## 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.

### Thermo-physical Properties of Poly(Bis A carbonate)

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
*The values in the 2nd column have been calculated with the software 3Ps-GC (Triton Road).

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.

### Pressure Dependence of Glass Transition

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

1. Laurence A. Belfiore, Physical Properties of Macromolecules, pp 177 (2010)
2. A. Belfiore, Physical Properties of Macromolecules, pp 177 (2010)
3. S. Saeki et al, Polymer, Vol 33, 3, 577–584 (1992)
• ## Summary

### Glass Transition Temperature

The glass transition temperature is a quasi-second-order Ehrenfest transition.

• ### Pressure Dependence

The effect of pressure on 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.

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