EXPLOSIVES SCIENCE

Raymond N. Rogers and Joan L. Rogers

Los Alamos, NM

Introduction:

Explosives are often played with as though they were toys. The persons
playing with explosives are often too young to have accumulated sufficient
formal education in chemistry and physics to understand the hazards involved.
One intent here is to supply sufficient information to allow intelligent choices
to be made in the handling and use of explosives.

The misuse of explosives causes a knee-jerk reaction against any scientific
discussion of the materials. This is unfortunate. They have unique properties
that can help us understand materials in general: they "talk to us" with energy.
You can build defects into crystals and watch the effects through changes in the
explosives' thermal properties and sensitivity. You can easily follow
absolute-rate processes. True scientific applications of explosives can be
fascinating and rewarding. We hope that the information presented here will
suggest methods for using explosives in research.

Three broad categories of hazards can be observed in the use of explosives:
sensitivity, stability, and toxicity. Each type of hazard must be considered
before explosives are handled.

Safety tests for impact, friction, shock, and sparks generate relative
scales for evaluating hazards. Different explosives are compared with
one another. It can be stated that TNT is less sensitive than PETN; however, a
quantitative statement can not be made about exactly how hard either must be hit
to cause initiation under all conditions. Relative scales lack credibility: some
small change in experimental conditions can cause errors in hazards
interpretations. Many different relative tests must be run to improve the
probability that all hazards have been identified.

Safety is estimated from experience with the materials. The experience
usually involves an accident and the subsequent accident investigation. If one
explosive rarely causes accidents and another is found to be less sensitive to
impact, you might jump to the assumption that it will be less hazardous. That is
a very dangerous assumption. Each explosive, formulation,
and application must be investigated by many different safety
tests.

All initiations are thermal in nature. Detonations are characterized by a
constant-velocity shock wave; however; the heat generated by chemical reactions
supports the shock wave. An understanding of explosives requires an
understanding of their thermochemical properties.

Thermochemistry of explosives:

Self-heating accidents have often occurred when small-scale procedures have
been scaled up without considering the effects of size. Safe amounts can be
estimated in very straightforward ways. Other accidents have occurred when
additional materials were added to previously safe operations. Such
"compatibility" problems can be observed before they become a hazard.

A large number of tests has been used to observe relative thermal
stabilities. In addition, some more recent quantitative methods can be applied
to predicting safe temperature ranges for many important explosives. Each
approach will be discussed; however, no attempt is being made to make a
comprehensive review. All comments and perspectives are based on our experience
alone.

Relative Tests for Thermal Stability and Compatibility:

Tests Involving Chemical Product Detection or Analysis:

All of the earliest tests are in this class, and many of the tests are still
in use in different parts of the world. Erroneous conclusions will always
be drawn from these tests when results are used to compare stabilities of
materials that decompose to produce different products.

Abel Test: One of the earliest tests is the Abel Test (1875). It observes
the time required to change the color of starch/iodide paper when 1-gram samples
are heated to 180° F. It is
still used in the quality control of commercial cellulose nitrate (NC),
nitroglycerin (NG), and nitroglycol. It can not be used to compare different
types of explosives.

Vieille Test: The sample is heated at 110° C with a strip of litmus paper (1896). The
sample is opened to the air overnight at room temperature, and the procedure is
repeated until the paper turns red within one hour. The overall heating time is
the quantity measured. A propellant powder passed by this test self heated to
explosion in 1911, and two ships were sunk.

Bergmann-Junk Test: The test involves heating the sample to
132° C and determining
extracted nitrites (1904). The test was much modified by Siebert in 1942, who
used H2O2 as the trapping liquid, added a better apparatus
for trapping the NO, and titrated total acidity. The test works well for quality
control of a single explosive, but it can not be used to compare dissimilar
materials.

Leclercq's Test: This test (1950) involves the determination of the
amount of NO and NO2 liberated at 90° C as a function of time.

Changes in product composition will confuse all of these tests. For example,
nitroguanidine decomposes to produce some ammonia. Ammonia changes total acidity
and can react with oxides of nitrogen. None of the chemical tests observe the
product of decomposition that causes self-heating accidents:
heat.

Differential Thermal Analysis (DTA):

When self-heating is the problem, it seems only logical to make heat the
quantity measured. DTA observes the production or absorption of heat by a
sample.

The figure shows a simple DTA cell for use with explosives. It uses two
thermocouples on the same axis. Components: A, stainless-steel hypodermic
tubing; B, ceramic plug; C, thermocouple insulators; D, thermocouples; E, sample
compartment; F, reference compartment. A 0.125-inch OD tube is suitable for
samples of about 3-30 milligrams. Caution: detonation of a 30 mg sample
can be extremely hazardous. The DTA cell should be isolated within a secure
shield. The cell can be slipped inside a ceramic or graphite tube furnace for
heating.

The next figure shows the DTA "thermogram" of reagent-grade ammonium nitrate
(the solid curve). The dashed curve is the "pyrolysis" (Effluent Gas Detection,
EGD) curve, a technique that will be discussed below.

The downward peaks with negative DTs indicate energy-absorbing processes. In the case of ammonium
nitrate, there are three different changes in crystalline structure and melting.
The melted ammonium nitrate starts to decompose exothermally immediately, and
the curve rises into the +DT
range. The pyrolysis curve shows concomitant gas evolution.

The qualitative information available from DTA is very useful; unfortunately,
quantitative measurements suffer from the fact that heat flow between the sample
and the reference cells depends on the temperature difference between them and
the average temperature of the system. The thermal sensitivity of a normal DTA
system is not constant. It is usually not safe to make quantitative comparisons
between dissimilar materials.

The first appearance of heat from a reaction (exotherm) is often used as a
criterion for thermal stability. Different samples of the same explosive can be
compared with some confidence when runs are made at the same heating rates;
however, simple DTA runs can not establish a reliable relative-stability
scale for comparing different explosives. This fact results from the
ways different explosives decompose.

Very few explosives decompose according to simple rate laws, for example the
first-order law shown to the left. When such a material is heated to some
temperature, its rate of decomposition is immediately as high as it can get at
that temperature. Its rate falls off exponentially as reactant is consumed over
time.

The "order" of a reaction is indicated by the exponent of the depletion
function in the rate equation. For example, a "second order" reaction has a
depletion function (1 - a)2.

Most explosives decompose according to "autocatalytic" rate laws, as shown to
the right. There is some delay at any temperature before they reach their
maximum rate of decomposition: the first appearance of a DTA exotherm will be
shifted to a relatively higher temperature. A very autocatalytic material
will appear to be more stable than it really is.

The assumption is often made that it is safe to handle an explosive at any
temperature below the first appearance of an exotherm in the DTA curve:
That assumption is dangerously
false! The highest safe temperature for handling
any energetic material depends on its size, shape, and previous thermal
history.

A normal DTA cell is somewhat sealed; therefore, the test is run in a
self-generated atmosphere. Important heterogeneous and secondary reactions can
often be observed. Tests involving reduced pressure or purging (for example, the
vacuum stability test or thermogravimetry) will usually miss these reactions.
Some of the most important compatibility problems can be identified by DTA in a
self-generated atmosphere. However, in explosives work it is advantageous to run
both confined DTA tests and unconfined or purged tests. The differences between
the types of tests will often help identify safety problems involving
confinement. An explosive in a can or a bomb does not age the same as an
explosive in the open.

Several methods have been published for determining chemical kinetics
constants with DTA apparatus. Erroneous results of different degrees will be
obtained with all such methods when decompositions are complex, eg,
autocatalytic. Simple decompositions are almost unheard of with explosives and
propellants. It is extremely dangerous to develop safety predictive models
that are based solely on kinetics constants determined by DTA methods (or any
other methods that use programmed temperatures). In any case, all predictive
models must be confirmed by independent thermal-ignition tests.

One of the most important applications of DTA is the detection of chemical
incompatibility. The explosive is run by itself at some controlled heating rate.
Then the mixture in question is run under identical conditions.

The figure shows the problem caused by adding lead powder to HMX. The lower
curve shows a production-grade HMX. Its major impurity is RDX, as shown by the
double endotherm below 200° C.
The upper curve shows the same HMX mixed with lead powder. The endotherms have
now become exotherms, and the sample explodes 50° C below HMX alone. The mixture is not
safe, and a similar system self-heated catastrophically in a large press during
fabrication procedures. Quantitative estimates of the difference between the HMX
and HMX with lead can be made, but they can not be made from the DTA curves
alone.

Pyrolysis (Effluent Gas Detection,
EGD):

In the pyrolysis (EGD) test, the explosive is heated at a linear rate under a
flow of gas, and the decomposition products and/or volatile materials are
detected in the gas stream as a function of temperature. Detection is
accomplished with one of the normal kinds of gas-chromatography detectors,
usually a thermal-conductivity detector.

Decomposition products are immediately removed from the reactant, and
heterogeneous reactions are usually eliminated. A comparison between DTA and EGD
results allows phase transitions and reactions to be differentiated, and
heterogeneous reactions can be detected. It provides a sensitive method for
detection of impurities, solvates, and clathrates. Very sensitive detectors are
available, and the sensitivity of the test can be very high, much higher than
thermogravimetry.

The pyrolysis curve for ammonium nitrate is shown above with the DTA curve.
The crystal transitions do not produce gas; however, materials that are trapped
in the crystal lattice are released when the crystal structure changes.

Pyrolysis can be used to determine the vapor pressure of purely volatile
materials.

EGD and most other gas-detection methods respond only to total gas evolved.
Changes in mechanism during a decomposition result in changes in the kinds of
gas produced as well as amounts and rates. Therefore, it is not safe to assume
that the rate of appearance of gaseous products is the same as the rate of
disappearance of reactant(s).

Comparisons between different samples of the same material, run at the same
heating rate, can be very useful for quality control; however, comparisons among
dissimilar materials must be carefully interpreted. Note that this same
statement was made with regard to DTA tests. It is almost a truism that each
type of test has its own shortcomings. It is far safer to compare the results
obtained from many different types of tests than to depend on a single
test.

Pyrolysis-TLC:

A simple method related to EGD combines pyrolysis with thin-layer
chromatography (TLC). The method involves programming a temperature-resistant
thin-layer plate across the exit port of a pyrolysis cell as a function of time
or temperature. The important distinction between constant-temperature and
programmed-temperature methods will be discussed later.

The TLC plate collects the higher molecular weight decomposition products
before secondary reactions can occur, and the TLC plate can be developed to
separate and identify the components. The individual decomposition products can
be identified from their Rf values (how fast they move on the plate)
and/or specific reagent sprays.

The figure shows an example that was produced with impure TNT. The
corresponding DTA and pyrolysis curves are superimposed for comparison. Changes
in decomposition mechanism can be detected, and subtle incompatibilities may be
quite obvious.

The volatile TNT impurities, the dinitrotoluenes, and TNT vapor can be
detected at temperatures slightly above the melting point (3, 4, and 5). True
decomposition products appear at temperatures above about 250° C, consistent with the DTA and EGD
results.

Kinetics constants can be determined by photometry of a TLC plate. However,
an important distinction must be made between methods based on the rate of
appearance of products and methods based on the rate of disappearance of
reactant. An explosive may appear to decompose according to a simple rate law,
but analysis of products usually shows that there are many component reactions:
the process is complex.

None of the product- or gas-analytical methods give direct information on
heat, the factor that causes self-heating accidents.

Thermogravimetry
(TGA):

In thermogravimetry a sample is heated at a linear rate while it is being
weighed. Since it is difficult to embed a thermocouple in a sample while it is
being weighed, there must be a compromise between weighing accuracy and
sensitivity and accuracy of temperature measurement. The thermocouple in DuPont
equipment is not in contact with the sample; therefore, a sample that self heats
significantly will have a largely unknown temperature. Volatile reactant will
escape as well as decomposition products, and the method will have all of the
disadvantages discussed under other gas measuring methods.

With explosives and propellants, rapid decomposition reactions produce a
thrust on the sample pan, causing erroneous mass measurements: the mass appears
to increase as reactant decomposes. Catastrophic decompositions or detonations
tend to destroy much expensive equipment.

Vacuum Stability
Test:

This old test is used all over the world for the determination of thermal
stability and compatibility. It is often the only thermal test used, a
situation that should be much discouraged.

The figure shows a schematic of the vacuum stability apparatus. In running
the test, a sample in a calibrated tube is connected to a manometer, mercury
(toxic) is placed in a cup at the base of the manometer, and the system is
evacuated to approximately 5 torr. When evacuation is stopped, mercury rises in
the manometer tube to some level, and the sample remains under vacuum. The
sample tube is heated to a constant temperature, usually 90° C for double-base propellants,
100° C for single-base
propellants, and as high as 200° C for some high explosives. The volume of gas produced is read as a
function of time or at some specified time. Volume of gas is the value
reported.

Volatile components and/or products distill into the manometer, some
materials and products react with mercury, and the reduced pressure inhibits
heterogeneous reactions. Explosives that decompose to produce different gaseous
products can not be compared with the test, and interpretation is important
under the best circumstances.

The test is cheap, and it can be a good control or acceptance test for
monitoring different batches of the same explosive or formulation. It has the
advantage of operating at a lower temperature than many other tests. It tends to
miss rapid initial-rate processes and secondary heterogeneous or gas-phase
reactions. Incidentally, RDX and HMX produce considerable formaldehyde on
thermal decomposition, and polyoxymethylenes condense on the manometer tube.

The test is much used for compatibility determinations, comparing gas volumes
obtained from a sample against volumes obtained from the sample mixed with a
material in question. There is considerable controversy concerning what
additional volume of gas indicates "incompatibility," and many arbitrary
specifications have been published. Since many thermally active reactions do not
produce much if any additional gas, and many multi-phase reactions require
interaction through the gas phase, the test tends to miss important
incompatibility hazards. Negative results are possible when the additive absorbs
a gaseous product. Interpretation of such results is tricky. One laboratory,
using the vacuum stability test as its only thermal test, lost a pressing
facility to a mixture that passed the test.

Taliani Test:

This test appeared in its basic form in 1904, before the introduction of the
vacuum stability test. It is quite similar to the vacuum stability test, but it
is designed to measure pressure at constant volume as a sample decomposes. A
schematic of the apparatus is shown in the figure.

Although it is normally run at reduced pressures (up to only about 100 torr),
it can be run at higher pressures. At higher pressures it may see heterogeneous
and/or gas-phase reactions. It is widely used in the propellant industry.

Gun Propellant Surveillance Program
(The "65.5° C
Test"):

The program was initiated early in the 20th Century after the Navy
had experienced several disastrous fires and explosions with smokeless
propellants. The Naval Ordnance Station, Indian Head, MD, is now field manager
for a program that keeps all gun propellants of the U. S. military establishment
under surveillance.

Samples of propellant are received in 8-oz glass-stoppered bottles, and they
are placed in an oven heated to 65.5° C (150° F). The
bottles are checked daily for visible fumes, and those samples that fume in less
than thirty days are believed to have reached their "safe-life" limit. Such
samples are retested in the same way, and the "German Bath Test" and "Available
Stabilizer Test" are added. Samples that fail these tests are destroyed or
expended in a specified time. A very large number of samples is under
surveillance at any given time. The test is not used for nonstandard
propellants.

Chemical Reactivity Test
(CRT):

The CRT test is an attempt to improve on the vacuum stability test by using a
higher pressure, maintaining volatile products in the vicinity of the sample,
and analyzing the products via gas chromatography.

In the standard test, the sample is heated at 120° C under 1 atm pressure for 22 hours. The
sample is positioned below a diffusion plug to help keep gaseous products near
the condensed phase. After the heating time, a two-stage chromatography unit is
used to measure the individual volumes of N2, NO, CO, N2O,
and CO2. Unfortunately, the most popular version does not normalize
the products measured against the total amount of volatiles fed into the GC
system. Volatile products that do not pass the columns are lost and are not
detected or identified.

The effects of additives on volumes of the specific gases can be measured,
providing some criteria for compatibility. In practice, total gas volume is the
usual value reported, and results do not usually differ much from vacuum
stability results. The test is much more expensive than the vacuum stability and
Taliani tests, and it is probably not worth the additional expense for routine
quality control operations.

Accelerating Rate Calorimeter
(ARC):

The ARC (Columbia Scientific Industries) is intended "to maintain a sample in
an adiabatic state and permit it to undergo thermal decomposition due to
self-heating while recording the time-temperature-pressure relationship of the
runaway process." The ARC automatically calculates kinetics constants and
reports them as "the" kinetics constants for the system. When used with solid
explosives and propellants, the ARC has serious limitations and gives spurious
results. It is dangerous to base predictive models on numbers obtained from the
ARC. The problems with the ARC follow from the basic functions of adiabatic
calorimetry.

The fundamental equation for adiabatic calorimetry is:

where cp is the heat capacity, T is the temperature, t is time, Q
is heat of reaction, a is the
fraction decomposed at any time, Z is the Arrhenius pre-exponential, E is the
Arrhenius activation energy, and R is the gas constant.

If the equipment were truly adiabatic, cp were constant over the
temperature range, a single temperature described the sample at any time, and
the mechanism did not change with depletion, the equation would accurately
describe the time-temperature history of a decomposition. None of these
requirements are accurately met when using the equipment with solid or viscous
samples of significant size and energy.

Explosives produce energy on decomposition, and they generally have very low
thermal conductivities: they tend to self heat. They get hotter on the inside
than they are on the outside. One temperature does not describe
the system. This provides a major error in using the ARC with solid explosives
and propellants.

When decompositions are complex, mechanisms change with temperature,
depletion, and pressure: Q and f(a ) are not constant. This provides another major source of
error.

Procedures do not currently exist for obtaining accurate kinetics constants
for the component reactions of complex processes involving solid explosives and
propellants from ARC measurements.

There are additional fundamental problems with the theory of adiabatic
calorimetry. When the basic equation is integrated, you obtain the following
equation that defines T(t).

An exact, explicit form for the solution of
that type of equation has not been discovered, and approximations of different
degrees of accuracy and complexity must be used. To make matters much worse,
f(a ) has never been observed
to be either a simple function or a single function for an explosive. The
ARC should not be used in an attempt to obtain meaningful kinetics constants for
solid explosives.

Time-To-Explosion Test:

Henkin and McGill published a time-to-explosion test in 1952 that was clever
and simple. They attempted to obtain kinetics constants for explosives with no
success. We now understand why their attempt failed, and we consider a
modification of their test to be one of the most important thermal tests to run
on explosives.

The "Henkin Test" used empty blasting-cap shells as containers for the
explosive samples, immersed the samples in a constant-temperature Wood's metal
bath, and measured the time to explosion. Henkin and McGill made Arrhenius Plots
of time to explosion versus 1/T, assuming that the slope of the line would be
E/R. It wasn't, but the test proved to be very useful for other things; for
example, it was a very good way to detect incompatible systems.

The Henkin Test has been much modified at the Los Alamos National Laboratory
in order to provide a relative scale of thermal stabilities that can be
justified on the basis of fundamental principles. The modified test can also be
used for the laboratory-scale experimental determination of critical
temperatures for a known size and shape of explosive. As such, it is the test
used to prove the accuracy of quantitative thermal-hazard models. It is a cheap
and useful test.

When the surface temperature of any explosive charge is increased, it will
either decompose quietly at a somewhat higher rate (ultimately rupturing its
confinement as a result of the production of gaseous products), self-heat to
explosion or detonation, or ignite and burn. Its response depends on its surface
temperature, its size and shape, and its chemical and physical
properties.

The most important criterion for thermal safety is the "critical temperature"
(Tc), defined as the lowest constant surface temperature at
which a specific material of a specific size and shape will self heat
catastrophically. The critical temperature is related to the size, shape,
chemical, and physical properties of a specific material.

Reactive heat flow equations have been solved with assumptions that are
appropriate for highly energetic materials, and critical temperatures can be
calculated for specific materials of a specific size and shape. The method used
for the calculation depends on whether the explosive is a solid (conductive heat
flow) or a liquid (convective heat flow). The two most important equations are
shown in the figure. E is the Arrhenius activation energy, Z is the Arrhenius
pre-exponential, Tc is the critical temperature, R is the gas
constant, a is a dimension (radius of a sphere or cylinder, half thickness of a
slab), d is essentially a
dimensionless shape factor (3.32 for spheres, 2.00 for infinite cylinders, and
0.88 for infinite slabs), l is
the thermal conductivity, r is
the density, Q is the heat of reaction, V is the volume, S is the surface area,
and b is a heat-flow
coefficient. A stirred liquid approaches the behavior predicted by the Semenov
equation; a solid that does not melt closely approaches the behavior predicted
by the Frank-Kamenetskii equation.

These equations can not be solved in the normal way: They must be
solved by successive approximations. It is quite laborious to do that by
hand. A programmable calculator can be used, or a much faster Basic program can
be written for the computer. When all of the values except Tc are
known, guess an arbitrary Tc and calculate values for each side of
the equation. Keep trying different guesses until the two sides are identical.
We usually set our programs to converge to within 0.1K.

Once a critical temperature has been determined experimentally for a specific
size, shape, and density of a specific material, the value of the expression
[r QZE/l R] is specified. No assumptions have to be
made about the material's properties at all.

Since the activation energy is specific to any material, a list of critical
temperatures at the same size, shape, and density will provide a general, valid,
relative scale for thermal stabilities. Different types of energetic
materials can be compared on the same scale. We believe that an
experimental determination of critical temperature is the most important single
test to be run on energetic materials.

The test as run at Los Alamos uses empty DuPont E-83 aluminum blasting-cap
shells (copper alloy cells are incompatible with many explosives). 40 mg of
explosive is weighed into the cell for the "standard" test, and it is confined
with an aluminum plug. The plugs are hollow anodized aluminum plugs 6.55-mm OD
by 5.33-mm ID and 5.64-mm long, and they can be produced in large numbers on a
screw machine. Standard Lee plugs have also been used. The sample, confining
shell, and plug are pressed with a conical punch to a pressure somewhat less
than 6100 p.s.i (400 pounds applied force), as required to expand the aluminum
plug to form a seal. After pressing, sample thickness can be measured. The low
thermal conductivity of explosives makes the thin wafer of sample act as an
infinite slab. The half thickness is the "a" of the Frank-Kamenetskii equation.
The completed assembly is dropped into a preheated metal bath at a known
temperature (T), and the time to explosion is recorded. The lowest temperature
at which an explosion (or other runaway reaction) can be obtained is
Tc.

CAUTION: Explosion or partial detonation of a 40-mg sample can be extremely
destructive. Tests must be run with adequate shielding.

The sealed cell maintains a positive pressure over the sample at all times;
however, the thin aluminum wall stretches allowing gas to leak at higher
pressures (somewhat like a Bunsen valve). The effect is a containment vessel
that maintains a constant pressure of a few hundred p.s.i. We have found these
cells very useful for other kinds of applications.

It is extremely important to recognize that the critical temperature
determined applies only to the size and shape of the test.

The sample does not stop decomposing at temperatures below the Tc
(see the discussion on the Arrhenius expression below), the rate is just
not sufficient to cause an explosion. When a cell is opened after a "no-go," it
is often found to be either empty or contain only a small amount of charred
decomposition product. The original sample has decomposed quietly and
completely.

An example of a relative stability scale, based on critical
temperatures, is shown in the figure. It is important to notice that for maximum
validity and accuracy, the samples should have as nearly as possible the same
thickness (the dimension, "a," is squared in the Frank-Kamenetskii equation,
making results sensitive to thickness). Density differences are much less
important. The critical temperatures shown apply only to
0.8-mm-thick slabs (a = 0.4 mm). Estimation of critical temperatures for other
sizes and shapes will be discussed below.

A useful feature of the test is that time to explosion can be used for
quality control purposes: A reduced time to explosion for a new sample of a
specific explosive indicates a less stable material. The figure shows a
comparison between time-to-explosion curves for pure and commercial ammonium
nitrates. The critical temperatures (the temperature at which the lines become
horizontal and explosions do not occur at any time) are nearly 100° C apart.

All of the tests in the figure were run on 0.8-mm-thick samples. A thicker
sample gives a lower critical temperature. Results are quite sensitive to
thickness, as would be expected from the a2 term in the
Frank-Kamenetskii equation. Some care in sample preparation is rewarded with
better precision in the results.

Similarly, when considering compatibility, reductions in time to explosion
and/or critical temperature when another material is mixed with the explosive
indicate incompatibilities.

However, the most important aspect of the test is that it can provide a
small-scale, totally independent test for quantitative thermal-hazard
predictions.

This test can also be used to make predictions for those situations where "no
answer is not the right answer." When some "guess" must be made on the safety of
an explosive, its Tc can be determined rapidly from a
time-to-explosion curve. This specifies the value of [r QZE/d l R]. If the
density does not change appreciably, predictions can be made for other sizes and
shapes. A familiarity with the properties of explosives makes it possible to
guess an activation energy, if one can not be obtained. The accuracy of the
resulting model can be tested to a first approximation by doubling the thickness
of the sample tested and measuring another Tc. Some very violent
reactions should be anticipated; however, this may be the only valid approach to
making a necessary prediction.

One Dimensional Time-to-Explosion
Test (ODTX):

The ODTX test was an attempt to simplify mathematical analysis of
time-to-explosion data. Its result was to complicate the problem and cause
considerable confusion.

In the ODTX test, a spherical sample is confined between O-ring-sealed,
heated "anvils," and the time to confinement failure is measured. A closing
pressure of 1500 atm is standard, but the pressure can be controlled. Shapes of
samples other than spheres have also been used.

The ODTX criterion for "explosion" is failure of confinement: failure does
not necessarily involve catastrophic self heating. Indeed, ODTX operators
recognize and report two different types of responses, "low order" and "high
order." A material that decomposed to gaseous products endothermically would
give an "explosion." Since different types of chemical processes can give the
same result, the ODTX is not a simple reactive-heat-flow test. It is also
extremely expensive.

Quantitative Predictions of Thermal Hazards:

All energetic materials, whether they are called explosives or propellants,
evolve heat when they decompose. The higher their temperature, the faster they
decompose. From a box full of oily rags or a barn full of hay to an ICBM rocket
motor filled with solid propellant, energetic materials can self heat with
unfortunate results. Processing, design, quality control, and operational
applications of systems using energetic materials all require an understanding
of thermal hazards and an ability to predict safety limits.

The safest approach to hazards predictions involves an understanding of the
fundamental chemical properties of the materials and the use of this knowledge
for the production of quantitative models for hazards
predictions.

The figure shows the basic problem: THERE IS NO SUCH THING AS A SINGLE AUTOIGNITION, COOKOFF, OR
CRITICAL TEMPERATURE FOR ANY ENERGETIC MATERIAL.

The temperature at which any specific energetic material will self heat to
ignition or explosion depends on its chemical properties, its size, and its
shape. The curves show that there is a specific critical temperature for
each explosive at each specific size of sphere.

The critical temperature is very sensitive to changes in size in the
small-size range. It can change by nearly 100° C in the first 5-cm size range. If we
were to make cookoff measurements in 1/2-inch geometry and make the assumption
that an 8-inch charge would survive the same temperature, an accident would
almost certainly be the result.

Even though a barn full of hay may ignite and burn, a handful of hay will not
burn your hand.

Differences in shape are not nearly so important as are changes in size. For
practical purposes, the critical temperature for some rather irregular shape can
be estimated by circumscribing it with a regular shape. The estimated
Tc will not be lower than that for the peculiar
shape.

The Concept of a Critical Temperature:

As discussed under the time-to-explosion test above, it can be demonstrated
experimentally that there is a specific constant surface temperature below which
a material of a specific size and shape will fail to self heat catastrophically.
The temperature that divides catastrophic events from simple decomposition is
called the critical temperature, Tc. The critical temperature
is the most important value to predict when the thermal safety of any material
or process is in question.

It must be remembered, however, that energetic materials still decompose at
temperatures below the critical temperature. If they are sealed in a container,
gas pressure will build up until the container ruptures. The result may look
like an "explosion"; however, extremely violent responses can be expected at
temperatures above Tc.

Mathematical Models for Critical Temperature:

As discussed under the time-to-explosion test, the Frank-Kamenetskii equation
provides a good model for a solid explosive or other energetic material; the
Semenov equation can be used to model energetic liquids. It was also mentioned
that the equations must be solved by successive approximations.

The Frank-Kamenetskii model assumes that a thermal gradient will be
established across a mass of the material: it will be hotter at its center than
at its surface. The Semenov model assumes a perfectly flat temperature
distribution, as approached by a rapidly stirred liquid. The heat-flow
coefficient, b , is usually
between about 0.0105 and 0.0135 cal cm-2 s-1
K-1 for thin glass walls (eg, a flask). It will be about 0.018
for fluid-jacketed melt kettles and about 0.0015 for steam-jacketed kettles.

The activation energy, E, and the pre-exponential, Z, are the largest numbers
in the equations, and it is important that they be determined with good
accuracy. The figure illustrates the problem. It shows different critical
temperature predictions for a material

(benzenetrifuroxan) that has an experimental critical temperature of
250° C as a 0.6-mm-thick slab.
An infinite number of compensating pairs of Es and Zs will predict the
experimental Tc, but only the correct set will predict the
critical temperature for all sizes and shapes.

Some idea of accuracy requirements can be obtained from the values of the
compensating pairs: E = 50 kcal/mole, Z = 3.16 X 1018 s-1;
E = 40 kcal/mole, Z = 2.62 X 1014 s-1; E = 37.2 kcal/mole,
Z = 1.92 X 1013 s-1; E = 35 kcal/mole, Z = 2.44 X
1012 s-1; and E = 20 kcal/mole, Z = 2.3 X 106
s-1. All of these curves go through the single experimental
Tc point, but only the 37.2 kcal/mole curve predicts Tc
for all sizes and shapes. The upper solid curve that completely misses the
experimental point is calculated from E = 37.2 kcal/mole and Z = 4.11 X
1012 s-1. It would give erroneously safe predictions for
the material. It is the curve that was obtained from an experimental
determination of E and Z. We were never able to get accurate measurements,
because BTF is remarkably sensitive to confinement and is incompatible with
almost everything (including sample holders).

The fact that kinetics constants can not always be determined with acceptable
accuracy makes it important to have at least one independent method for the
determination of critical temperatures to check predictive models.

The time-to-explosion test described above can be used to test predictive
models.

Determination of Chemical Kinetics Constants for Use in Thermal Hazard
Predictive Models:

As discussed above, the accuracy of the kinetics constants is critical. We
have found constants determined by DTA, ARC, or time-to-explosion alone to be
too inaccurate for safety purposes.

Several calorimetric methods have been used for the determination of kinetics
constants. Several can be found in the literature that give good results, but we
believe that the method that gives the most information on decomposition
complexity and is the most generally applicable is that using a differential
scanning calorimeter (DSC) in the isothermal (constant
temperature) mode.

A DSC operates much like a DTA, and it looks very similar. Two sample holders
are used, one for the sample and one for a reference; however, energy is
partitioned between

them to keep their temperatures exactly the same: there is no heat flow
between them. The energy required to keep the temperatures the same is
the quantity measured. If the sample melts, energy is supplied to the sample to
keep its temperature the same as the reference. If the sample decomposes
exothermically, energy is supplied to the reference to keep its temperature the
same as the sample. The energy measured is the energy of the transition
or reaction. The measurements are quantitative.

A number of methods have been published that use the DSC in a
temperature-scanning mode. None of them can be used with complex reactions to
give sufficiently accurate kinetics constants for hazards predictions.

When the DSC is operated at constant temperature, a record is obtained of the
rate of energy evolution as a function of time.

The figure shows isothermal DSC rate curves for several different types of
energetic materials, as follows: 1) Comp B (65/35-RDX/TNT), 2) a high energy
rocket propellant, 3) HMX, and 4) pure TATB.

It can be seen that rate processes are very much different for the different
materials. Use of assumed rate laws could lead to hazardously wrong
predictions.

Reaction rate and amount of reactant(s) are the fundamental data required for
any kinetics study. All of the values required can be obtained from an
isothermal DSC rate curve.

Isothermal DSC Kinetics Determinations:

An isothermal rate curve obtained from a 3-mg sample of TATB
(1,3,5-triamino-2,4,6-trinitrobenzene) at 636K is shown in the figure to
illustrate the method used to obtain kinetics constants.

The fraction decomposed at any time (a ) can be calculated from:

a = area to time t/total area =
a/A

The absolute rate at any time can be obtained from:

da/dt = height above the
baseline at t/total area = h(t)/A

The quantitative rate of heat evolution (as measured with the DSC) is
proportional to the rate of the (global) chemical reaction, as follows:

dq/dt = Qda/dt =
kQf(a
),

where q is the measured heat flux, Q is the heat of reaction (for the
specific reaction), and k is the chemical rate constant. However, although heat
evolution and rate are proportional, changes in mechanism associated with
complex reactions can cause changes in heat of reaction (Q) and the depletion
function [f(a )] as the
reaction proceeds. When mechanisms
change during the course of a reaction, it is not valid to "linearize" the rate
data for the entire process to obtain a single rate constant.

A single depletion function that will model a specific part of a reaction is
a necessary but not sufficient proof of a consistent mechanism. VALID KINETICS CONSTANTS CAN BE OBTAINED ONLY FOR
CONSISTENT REACTIONS. Isothermal DSC often makes it
possible to measure the kinetics constants for the different component reactions
of a complex process, even those that operate as the rate-controlling components
at lower temperatures.

It will be discussed below that a reaction regime that both obeys a single
depletion function and shows a constant kinetic isotope effect represents a
consistent reaction.

It is important to measure all of the component reactions. The low-rate,
induction-time reactions will largely determine time to explosion; the most
rapid reaction will be responsible for catastrophic self heating. It is seldom
possible to make both time-to-explosion and critical temperature calculations
with the same set of chemical rate constants.

The assumption is often made in the literature that the decomposition of an
energetic material will obey a rate law of the following form:

da/dt = k(1 - a
)n

where n is the "reaction order." When working with explosives and
propellants, that assumption is not often true. It is necessary to
analyze the data in such a way that consistent reactions can be identified and
measured.

Autocatalytic-type processes (reactions in which the early rate increases
with time and depletion at constant temperature) are common. Some causes for
autocatalytic processes with explosives can be melting with decomposition (RDX,
HMX, etc.), chemical autocatalysis (PETN, NC, NG, etc.), inhibition (stabilized
propellants), and solid-state systems (nucleation-growth processes). The search
for appropriate rate laws for the analysis of rate curves must include such
systems. The reaction products observed during the early (induction),
intermediate (acceleratory), and late (decay) parts of an autocatalytic reaction
are nearly always different.

A first attempt to find appropriate rate laws can be made by making an
"order plot." Once da/dt
and a series of (a ,t) values
have been obtained from the rate curves, they can be tested for simple rate laws
(n ³ 0). From the simple rate
law above, you can see that a plot of ln da/dt versus ln(1 - a ) should give a straight line with a slope
of n (the reaction order). Any curvature, discontinuity, or negative slope in
the order plot indicates complexity in the reaction. If negative slopes are
observed, autocatalytic-type rate laws should be tested.

A general autocatalytic rate law has the form: da/dt = ka p(1 - a )q.

When the peak of an autocatalytic rate curve occurs after 50% depletion, p
> q.

TATB decomposes by a complex mechanism, and it provides a good example of the
methods that allow analysis of such rate curves. TATB rate curves show an
increasing rate early in the process, and the curve shows two distinct peaks: it
is clearly complex.

The TATB order plot shows that almost 60% has decomposed before the slope
becomes positive.

However, a plot of the TATB rate data according to a simple autocatalytic law
[da/dt = ka (1 - a )] shows that a major part of the process
can be modeled with such a law. In this type of plot, the slope is k, but the
curve folds back on itself at a(1 - a ) = 0.25.

The autocatalytic order plot for TATB shows that the slope of the early
consistent reaction between a =
0 and a = 0.5 is reduced by
deuterating the TATB. There is a kinetic isotope effect (KIE).

The KIE is constant through exactly the same range of depletion that showed
the constant slope (k). If a KIE is constant through a specific part of a
complex decomposition, you can feel confident that a consistent component
reaction has been identified. This is a time-consuming and expensive way to
identify consistent reactions, but it may be the only positive way to unravel
some nasty surprises by explosives.

Rate laws of all of the different types that can be expected have been
observed in working with energetic materials; however, most consistent reactions
can be described according to one of the rate laws shown in the table.

Some Rate Laws and their Integrals:

It is not usually necessary to go to such lengths as KIE measurements to
prove that a useful consistent reaction has been identified. Rate constants (k)
determined from straight-line portions of order plots can be used to calculate
kinetics constants for the processes. Predictive models can be derived from the
kinetics constants (E and Z), and the models can be tested by time-to-explosion
tests.

The Arrhenius Law describes the effect of temperature on rate constants for
consistent reactions, as follows:

k = Ze-E/RT.

Therefore, a plot of ln k versus 1/T should give a straight line for
each consistent reaction, and the slope of the straight line will be
-E/R.

The Arrhenius plot for theTATB data is shown in the figure. The slope of the
"autocatalytic process" gives an activation energy (E) of 59.1 kcal/mole and the
intercept gives a Z of 3.75 X 1018 s-1.

With TATB, only the E and Z for the "autocatalytic" process can be used
correctly to predict experimental critical temperatures. This is exactly what
you would predict from the KIE results. They are, therefore, the constants to
use for Tc versus size and shape predictions.

Kinetics constants can usually be determined for explosives, even when the
decompositions are complex, by using isothermal methods. The kinetics constants
can be used in suitable reactive-heat-flow mathematical models (eg, the
Frank-Kamenetskii or Semenov equations) to predict the critical temperatures
(Tc) for any size and shape of a specific explosive. The predictive
models can be tested for accuracy against time-to-explosion tests.

Some examples of explosives that have been studied by the above methods are
shown in the table. The prediction for BTF did not agree with the experimental
critical temperature; therefore, we know that incorrect kinetics constants were
determined. It would be hazardous to use such a model for large-scale
predictions.

Experimental and Predicted Critical Temperatures (With values used for
calculations):

When the predictive model needs further verification (as with explosives for
a nuclear weapon), or when kinetics constants have been impossible to determine,
we do large-scale testing at a firing site. The cheapest system we have tried
involves 1-liter heating mantles. We put castable explosives (that melt well
below the test temperatures) in 1-liter round-bottom flasks. Explosives that do
not melt at the test temperatures are machined into 13-cm-diameter hemispheres.
Thermocouples are placed in the center of the samples and at several positions
in each mantle. Two hemispheres are joined to make a sphere. Temperature
controllers are adjusted so that the hottest spot in each mantle controls its
temperature. Recorders chart the temperatures of the mantles and sample. We
shield the sample in a 6-foot-diameter high-tensile steel containment vessel. We
heat the mantles as quickly as possible to the desired test temperature. The
sample is left until it self heats. Times may be as long as several weeks when
the test temperature is close to the critical temperature. Tests run below the
critical temperature show an increase in the central temperature of the sample,
but the temperature ultimately begins to drop. The explosive decomposes, but
there is no ignition or explosion. Large-scale tests require considerable time
--- and stable power sources.

Kinetic Isotope Effects and Explosives Sensitivity:

As discussed above, kinetic-isotope effects can be used to detect the
specific functional groups involved in the elementary reactions of complex
explosives decomposition processes. Isothermal kinetics methods must be used to
correlate component reactions with specific reaction regimes. When component
reactions can be identified at different temperatures, kinetics constants can be
determined. Conditions for self heating to explosion or detonation can be
calculated from the kinetics constants, and predictions can be tested against
independent time-to-explosion measurements.

However, much more can be learned from KIE. Pressure effects on the
elementary reaction can be explained in terms of transition-state theory. It can
be shown that the rate depends on pressure according to the expression:

where D V is the volume of
activation. The volume of activation is defined as the difference in molar
volume between the reactants and the activated complex. Pressure applied to a
system that has a positive volume of activation decreases the rate of the
reaction; pressure applied to a system that has a negative volume of activation
increases the rate.

The sign of the volume of activation can be determined from the magnitude of
the KIE. In the case of TATB (above), kH > kD, and the
ratio is 1.5. It is a "normal" effect, and it is a "primary" effect. The
elementary reaction involves motion of the hydrogens. Isotope effects are
determined by changes in the force constants describing motions at the position
of isotopic substitution for the process leading from reactant to transition
state (the "activated" state). A decreased force constant can be correlated with
a normal isotope effect. When there is a decrease in force constant leading to
activation, bond lengths will be greater in the transition state: there will
be a positive change in the volume of activation.

TATB is recognized as an intrinsically "insensitive" explosive, and it has a
positive volume of activation. All other factors being equal, an explosive with
a positive volume of activation will be more difficult to initiate with a shock
wave than an explosive with a zero or negative volume of activation. We have not
had the opportunity to study other explosives as completely as TATB, but it has
appeared that kH < kD for HMX during the decomposition
in the liquid phase, and the ratio for PETN appeared to be nearly zero.

We propose that observations of KIE could make it possible to predict
sensitivities. A long-range goal would be a quantitative model for
"sensitivity."

Compatibility:

Compatibility problems can be handled in exactly the same way as are pure
explosives. A reaction regime will normally be found that corresponds to the
reaction between the explosive and the additive. The stoichiometry of the
reaction can be obtained from the rate curve or order plot. The rate curves must
be evaluated with the correct rate laws.

Mixtures of explosives with metals often show a zero order rate law,
especially when the metal is a catalyst for the decomposition of the explosive.
This is because the reaction takes place at the surface of the metal, and the
surface area of the metal does not change.

Note that lead is not a true catalyst for the decomposition of RDX and HMX;
it takes part in the reaction. Elemental lead is oxidized to plumbic oxide by
the oxides of nitrogen produced by the nitramines, then plumbic oxide oxidizes
formaldehyde (another decomposition product). The lower oxides on the surface of
the lead are then re-oxidized by oxides of nitrogen. The lead particles do not
undergo significant size changes, so the reaction is best described by a
zero-order rate law. More energy is obtained from the overall reaction, making
the system more hazardous.

Zero order is defined as the situation where da/dt = k(1 - a )0; that is, da/dt = k (a constant). The rate does not
change with time at any given temperature. The data must be evaluated with a
zero-order rate law. Predictions can be made.

Time to Explosion:

Time to explosion gets longer as systems get larger. Times to explosion of a
few weeks have been measured at temperatures slightly above the critical
temperature in 13-cm diameter spherical geometry at Los Alamos.

In view of the long times, it would appear to be safe to do some operations
at temperatures above the critical temperature. Indeed, that is often done;
however, factors that change time to explosion must be understood in complete
detail. Slight changes in purity or composition, changes in crystal perfection
(as defects caused by pressing), past history of a charge, and/or fabrication or
formulation methods can cause major changes in time to explosion. The changes
can be very large and unexpected. WE
STRONGLY RECOMMEND AGAINST HANDLING ENERGETIC MATERIALS ABOVE THE CRITICAL
TEMPERATURE.

BIBLIOGRAPHY

DTA:

G. Krien, Explosivstoffe 8, 205, August 1965.

R. N. Rogers, Microchemical J. 5, 91 (1961).

H. J. Borchardt and F. Daniels, JACS 79, 41 (1957). This is the
first kinetics article on DTA.

H. E. Kissinger, Analytical Chemistry 29, 1702 (1957).
Kissinger proposed his method for simple reactions only (clays). The method is
often used for explosives, giving erroneous results.

Review of Thermal Methods:

L. W. Collins and L. D. Haws, Thermochimica Acta 21, 1 - 38
(1977).

ASTM, American National Standard, ANSI/ASTM E698 - 79, pp. 1009
ff.

Pyrolysis (EGD):

R. N. Rogers, S. K. Yasuda, and J. Zinn, Analytical Chemistry
32, 672 (1960).

J. F. Baytos, "Evaluation of High Explosives by Pyrolysis," LA-3249, Los
Alamos National Laboratory, December 1964.

Combined Pyrolysis and Thin-Layer Chromatography:

R. N. Rogers, Analytical Chemistry 39, 730 (1967).

R. N. Rogers and L. C. Smith, J. Chromatography 48, 268
(1970).

Vacuum Stability:

MIL-STD-286B, 20 December 1975, Method 403.1.3.

J. F. Baytos, LAUR-84-1333, Los Alamos National Laboratory, June 1984.

J. F. Baytos, "High-Temperature Vacuum Thermal Stability Tests of
Explosives," LA-5829-MS, Los Alamos National Laboratory, January 1975.

Taliani:

MIL-STD-286B, 1 December 1967, Method 406.1.2.

Critical-Temperature Predictive Models:

A. G. Merzhanov and V. G. Abramov, Propellants and Explosives
6, 130-148 (1981). A review of models.

D. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical
Kinetics, Plenum Press, New York, NY (1969).

N. N. Semenov, Chemical Kinetics and Chain Reactions, Oxford
University Press, London (1935).

Thermal-initiation Testing:

J. Zinn and C. L. Mader, J. Applied Physics 31, 323
(1960).

J. Zinn and R. N. Rogers, J. Phys. Chem. 66, 2646
(1962).

R. N. Rogers, Thermochimica Acta 11, 131 (1975).

D. L. Jaeger, LA-8332, Los Alamos National Laboratory, August 1980. This
reports a critique on the ODTX.

Heat-Flow Calorimetry:

J. L. C. Van Geel, Ind. And Eng. Chem. 58, 24
(1966).

DSC Kinetics Methods:

R. N. Rogers and L. C. Smith, Thermochimica Acta 1, 1
(1970). This shows some of the problems with programmed-temperature kinetics
methods.

R. N. Rogers, Analytical Chemistry 44, 1336 (1972).
Discusses isothermal rate constants.

R. N. Rogers, "Differential Scanning Calorimetric Determination of Kinetics
Constants of Systems that Melt with Decomposition," Thermochimica Acta
3, 437 (1972).

R. N. Rogers and G. W. Daub, "Scanning Calorimetric Determination of
Vapor-Phase Kinetics Data," Analytical Chemistry 45, 596
(1973).

R. N. Rogers and G. W. Daub, "Determination of Condensed-Phase Kinetics
Constants," Thermochimica Acta 9, 855 (1974).

A. A. Duswalt, "The Practice of Obtaining Kinetic Data by Differential
Scanning Calorimetry," Thermochimica Acta 8, 57 (1974).

R. Bruce Cassel, "ASTM Method of Testing for Determining the Arrhenius
Kinetic Constants for the Screening of Potentially Hazardous Materials,"
Perkin-Elmer Thermal Analysis Application Study 28
[Pittsburgh Conference Paper No. 688, 1979].

Complex Reactions, KIE:

R. N. Rogers, J. L. Janney, and M. H. Ebinger, Thermochimica Acta
59, 287-298 (1982).

When All Else Fails (and you still have to make a prediction):

R. N. Rogers, J. L. Janney, and N. P. Loverro, Journal of Energetic
Materials 2, 293-330 (1984).