Chemistry Reference
In-Depth Information
pyrolysis of polymeric materials), the temperature of the hot plate,
T
0
, separated
from the decomposing compound by a gas layer can significantly exceed the tem-
perature of the pyrolysis surface,
T
S
. This effect was first mentioned by Cantrell
[19], who analyzed the hydrodynamics of the gas layer and obtained the following
relationship between its thickness,
Z
, and basic parameters of the process:
Z
=
3
1
/
3
g
b
4
32
U
ρ
s
g
ν
,
(1.56)
W
where
ν
g
is the viscosity of the gas pro-
duced by linear pyrolysis,
b
is the sample diameter, and
W
is the force pressing
the sample to the heater. Cantrell showed that the heat transfer to the surface of
the reacting compound occurs mostly due to conduction, estimated the
T
S
for the
linear pyrolysis of solid carbonic acid at
T
0
ρ
s
is the density of the solid compound,
50
◦
C, and found out that the temper-
ature drop across the gas gap can be as high as 100
◦
C. For his experimental and
theoretical studies, Cantrell used data obtained by direct calorimetric measurements
of the heat flow maintaining the linear pyrolysis and highly accurate thermophysi-
cal parameters for carbonic acid gas. The results of Cantrell's work were not used
in subsequent studies of linear pyrolysis for compounds that are important from a
practical viewpoint (specifically polymers). Most likely, this was usually caused by
the lack of data on the thermophysical parameters, the viscosity and the composition
of the gap-filling gas produced by linear pyrolysis. In addition, calorimetric equip-
ment used for studying high-temperature linear pyrolysis experimentally is much
more sophisticated than the experimental setup used by Cantrell. In fact, the appli-
cation of high-temperature calorimetry eliminates some of the main advantages of
the method based on linear pyrolysis: its simplicity and reliability. Therefore, the
direct calculation of the pyrolysis surface temperature,
T
S
, using experimental data
on the linear pyrolysis rate,
U
, at a certain temperature of the heater,
T
0
, is of great
interest. A method of calculating this is given below.
The equation for the balance of heat maintaining linear pyrolysis is
≈
λ
g
T
0
−
T
S
=
m
[
c
s
(
T
S
−
T
∞
)+
Q
]
,
(1.57)
Z
where
m
=
U
is the thermal conductivity of
the gas produced by linear pyrolysis, and
c
s
is the thermal conductivity of the solid
compound. Substituting Eq. (1.56) into Eq. (1.57) and neglecting the temperature
dependence of the thermophysical parameters of the gas in the first approximation,
one can obtain
ρ
s
is the mass rate of linear pyrolysis,
λ
=
32
3
1
/
3
B
(
mb
)
4
/
3
W
1
/
3
λ
g
(
T
0
−
T
S
)
T
∞
)+
Q
]
,
(1.58)
π
1
/
3
[
c
s
(
T
S
−
ν
where
B
=(
W
/
SP
∞
+ 1)
−
1
/
3
= const and
S
is the area of the linear pyrolysis surface.
The situation of a weak dependence of
T
S
on increasing
T
0
and
U
at fast linear py-
rolysis corresponds to a linear relationship between the left hand side of Eq. (1.58)
