Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.2 Prediction of solubility parameter 255
Figure 5.2.1. Schematic curves of H a and C p in the vicinity
of T g for an amorphous polymer. Two lines of short
and long dashes show H a for a supercooled liquid and C p
for a superheated glass (hypothesized), respectively. T e is
the end temperature of C p jump. [after reference 10]
{ ( ) }
conf
2 2
h = RT d ln Z / dT ) / x = RT d ln v / dT −h
g
g g f
int
g
{ ( ) }
[5.2.10]
conf
s = Rln Z+ RT d ln Z/ dT / x = Rlnv + RT d ln V / dT −S
[5.2.11]
g
g f g f d
Rewriting equation [5.2.10], the glass transition enthalpy per molar structural unit,
int conf
h ( =h + h ) , is obtained:
g g
g
2 2
h = RT dln v / dT ≈RT
/ c
[5.2.12]
g g f g
2
with c ≈φg/β where:
int
hg h int at Tg c2 the constant in the WLF equation 20
β the difference between volume expansion coefficients below and above Tg φ g the fractional free volume at Tg The WLF equation on the time - temperature superposition of viscoelastic relaxation
phenomena is given by: 20
( ) ( )
log a =−c T − T / c + T −T
Figure 5.2.2. State models for an amorphous
polymer in each temperature range
of (a) T≤T g, (b) T g