blake, Havenith, Lee and Saykally [62], This instrument was used to study rare gas/water clusters. 

Such considerations also provide a rationale of the inability of the dielectric continuum model, as conventionally expressed with a fixed frequency factor, to describe the solvent-dependent kinetics of some other outer-sphere reactions [45b, 95b]. As noted in Sect. 3.3.1, the influence of solvent dynamics upon vn should disappear for reactions having moderate or large inner-shell barriers, the frequency factor being determined by vis instead [eqns. (22) and (25)] this can account for the success of the conventional (fixed-frequency) dielectric-continuum treatment in describing solvent-dependent kinetics for some reactant systems [45],... 

However, the experimental studies relate to spatial growth of disturbances as the flow system is always excited by fixed frequency sources. Hence a spatial theory is preferred to study the stability of non-isothermal flows. Despite the distinction between temporal and spatial methods, the neutral curve, however, is identical. Iyer Kelly (1974) reported results using linear spatial theory under parallel flow approximation for free-convection flow past heated, inclined plates. Tumin (2003) also reports the spatial stability of natural convection flow on inclined plates providing the eigen spectrum. 

The main advantage of the computer-controUed phase-locked loop configuration is that it is nearly as rugged as the fixed-frequency perturbation measurement system in terms of continuing to function during large changes in at-... 

The DMTA operates at fixed frequencies over a broad temperature range. Sixteen discrete frequencies from 0.01 Hz to 200 Hz are available. The very low frequencies, below about 0.1 Hz, require a long time to complete, while frequencies above 30 Hz are often near or above the system resonance and require special consideration. Though the system is capable of a... 

Of the four types of laboratory ultrasonic apparatus commercially available for practising chemists in general (namely, whistle reactors, ultrasonic cleaning baths, probes and cup-horn devices) analytical chemists, except for a few specialists working in (or with) ultrasound detectors, use mainly cleaning baths and probes both of which are usually operated at a fixed frequency dependent on the particular type of transducer, that is usually 20 kHz for common probe systems and 40 kHz for baths. Both types of devices are described below. 

As with all systems which operate using piezoelectric transducers, optimum performance is obtained at a fixed frequency. For most commercial probe systems such a frequency is 20 kHz and, although it is possible to drive them at their overtones i.e. 40 or 80 kHz), the power dissipation at overtones is very much reduced. In order to operate successfully at different frequencies, it is best to purchase individual amplifier-horn systems tailored to one s individual requirements. 

C, Li3 spin systems). The HMQC experiment, which also allows a straightfoward determination of the involved C, Li coupling constants, is especially easy to perform with a triple resonance probehead which has, aside from the H and the lock channel, a fixed frequency for and a variable X frequency (see Chapter 2). It is of interest to note that Li, C cross peaks can also be observed in cases where the corresponding Li, C coupling is not resolved in the ID spectrum [14]. An example for an experiment using sequence (v) is shown in Figure 14 with the spectrum of isopropyllithium, where in hydrocarbon solvents solvation leads to the formation of tetramers and hexamers [76]. 

The macroscopic property observed in sum-frequency experiments, Xs . is a sum of the molecular hyperpolarizabilities, over all vibrational modes and all of the molecules at the interface, which takes into account the orientation of each molecule. Orientational information is obtained from the experimental spectra through consideration of the relationship between the observed Cartesian components of the macroscopic second-order susceptibility Xuk, the corresponding spectroscopically active components of the molecular hyperpolarizability, This is accomplished through an Euler angle rotation of the molecular axis system into the laboratory axis system as defined through the use of the rotational matrix iiuK imn- The general expression for the transformation from a molecular-fixed axis system to a laboratory-fixed system is... 

Both the dielectric and the calorimetric results were found to be quite well reproducible in the whole concentration range studied but for two concentration values, C=0.270 and 0=0.353> where time dependent phenomena were observed upon ageing of the samples. Because of the latter effect, the two analyses were performed by taking the measurements respectively, 3-7-10-15-20 and 30 days after the preparation of each concentration tested. The latter study had the aim to follow the spontaneous evolution of the system until time independent both dielectric and calorimetric behaviors were obtained. The dielectric study of the time dependent phenomena was carried out at the fixed frequency of 10 KHz. 

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