Maximum dipole loss, frequency

Fig. 24. Arrhenius plot of the frequency of maximum dipole loss for DGEBA epoxy resins of varying molecular weights, a) n = 12.1 b) 5.1 c) 3.4 d) 2.1 e) 0.6 0 0.2 g) 0. (Reprinted from Ref.46> with permission of the authors)...

When a dielectric is placed in an alternating electric field the dipoles attempt to maintain alignment with the field. This process requires a finite time that is different for each polarization mechanism. At the relaxation frequency the dipoles will only just be able to reorient themselves in time with the applied field. At this frequency the dielectic is lossy and energy is lost in the form of heat. The dielectric loss is at a maximum when the frequency of the external field coincides with the relaxation frequency of a given polarization mechanism. This is the principle behind the microwave oven. It operates at the relaxation frequency of water molecules and the heat generated warms the food. 

Relaxations tend to divide into two types those that obey a simple Arrhenius temperature dependence and those that do not. For simple thermally activated processes Arrhenius behaviour is observed. The probability of the dipole reorientating depends directly on the thermal energy distribution. The relaxation time is related to the frequency of maximum dielectric loss ... 

Experimentally the maximum loss frequency is typically measured for lower temperatures [23, 24] to study the temperature dependence of the structural glass transition or a process. Two sets of experiments in the literature show some discrepancies in an intermediate temperature window but agree with each other and with our simulation data at higher temperatures where we have an overlap temperature window between simulation and experiment. Prom this we can conclude, that also in the experiment one sees no correlations between the dipole moments of different chains. When we furthermore compare the time scale given by the maximum loss frequency with the time scales of the Rouse modes for our chains we can obtain from the simulation, we can say that the dielectric measurements on PB see the relaxation of a chain segment of about 6 backbone carbons, which is exactly the length of a statistical segment of the chains. 

A second type of relaxation mechanism, the spin-spm relaxation, will cause a decay of the phase coherence of the spin motion introduced by the coherent excitation of tire spins by the MW radiation. The mechanism involves slight perturbations of the Lannor frequency by stochastically fluctuating magnetic dipoles, for example those arising from nearby magnetic nuclei. Due to the randomization of spin directions and the concomitant loss of phase coherence, the spin system approaches a state of maximum entropy. The spin-spin relaxation disturbing the phase coherence is characterized by T. ... 

The dielectric loss or absorption behaves differently. At very low frequencies the dipole follows the field freely, but little energy is transferred to the surrounding molecules and thus little absorption occurs. As the frequency increases, molecular motion increases and more energy is transferred to the surrounding molecules. As the frequency increases further, molecular inertia begins to impede motion and a maximum absorption is reached. As the frequency is raised still further, the dipoles... 

Part of the work performed on a sample will be converted irreversibly into random thermal motion by movement of the molecules or molecule segments. This loss passes through a maximum at the appropriate transition temperature or relaxation frequency in the associated alternating mechanical field (torsion pendulum test). A similar effect is obtained by the delayed response of the dipoles with dielectric measurements. Therefore, dielectric measurements can be made only on polar polymers. According to the... 

For polymers, dielectric spectroscopy is sensitive to fluctuations of dipoles, which are related to the molecular mobility of groups, segments, or the polymer chain as well [38]. The molecular mobility is taken as a probe for structure. The basic quantity is the complex dielectric function e f) = t (f) - it"(f) as a function of the frequency/and the temperature T. s (/) is the real whereas e"(/) is the loss part i = >f ). A relaxation process is indicated by a step-like decrease of s (/) with increasing frequency and a peak in e"(/). From the maximum position of the peak a mean relaxation rate can be deduced, which corresponds to the relaxation time of the fluctuation of the dipole moment of a given structural imit. For details see reference [49]. All shown measurements were carried out isothermally in the frequency range from 10 to 10 Hz by an ALPHA analyzer (NovocontroF). The temperature of the sample is controlled by a Quatro Novocontrol system with stability better than 0.1 K. 

When the frequency of an applied electric field is the same as the collision frequency, the field and the fluctuating dipoles interact and we get relaxation or resonance phenomena. In other words, the frequency of maximum loss, of energy absorption, is the molecular collision frequency. 

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