Static and Dynamic Glass-Transition Temperatures

Chain segments move with a definite frequency above the glass transition temperature. Consequently, the frequency of the measurement method used or the deformation time of the sample must determine the numerical value of the glass transition temperature observed. Thus, the methods of measurement are classified as static or dynamic according to the speed of the measurement. 

The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. 

Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free-volume fraction /wi.F increases (see also Section 5.6.1). For/wlf = 0, of necessity, p = 0. For /wLF it follows thatp =. The functionality is consequently 

The extent of the deformation depends on the time /. To a good approximation, it can be assumed that pt = const, and Equation (10-53) becomes 

For the differences in the logarithms of the times ti and t, therefore, we have, with the corresponding fractions of free volumes, 

The numerical value of the glass-transition temperature depends on the rate of measurement (see Section 10.1.2). The techniques are therefore subdivided into static and dynamic measurements. The static methods include determinations of heat capacities (including differential thermal analysis), volume change, and, as a consequence of the Lorentz-Lorenz volume-refractive index relationship, the change in refractive index as a function of temperature. Dynamic methods are represented by techniques such as broad-line nuclear magnetic resonance, mechanical loss, and dielectric-loss measurements. Static and dynamic glass transition temperatures can be interconverted. The probability p of segmental mobility increases as the free volume fraction / Lp increases (see also Section 5.5.1). For /wlf = of necessity, p = 0. For / Lp oo, it follows that p = 1. The functionality is consequently 

A change in the time scale consequently corresponds to a change in the free volume (a smaller time corresponds to a larger volume). On the other hand, the free volume fraction must increase with increasing temperature. This increase is linear in the vicinity of the glass-transition temperature 

It has been found empirically that (/wlf)g - 0.025 (see Section 5.5.1). B can, to a good approximation, be made equal to unity. Since - aa is about 4.8 x 10 K for many materials (see also Table 10-2), equation (10-49) can be given as 

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Transitions temperatures vary with the method and the rate of measurements. This is a potentially confusing situation. The transitions associated with the relaxation processes are highly frequency-dependent. Glass transition temperature obtained in measurement by dynamic methods [acoustic, dynamic mechanical analysis (DMA), ultrasonic, or dielectric methods] should reasonably be denoted as T to differ it from Tg measured, for instance, by DSC. At low fi equen-cies, that is, at 1 Hz or least, Ta is close to Tg. As the measurement fi equency is increased, increases while Tg remains the same, giving rise to two separate transition temperatures. In the literature, the distinction between the static and dynamic glass transitions is not always made clear. 

Table III also shows that E increases with increasing DSC T. This would be expected from restricted segmental mobility of trie high T samples. Lewis iH found that Arrhenius plots of log frequency versus reciprocal dynamic glass transition temperature for restricted and nonrestricted polymers converges to a different point in the frequency/temperature scale. From this finding, equations were derived to predict static T from the dynamic T value and vice versa. ...

The WLF equation enables static glass transition temperatures Tg and various dynamic glass transition temperatures Tto be interconverted. To do this, the deformation times of the various individual methods must be known... 

In the present study, we have made X-ray diffraction, neutron diffraction with isotopic substitution, and quasi-elastic neutron scattering measurements on highly concentrated aqueous solutions of lithium halides in a wide temperature range from room temperature to below glass transition temperature, from which the microscopic behaviors of the static structure and dynamic properties of the solutions are revealed with lowering temperature. The results obtained are discussed in connection with ice nucleation, anisotropic motion of water, crystallization, and the partial recovery of hydrogen bonds. 

Semi-empirical rules, which correlate the static glass transition temperature Ty from differential thermal analysis or dilatometry with the dynamic T(J taken from the tan 8 or E" peak, may be used with caution in analyzing two-phase systems with a dispersed rubbery phase. The dynamic Tg depends on the rubber phase volume, and it may be shifted further toward lower temperature for effectively crosslinked and grafted rubber particles because of dilatation. 

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