Modulus electric

The temperature and frequency dependence of the complex dielectric permittivity a for both 2-chlorocydohexyi isobutyrate (CCHI) and poly(2-chlorocyclohexyl acrylate) (PCCHA) is reported. The analysis of the dielectric results in terms of the electric modulus suggests that whereas the conductive processes in CCHI are produced only by free charges, the conductivity observed in PCCHA involves both free charges and interfacial phenomena. The 4x4 RIS scheme presented which accounts for two rotational states about the CH-CO bonds of the side group reproduces the intramolecular correlation coefficient of the polymer. 

This is a procedure which was used successfully by Pathmanathan and Johari and allow to calculate the real an imaginary part of electrical modulus and corresponding spectra as shown in Fig. 2.9... 

Sanchis and coworker [64] in order to insight something about this fact and in order to get confidence about this phenomenon, have used the electric modulus formalism [146], (M = l/e ) to represent the experimental data. The advantages of this kind of representation are evident due to the better resolution observed for dipolar and conductive processes. The imaginary part of M as a function of frequency at 423 K, for both polymers, is shown in Fig. 2.45. The curve corresponding to PTHFM shows a complex behavior at low frequencies, which presumably is the result of the superposition of the two conductive processes. 

Several comprehensive reviews on the BDS measurement technique and its application have been published recently [3,4,95,98], and the details of experimental tools, sample holders for solids, powders, thin films, and liquids were described there. Note that in the frequency range 10 6-3 x 1010 Hz the complex dielectric permittivity e (co) can be also evaluated from time-domain measurements of the dielectric relaxation function (t) which is related to ( ) by (14). In the frequency range 10-6-105 Hz the experimental approach is simple and less time-consuming than measurement in the frequency domain [3,99-102], However, the evaluation of complex dielectric permittivity in the frequency domain requires the Fourier transform. The details of this technique and different approaches including electrical modulus M oo) = 1/ ( ) measurements in the low-frequency range were presented recently in a very detailed review [3]. Here we will concentrate more on the time-domain measurements in the high-frequency range 105—3 x 1010, usually called time-domain reflectometry (TDR) methods. These will still be called TDS methods. 

Figure 7.03. Real and imaginary parts of the electric modulus vs. reduced frequency coTf) for 0.4 Ca(N03)2 0.6KNOj glass (After Howell ct. al.. 1974)...

Secondary relaxation in sodium trisilicate glass has been observed in the measurements of electrical modulus (M ) and shear modulus (G ) as shown in Figure 9.02. It can be seen from the figure that behaviours of... 

Figure 9.02 Shear modulus and electrical modulus for sodium trisilicate glass. Note the relaxation step in G around 0 C and that of M at 0.4 Hz at 0 C (After Angell, 1988).

Figure 1 shows an example from electric modulus spectra of the room temperature ionic liquid (an environmental friendly material that have many applications), 1-butyl-1-methylpyrrolidinium bis[oxalato]borate (BMP-BOB) measured over wide temperature (123-300 K) and pressure (0.1-500 MPa) ranges. ... 

Figure 1. Electric modulus relaxation spectra (M") of the ionic liquid BMP-BOB at ambient pressure and 231 and 245 K are plotted as solid lines. High pressure M" data (0.5 GPa) at the temperatures that yield relaxation times similar to those of the ambient pressure data, 283 and 308 K, are included in the figure as squares. Data at 0.5 GPa data are slightly shifted in frequency to match perfectly the atmospheric peak frequencies. Long and short dashed lines are fits to a Kohlrausch relaxation function with fi=(l-n)= 0.56 and 0.50, respectively. The inset shows the good correspondence between the stretching parameter fi and the relaxation time at different temperatures and at atmospheric pressure and at 0.5 GPa.

The electric modulus approach (AT = 1/e ) used in the case of polyacetylene [3] has shown that this contribution is more important. With the assumption of a conductivity distribution, this description allow the explanation of the dispersion of t with frequency without any molecular polarisation phenomenon. 

In Section 4.2.1 we present theoretical results concerning the electric modulus. Those results have been widely obtained in the field of ionic conductors [128]. In Section 4.2.2, we show how a molecular polarisation phenomenon would appear in the curv es AT = f u>). In Section 4.2.3, we present experimental results of relaxation phenomena in conducting polymer based materials. We will give here an example of a calculation using the electric modulus description and a comparison with experimental results will be made. We will show that a correlation between relaxation frequency and static conductivity level, already found for other materials, also holds in conducting polymers. 

The effect of a molecular polarisation on the evolution of M with frequency is investigated. The ideal material is characterised by electric field relaxation time under constant electrical induction D. If a molecular polarisation phenomenon, different from the long-range conducting process does exist, it is characterised by (relaxation time of the molecular process under the constraint of constant electrical induction). In this case Ambrus [135] has given an expression for the electric modulus ... 

Actually, the two terms of equation (8.7) have to be modified in order to account for a relaxation time distribution on both polarisation and conduction phenomena. As x is the time constant describing the electric field delay to 0, only a molecular relaxation process having Tj dielectric measurements using the electric modulus, the lower frequency relaxation will always be associated with the relaxation of long-range transport phenomena. Nevertheless, due to the similarity of equation (8.3) and (8.7), the first sight of a relaxation curve doesn t allow us to distinguish a relaxation caused by a conduction mechanism coupled with a polarisation mechanism from a relaxation of the conduction mechanism characterised by a broad distribution of relaxation times. A more precise study on several samples has then to be done. 

Figure 8.12. Generic representation of relaxation phenomena due either to conduction or polarisation in the electric modulus description.

The electric modulus analysis is able to describe relaxation phenomena from static to high frequency... 

The development of conductive polymer based micro-wave absorbing materials implies the knowledge of radioelectrical characteristics of these compounds, in terms of level and frequency evolution. The need to associate a theoretical approach with our experimental process appears very early, allowing us to optimise the use of some materials. The later approach, based on the description of the phenomena in term of electrical modulus permits us to obtain important results. The correlation of the relaxation frequency with the level of... 

However, generally in composites with conductive inclusions, ionic current and interfacial polarization could often mask the real dielectric relaxation processes in the low frequency range. Therefore, to analyze the dielectric process in detail, the complex permittivity e can be converted to the complex electric modulus M by using the following equation ... 

In this case, this chapter presents both analyses in the case of chitin and CS, the analysis by means of the real s ) and the imaginary (e") parts of permittivity and for PVA the case of the analysis by the complex electric modulus, M. ... 

In analogy to mechanical relaxation, the complex electric modulus M is defined as the inverse of the complex permittivity, originally given by McCrum et al. [2] according to the equation ... 

The relationship between complex electrical modulus and impedance is given by ... 

Alternatively, complex electrical modulus can also represented by ... 

FIGURE 26 Frequency dependence of real part of electrical modulus, M for hexanoyl chitosan-30% LiCF3S03 electrolyte system at selected temperatures. 

Macedo and others (Hodge et al. [1975, 1976]) have stressed the electric modulus formalism (M = 1/c ) for dealing with conducting materials, for the reason that it emphasizes bulk properties at the expense of interfacial polarization. Equation (112) transforms to... 

Mechanical and thermal characterization of ultra low k dielecteics is very similar to the characterization of dense low k dielectrics however the introduction of porosity requires the development of new characterization techniques in order to understand the pore structure. The dielectric constant, dielectric breakdown and coefficient of diermal expansion can be measured using the same techniques used for dense low k electrics. Modulus and hardness can also be measured by die same techniques, however, if using nanoindentation, measurements firom porous dielectrics may have larger substrate contributions at equivalent film thicknesses. Therefore, the modulus values... 

For better comparison the electric modulus representation as introduced by Macedo et al. as an analytical scheme to extract long range ionic conduction processes in impedance spectra were used as ... 

The separate ot-mode contribution of NR in the NR/PUR blend can be clearly observed in Figure 9.9 where the imaginary part of the electric modulus is depicted versus temperature and frequency. The temperature and frequency range was from -100 to 50 °C and 10 to 10 Hz, respectively. Generally speaking, the frequency-temperature superposition shifts the loss peak position... 

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