Spectroscopy modulus

Some authors have used the designation modulus spectroscopy to denote small-signal measurement of M vs. v or co. Clearly, one could also define admittance and dielectric permittivity spectroscopy. The latter is just another way of referring to ordinary dielectric constant and loss measurements. Here we shall take the general term impedance spectroscopy to include aU these other very closely related approaches. Thus IS also stands for immittance spectroscopy. The measurement and use of the complex (< ) function is particularly appropriate for dielectric materials, those with very low or vanishing conductivity, but aU four functions are valuable in IS, particularly because of their different dependence on and weighting with frequency. 

In this section we shall first summarize a number of previous methods of data presentation and then illustrate preferred methods. A common method of showing data has been to plot the imaginary parts (or sometimes their logarithms when they show considerable variation) of such quantities as Z, Y, M, or e vs. v or log(v). More rarely, real parts have been plotted vs. v. Such plotting of the individual parts of Z or M data has itself been termed impedance or modulus spectroscopy (e.g. Hodge et al. [1976], Almond and West [1983( ]). As mentioned earlier, however, we believe that this approach represents only a part of the umbrella term impedance spectroscopy and that complex plane and 3-D plots can much better show full-function frequency dependence and interrelationships of real and imaginary parts. 

Impedance and Modulus Spectroscopy of Polycrystalline Solid Electrolytes, J. Electroanal. Chem. 74, 125-143. 

In addition to the AC inputs such as voltage amplitude and radial frequency CO, impedance spectroscopy also actively employs DC voltage modulation (which is sometimes referred to as "offset voltage" or "offset electrochemical potential") as an important tool to study electrochemical processes. Alternative terms, such as "dielectric spectroscopy" or "modulus spectroscopy," are often used to describe impedance analysis that is effectively conducted only with AC modulation in the absence of a DC offset voltage (Figure 1-4). 

Clip acts in phase (the same Fourier component) with the first action of cii to produce a polarization that is anti-Stokes shifted from oi (see fV (E) and IFj (F) of figure B 1.3.2(b)). For the case of CSRS the third field action has frequency CO2 and acts in phase with the earlier action of CO2 (W (C) and IFj (D) of figure Bl.3.2 (b). Unlike the Class I spectroscopies, no fields in CARS or CSRS (or any homodyne detected Class II spectroscopies) are in quadrature at the polarization level. Since homodyne detected CRS is governed by the modulus square of hs lineshape is not a synmretric lineshape like those in the Class I... 

The excellent low temperature properties of FZ have been iadicated ia Table 1. Modulus curves were obtained usiag dynamic mechanical spectroscopy to compare several elastomer types at a constant 75 durometer hardness. These curves iadicate the low temperature flexibiUty of FZ is similar to fluorosihcone and ia great contrast to that of a fluorocarbon elastomer (vinyUdene fluoride copolymer) (Fig. 3) (15). 

The elastic constants of bulk amorphous Pd-Ni-P and Pd-Cu-P alloys were determined using a resonant i rasound spectroscopy technique. The Pd-Ni-P glasses are slightly stiffer than the Pd-Cu-P glasses. Within each alloy system, the Young s modulus and the bulk modulus show little change with alloy composition. 

To examine this peculiar behavior, we have converted the elastic compressibility modulus, per unit area, Y (Fig. 12a), to the modulus per chain, Y = F/10 F (Fig. 12b). The elastic compressibility modulus per chain is practically constant, 0.6 0.1 pN/chain, at high densities and jumps to another constant value, 4.4 0.7 pN/chain, when the density decreases below the critical value. The ionization degree, a, of the carboxylic acid determined by FTIR spectroscopy gradually decreases with increasing chain density due to the charge regulation mechanism (also plotted in Fig. 12b). This shows that a does not account for the abrupt change in the elastic compressibihty modulus. 

From the dynamic mechanical spectroscopy, an increase of PTMO molecular weight from 650 to 2000 results in a decrease in both the modulus and the glass transition temperature of the final product. The SAXS results indicate that a correlation distance exists in the samples, and this distance increases as PTMO molecular weight increases. A cluster model is thus suggested to account for the experimental results. 

Alternatively, NIR spectroscopy has been applied to relate NIR data to mechanical properties [4], A multivariate data analysis was performed on a series of commercial ethene copolymers with 1-butene and 1-octene. For the density correlation, a coefficient of determination better than 99% was obtained, whereas this was 97.7% for the flexural modulus, and only 85% for the tensile strength. 

The behavior of cristobalite PON has been studied as a function of pressure. No in situ evidence for pressure-induced amorphization was noticed. Whereas cristobalite Si02 displays four crystalline phases up to 50 GPa (195), PON remains in a cristobalite phase (193, 196). By using Raman spectroscopy and synchrotron X-ray diffraction, Kingma et al. (193, 197) observe a displacive transformation below 20 GPa to a high-pressure cristobalite-related structure, which then remains stable to at least 70 GPa. The high value of the calculated bulk modulus (71 GPa) (196) is indicative of the remarkable stiffness of the phase. 

The elastic properties of PS depend on its microstructure and porosity. The Young s modulus for meso PS, as measured by X-ray diffraction (XRD) [Ba8], acoustic wave propagation [Da5], nanoindentation [Bel3] and Brillouin spectroscopy [An2], shows a roughly (1-p)2 dependence. For the same values of porosity (70%), micro PS shows a significantly lower Young s modulus (2.4 GPa) than meso PS (12 GPa). The Poisson ratio for meso PS (0.09 for p=54%) is found to be much smaller than the value for bulk silicon (0.26) [Ba8]. 

At low temperature the material is in the glassy state and only small ampU-tude motions hke vibrations, short range rotations or secondary relaxations are possible. Below the glass transition temperature Tg the secondary /J-re-laxation as observed by dielectric spectroscopy and the methyl group rotations maybe observed. In addition, at high frequencies the vibrational dynamics, in particular the so called Boson peak, characterizes the dynamic behaviour of amorphous polyisoprene. The secondary relaxations cause the first small step in the dynamic modulus of such a polymer system. 

Day, R.J., Robinson, I.M., Zakikhani, M. and Young, R.J. (1987). Raman spectroscopy of stresses high modulus poly(/)-phenylene benzobislhiazole) fibers. Polymer 2S, 1833-1840. 

Choudhury et al. [86] have studied the effect of polymer-solvent and clay-solvent interaction on the mechanical properties of the HNBR/sepiolite nanocomposites. They chose nine different sets of solvent composition and found that chloroform/methyl ethyl ketone (Qi/MEK) (i.e., HNBR dissolved in Ch and sepio-lite dissolved in MEK) is the best solvent combination for improvement in mechanical properties. XRD, AFM, , and UV-vis spectroscopy studies show that the dispersion of clay is best in the Ch/MEK solvent combination and hence polymer-filler interaction is also the highest. images shown in Fig. 14a, b clearly elucidate the aforementioned phenomena. Consequently, the tensile strength and modulus are found to be higher (5.89 MPa and 1.50 MPa, respectively) for the Ch/MEK system due to the minimum difference in interaction parameter of HNBR-solvent (xab) and sepiolite-solvent (Xcd)- Choudhury et al. have also studied the effect of different nanoclays [NA, , 15A, and sepiolite (SP)] and nanosilica (Aerosil 300) on the mechanical properties of HNBR [36]. The tensile... 

T = 140 °C. Here, during solidification, the H increase from 140 °C down to about 100 °C is the result of a double contribution of (a) the crystallization of the fraction of molten crystals and (b) the thermal contraction of the nonpolar phase crystals. The hysteresis behavior is also found in other mechanical properties (dynamic modulus) derived from micromechanical spectroscopy [66, 67], where it is shown that the hysteresis cycle shifts to lower temperatures if the samples are irradiated with electrons. It has also been pointed out that the samples remain in the paraelectric phase, when cooling, if the irradiation dose is larger than 100 Mrad. 

Thus, the relaxation function observed by photon correlation spectroscopy will be a direct measure of the relaxational part of the longitudinal modulus. 

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