Temperature-frequency dependence

The principal regularities of viscoelastic properties of pc ymers are revealed in analysis of their temperature-frequency dependence. Such prr rties are described in the theory of reduced variables (i 05). WUliams, LandeU, and Ferry worked out a method of transformation of temperature and frequeru scales with the aid of which experim tal data, specifically the dynamic modulus, can be pat on one generalized curve, covering a very wide range of fr iuencies and temperatures (WLF-method). In a number of studies carried out up till now the licsbiUty of the WLF equation to filled systems, mainly to rubbers, has been proved (121—126). 

The jplication of the WLF theory to filled rubbers has indicated that the filler has little effect on the temperature-frequency dependence, and that is roximately linear-dependent on the filler contort (127). 

C3.5.6.5 POLYATOMIC MOLECULES IN LOW-TEMPERATURE CRYSTALS—FREQUENCY DEPENDENCE... 

Much of our knowledge of the frequency dependence of VER rates in polyatomic molecules stems from low-temperature studies of molecular crystals [2] such as pentacene (PTC 221 4) guest molecules in a crystalline naphthalene (N C,., H ) host. In naphthalene, the phonon cut-off frequency is -180 cm [97]. At low temperature,... 

Because of very high dielectric constants k > 20, 000), lead-based relaxor ferroelectrics, Pb(B, B2)02, where B is typically a low valence cation and B2 is a high valence cation, have been iavestigated for multilayer capacitor appHcations. Relaxor ferroelectrics are dielectric materials that display frequency dependent dielectric constant versus temperature behavior near the Curie transition. Dielectric properties result from the compositional disorder ia the B and B2 cation distribution and the associated dipolar and ferroelectric polarization mechanisms. Close control of the processiag conditions is requited for property optimization. Capacitor compositions are often based on lead magnesium niobate (PMN), Pb(Mg2 3Nb2 3)02, and lead ziac niobate (PZN), Pb(Zn 3Nb2 3)03. 

In comparing the radiative properties of materials to those of a blackbody, fhe terms absorptivity and emissivity are used. Absorptivity is the amount of radiant energy absorbed as a fraction of the total amount that falls on the object. Absorptivity depends on both frequency and temperature for a blackbody if is 1. Emissivity is the ratio of the energy emitted by an object to that of a blackbody at the same temperature. It depends on both the properties of fhe subsfance and the frequency. Kirchhoff s law states that for any substance, its emissivity at a given wavelength and temperature equals its absorptivity. Note that the absorptivity and emissivity of a given substance may be quite variable for different frequencies. 

A role is also played by the temperature and frequency dependence of the photocurrent, the variable surface sensitivity at various parts of the cathode and the vector effect of polarized radiation [40]. All the detectors discussed below are electronic components whose electrical properties vary on irradiation. The effects depend on external (photocells, photomultipliers) or internal photo effects (photoelements, photodiodes). 

For demonstrations add to a 1 -L beaker, 600 mL water, 60 mL cone, sulfuric acid, 20 g malonic acid, 7.8 g potassium bromate, 0.7-0.8 g (NHj ),Ce(NCL), and about 1 mL 0.025 M [Fe(phen)i]S04 ( ferroin indicator) to give a visible color. Stir magnetically. A short but variable length of time can be expected before oscillations begin their frequency depends on the temperature. 

Although the mean relative speed of the molecules increases with temperature, and the collision frequency therefore increases as well, Eq. 16 shows that the mean relative speed increases only as the square root of the temperature. This dependence is far too weak to account for observation. If we used Eq. 16 to predict the temperature dependence of reaction rates, we would conclude that an increase in temperature of 10°C at about room temperature (from 273 K to 283 K) increases the collision frequency by a factor of only 1.02, whereas experiments show that many reaction rates double over that range. Another factor must be affecting the rate. 

The dramatic slowing down of molecular motions is seen explicitly in a vast area of different probes of liquid local structures. Slow motion is evident in viscosity, dielectric relaxation, frequency-dependent ionic conductance, and in the speed of crystallization itself. In all cases, the temperature dependence of the generic relaxation time obeys to a reasonable, but not perfect, approximation the empirical Vogel-Fulcher law ... 

However, these parameters are temperature and Larmor frequency dependent. Such a model can be conveniently parameterized in terms of collision frequency (/), so that the rate of decorrelation is given by... 

Figure A2.1 Microwave frequency dependent HF-EPR spectra of aqueous Cr2+ (0.1-0.2 m), sulfate counterion. Experimental conditions temperature 10 K microwave frequency as indicated. In the spectrum taken at 329 GHz a sharp signal from aqueous Cr3+ impurity at g = 2 is indicated and the resonances due to Cr2+ are labeled (Figure A2.2).

Plots of G at 0.5 Hz and the reduced stress ore(j obtained from stress-strain measurements at small strains against temperature, give almost identical straight lines (Figure 5). This similarity was expected because no frequency dependence of G had been observed. Hence G equals the equilibrium modulus G G moreover equals the reduced stress ore(j, if the latter is measured in the vicinity of X= 1. The measurements were always performed at X = 1.02 - 1.04, so that this requirement is fulfilled. 

Six [Ln(Pc)2] complexes with heavy lanthanide ions (Ln = Tb, Dy, Ho, Er, Tm or Yb) were investigated by the measurements of alternating current (AC) magnetic susceptibility [18]. Out of the six compounds, [TbPc2] and [DyPc2] were found to show temperature and frequency dependence on AC magnetic susceptibility similar to that observed for the transition-metal SMMs, while the rest did not. Their SMM behaviour have been observed either in bulk, in dilute solid solutions... 

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