Handbook of Solvents - George Wypych - ChemTech - Ventech!

256 Nobuyuki Tanaka
N66, -CH(CH 3)- for iPP, -CH(C 6H 5)- for iPS, and -C 6H 4- for PET, was used. 21 The predicted
values of c 2 for PS and PET are close to the experimental values, 56.6K and 55.3K, respectively.
20,22 The standard values of c 1 and c 2 in equation [5.2.13] are 17.44 and 51.6K, respectively.
20,23
Table 5.2.1
Polymer
Tg
K
hg int
cal/mol
hg conf
cal/mol
sg conf
cal/(K mol)
hg (=hg int +hg conf )
cal/mol
N6 313 8500 475 11.2 8980 21.7
N66 323 17000 976 22.6 17980 11.5
iPP 270 1360 180 0.98 1540 94.1
iPS 359 16
4300 520 2.03
PET 342 3900 282 7.10
4820
(4520)
4180
(4200)
c2
K
53.1
(56.6)
55.6
(55.3)
The numerical values in parentheses are the experimental values 20,22 of c2 and hg (from c2). N6: polycaproamide
(nylon-6), N66: poly(hexamethylene adipamide) (nylon-6,6), iPP: isotactic polypropylene, iPS: isotactic polystyrene,
PET: poly(ethylene terephthalate).
5.2.2.2 Cp jump at the glass transition
The mechanism of Cp jump at the glass transition could be illustrated by the melting of ordered
parts released from the glassy states. 10 Figure 5.2.2 shows the state models for an
amorphous polymer below and above Tg. The ordered parts are generated near Tg in the cooling process; in the glasses, the ordered
parts are contained. In the heating process, right after the glassy state was removed at
Tg, the melting of ordered parts starts and continues up to Te, keeping an equilibrium state
between ordered parts and flow parts. In this temperature range, the free energy per molar
structural unit for polymer liquids contained ordered parts, fm, is given by: 10
( )
f = f X + f 1 −X
[5.2.14]
m x x flow x
where:
fx the free energy per molar structural unit for ordered parts
fflow the free energy per molar structural unit for flow parts
Xx the mole fraction of ordered parts
From (dfm/dXx) p = 0, an equilibrium relation is derived:
fm = fx = fflow
[5.2.15]
Whereas, C p is defined as:
( )
C = dh / dT
[5.2.16]
p q p
with h q =f q- T(df q/dT) p, q = m, x or flow