Chemistry Reference
In-Depth Information
simultaneously the associated thermal effect (
d
Q
/d
t
)
T
and the mechanical effect
(
V
/d
t
)
T
;and(
2
) the use of temperature as scanned variable along isobars while
recording simultaneously the associated thermal effect (
∂
d
Q
/d
t
)
p
and the mechanical
effect (
V
/d
t
)
p
.
In the case of the first mode, the straightforward thermodynamic relation [
23
]:
∂
d
HT
ð
;
p
Þ¼@
ð
H
=@
T
Þ
p
d
T
þ @
ð
H
=@
p
Þ
T
d
p
(4)
with:
d
HT
ð
;
p
Þ¼dQ
þ
V
d
p
;
(5)
allows one to express finally that the thermal effect
q
T
(
p
) along the scan is:
¼
q
T
p
ðÞ¼dQ
ð
=
d
t
Þ
T
¼
a
ð
@
H
=@
p
Þ
T
V
aT
ð
@
S
=@
p
Þ
T
(6)
¼
aT
ð
@
V
=@
T
Þ
p
¼
aTVa
p
;
where
H, S, a
,and
a
p
are the enthalpy, entropy, pressure scanning rate and isobaric
thermal expansion, respectively. In addition, the associated mechanical effect (
V
/
∂
d
t
)
T
, (or equivalently (
p
)
T
) allows one to obtain the isothermal compressibility
k
T
. Similarly, in the second mode, from (
4
)and(
5
), at constant pressure (e.g., d
p
V
/
∂
∂
¼
0)
one obtains for the thermal effect
q
p
(
T
) an equation equivalent to (
4
),
C
p
being the
heat capacity:
q
p
T
ðÞ¼
b
ð
@
H
=@
T
Þ
p
¼
bC
p
:
(7)
In the same way as above, the mechanical effect (
V
/
T
)
p
allows one to obtain
∂
∂
the isobaric thermal expansion
a
p
.
The transitiometric technique can be used for fluids (gases and liquids) as well as
for solid materials (polymers and metals). Remarkably, measurements can be
performed in the vicinity of and above the critical point. Concretely, the investi-
gated polymer samples are placed in ampoules, i.e., open mini test-tubes seated in
the transitiometric measuring vessel in such a way that the sample is in direct
contact with the pressurizing fluid. More details on the technique can be found
elsewhere [
24
,
25
]. The transitiometers (from BGR TECH, Warsaw) used in these
studies of polymers, built according to the above principle, can be operated over the
following ranges of temperature and pressure: 173 K
<
T
<
<
673 K and 0.1 MPa
p
200 MPa (or 400 MPa). A detailed description of a basic scanning transiti-
ometer is given elsewhere [
26
].
A schematic representation of the instruments is shown in Fig.
4
.Thetransi-
tiometer itself is constructed as a twin calorimeter with a variable operating
volume. It is equipped with high-pressure vessels, a
pVT
system, and Lab-
VIEW-based virtual instrument software. Two cylindrical fluxmeters or calori-
metric detectors (internal diameter 17 mm, length 80 mm), each made from 622
<
