Biomedical Engineering Reference
In-Depth Information
However, in thermodynamics the melting or crystallization enthalpies are de
ned for
in
nite phases, where surface energies are neglected. In practice the heat of melting of
fine powders differs from large crystals and so the melting temperature changes as well.
The crystalline junctions in physical gels are necessarily small and their thermal behav-
iour normally depends on the whole thermal history of the sample.
Chemical reactions may be carried out isothermally or non-isothermally, in a scanning
mode or following a special temperature programme, and can be analysed by DSC. In
(
2.19
), the reaction enthalpy (
∂
H/
∂χ
)
T, p
=
Δ
H
r
is generally replaced by the average
reaction enthalpy
, independent of the instantaneous composition of the system.
To carry out chemical reactions in the isothermal mode, the sample has to be brought
extremely rapidly from the initial inert state to the desired reaction temperature. Then
(
2.19
) can be written in a simple form:
〈
Δ
H
r
〉
d
dt
:
m
ð
T
;
p
; χÞ¼hD
H
r
i
ð
2
:
20
Þ
When the reaction progresses, the total heat exchanged is obtained by integration of the
heat
flux over time, between 0 and time t:
ð
t
0
m
ð
ð
χ
t
0
Þ
dt
0
¼hD
χ
0
:
Q
m
ð
t
Þ¼
H
r
i
d
ð
2
:
21
Þ
0
When the reaction is completed,
.
In the scanning mode, the heat of reaction is generally obtained by integrating the total
area of the heat
χ
=1,Q
m
=
〈
Δ
H
r
〉
flux below the baseline.
2.3.3
Microcalorimetry: µDSC
Microcalorimetry is an alternative to heat
flux DSC measurement, and operates with a
cylindrical type of measuring system. The microcalorimeter has a sensitivity of the order
of 1 μW. The block type furnace is provided with two cylindrical cavities which contain
identical cells. In the μDSC III instrument (Setaram, Caluire, France), the cells are
surrounded by high-sensitivity Peltier elements ensuring thermal contact with the calo-
rimetric block. Closed batch cells and mixing cells of the special thermal conducting
alloy Hastelloy
®
are available with a volume of 850 μL, as shown in
Figure 2.8
. The
mixing cells contain two containers (
Figure 2.8b
): the upper one is
filled with the reactant
and the lower one with the polymer solution. By pushing on the piston separating the two
compartments and stirring rapidly, the two liquids are brought into contact and rapidly
mixed and the chemical reaction starts. Such microcalorimetric measurements are well
suited both to studies of thermal gelation using batch cells and to isothermal chemical
cross-linking using mixing cells.
Such a microcalorimeter has the advantages of relatively large sample size, very high
sensitivity (resolution 0.02 μW) and operation in either isothermal or scanning mode.
Scan rates are necessarily low, at 10
-
3
1°C min
−
1
(typically 0.1°C min
−
1
), to allow a
uniform temperature inside the sample. The basic principles of operation are the same as
in DSC.
-
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