Handbook of Solvents - George Wypych - ChemTech - Ventech!

5.2 Prediction of solubility parameter 257
From equations [5.2.15] and [5.2.16], it is shown that C p of ordered parts is equal to
that of flow parts. Therefore, h x is given by: 10
hx ≈ hg + Δ h
[5.2.17]
Te
conf
with Δh = ∫ ΔCpdTand
{RTgln(Zg/Z0)}/x ≤Δh≤Tg{sg - (RlnZ0)/x},
Tg
where:
ΔCp the difference in the observed Cp and the hypothesized super heated glass Cp at the glass transition
Zg the conformational partition function per a chain at Tg Z0 the component conformational partition function per chain regardless of
the temperature in Z
conf
sg the conformational entropy per molar structural unit at Tg hx is also given by rewriting the modified Flory’s equation, which expresses the melting
point depression as a function of the mole fraction of major component, X, for binary random
copolymers: 24-27
( )
h ≈2h 1−1/ a
[5.2.18]
x u
0
witha=-hu(1/Tm(X)-1/Tm)/(RlnX) where:
Tm(X) the melting temperature for a copolymer with X
0
the melting temperature for a homopolymer of major component
T m
Table 5.2.2
Polymer
hu
cal/mol
N6 5100
N66 10300
hx(eq.[5.2.17])
cal/mol
9590
(10070)
19300
(20280)
iPP 1900
1600
(1780)
iPS 2390 12 5030
(5550)
PET 5500
5380
(5670)
hx(eq.[5.2.17]) - hu
cal/mol
4490
(4970)
9000
(9980)
hx (eq.[5.2.18])
cal/mol
hx from δ p
cal/mol
4830 -
9580 10070
- 1470 1420
2640
(3160)
- 2410 - 5790
- 6600 6790
The numerical values in parentheses were calculated using equation [5.2.17] with the second term of T g{s g conf -
(RlnZ 0)/x}.
Table 5.2.2 shows the numerical values of h x from equations [5.2.17] and [5.2.18], and
from the reference values 7,8 of δ p using equations [5.2.1] ~ [5.2.4], together with the
values 12,28,29 of h u, for several polymers. The second term in the right hand side of equation
[5.2.17] was calculated from {RT gln(Z g/Z 0)}/x. The numerical values in parentheses, which
were calculated using equation [5.2.17] with the second term of T g{s g conf - (RlnZ0)/x}, are a
little more than in the case of {RT gln(Z g/Z 0)}/x. The relationship of h x(eq.[5.2.17]) � � �
found for N6 and N66 suggests two layer structure of ordered parts in the glasses, because,