Frequency dependence, isothermal measurement

Surface Acoustic Waves (SA Ws). The basic idea of this technique is to use the dependence of the frequency and propagation of surface acoustic waves on mass loading in a film. The porous film has to be deposited on a piezoelectric substrate (quartz), which is then placed into a physisorption setup to condense nitrogen at 77 K. Adsorption and condensation of N2 result in a shift of the oscillation frequency, and thus measurements of the oscillation frequency as a function of N2 partial pressure provide an adsorption-desorption isotherm.30 Although the technique has proven to provide a concise characterization of porous films,29,30 the requirement for the deposition directly onto the SAW piezoelectric substrate represents a certain restriction. 

In situ frequency dependent electromagnetic-impedence measurements provide a sensitive, convenient, automated technique to monitor the changes in macroscopic cure processing properties and the advancement of the reaction in situ in the fabrication tool. This chapter discusses the instrumentation, theory, and several applications of the techniques, including isothermal cure, complex time—temperature cure, resin film infusion, thick laminates, and smart, automated control of the cure process. 

P-Rdaxation. To analyze the p-rdaxation in more detail from the isothermal measured frequency scans temperature dependent charts at fixed frequency were constructed. From these plots the temperature of maximal loss was taken at the selected frequency. The results are shown in Figure 5 where the logarithm of the relaxation rate of the P-process log is plotted versus the reciprocal temperature. For all samples the temperature dependence of the relaxation rate i p can be described by an Arrhenius-equation... 

Saruyama Y (1999) Quasi-isothermal Measurement of Frequency Dependent Heat Capacity of Semicrystalline Polyethylene at the Melting Temperature using Light Heating Modulated Temperature DSC. Thermochim Acta 330 101-107. 

In addition to the adiabatic or isothermal difference, acoustically determined elastic constants of polymers differ from static values because polymer moduli are frequency-dependent. The deformation produced by a given stress depends on how long the stress is applied. During the short period of a sound wave, not as much strain occurs as in a typical static measurement, and the acoustic modulus is higher than the static modulus. This effect is small for the bulk modulus (on the order of 20%), but can be significant for the shear and Young s modulus (a factor of 10 or more) (5,6). 

The temperature-modulated mode of operation has been well known for many decades in calorimetry [33], but became well established only during the 1990s, when commercial DSC was modified this way [34], The idea is to examine the behavior of the sample for periodic rather than for isothermal or constant-heating-rate temperature changes. In this way it is possible to obtain information on time-dependent processes within the sample that result in a time-dependent generalized (excess) heat capacity function or, equivalently, in a complex frequency-dependent quantity. Similar complex quantities (electric susceptibility, Young s modulus) are known from other dynamic (dielectric or mechanical) measurement methods. They are widely u.sed to investigate, say, relaxation processes of the material. 

Figure 126 shows the frequency dependence of E", in which nine points per decade were measured. E" increases with increasing frequency to a maximum and then decreases rather slowly. All the E" (o) data exhibit a kink at a frequency about one and half decades higher than each maximum point, as marked with arrows. The kink at the higher frequency corresponds to the first Tg peak in the E"(T) curve. During the isothermal measurements, the sample has relaxed spontaneously and hence the resolution of the two peaks is decreased. With increasing temperature, the two peaks shift to a higher frequency. 

Figure 6.6. Schematic presentation of the frequency dependences of e and e" for typical dielectric relaxation modes in polymers. The traces of relaxation mechanisms with higher molecular mobility (shorter relaxation time) are recorded at higher frequencies. Compare with the isochronal dielectric spectrum of Fig. 6.4. Considering the temperature dependence of the dielectric strength (Ae), it becomes clear that the Ae values measured from isothermal or isochronal isothermal spectra alone are not necessarily equal.

The isothermal time dependence of relaxation and fluctuation due to molecular motions in liquids at equilibrium usually cannot be described by the simple linear exponential function exp(-t/r), where t is the relaxation time. This fact is well known, especially for polymers, from measurements of the time or frequency dependence of the response of the equilibrium liquid to external stimuli such as in mechanical [6], dielectric [7, 33], and light-scattering [15, 34] measurements, and nuclear-magnetic-resonance spectroscopy [14]. The correlation or relaxation function measured usually decays slower than the exponential function and this feature is often referred to as non-exponential decay or non-exponentiality. Since the same molecular motions are responsible for structural recovery, certainly we can expect that the time dependence of the structural-relaxation function under non-equilibrium conditions is also non-exponential. An experiment by Kovacs on structural relaxation involving a more complicated thermal history showed that the structural-relaxation function even far from equilibrium is non-exponential. For example (Fig. 2.7), poly(vinyl acetate) is first subjected to a down-quench from Tq = 40 °C to 10 °C, and then, holding the temperature constant, the sample... 

The non-isothermal crystallisation of PETP was examined by temp, modulated DSC(TMDSC). A new analytical model of TMDSC was applied to the process, taking account of the response of exothermic heat flow to temp, modulation in an apparent heat capacity of complex quantity. By examining the frequency dependence of the apparent heat capacity, the applicability was successfully examined for the non-isothermal process. The method was capable of determining the temp, dependence of crystal growth rate from TMDSC data analysis. The results were in good agreement with the dependence determined from literature values of spherulite growth rate measured by optical microscopy. 12 refs. 

Generally, the rheology of polymer melts depends strongly on the temperature at which the measurement is carried out. It is well known that for thermorheological simplicity, isotherms of storage modulus (G (co)), loss modulus (G"(complex viscosity (r (co)) can be superimposed by horizontal shifts along the frequency axis ... 

Very few experiments have been performed on vibrational dynamics in supercritical fluids (47). A few spectral line experiments, both Raman and infrared, have been conducted (48-58). While some studies show nothing unique occurring near the critical point (48,51,53), other work finds anomalous behavior, such as significant line broadening in the vicinity of the critical point (52,54-60). Troe and coworkers examined the excited electronic state vibrational relaxation of azulene in supercritical ethane and propane (61-64). Relaxation rates of azulene in propane along a near-critical isotherm show the three-region dependence on density, as does the shift in the electronic absorption frequency. Their relaxation experiments in supercritical carbon dioxide, xenon, and ethane were done farther from the critical point, and the three-region behavior was not observed. The measured density dependence of vibrational relaxation in these fluids was... 

Dielectric Measurements. The dielectric properties of Resin 5208 were followed for isothermal cures of 110, 125, 137, 148, and 162"C at several frequencies. Figure 7 shows the time dependence of the dielectric loss tangent for the combination of the PTFE... 

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