Kinetics of the glass transition

Fig. 3. Calculated equilibrium and nonequilibrium volumes of PVAc as a function of temperature and cooling rate [28]. Circles are experimental data [29]. The lattice thermal expansion coefficient (a ) is related to the occupied volume and has nothing to do with Tg. The kinetics of the glass transition is determined by the dynamics of hole motion...

Tool-Narayanaswamy-Moynihan (model of kinetics of the glass transition) [Tool, 1946a,b Narayanaswamy, 1971 Moynihan et al., 1976] two-parameter theory... 

A more detailed analysis of the kinetics of the glass transition was carried out by quasi-isothermal TMDSC [66,67]. Figure 6.132 is a representation of plots of the reversing, apparent heat capacities of some of these samples after extrapolation to zero modulation amplitude. All traces of hysteresis are absent. The same methods as described in Sects. 6.3.1 and 6.3.2 were used for the analyses of the glass transitions. For the amorphous PET, the analysis is shown in Figs. 4.129-133 and 6.119-121. 

Wunderlich B, Boiler A, Okazaki I, Kreitmeier S (1996) Modulated Differential Scanning Calorimetry in the Glass Transition Region II. The Mathematical Treatment of the Kinetics of the Glass Transition. J Thermal Anal 47 1013-1026. 

Figure 4.54 is a quantitative quasi-isothermal MTDSC trace for quenched, poorly crystallised PTT. The corresponding semiquantitative MTDSC is depicted in Figure 4.38. The cold crystallisation at about 325 K, the recrystallisation, 450 K, and the small enthalpy relaxation at 320 K are seen to be fully irreversible, and as in PET, the kinetics of the glass transition and the cold crystallisation can be further analysed quantitatively making use of the reversing heat capacity. It is also clear that during the standard DSC measurement, the cold crystallisation never stops completely between the two peaks and considerable errors in the crystallinity may result from choosing a baseline without MTDSC data.

In Section 4.3, it is shown with Figure 4.55 that the heat of fusion and its calibration to 100% crystallinity can be best accomplished by standard DSC, but the baseline is best checked or established by MTDSC. A well-established baseline of heat flow rate of the liquid is sufficient if the temperature dependence of the heat capacity is known (see Figures 4.23,4.25 and 4.57). A detailed, simple description of the kinetics of the glass transition of semicrystalline samples is illustrated in the example of PET (Figures 4.58. 60). Both frequency of measurement and the existing crystallinity affect the appearance of the glass transition as can be seen from the data in Table 4.1. 

To get a kinetic expression, one makes use of the first-order kinetics of Fig. 2.8 and writes Eq. (3), with N (T) being the equilibrium number of holes, and N its instantaneous value. The rate constant, which was called k in Fig. 2.8, is replaced by 1/r, the relaxation time. By introduction of the heating rate q - (dr/dt), the change of time dependence to temperature dependence at constant heating rate is accomplished. Equation (3) describes the nottiso-thermal kinetics of the glass transition. A full solution of the equation is... 

The kinetic nature of the glass transition should be clear from the last chapter, where we first identified this transition by a change in the mechanical properties of a sample in very rapid deformations. In that chapter we concluded that molecular motion could simply not keep up with these high-frequency deformations. The complementarity between time and temperature enters the picture in this way. At lower temperatures the motion of molecules becomes more sluggish and equivalent effects on mechanical properties are produced by cooling as by frequency variations. We shall return to an examination of this time-temperature equivalency in Sec. 4.10. First, however, it will be profitable to consider the possibility of a thermodynamic description of the transition which occurs at Tg. 

Figure 10 Oscillating differential scanning calorimetric (ODSC) curves showing the separation of the glass transition (reversible, i.e., thermodynamic component) and enthal-pic relaxation (irreversible, i.e., kinetic component) which overlap in the full DSC scan. (Reprinted with permission from Ref. 38.)... 

Crosslinked polymer networks formed from multifunctional acrylates are completely insoluble. Consequently, solid-state nuclear magnetic resonance (NMR) spectroscopy becomes an attractive method to determine the degree of crosslinking of such polymers (1-4). Solid-state NMR spectroscopy has been used to study the homopolymerization kinetics of various diacrylates and to distinguish between constrained and unconstrained, or unreacted double bonds in polymers (5,6). Solid-state NMR techniques can also be used to determine the domain sizes of different polymer phases and to determine the presence of microgels within a poly multiacrylate sample (7). The results of solid-state NMR experiments have also been correlated to dynamic mechanical analysis measurements of the glass transition (1,8,9) of various polydiacrylates. 

Craig, I.D., Parker, R., Rigby, N.M., Cairns, P., and Ring, S.G. 2001. Maillard reaction kinetics in model preservation systems in the vicinity of the glass transition Experiment and theory. J. Agric. 

The thermodynamic theories [7,8] deny the pure kinetic nature of the glass transition and link it directly to thermodynamic quantities like the configurational entropy of the material. Some recent results suggest a correlation between kinetic quantities and thermodynamic parameters [9]. Also recently, this theory was successfully merged with a potential landscape approach [10]. The thermodynamic approach is interesting since it reflects the different configurations that are allowed not only for the whole ensemble but also for the internal conformations... 

Figure 4.3 shows a plot of both characteristic times as a function of 1/T. When xc < xq, the polymer is able to reach, continuously, the equilibrium distribution of conformations. So it remains in the rubbery (or liquid) state. But when x > xq, the polymer cannot reach equilibrium in the time-scale of the experiment and it behaves as a glass. In the frame of this kinetic model, the glass transition may be defined as the temperature at which xc = xq (Fig. 4.3). 

The kinetic character of the glass transition and the resulting non-equilibrium character of the glassy state are responsible for the phenomena of structural relaxation, glass transition hysteresis, and physical aging (Kovacs, 1963 Struik, 1978). 

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