Arrhenius-type relaxation

The two different temperature dependencies described above for giass-forming liquids are present in a-chitin, and the simiiarity between dc conductivity and relaxation time for the two low frequency relaxations is clearly observed in Figure 2.12a and b. Both dependencies (dc conductivity (a, .) and relaxation time (t) versus T plots) show the same features an Arrhenius type relaxation will yield a straight line above 80 °C, whereas a non-Arrhenius relaxation will manifest as a curved line that suggests a VFTH type or glass transition below 80 °C in dry annealed samples. For wet and dry samples, the decrease of conductivity as the temperature is increased from 20 to 80 °C is likely due to the motion of water-polymer complex since water could be modifying the relaxation mechanism of the matrix material. 

C) and high temperature (above 120 °C) ranges. Previously, these two regions were erroneously assigned to two Arrhenius-type relaxations. While dry PVA shows a single a-relaxation non-Arrhenius, VFT-type relaxation clearly revealed after water evaporation. 

Several studies on thin polymer films also indicated a sub-T Arrhenius-type relaxation process, which was related to the motion within a distinct surface layer of higher mobility or to increased heterogeneity [35, 44, 63, 64], yielding Ea 100 kJ/mol [44] and Ea = 185 3 kJ/mol [14]. Lateral force microscopy measurements on thin PS films [63] found a thickness dependent surface y -relax-ation process, with Ea = 55 kJ/mol for a 65 nm thick film. Fast sub-T -relaxations at surfaces of thin polymer films were measured by AFM, including the relaxation of... 

Steady-state behavior and lifetime dynamics can be expected to be different because molecular rotors normally exhibit multiexponential decay dynamics, and the quantum yield that determines steady-state intensity reflects the average decay. Vogel and Rettig [73] found decay dynamics of triphenylamine molecular rotors that fitted a double-exponential model and explained the two different decay times by contributions from Stokes diffusion and free volume diffusion where the orientational relaxation rate kOI is determined by two Arrhenius-type terms ... 

Several attempts have been made to superimpose creep and stress-relaxation data obtained at different temperatures on styrcne-butadiene-styrene block polymers. Shen and Kaelble (258) found that Williams-Landel-Ferry (WLF) (27) shift factors held around each of the glass transition temperatures of the polystyrene and the poly butadiene, but at intermediate temperatures a different type of shift factor had to be used to make a master curve. However, on very similar block polymers, Lim et ai. (25 )) found that a WLF shift factor held only below 15°C in the region between the glass transitions, and at higher temperatures an Arrhenius type of shift factor held. The reason for this difference in the shift factors is not known. Master curves have been made from creep and stress-relaxation data on partially miscible graft polymers of poly(ethyl acrylate) and poly(mcthyl methacrylate) (260). WLF shift factors held approximately, but the master curves covered 20 to 25 decades of time rather than the 10 to 15 decades for normal one-phase polymers. 

Tg, the stress relaxation data can be described by the WLF temperature dependence (8). However, an Arrhenius type of... 

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... 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the... 

An Arrhenius-type analysis of temperature dependence can be used to calculate the enthalpy and entropy of activation for the relaxation process. For liquid water, the enthalpy of activation is 19 kjmol-1, which corresponds approximately to the energy required to break one hydrogen bond. For ice, the equivalent enthalpy is 54 kj mol-1,... 

From an Arrhenius type plot like that of Fig. 2.82 the activation energies for these processes are obtained an the values are 14.6 and 57.0 kcal mol-1. these results give some idea about the differences in sizes of groups involved in the relaxation. 

The pre-exponential factor Df (or rf) is the diffusion constant (or correlation time) of a freely rotating methyl group and is given by an equation analogous to Eq. 21. A rigorous approach to this problem is to calculate activation energies from variable-temperature relaxation measurements, using an Arrhenius-type plot of D, (or tc i ) versus 1/T(K).67... 

This expression is of the same shape as that of stress relaxation of viscoelastic materials (Chap. 13). By analogy 1/k is called the "relaxation time" (t). Since chemical reactions normally satisfy an Arrhenius type of equation in their temperature dependence, the variation of relaxation time with temperature may be expressed as follows ... 

As mentioned above, the frequency dependence of the complex dielectric permittivity (e ) of the main relaxation process of glycerol [17,186] can be described by the Cole-Davidson (CD) empirical function [see (21) with a = 1, 0 < Pcd < 1], Now Tcd is the relaxation time which has non-Arrhenius type temperature dependence for glycerol (see Fig. 23). Another well-known possibility is to fit the BDS spectra of glycerol in time domain using the KWW relaxation function (23) < )(t) (see Fig. 24) ... 

Fast relaxation processes ( , 0) show a Williams-Landel-Ferry (WLF) type temperature dependence which is typical for the dynamics of polymer chains in the glass transition range. In accordance with NMR results, which are shown in Fig. 9, these relaxations are assigned to motions of chain units inside and outside the adsorption layer (0 and , respectively). The slowest dielectric relaxation (O) shows an Arrhenius-type behavior. It appears that the frequency of this relaxation is close to 1-10 kHz at 240 K, which was also estimated for the adsorption-desorption process by NMR (Fig. 9) [9]. Therefore, the slowest relaxation process is assigned to the dielectric losses from chain motion related to the adsorption-desorption. 

Av is the frequency difference between two anisotropic ESR resonance lines, the resulting spectrum is the superposition of the individual configurations. On the contrary, if r < (2 JtAv), we have an isotropic spectrum the resonance frequency is the average of the anisotropic components of the individual configurations As discussed in detail by Ham , motional narrowing can be produced by three relaxation mechanisms, which are characterized by a different temperature dependence an Arrhenius-type dependence (r" = Voe ) for an Orbach process, and a linear dependence or proportional to T for direct and Raman processes, respectively. Therefore, the temperature dependence of the isotropic spectrum gives information about the relaxation mechanism and consequently on the vibronic level scheme. 

The variation of the maximum relaxation time with temperature indicates that the rate constant for the second mechanism is of the Arrhenius type. This is particularly pronounced in the sulfur case. 

The relaxation rates are dominated by the behaviour of the spectral density function at frequencies related to the spectral densities at o)o (TO, coi (Tip) and 0 (T2). The correlation time Tc follows an Arrhenius-type activation so that... 

The reciprocals of the quadrupole relaxation time, l/T and l/T, are reasonably represented by an Arrhenius-type equation as given in Eq. (8),... 

In some epoxy systems ( 1, ), it has been shown that, as expected, creep and stress relaxation depend on the stoichiometry and degree of cure. The time-temperature superposition principle ( 3) has been applied successfully to creep and relaxation behavior in some epoxies (4-6)as well as to other mechanical properties (5-7). More recently, Kitoh and Suzuki ( ) showed that the Williams-Landel-Ferry (WLF) equation (3 ) was applicable to networks (with equivalence of functional groups) based on nineteen-carbon aliphatic segments between crosslinks but not to tighter networks such as those based on bisphenol-A-type prepolymers cured with m-phenylene diamine. Relaxation in the latter resin followed an Arrhenius-type equation. 

The secondary f)-relaxation is also observed in a-chitin from 80 °C to the onset of thermal degradation ( 210°C). It exhibits a normal Arrhenius-type temperature dependence with activation energy of 113 3 kJ/mol. 

High Temperature Relaxation The high temperature relaxation arises at 80 °C until the onset of degradation 210 °C (Figs. 2.13a and b). It can be well described by the Arrhenius model and is present in both neutralized and nonneutralized CS. The slope of these curve represent the activation energy of each process. The temperature dependence of dc conductivity and relaxation time are Arrhenius type. For this relaxation, nonneutralized CS films seem to be more sensitive to water, since in the dry state... 

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