Effect of Pressure on Tg

The discussion above has assumed constant pressure at 1 atm (1 bar). Since an increased pressure causes a decrease in the total volume [see equation (8.8)], an increase in Tg is expected based on the prediction of decreased free volume. 

The results in Rgure 8.33 can easily be interpreted in terms of the free-volume theory of Tg. In developing the WLF equation (Section 8.6.1.2), it was shown that the free-volume fraction at any temperature above Tg could be expressed f=fo+ 0Cf(T- Tg). If the free-volume compressibility is Pf, then 

For polyurethanes. Quested et al. (148) found that A)3//Aa was greater than dTgIdP, except at pressures close to 1 bar. At high pressures, dTJdP reached a limiting value of 10.4°C/kbar. The effect of pressure has been studied for ultrasonic frequencies (149) and fracture stress differences (150). 

In the above, it was demonstrated that an increase in pressure can bring about vitrification. This result is important in engineering operations such as molding or extrusion, where operation too close to Tg (1 bar) can result in a stiffening of the material. 

Thus we may refer to a glass transition pressure. In a broader sense, the glass transition is multidimensional. We could also refer to the glass transition molecular weight (Section 8.7), the glass transition concentration (for diluted or plasticized species), and so forth. 

---

Fig. 4. Comparison of calculated [27] and measured [29] PVT behavior of PVAc. It clearly reveals the effect of pressure on Tg...

When a system is under pressure with negligible pressure rate, the PVT behaviour is again calculated from Eqs. (2), (15) and (35) by replacing e with e + pv. The result of PVAc is shown in Fig. 4, where the circles are isobaric volume data [29] and the curves represent the theoretical calculation. The effect of pressure on Tg... 

---