Dielectric relaxation, analysis

Dielectric Relaxations Analysis Figure 2.11 shows the permittivity loss coefficient (e") data for dry annealed chitin before (80 °C, solid triangles) and after dc conductivity correction (open triangles). From dielectric measurements the frequencies at which contact/polarization effects become relevant (about 2 Hz for the contact effects... 

MeiBner, D. and Einfeldt, J. 2004. Dielectric relaxation analysis of starch oligomers and polymers with respect to their chain length. J. Polym. Sci. B Polym. Phys. 42 188-197. 

However, if possible, it is better to determine specific values of C, and Cj by dynamic mechanical or dielectric relaxation analysis. Conversion from one reference T to another T, can always be accomplished using the equation ... 

The relaxation methods employed are Dynamic Mechanical Thermal Analysis (DMTA) and Dielectric Thermal Analysis (DETA). Generally in both cases a single excitation frequency is used and the temperature is varied,... 

Glass-Forming Liquids I. Temperature Derivative Analysis of Dielectric Relaxation Data. 

It was soon realized that a distribution of exponential correlation times is required to characterize backbone motion for a successful Interpretation of both carbon-13 Ti and NOE values in many polymers (, lO). A correlation function corresponding to a distribution of exponential correlation times can be generated in two ways. First, a convenient mathematical form can serve as the basis for generating and adjusting a distribution of correlation times. Functions used earlier for the analysis of dielectric relaxation such as the Cole-Cole (U.) and Fuoss-Kirkwood (l2) descriptions can be applied to the interpretation of carbon-13 relaxation. Probably the most proficient of the mathematical form models is the log-X distribution introduced by Schaefer (lO). These models are able to account for carbon-13 Ti and NOE data although some authors have questioned the physical insight provided by the fitting parameters (], 13) ... 

For positive lit electrodes one can register the drift of holes, and for negative ones- the drift of the electrons. The photosensitizer (for example Se) may be used for carrier photoinjection in the polymer materials if the polymer has poor photosensitivity itself. The analysis of the electrical pulse shape permits direct measurement of the effective drift mobility and photogeneration efficiency. The transit time is defined when the carriers reach the opposite electrode and the photocurrent becomes zero. The condition RC < tlr and tr > t,r should be obeyed for correct transit time measurement. Here R - the load resistance, Tr -dielectric relaxation time. Usually ttras 0, 1-100 ms, RC < 0.1 ms and rr > 1 s. Effective drift mobility may be calculated from Eq. (4). The quantum yield (photogenerated charge carriers per absorbed photon) may be obtained from the photocurrent pulse shape analysis. 

Attempts have been made to identify primitive motions from measurements of mechanical and dielectric relaxation (89) and to model the short time end of the relaxation spectrum (90). Methods have been developed recently for calculating the complete dynamical behavior of chains with idealized local structure (91,92). An apparent internal chain viscosity has been observed at high frequencies in dilute polymer solutions which is proportional to solvent viscosity (93) and which presumably appears when the external driving frequency is comparable to the frequency of the primitive rotations (94,95). The beginnings of an analysis of dynamics in the rotational isomeric model have been made (96). However, no general solution applicable for all frequency ranges has been found for chains with realistic local structure. 

The dielectric relaxation of bulk mixtures of poly(2jS-di-methylphenylene oxide) and atactic polystyrene has been measured as a function of sample composition, frequency, and temperature. The results are compared with earlier dynamic mechanical and (differential scanning) calorimetric studies of the same samples. It is concluded that the polymers are miscible but probably not at a segmental level. A detailed analysis suggests that the particular samples investigated may be considered in terms of a continuous phase-dispersed phase concept, in which the former is a PS-rich and the latter a PPO-rich material, except for the sample containing 75% PPO-25% PS in which the converse is postulated. 

Figures 3-5 that the dielectric relaxation again reveals only a single a relaxation for the mixtures. These are, however, noticeably broader than the a relaxation of the pure polymers. The temperatures of the loss maxima, when plotted (Figure 7) as a function of wu the weight fraction of PPO in the mixtures, do not display the smooth monotonic increase in T0 vs. Wi that was shown by both the Vibron and the DSC results. Instead, there is a pronounced increase in Tg above = 0.5 to give a sigmoid curve for this relation. Some reservations should be attached to this observation inasmuch as data for only three polyblend compositions are available nevertheless a qualitatively similar phenomenon is observed in the analysis of the intensity of the y peak (below). Further, if only the stronger maxima in the dynamical mechanical data are considered— i.e.y if the secondary peaks and shoulders which led to the identification of two phases are omitted—then a similar sigmoid curve is found. The significance of this observation is discussed later.

The investigation of pure PET and PET/additive blends by combining dynamic mechanical analysis, dielectric relaxation and solid-state NMR techniques, leads to a clear attribution of the molecular processes involved in the ft relaxation of PET, as well as an understanding of the effect of an antiplasticiser additive ... 

The frequency analysis of this peak has been performed [18] and is shown in Fig. 27 in the temperature range - 112 to - 38 °C. In addition to the expected shift of the frequency at the peak maximum with increasing temperature, there was a large increase of ax, as we as a narrowing of the peak. Such a behaviour indicates that the dielectric / relaxation does not correspond to a unique process, but contains different processes with various activation energies, which gradually merge when the frequency is increased. 

Various experimental techniques (dielectric relaxation, dynamic mechanical analysis, 1H, 2H and 13C solid-state NMR) have been used for investigating the secondary transitions of BPA-PC, and the block copolymers of BPA and TMBPA carbonates as well as compatible blends of BPA-PC and TMBPA-PC. They have provided lots of information on the motions of methyl, phenyl ring and carbonate units in bulk BPA-PC. The effect of intermolecular packing has also been clearly evidenced. 

It is worth noticing that a molecular modelling approach is used to complement the experimental techniques of dynamic mechanical analysis, dielectric relaxation, solid-state 13C and 2H NMR. 

Furthermore, the activation energies (83 =t 5 kj mol-1 from mechanical analysis and 82 2 kj mol-1 from dielectric relaxation) as well as the activation entropies (51 3 J K-1 mol-1 from mechanical analysis and 58 33 J K-1 mol-1 from dielectric relaxation) are identical, confirming that the processes are the same. 

The quasi-static modelling of the dynamics of the ester group flip in an amorphous cell of atactic PMMA has yielded information complementary to that derived from dynamic mechanical analysis, dielectric relaxation and, mainly, multidimensional 13C and 2H solid-state NMR. The main results are ... 

The approach developed in this paper, combining on the one side experimental techniques (dynamic mechanical analysis, dielectric relaxation, solid-state 1H, 2H and 13C NMR on nuclei at natural abundance or through specific labelling), and on the other side atomistic modelling, allows one to reach quite a detailed description of the motions involved in the solid-state transitions of amorphous polymers. Bisphenol A polycarbonate, poly(methyl methacrylate) and its maleimide and glutarimide copolymers give perfect illustrations of the level of detail that can be achieved. 

Complex dielectric susceptibility data such as those in Figure 15.6 provide a detailed view of the dynamics of polar nanodomains in rls. They define relaxation frequencies, /, corresponding to the e (T) peak temperatures Tm, characteristic relaxation times, r = 1/tu (where uj = 2nf is the angular frequency), and a measure of the interaction among nanodomains as represented by the deviation of the relaxation process from a Debye relaxation. Analysis of data on pmn and other rls clearly shows that their dipolar relaxations cannot be described by a single relaxation time represented by the Debye expression... 

The transformation performed by this equation is a good way for the analysis of the dielectric relaxations in the zone of high temperatures and low frequencies of the spectrum. 

The considered model of a straight line of M nanoparticles illustrates only general features of dielectric losses caused by an M nanoparticle cluster in polymer matrix. Actually such cluster is a complex fractal system. Analysis of dielectric relaxation parameters of this process allowed the determination of fractal properties of the percolation cluster [104], The dielectric response for this process in the time domain can be described by the Kohlrausch-Williams-Watts (KWW) expression... 

The structural interpretation of dielectric relaxation is a difficult problem in statistical thermodynamics. It can for many materials be approached by considering dipoles of molecular size whose orientation or magnitude fluctuates spontaneously, in thermal motion. The dielectric constant of the material as a whole is arrived at by way of these fluctuations but the theory is very difficult because of the electrostatic interaction between dipoles. In some ionic crystals the analysis in terms of dipoles is less fruitful than an analysis in terms of thermal vibrations. This also is a theoretically difficult task forming part of lattice dynamics. In still other materials relaxation is due to electrical conduction over paths of limited length. Here dielectric relaxation borders on semiconductor physics. 

We discuss briefly some basic topics in materials physics such as crystallography, lattice vibrations, band structure, x-ray diffraction, dielectric relaxation, nuclear magnetic resonance and Mossbauer effects in this chapter. These topics are an important part of the core of this book. Therefore, an initial analysis of these topics is useful, especially for those readers who do not have a solid background in materials physics, to understand some of the different problems that are examined later in the rest of the book. 

The best evidence so far for the glassy nature of HDA was provided (1) by measurements of the dielectric relaxation time under pressure at 140 K [206, 251], (2) by the direct vitrification of a pressurized liquid water emulsion to HDA [252], and (3) by a high-pressure study of the glass >liquid transition using differential thermal analysis (DTA) [253], We note here that these studies probe structurally relaxed HDA (eHDA) rather than unrelaxed HDA. It is possible that structurally relaxed HDA behaves glass like, whereas structurally uHDA shows a distinct behavior. Thus, more studies are needed in the future, which directly compare structurally relaxed and unrelaxed HDA. 

The epoxy resin data and the post-cure data, taken together, show that the dipolar relaxation is associated with the temperature dependence of the polymer chain mobility in the vicinity of the glass transition. The WLF analysis of the dipolar relaxation during cure has not been carried out. In order to complete the analysis, correlated measurements of Tg, extent of cure, and dielectric properties must be made as functions of cure time and temperature. In the absence of such definitive studies, various indirect methods have been employed to analyze dielectric relaxations in curing systems, as described below. 

The analysis of the dynamics and dielectric relaxation is made by means of the collective dipole time-correlation function (t) = (M(/).M(0)> /( M(0) 2), from which one can obtain the far-infrared spectrum by a Fourier-Laplace transformation and the main dielectric relaxation time by fitting < >(/) by exponential or multi-exponentials in the long-time rotational-diffusion regime. Results for (t) and the corresponding frequency-dependent absorption coefficient, A" = ilf < >(/) cos (cot)dt are shown in Figure 16-6 for several simulated states. The main spectra capture essentially the microwave region whereas the insert shows the far-infrared spectral region. 

Dielectric relaxation of complex materials over wide frequency and temperature ranges in general may be described in terms of several non-Debye relaxation processes. A quantitative analysis of the dielectric spectra begins with the construction of a fitting function in selected frequency and temperature intervals, which corresponds to the relaxation processes in the spectra. This fitting function is a linear superposition of the model functions (such as HN, Jonscher, dc-conductivity terms see Section II.B.l) that describes the frequency dependence of the isothermal data of the complex dielectric permittivity. The temperature behavior of the fitting parameters reflects the structural and dynamic properties of the material. 

The dielectric relaxation properties in nano-PS with different thicknesses have been investigated recently over a wide range of frequency and temperature [160,161]. The dielectric properties of the PS samples were measured in the 20-Hz to 1-MHz frequency range and in the 173 to 493 K temperature interval. For all the dielectric measurements, the amplitude of a sinusoidal ac-voltage source was maintained 1 V so that the average electric field across our sample was of the order of hundreds of volts per centimeter depending on the sample thickness. It was verified that the response was linear with respect to the ac-voltage amplitude such that a linear response analysis could be utilized for our sample. 

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