Spencer-Gilmore equation

This equation of state when applied to a polymer is known as the Spencer-Gilmore equation.)... 

As the melt cools in the cavity, so long as the pressure exceeds atmospheric, it is pressed against the walls of the mould and the specific volume remains constant. In order to compensate for the falling temperature at constant Vq, there is a corresponding fall in pressure. Eventual, pressure P falls to atmospheric (=1.013 X 103 Pa). The temperature T at which this point is reached can be found by applying the Spencer-Gilmore equation again ... 

Several semi-empirical equations have been proposed, out of which we shall discuss two the Spencer-Gilmore and the Hartmann-Haque equations. 

Reviews of the Equation of State for Polymer Melts There are many publications comparing different equations of state to each other, and a few more ambitious reviews that discuss theoretical fundamentals, derivation, and application, and provide tabulated characteristic reducing parameters and deviation from the experimental volume [Curro, 1974 Zoller, 1989 Rodgers, 1993 Rudolf et al., 1995, 1996 Lambert et al 2000], For example, Zoller [1989] examined the equations of state by Spencer-Gilmore (S-G) [1949, 1950], Flory-Orwoll-Vrij (FOV), Sanchez-Lacombe (S-L), and Simha-Somcynsky (S-S). Large deviations (<0.01 mL/g) were observed for S-G. While the FOV and S-L expressions were useful at low P, the S-S equations of state consistently provided the best representation of data over extended ranges of T and P, with deviations AV< 0.003 mL/g, eomparable to the experimental error for density. 

TABLE 13.1 The Equation of State of Spencer and Gilmore and the Experimental Data... 

The internal pressure n is closely related to the cohesive energy density ecoh. Therefore we pay some attention to this subject. Spencer and Gilmore (1949,1950) showed that the p-v-T behaviour of polymer melts can be represented reasonably well by the following modified Van der Waals equation of state4 ... 

Various workers have developed empirical relationships between P, V, and T. Among those are the equations of Spencer and Gilmore [77], Breuer and Rehage [78], Kamal and Levan [79], and Simha and Olablsi [80]. 

---