Polymer relaxation times related

It is commonly observed that the temperature and frequency dependence of polymer relaxations are related. This is expressed qualitatively as the time-temperature superposition principle, or the frequency-temperature equivalence,... 

It is commonly observed that the temperature and frequency dependence of polymer relaxations are related. This is expressed qualitatively as the time-temperature superposition principle, or the frequency-temperature equivalence, or the method of reduced variables. A mathematical way to describe this behavior is to note that if the dispersion relation for the relaxation [eqs. 29,30, and 44] depends on frequency and temperature only through the product of frequency and a function of temperature, cor T), then the effect of a change in frequency is indistinguishable from a change in temperature. In other words, a measurement... 

For practical purposes, it is convenient to define the relaxation time in terms of macroscopic quantities which can be readily determined. Within the validity limit of Hookean connectors (Eq. 13), the low-shear viscosity of a polymer solution is given by the relation ... 

This equation offers a simple relationship between magnitudes related to electrochemistry (rjc, and through tjc and the relaxation time, all the other electrochemical and chemical magnitudes) and those specifically from polymer science. According to this result, coefficient zc will be lower and coefficient zr higher, as stronger interactions are present, which is confirmed by experimental results. On the other hand, high values of zr are... 

The equations of motion (75) can also be solved for polymers in good solvents. Averaging the Oseen tensor over the equilibrium segment distribution then gives = l/ n — m Y t 1 = p3v/rz and Dz kBT/r sNY are obtained for the relaxation times and the diffusion constant. The same relations as (80) and (82) follow as a function of the end-to-end distance with slightly altered numerical factors. In the same way, a solution of equations of motion (75), without any orientational averaging of the hydrodynamic field, merely leads to slightly modified numerical factors [35], In conclusion, Table 4 summarizes the essential assertions for the Zimm and Rouse model and compares them. 

Time-temperature superposition is frequently applied to the creep of thermoplastics. As mentioned above, a simple power law equation has proved to be useful in the modelling of the creep of thermoplastics. However, for many polymers the early stages of creep are associated with a physical relaxation process in which the compliance (D t)) changes progressively from a lower limit (Du) to an upper limit (DR). The rate of change in compliance is related to a characteristic relaxation time (x) by the equation ... 

Moreover, real polymers are thought to have five regions that relate the stress relaxation modulus of fluid and solid models to temperature as shown in Fig. 3.13. In a stress relaxation test the polymer is strained instantaneously to a strain e, and the resulting stress is measured as it relaxes with time. Below the a solid model should be used. Above the Tg but near the 7/, a rubbery viscoelastic model should be used, and at high temperatures well above the rubbery plateau a fluid model may be used. These regions of stress relaxation modulus relate to the specific volume as a function of temperature and can be related to the Williams-Landel-Ferry (WLF) equation [10]. 

Table 4.1 Parameters related to the structural relaxation for the polymers investigated by NSE glass transition temperature Tg, position of the first static structure factor peak Qmax> shape parameter magnitude considered to perform the scaling of the NSE data, and temperature dependence of the structural relaxation time...

Material response is typically studied using either direct (constant) applied voltage (DC) or alternating applied voltage (AC). The AC response as a function of frequency is characteristic of a material. In the future, such electric spectra may be used as a product identification tool, much like IR spectroscopy. Factors such as current strength, duration of measurement, specimen shape, temperature, and applied pressure affect the electric responses of materials. The response may be delayed because of a number of factors including the interaction between polymer chains, the presence within the chain of specific molecular groupings, and effects related to interactions in the specific atoms themselves. A number of properties, such as relaxation time, power loss, dissipation factor, and power factor are measures of this lag. The movement of dipoles (related to the dipole polarization (P) within a polymer can be divided into two types an orientation polarization (P ) and a dislocation or induced polarization. 

The electrical properties of materials are important for many of the higher technology applications. Measurements can be made using AC and/or DC. The electrical properties are dependent on voltage and frequency. Important electrical properties include dielectric loss, loss factor, dielectric constant, conductivity, relaxation time, induced dipole moment, electrical resistance, power loss, dissipation factor, and electrical breakdown. Electrical properties are related to polymer structure. Most organic polymers are nonconductors, but some are conductors. 

This relation enables evaluating the fragility parameter Ks as well as the structural relaxation times r over the whole temperamre range To < T < Ta-Because T] depends on polymer microstructure and molar mass, Ap likewise exhibits the same dependence. Computations of Ks within the entropy theory have not been possible before. 

Work in groups of three. The shift factor, or, in the WLF Equation [Eq. (5.76)], is actually a ratio of stress relaxation times, f , in the polymer at an elevated temperature, T, relative to some reference temperature. To, and can be related via an Arrhenius-type expression to the activation energy for relaxation, Erei as... 

The electric properties of a material vary with the frequency of the applied current. The response of a polymer to an applied current is delayed because of a number of factors including the interaction between polymer chains, the presence within the chain of specific molecular groupings, and effects related to interactions within the specific atoms themselves. A number of parameters are employed as measures of this lag, such as relaxation time, power loss, dissipation factor, and power factor. 

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