Ideal glass transition temperature

Simulations [73] have recently provided some insights into the formal 5c —> 0 limit predicted by mean field lattice model theories of glass formation. While Monte Carlo estimates of x for a Flory-Huggins (FH) lattice model of a semifiexible polymer melt extrapolate to infinity near the ideal glass transition temperature Tq, where 5c extrapolates to zero, the values of 5c computed from GD theory are too low by roughly a constant compared to the simulation estimates, and this constant shift is suggested to be sufficient to prevent 5c from strictly vanishing [73, 74]. Hence, we can reasonably infer that 5 approaches a small, but nonzero asymptotic low temperature limit and that 5c similarly becomes critically small near Tq. The possibility of a constant... 

In summary, Fig. 6 exhibits the four characteristic temperatures of glass formation the Arrhenius temperature 7a, the crossover temperature Tj, the ideal glass transition temperature Tb, and a kinetic glass-formation temperature Tg (dehned in Section VI), to illustrate their relative locations with respect to the temperature variation of s. ... 

Figure 8. (a) The ideal glass transition temperature Tq, the glass transition temperature Tg, the... 

Figure 10. LCT configurational entropy ScT as a function of the reduced temperature 5T = (T — To)/To for low and high molar mass F-F and F-S polymer fluids at constant pressure of P = 1 atm (0.101325 MPa). The product ScT is normalized by the thermal energy k To at the ideal glass transition temperature To- (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005 American Chemical Society.)...

Figure 22. The configurational entropy Sc per lattice site as calculated from the LCT for a constant pressure, high molar mass (M = 40001) F-S polymer melt as a function of the reduced temperature ST = (T — To)/Tq, defined relative to the ideal glass transition temperature To at which Sc extrapolates to zero. The specific entropy is normalized by its maximum value i = Sc T = Ta), as in Fig. 6. Solid and dashed curves refer to pressures of F = 1 atm (0.101325 MPa) and P = 240 atm (24.3 MPa), respectively. The characteristic temperatures of glass formation, the ideal glass transition temperature To, the glass transition temperature Tg, the crossover temperature Tj, and the Arrhenius temperature Ta are indicated in the figure. The inset presents the LCT estimates for the size z = 1/of the CRR in the same system as a function of the reduced temperature 5Ta = T — TaI/Ta. Solid and dashed curves in the inset correspond to pressures of P = 1 atm (0.101325 MPa) and F = 240 atm (24.3 MPa), respectively. (Used with permission from J. Dudowicz, K. F. Freed, and J. F. Douglas, Journal of Physical Chemistry B 109, 21350 (2005). Copyright 2005, American Chemical Society.)...

Besides the desired dehydrocoupling, Si-N bond cleavage of HPZ and formation of DEB-NHSiMej occurred. Nevertheless, the polymeric precursor had an ideal glass-transition temperature for melt spinning and stable melt viscosity. Melt spun Si-B-C-N-H green fibers were subsequently transformed into ceramic fibers by thermolysis at 1400°C. 

A is a constant related to the free carrier concentration, the ideal glass transition temperature, a pseudo activation energy. Examples of conductivity temperature relations are shown in Figure 1.9. 

To Vogel temperature, ideal glass transition temperature... 

The group-entropy S(T) remains zero below Tes> which will make S(T) a singular function ofthe temperature. Similarly, the class-entropy Sbc(T) = 0 below Tr, which makes the dass-entropy also singular at Tr, the ideal glass transition temperature as said above. It is interesting to investigate if Tes has any relation to Tmc- We will not pursue this issue here. 

Aar can vanish at the transition if dTyi/dP is to remain nonzero and finite. In other words, any nonzero discontinuity in one quantity implies that all these quantities must have nonzero discontinuities simultaneously. Thus, the actual value of the ideal glass transition temperature Tr does not depend on whether we consider the volume V, enthalpy H, or entropy S in Figure 10.6, as a singular behavior (nonzero discontinuity) in any one of these quantities reflects a singular behavior in other thermodynamic quantities. This can be seen directly from the following thermodynamic identities ... 

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