The a-relaxation

The more direct identification of the molecular character of a secondary relaxation or information regarding the processes that are involved in the a-relaxation requires more information of a kinetic nature. This is accomplished by complementary experiments under different frequencies of probing to observe a temperature shift of the specific relaxation or by conducting stress-relaxation experiments at different temperatures and noting related shifts in the relaxation time of the specific transition. We explore these shifts in the following sections. 

The ratio of the relaxation times t T) of the steepest drops of the different curves to that of the central reference curve which is an important 

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The relaxatioa temperature appears to iacrease with increa sing HFP coateat. Relaxatioa iavolves 5—13 of the chaia carboa atoms. Besides a and y relaxations, one other dielectric relaxation was observed below —150° C, which did not vary ia temperature or ia magnitude with comonomer content or copolymer density (55). The a relaxation (also called Glass 1) is a high temperature transition (157°C) andy relaxation (Glass 11) (internal friction maxima) occurs between —5 and 29°C. 

Figure 5 Summary plot of the transition temperatures (lower), inverse of the smectic layer spacing (middle), and temperature of the a relaxation (upper) of polybibenzoates as a function of the number of methylene units in the spacer Ti, [Ref. 9] T, , [Ref. 9] A I/d, [Ref. 7] T T , [Ref. 9] open symbols our results.

Interestingly, tetrazetine 78 and tetracyclophosphene 79 are 6e it systems, but p-systems, but not planar, and saturated N and P atoms are pyramidalized. The lone pair must be pyramidahzed to have high s character for the a-relaxation. 

Figure 8.2. Temperature dependence on tan 8 at 1 Hz in the a-relaxation region for 6FNE.

This time t a actually is the maximum time for which Eq. [48] is valid, to structural relaxation. Typical a time scales diverge as... 

Figure 20 Temperature dependence of the a-relaxation time scale for PB. The time is defined as the time it takes for the incoherent (circles) or coherent (squares) intermediate scattering function at a momentum transfer given by the position of the amorphous halo (q — 1.4A-1) to decay to a value of 0.3. The full line is a fit using a VF law with the Vogel-Fulcher temperature T0 fixed to a value obtained from the temperature dependence of the dielectric a relaxation in PB. The dashed line is a superposition of two Arrhenius laws (see text).

Simulation Study of the a-Relaxation in a 1,4-Polybutadiene Melt as Probed by the Coherent Dynamic Structure Factor. 

Polymer Melts Coherent Scattering and van Hove Correlation Functions. Part II Dynamics in the a-Relaxation Regime. 

Phys. Condens. Matter, 15, S1127 (2003). Self-Motion and the a-Relaxation in Glass-Forming Polymers. Molecular Dynamic Simulation and Quasielastic Neutron Scattering Results in Polyisoprene. 

Fig. 3.22 Frequency-dependent dynamic modulus G"(co) from a PE chain of M =800 kg/mol at 509 K. The solid line gives the reptation prediction of G co)-cor . The peak here may not be confused with the a-relaxation of the glass dynamics. It immediately follows from the Fourier transform of strongly depends on molecular weight. The glass relaxation...

Thereby, the features of the a-relaxation observed by different techniques are different projections of the actual structural a-relaxation. Since the glass transition occurs when this relaxation freezes, the investigation of the dynamics of this process is of crucial interest in order to understand the intriguing phenomenon of the glass transition. The only microscopic theory available to date dealing with this transition is the so-called mode coupling theory (MCT) (see, e.g. [95,96,106] and references therein) recently, landscape models (see, e.g. [107-110]) have also been proposed to account for some of its features. 

In the case of polymers, the a-relaxation has been well characterized for many years, e.g. by dielectric spectroscopy and mechanical relaxation (see, e.g. [34, 111]).The main experimental features extracted from relaxation spectroscopies are ... 

However, though the establishment of such general features is very important, the relaxation techniques employed provide only indirect observations of the structural relaxation. In fact, the decay of different correlators in the a-relaxation regime may differ, as shown in Fig. 4. lb. 

At this point the question arises whether the feature usually termed as universality is also fulfilled do the timescales deduced from the investigation of different correlators in the a-relaxation regime show the same temperature... 

Fig. 4.8 Temperature dependence of the dielectric characteristic times obtained for PB for the a-relaxation (empty triangle) for the r -relaxation (empty diamond), and for the contribution of the -relaxation modified by the presence of the a-relaxation (filled diamond). They have been obtained assuming the a- and -processes as statistically independent. The Arrhenius law shows the extrapolation of the temperature behaviour of the -relaxation. The solid line through points shows the temperature behaviour of the time-scale associated to the viscosity. The dotted line corresponds to the temperature dependence of the characteristic timescale for the main peak. (Reprinted with permission from [133]. Copyright 1996 The American Physical Society)...

Fig. 4.9 Temperature dependence of the characteristic time of the a-relaxation in PIB as measured by dielectric spectroscopy (defined as (2nf ) ) (empty diamond) and of the shift factor obtained from the NSE spectra at Qmax=l-0 (filled square). The different lines show the temperature laws proposed by Tormala [135] from spectroscopic data (dashed-dotted), by Ferry [34] from compliance data (solid) and by Dejean de la Batie et al. from NMR data (dotted) [136]. (Reprinted with permission from [125]. Copyright 1998 American Chemical Society)...

From this comparison it follows that the observation of the structural relaxation by standard relaxation techniques in general might be hampered by contributions of other dynamic processes. It is also noteworthy that the structural relaxation time at a given temperature is slower than the characteristic time determined for the a-relaxation by spectroscopic techniques [105]. An isolation of the structural relaxation and its direct microscopic study is only possible through investigation of the dynamic structure factor at the interchain peak - and NSE is essential for this purpose. 

To date, incoherent quasi-elastic neutron scattering experiments on the a-relaxation regime of glass-forming polymers have revealed the following main features for the self-motion of hydrogens ... 

Fig. 4.13 Momentum transfer dependence of the characteristic time associated to the self-motion of protons in the a-relaxation regime Master curve (time exponentiated to p) constructed with results from six polymers polyisoprene (340 K, p=0.57) (filled square) [9] polybutadiene (280 K, p=0Al) (filled circle) [146] polyisobutylene (390 K, p=0.55) (empty circle) [147] poly (vinyl methyl ether) (375 K, f=0A4) (filled triangle) [148] phenoxy (480 K, p=0A0) (filled diamond) [148] and poly(vinyl ethylene) (340 K, p=0A3) (empty diamond) [ 146]. The data have been shifted by a polymer dependent factor Tp to obtain superposition. The solid line displays a Q -dependence corresponding to the Gaussian approximation (Eq. 4.11). (Reprinted with permission from [149]. Copyright 2003 Institute of Physics)...

We may now discuss the imphcations of the results foimd for the self-motion of hydrogens in the a-relaxation regime by neutron scattering. It is well known that for some simple cases - free nuclei in a gas, harmonic crystals. 

Fig. 4.15 Momentum transfer (Q)-dependence of the characteristic time r(Q) of the a-relaxation obtained from the slow decay of the incoherent intermediate scattering function of the main chain protons in PI (O) (MD-simulations). The solid lines through the points show the Q-dependencies of z(Q) indicated. The estimated error bars are shown for two Q-values. The Q-dependence of the value of the non-Gaussian parameter at r(Q) is also included (filled triangle) as well as the static structure factor S(Q) on the linear scale in arbitrary units. The horizontal shadowed area marks the range of the characteristic times t mr- The values of the structural relaxation time and are indicated by the dashed-dotted and dotted lines, respectively (see the text for the definitions of the timescales). The temperature is 363 K in all cases. (Reprinted with permission from [105]. Copyright 2002 The American Physical Society)...

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