The Thermodynamics and Kinetics of Explosives

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The Thermodynamics and Kinetics of Explosives

• Thomas M. Jerant

Cindy D. Spangler
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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

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The Decomposition of TNAZ
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The Method - DSC

• Differential Scanning Calorimetry
• Usually DSC analysis employs a temperature
  gradient that increases as a function of time.

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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

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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.

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Heat Flux DSC
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DSC Curve
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Determination of Kinetics

• Finding the accuracy of activation energy
  evaluations using the isoconversional method
• A single step kinetic equation is usually used
  for solid state decompositions given by
• Where a is the extent of conversion and f(a) is
  the reaction model

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Determination of Kinetics

• To find a, it requires differentiation of
  experimental measurements but produces
  unacceptably noisy data
• So the integral form is used
• 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

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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

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Statistical Procedure Validation

• Used five heating rates and nine independent sets
  of experimental measurements at each rate to
  determine the activation energies

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The Method

• Applications
• The DSC is used to measure specific heat capacity
  (100 to 1200C) and heats of transition as well
  as to detect the temperature of phase changes and
  melting points in the range of 20 to 1500C.
  Specific heat capacity can be used in conjunction
  with thermal diffusivity to obtain thermal
  conductivity.

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Kinetic Analysis

• The decomposition kinetics of a heterogeneous
  solid state reaction
• a is the extent of reaction.
• f(a) is the reaction model
• k(T) is the temperature-dependent rate constant

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Kinetic Analysis

• To determine Ea, the function S2(Ea), 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

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Kinetic Analysis

• a is broken down into 50 segments for the entire
  process.
• The plot of Ea vs. ? is shown below for the
  nonisothermal DSC trace where ß 10 C min-1 for
  the closed pan sample of TNAZ
• A built up dependence of a is established for the
  entire reaction, Af(a).

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Kinetic Analysis

• Decrease in Ea 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.

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Results for TNAZ

• The Ea determined in this study matched Ea 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.

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