Glass transition temperature estimation

FIGURE 20.15 Temperature dependence of the relaxation times of both poly(ATRIF) homopolymer (squares) and poly(AN- faf-ATRIF) copolymer (circles) the arrows indicate the glass transition temperatures estimated from the VFTH equations at x = 100 s [68],... 

In addition to thermodynamic appUcations, 62 values have also been related to the glass transition temperature of a polymer, and the difference 62-61 to the viscosity of polymer solutions. The best values of 6 have been analyzed into group contributions, the sum of which can be used to estimate 62 for polymers which have not been characterized experimentally. 

Solution Polymers. Methacryhc solution polymers are usually characterized by thek composition, soHds content, viscosity, molecular weight, glass-transition temperature, and solvent type. The compositions of methacryhc polymers are most readily determined by physicochemical methods such as spectroscopy, pyrolytic gas—Hquid chromatography, and refractive index measurements. The soHds content is determined by dilution followed by solvent evaporation to constant weight. Solution viscosities are most conveniendy determined with a Brookfield viscometer. Methods for estimating molecular weights by intrinsic viscosity are available (103). 

The thermal glass-transition temperatures of poly(vinyl acetal)s can be determined by dynamic mechanical analysis, differential scanning calorimetry, and nmr techniques (31). The thermal glass-transition temperature of poly(vinyl acetal) resins prepared from aliphatic aldehydes can be estimated from empirical relationships such as equation 1 where OH and OAc are the weight percent of vinyl alcohol and vinyl acetate units and C is the number of carbons in the chain derived from the aldehyde. The symbols with subscripts are the corresponding values for a standard (s) resin with known parameters (32). The formula accurately predicts that resin T increases as vinyl alcohol content increases, and decreases as vinyl acetate content and aldehyde carbon chain length increases. 

The simple relation (6.1) is quite useful. It allows an estimate of the gain or loss in yield strength if the glass transition temperature is changed, as for instance by the progress of the curing reaction, by radiation damage, or by absorption of water and of solvents. The ATe is determined fairly easily by thermoanalytical measurements. 

Plasticixers arc low-molecular-weight liquids that lower the glass transition temperature of a polymer. A typical example is the use of dioctyl phthalate in poly(vinyl chloride) to convert the polymer from a rigid material to a soft, flexible one. It the glass transition of the two components A and B are known, an estimate can be made of the Tg value of the mixture by one or the other of the equations... 

The heat distortion temperature of impact-resistant polystyrene may also be improved by polymer blends. Those of impact-resistant polystyrene with poly-2,5-dimethylphenylene-1,4-oxide (PPO) are particularly interesting (90). Polystyrene and PPO are molecularly compatible and mixtures of them have glass transition temperatures which vary virtually linearly with composition. A further advantage of these compositions which should not be under-estimated is their better flame resistance. 

In the above table, Mj, Vi, Yj and Hj are the contributions for group i for estimating the molecular weight, the molar volume, the glass-transition temperature, and the water absorption, respectively. The model equations for each of these properties are as follows ... 

Hopfinger AJ, Koehler MG, Pearlstein RA (1988) Molecular modUng of polymers. IV. Estimation of glass transition temperatures. J Polym Sci Part B 26 2007-2028... 

Figure 2-13 Schematic drawing of (a) density as a function of temperature, and (b) entropy as a function of temperature for glasses with different cooling rates and hence different glass transition temperature (Martens et al., 1987). The entropy of the undercooled liquid is estimated assuming constant heat capacity.

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... 

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