Transcript The Thermodynamics of Blowin’ Shit Up

The Thermodynamics and
Kinetics of Explosives
Thomas M. Jerant
Cindy D. Spangler
TNAZ
• 1,3,3-trinitroazetidine (TNAZ) is a
the only widely used melt castable
explosive.
• TNAZ can be molded into the liquid
state.
• TNAZ is being considered as an
alternative for trinitrotoluene (TNT)
because of power and sensitivity.
• Thermally stable above its melting
point
• TNAZ has approximately 30% more
energy than TNT
NO2
NO2
N
O2 N
The Decomposition of TNAZ
NO2
NO2
N
O2 N
NO2
NO2
Heat
N
+
NO2
The Method - DSC
• Differential Scanning
Calorimetry
• Usually DSC analysis
employs a temperature
gradient that increases
as a function of time.
Power Compensated DSC
• Both the sample and
the reference are kept
at the same
temperature while
electrical power used
by the heaters is
monitored
• Small samples are used
to insure that thermal
equilibration will occur
fast
Heat Flux DSC
• A reference and sample
pan are connected to an
allow constantan (Cu &
Ni allow. Constant
resistance over a wide
range of temperatures).
• Two chromel wafers are
used to establish a
thermocouple between
itself and the
constantan.
Heat Flux DSC
Reference
Sample
Constantan Heating Disk
Thermocouple
Chromel
Chromel
Heat
Signal Out
Red = Thermal Energy Difference; ΔUtherm
Black = Electrical Energy Difference; ΔUelec
DSC Curve
Determination of Kinetics
 Finding the accuracy of activation energy
evaluations using the isoconversional method
o A single step kinetic equation is usually used for
solid state decompositions; given by
d
 k (T ) f ( )
dt
o Where α is the extent of conversion and f(α) is the
reaction model
Determination of Kinetics
To find α, it requires differentiation of experimental
measurements but produces unacceptably noisy data
o So the integral form is used

g ( )  
0
 E 
d
dt  AJ[ E , T (t )]
A  exp
f ( )
 RT (t ) 
0
t
o The integral of the reaction model can have useful approximations
used in it in order to lead to simple linear equations and estimation
of Arrhenius parameters
Reaction Model Importance
• The activation energy
depends on the choice
of reaction model
– Model is usually chosen
based on statistics;
however within a
confidence level,
models can be
statistically equivalent
Statistical Procedure Validation
• Used five heating
rates and nine
independent sets of
experimental
measurements at
each rate to
determine the
activation energies
The Method
• Applications:
– The DSC is used to measure specific heat capacity
(100 to 1200°C) and heats of transition as well as
to detect the temperature of phase changes and
melting points in the range of 20 to 1500°C.
Specific heat capacity can be used in conjunction
with thermal diffusivity to obtain thermal
conductivity.
Kinetic Analysis
The decomposition kinetics of a heterogeneous solid
state reaction
• α is the extent of reaction.
• f(α) is the reaction model
• k(T) is the temperature-dependent rate constant
d
 k (T ) f ( )  A( )e
dt

E
RT
f ( )
Kinetic Analysis
To determine Eα, the function S2(Eα), the variance, is
minimized.
• n is the number of experiments
• j and i are indices for heating programs for two separate
experiments
• J is the Arrhenius integral solved by the trapezoid rule
• T(t) is the temperature dependence on time
t
J [ E , Ti (t )]   e
t 

E
RTt ( t )
dt
 J [ E , Ti (t )] 
1

S ( E ) 
 1

n(n  1) i 1 j i  J [ E , T j (t )] 
n
2
n
2
Kinetic Analysis
• α is broken down into 50 segments for the entire process.
• The plot of Eα vs. Α is shown below for the nonisothermal
DSC trace where β = 10 °C min-1 for the closed pan sample of
TNAZ
• A built up dependence of α is established for the entire
reaction, Af(α).
Kinetic Analysis
• Decrease in Eα leads to evidence of
autocatalysis during the thermal decomposition
TNAZ.
• The final products gained in the experiments
are not the thermodynamically stable end
products of TNAZ combustion.
Results for TNAZ
• The Eα determined in this study matched Eα values for
the decomposition of TNAZ.
• It was then determined that the bond cleaved during
the initial decomposition was the N-NO2 bond based
on such values.
Bond Cleavage
Bond Dissociation Energy
Initial Eα
N-NO2
187 kJ mol-1
184 kJ mol-1
C-NO2
195 kJ mol-1