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Relaxation Vogel-Tammann-Fulcher

If the relaxation time of the supercooled liquid is described by the Vogel-Tammann-Fulcher (VTF) equation... [Pg.76]

Figure 1.18. Arrhenius plots for the relaxation time of the total energy of M13 at (a) p = 4 and (b) p = 14. Circles are mean relaxation times from the master equation, dashed lines are fits to the Arrhenius form, and the solid line in (a) is a fit to the Vogel-Tammann-Fulcher (VTF) form. Figure 1.18. Arrhenius plots for the relaxation time of the total energy of M13 at (a) p = 4 and (b) p = 14. Circles are mean relaxation times from the master equation, dashed lines are fits to the Arrhenius form, and the solid line in (a) is a fit to the Vogel-Tammann-Fulcher (VTF) form.
The K values shown in Table 14.3 for sample C can be well fitted by the Vogel-Tammann-Fulcher (VTF) equation or the Williams-Landel-Ferry (WLF) equation.Prom the VTF equation with the parameters obtained from the fitting, the K values at 127.5 and 93.7gC are calculated and listed in Table 14.3, with the former also listed in Table 14.1. The result of K (andrs) at 93.7gC is used in sections 14.8 and 14.10.a where the structural relaxation time and the length scale at Tg are defined or studied. [Pg.293]

Limitations of the widely used KWW equation have been discussed and addressed by employing the Vogel-Tammann-Fulcher (VTF) and AG equations in order to calculate the relaxation time above and below the glass transition temperature more precisely (Shamblin et al. 1999). [Pg.49]

Figure 6.5. Schematic of an Arrhenius plot for mechanisms commonly observed in polymers. The lines correspond to Arrhenius [Eq. (6.8) for y, p, and Maxwell-Wagner-Sillars (MWS) relaxations] and Vogel-Tammann-Fulcher-Hesse [VTFH Eq. (6.10)], for a and normal-mode (n-) relaxation] temperature dependences for the relaxation time t(T). Relaxations ascribed to small, highly mobile, dipolar units appear in the upper right side of the plot, while those originating from bulky dipolar segments, slowly moving ions, and MWS mechanisms are located in the lower-left part of the plot. Figure 6.5. Schematic of an Arrhenius plot for mechanisms commonly observed in polymers. The lines correspond to Arrhenius [Eq. (6.8) for y, p, and Maxwell-Wagner-Sillars (MWS) relaxations] and Vogel-Tammann-Fulcher-Hesse [VTFH Eq. (6.10)], for a and normal-mode (n-) relaxation] temperature dependences for the relaxation time t(T). Relaxations ascribed to small, highly mobile, dipolar units appear in the upper right side of the plot, while those originating from bulky dipolar segments, slowly moving ions, and MWS mechanisms are located in the lower-left part of the plot.
Figure 6.25. Representative Arrhenius diagram for Odc and relaxations isolated in thermoplastics [PU(Cu )].The lines correspond to Arrhenius [y relaxation E = 38kJ/ mol Eq. (6.8)] and Vogel-Tammann-Fulcher-Hesse [a relaxation, 7V = -112°C, Eq. (6.10) DC conductivity, Tq = -85 °C, Eq. (6.24)] function fittings of the data. The TSC glass transition temperature was obtained from a scan at a heating rate of 5 °C/min, and the DSC Eg is the midpoint of the heat capacity change (second heating at a rate of 20°C/min). For the method used to determine Eg did the reader is referred to Section 6.5.2.2. (Kalogeras and Vassilikou-Dova, unpublished data.)... Figure 6.25. Representative Arrhenius diagram for Odc and relaxations isolated in thermoplastics [PU(Cu )].The lines correspond to Arrhenius [y relaxation E = 38kJ/ mol Eq. (6.8)] and Vogel-Tammann-Fulcher-Hesse [a relaxation, 7V = -112°C, Eq. (6.10) DC conductivity, Tq = -85 °C, Eq. (6.24)] function fittings of the data. The TSC glass transition temperature was obtained from a scan at a heating rate of 5 °C/min, and the DSC Eg is the midpoint of the heat capacity change (second heating at a rate of 20°C/min). For the method used to determine Eg did the reader is referred to Section 6.5.2.2. (Kalogeras and Vassilikou-Dova, unpublished data.)...
A Vogel-Fulcher-Tammann-Hesse equation can be used to characterize the temperature dependence of the relaxation times for these six different degrees of cure, 0.70, 0.75, 0.80, 0.825, 0.90, and 0.95 ... [Pg.143]

The relaxation kinetics of the Arrhenius and Eyring types were found for an extremely wide class of systems in different aggregative states [7,52-54]. Nevertheless, in many cases, these laws cannot explain the experimentally observed temperature dependences of relaxation rates. Thus, to describe the relaxation kinetics, especially for amorphous and glass-forming substances [55-59], many authors have used the Vogel-Fulcher-Tammann (VFT) law ... [Pg.13]

It appears, however, that the mode-coupling theory is not able to explain some of the most significant slow-relaxation processes of these more complex glass formers. In particular, it cannot explain the success of the Vogel-Fulcher-Tammann-Hesse (VFTH) equation for the temperature-dependence of the relaxation time near the glass transition. The mode-coupling theory predicts instead a power-law dependence of the longest relaxation... [Pg.216]

In order to determine the structural relaxation times for the octa-O-acetyl-lactose we analyzed dielectric loss spectra of this carbohydrate with use of the Havriliak- Negami function. The temperature dependence of logioTa was fitted to the Vogel- Fulcher- Tammann (VFT) function... [Pg.371]

E0 and the infinite temperature relaxation time To are independent of temperature, and (ii) in the isotropic phase near the I-N transition, the temperature dependence of ts2(T) shows marked deviation from Arrhenius behavior and can be well-described by the Vogel-Fulcher-Tammann (VFT) equation ts2(T) = TyFrQxp[B/(T — TVFF), where tvff, B, and tvft are constants, independent of temperature. Again these features bear remarkable similarity with... [Pg.295]

In polymers, the glass transition phenomenon has been related to the dielectric a-relaxation processes through the Vogel-Fulcher-Tammann (VET) equation [9], and it can be characterized by means of their molecular dynamics analysis. [Pg.16]

In the a-process, the viscosity and consequently the relaxation time increase drastically as the temperature decreases. Thus, molecular dynamics is characterized by a wide distribution of relaxation times. A strong temperature dependence presenting departure from linearity or non-Arrhenius thermal activation is present, owing to the abrupt increase in relaxation time with the temperature decrease, thus developing a curvature near T. This dependence can be well described by the Vogel-Fulcher-Tammann-Hesse (VFTH) equation [40, 41], given by Equation 2.1 ... [Pg.17]

The relaxation-time dependence could be described by the Vogel-Fulcher-Tammann-Hesse equation [88] ... [Pg.232]

The polymer dynamics involves several relaxation processes, some of which start within the vitreous region and cross into high-temperature melts. For example, the fast relaxations of the backbone chain or side groups start near the Vogel-Fulcher-Tammann-Hesse (VFTH) temperature and extend io T>Tc. The linearized VFTH expression is... [Pg.261]

In the high-temperature range, both relaxation modes exhibit Vogel-Fulcher-Tammann-Hesse (VFTH) behavior ... [Pg.533]

See other pages where Relaxation Vogel-Tammann-Fulcher is mentioned: [Pg.179]    [Pg.7]    [Pg.446]    [Pg.40]    [Pg.236]    [Pg.104]    [Pg.8]    [Pg.511]    [Pg.519]    [Pg.533]    [Pg.551]    [Pg.570]    [Pg.598]    [Pg.127]    [Pg.194]    [Pg.421]    [Pg.121]    [Pg.140]    [Pg.13]    [Pg.47]    [Pg.169]    [Pg.324]    [Pg.499]    [Pg.211]    [Pg.10]    [Pg.142]    [Pg.264]    [Pg.65]    [Pg.67]    [Pg.129]    [Pg.235]    [Pg.231]   


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