Glass transition temperature polymer lattices

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... 

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.)...

In a further development of the above model, Kalospiros and Paulaitis [101] use the glass-transition temperature of the pure polymer to calibrate the value of the order parameter (fraction of holes in the lattice). This value is kept constant, even if a swelling agent is added to the system, so the glass transition-temperature depression induced by the SCF can be predicted. 

The concept of polymer free volume is illustrated in Figure 2.22, which shows polymer specific volume (cm3/g) as a function of temperature. At high temperatures the polymer is in the rubbery state. Because the polymer chains do not pack perfectly, some unoccupied space—free volume—exists between the polymer chains. This free volume is over and above the space normally present between molecules in a crystal lattice free volume in a rubbery polymer results from its amorphous structure. Although this free volume is only a few percent of the total volume, it is sufficient to allow some rotation of segments of the polymer backbone at high temperatures. In this sense a rubbery polymer, although solid at the macroscopic level, has some of the characteristics of a liquid. As the temperature of the polymer decreases, the free volume also decreases. At the glass transition temperature, the free volume is reduced to a point at which the... 

If the host polymer does not have a high glass transition temperature then the structures of polymer and chromophore must be such that post-poling lattice hardening can be carried out to assure thermally stable electro-optic activity [2, 5,50,63,64,110,132-150]. 

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