Dielectric analysis method temperature dependence

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 numerical value of the glass-transition temperature depends on the rate of measurement (see Section 10.1.2). The techniques are therefore subdivided into static and dynamic measurements. The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free volume fraction / Lp increases (see also Section 5.5.1). For /wlf = of necessity, p = 0. For / Lp oo, it follows that p = 1. The functionality is consequently... 

It is not a trivial problem to obtain a complete characterization of a material responding over many decades of time. The brute force method would be to carry out experiments over many decades of time. More efficient is to employ more than one instrument, and cover a time span that includes high frequencies. This is now possible with broad dielectric spectroscopy, with which the frequency reuige from 10 to 10 can be attained by using different techniques - time domain spectroscopy, frequency response analysis using AC-bridges, and coaxial line reflectrometry. Of course, each isothermal experiment has to be repeated at various temperatures in order to determine the temperature dependence. 

More exotic —that is, so far, less frequently used—methods are also worth noting dielectric relaxation on which we have a whole chapter by Jozef Moscicki thermally stimulated depolarization " electro-optical behavior" (time dependence of transmitted light intensity under a low frequency electric field) thermo-optical analysis" " (temperature dependence of the transmission of light through birefringent... 

The principles behind kinetic methods are described below on the basis of uncatalyzed reactions in homogeneous solutions. The rate at which a given chemical reaction develops depends on several factors including temperature, reactant concentrations, the presence or absence of catalysts, activators, and inhibitors, and dielectric constant or ionic strength. Most of the reactions employed in kinetic analysis are influenced by temperature, which usually accelerates reaction development. Hence, a thermostatting device is typically needed for kinetic applications. 

The measurement of the dipole moments of copolymers and its analysis in terms of both sequence distribution and local chain configurations has received attention Modern computer aided analytical procedures provide in ght into the dependence of mean square dipole moment per residue on reactivity ratios, polymer composition and rotamer probabilities. One such calculation for atactic cc ly-(p-chlorostyrene-p-methylstyrene) has shovm that at constant composition, the dipole moment is quite sensitive to the sequence distribution and thus to the reactivity ratios. This dependence would be even more marked for syndiotactic chains. For cop61y(propylene-vinyl chloride) and copoly(ethylene-vinyl chloride) d le moments are again very sequence dependent, much more so than the diaracteristk ratio. It would appear that in copolymer systems dielectric measurements can be a powerful method of investigating sequence distributions. Two copolymers, p-dilcxo-styrene with styrene and with p-methylstyrene have been examined experimentally The meamrements were made on solid amorphous samples above the ass-rubber transition temperature (Tg) and they are consistent with the predictions of the rotational isomeric state model udi known reactivity ratios and rea nable replication probabilities . However, it is the view of this author that deduc-... 

Unlike crystalline melting, the glass transition temperature is a relaxation transition. This means that it is dependent on the effective frequency of the measureirtent. This frequency is found by dynamic mechanical (DMA), dielectric relaxation, and pulsed nuclear magnetic methods. Quasi-static methods, such as dilatometry, differential scanning calorimetry (DSC), and thermomechanical analysis (TMA), show that the effective frequency depends on the rate of temperature scan. This is one of the reasons why the glass transition temperatures reported for various amorphous materials appear so diverse. 

Transitions temperatures vary with the method and the rate of measurements. This is a potentially confusing situation. The transitions associated with the relaxation processes are highly frequency-dependent. Glass transition temperature obtained in measurement by dynamic methods [acoustic, dynamic mechanical analysis (DMA), ultrasonic, or dielectric methods] should reasonably be denoted as T to differ it from Tg measured, for instance, by DSC. At low fi equen-cies, that is, at 1 Hz or least, Ta is close to Tg. As the measurement fi equency is increased, increases while Tg remains the same, giving rise to two separate transition temperatures. In the literature, the distinction between the static and dynamic glass transitions is not always made clear. 

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