T>Tg transition

Fig. 10. T>Tg transitions fornr-PS from self diffusion constants, Dg. Bottom, Tp by DSC from Fig. 3 for reference. Top lines are from intersections in Fig. 9 type plots for different molecular weight tagged molecules in a host of = 114,000, obtained by us from published Fig. 2 of ref 84. There is a suggestion that points labeled "Tp (host)" are reflecting (guest), as if guests are entangling with host.

As is documented in Section 111, Ueberreiter published a molecular mechanism for T>Tg transitions in 1943 which anticipated some aspects of the Lobanov-Ftenkel mechanism. 

Various instrumental methods applied or developed at MMI over the past ten years to study liquid state transitions are presented. T>Tg transition studies with an emf asis on polystyrene are discussed. Instrumental techniques cover the areas of dielectric relaxation, thermal methods, dynamic mechanical relaxation, and computer statistical analysis of tabulated literature data, as well as the spectroscopic methods of Fourier transform infrared and electron spin resonance. 

Various instrumental methods have been applied or developed to study liquid state transitions. All of the methods discussed in this paper stem directly from collaborations between Raymond F. Boyer and various researchers at MMI over the period 1975 to 1985. For the sake of brevity, the emphasis in this review will be on T>Tg transitions in amorphous styrenic polymers. The reader is referred to the article by Boyer for a discussion of liquid state transition studies for a... 

In order to study a polymer system by dielectric relaxation, the polymer must possess a net dipole moment, either along the chain, or through polar side groups. Successful studies of and T>Tg transitions have been carried out in our laboratory on poly(propytene oxide) oligomers, copolymers of ortho- and para-chlorostyrene, cellulose acetate and cellulose acetate butyrate copolymers,and random copolymers of styrene acrylonitrile. ... 

Fig. 4. Arrhenius plot of log versus l/T for plasticized PS. Three AfWs were studied at two different levels of plasticization, as shown. Slope changes indicate T>Tg transitions (see text). The structure of BzONO, the nitroxide spin probe used, is given in the inset. After Smith et al., refs. 18 and 20.

The main glass transition and the T>Tg liquid-liquid transition can also be seen in the plots of e" as a function of temperature at 0.1, 1.0, and 10 kHz, given in Figure 2. The T>Tg transition temperature exhibits a greater increase with increasing frequency than the Tg transition as shown in Table I. 

The presence of ionic impurities results in conduction losses in polymers in the liquid region.23 This dc conductivity dominates in contributing to e" at low frequencies. The dc conductivity in most cases would mask any T>Tg transition. In this study, however, due to the low TiilTg ratio, Tn can be clearly seen even at 0.1 kHz. Boyet24 has summarized five different methods for circumventing this difficulty in analyzing low frequency dielectric loss data of polymers in the liquid state. 

In the introduction of this communication we pointed out the similarities between the pressure dependence, the activation energy, and the annealing effects of the (Tp< Tg) and the (T/ > Tg) transitions, which strongly suggests that these transitions are the manifestation of the same relaxation process, probably issued from the complexity of the kinetic mechanism responsible for the glass transition temperature itself. In the second part of this communication we present and reanalyze DSC studies of atactic Rheomolded polystyrene specimens treated with various thermal-mechanical histories. The effect of frequency, amplitude of vibration, and annealing time... 

In liquids, and in glasses at temperatures above their glass transition (T > Tg), the shear stresses are usually very small. The equation for the viscosity T can be derived if xv kT is a reasonable assumption... 

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

The segmental mobility can be related to the T -Tg difference using a theory of the glass transition. For example, if the reac-... 

This transition is a kinetical, relaxational process. The variation of the temperature above Tg is followed by the shift of the equilibrium between free and bonded hydroxyl groups. This shift sets in practically instantly, as the relaxation times x are very small above Tr At the temperatures below Tg the relaxation times are very long and the variation of the temperature in this region is not connected with the change of equilibrium. The fraction of free hydroxyls v at T < Tg is not equal to ve, the equilibrium fraction at this temperature. 

This is a very useful approach, which can be recommended for practical applications. A simplified version of this general treatment may also be useful. It is possible to consider vitrification of a material as a jump-like transition from a liquid to a solid state. This idea was advanced elsewhere, where residual stresses in inorganic glasses were calculated by treating vitrification as a sequential solidification of layers of a viscous liquid on the rigid surface of a previously solidified material. In a liquid layer (not yet solidified) at T > Tg, only flow deformations can occur. In the transition through Tg, this deformation is frozen in and cannot change later on. 

The tensile and shear modulus differ from the bulk modulus in fact that they are influenced by the molecular mobility, and therefore display an almost discontinuous decrease at each secondary transition. Their relative variation at Tg is 10-100 times higher than that of the bulk modulus. The Poisson s ratio varies in the opposite sense in the region T < Tg. It tends toward 0.5 when the temperature increases beyond Tg. 

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