Free-volume dilatation coefficient

Eisenbach also discussed the significance of the WLF-parameters with respect to the fractional free volume at Tg and to the difference of thermal dilation coefficients of rubbery and glassy states. 

Increases in system temperature give rise to volume dilation, resulting in increased amounts of free volume. This explains the strong tendency for the diffusion coefficient to increase with temperature. The free-volume fraction in Eq (20.4-4) may be represented as a linear addition of the several variables that affect its value ... 

In eq. (5.28) /g is the critical free-volume fraction at Tg and a is the volumetric (dilatational) thermal coefficient of expansion of the sub-cooled liquid. Then, the shift factor discussed in Section 5.3.1 is... 

These values are considered as the universal WLF constants, giving the widest range of agreement over many prominent amorphous polymers. From these choices one calculates that the free-volume fraction /g at the glass-transition temperature is 0.025 and the dilatational thermal coefficient of expansion of a sub-cooled polymer melt at the glass-transition temperature is a = 2.8 x 10 ... 

On the basis of increase in the sorption coefficient, it is suggested that the deformation causes dilation of the amorphous regions. At larger deformations, D falls below its original value for the imoriented crystalline material, since small increases in free volume are unable to offset the very large increase in tortuosity. 

Sanchez et al. re-examined polymer bulk data in a rigorous classical thermodynamic analysis (7,8). A new principle of temperature-pressure (T-P) superposition of compression response was foimd. Stated briefly, a dimensionless pressure variable is used to superpose compression data as a function of temperature into a universal curve. The governing parameter of compression is the first pressure coefficient B (= CiB/QP)p, of the bulk modulus B. It is related to the asymmetry of the free energy aroimd its minimum, between dilation and compression. For polymers, Bi is aroimd 10, and universal. A new isothermal equation of state was formulated through a Fade analysis of the pressure dependence of the bulk modulus (8). Both the Tait and the Fade equations describe almost perfectly the isothermal pressure dependence of volume. Both can be used to smoothen experimental PVT data. 

---