Pressure Dependence of Glass Transition Temperature
At the glass transition temperature Tg, a discontinuity in the in the specific heat
(among many other properties) is observed. This discontinuity is usually about 0.2 - 0.3 J /
mol-K.
The
glass transition can be approximated as a second-order Ehrenfest
transition. The assumption of entropy and volume continuity at Tg
yields two Ehrenfest equations for the pressure dependence:
(∂Tg / ∂p) = Δβ / Δα
(∂Tg / ∂p) = v Tg Δα / ΔCp
The pressure dependence of the glass transition temperature is rather weak when compared to the effect of molecular weight and plasticizer. A rule of thumbs says, the Tg will increase by approximately 20-50 K per kbar of pressure.
| Property | Predicted* | Measured1 |
| Discontinuity of Heat Capacity, ΔCp (J/mol-K) | 0.243 | 0.290 |
| Density at Tg, ρ (g/cm3) | 1.175 | 1.176 |
| Molar Volume at Tg, Vm (cm3/mol) | 216.5 | 216.2 |
| Discontinuity in thermal expansion at Tg, Δα (1/K) | 3.20 10-4 | 3.78 10-4 |
| Glass Transition Temperature, Tg (K) | 424 (GIM: 427) | 423 |
To give a practical example, we calculate the pressure dependence of poly(bisphenol A carbonate). Its typical thermo-physical properties are shown in the table above. The values in the second column have been predicted with the software 3Ps-Tg from Triton Road and the values in the third column have been taken from Laurence Belfore's book "Physical Properties of Macromolecules" (2010). Using these values, yields the results: v Tg Δα / ΔCp = 4.75 10-2 K/bar and 4.69 10-2 K/bar. The experimental value is approximately 4.3 10-2 K/bar(1). This shows that the effect of pressure on the glass transition is usually negligible unless the change in pressure is in the range of several hundred bars.
| Polymer | (∂Tg / ∂p) |
| Polycarbonate, PC(1) | 4.4 10-2 K/bar |
| Polyvinylacetate, PVAC(2) | 3.7 10-2 K/bar |
| Polyvinylchloride, PVC(2) | 3.8 10-2 K/bar |
| Polystyrene, PS(3) | 3.6 - 5.5 10-2 K/bar |
| Polymethylmethacrylate, PMMA(3) | 1.8 - 3.6 10-2 K/bar |
References
- Laurence A. Belfiore, Physical Properties of Macromolecules, pp 177 (2010)
- A. Belfiore, Physical Properties of Macromolecules, pp 177 (2010)
- S. Saeki et al, Polymer, Vol 33, 3, 577–584 (1992)