molecular characterization of energetic materials
TRANSCRIPT
MOLECULAR CHARACTERIZATION
OF
ENERGETIC MATERIALS
A Dissertation
by
SANJEEV R. SARAF
Submitted to the Office of Graduate Studies of Texas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
December 2003
Major Subject: Chemical Engineering
MOLECULAR CHARACTERIZATION
OF
ENERGETIC MATERIALS
A Dissertation
by
SANJEEV R. SARAF
Submitted to Texas A&M University in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Approved as to style and content by: _____________________________ _____________________________ _____________________________ _____________________________ _____________________________
December 2003
Major Subject: Chemical Engineering
M. Sam Mannan (Chair of committee)
David M. Ford (Member)
Michael B. Hall (Member)
Dan F. Shantz (Member)
Kenneth R. Hall (Head of Department)
iii
ABSTRACT
Molecular Characterization of Energetic Materials. (December 2003)
Sanjeev R. Saraf, B. Chem. Engg., U.D.C.T, Mumbai, India
Chair of Advisory Committee: Dr. M. Sam Mannan
Assessing hazards due to energetic or reactive chemicals is a challenging and
complicated task and has received considerable attention from industry and regulatory
bodies. Thermal analysis techniques, such as Differential Scanning Calorimeter (DSC),
are commonly employed to evaluate reactivity hazards. A simple classification based on
energy of reaction (-∆H), a thermodynamic parameter, and onset temperature (To), a
kinetic parameter, is proposed with the aim of recognizing more hazardous
compositions. The utility of other DSC parameters in predicting explosive properties is
discussed.
Calorimetric measurements to determine reactivity can be resource consuming,
so computational methods to predict reactivity hazards present an attractive option.
Molecular modeling techniques were employed to gain information at the molecular
scale to predict calorimetric data. Molecular descriptors, calculated at density functional
level of theory, were correlated with DSC data for mono nitro compounds applying
Quantitative Structure Property Relationships (QSPR) and yielded reasonable
predictions. Such correlations can be incorporated into a software program for apriori
prediction of potential reactivity hazards. Estimations of potential hazards can greatly
help to focus attention on more hazardous substances, such as hydroxylamine (HA),
which was involved in two major industrial incidents in the past four years. A detailed
discussion of HA investigation is presented.
iv
To mom, dad, aka, aaji
and
all my family members in Nagpur
v
ACKNOWLEDGEMENTS
I would like to thank Dr. Sam Mannan for all his guidance and encouragement
during this study and for his invaluable mentorship. I’m grateful to Dr. Rogers for his
contributions to all the projects and for being extremely patient. I would like to thank Dr.
Ford for serving on my committee and allowing me access to his SGI. I would like to
express my appreciation to my committee members: Dr. Dan Shantz and Dr. Michael
Hall.
I learnt a lot from my collaborators and would like to express my gratitude to
individuals I worked with: David Frurip, Sima Chervin, Seshu Dharmavarm, and
Abdulrehman Aldeeb. I would like to thank Dr. Lisa Pérez for her help with theoretical
calculations; she has always been a source of inspiration. I thank the Texas A&M
Supercomputing Facility for computer time and the Laboratory for Molecular Simulation
(LMS) for software and support.
I would like to acknowledge my family members, friends, roommates, former
teachers, and students and staff of the Mary Kay O’ Connor Process Safety Center for
being supportive of my work.
Everyday I promise myself not to commit any faux pas and tell God that I’ve
been good so far; but soon I wake up. Therefore I would like to take this opportunity to
apologize for any misconduct.
vi
TABLE OF CONTENTS
Page
ABSTRACT………………………………………………………………………… iii
DEDICATION……………………………………………………………………… iv
ACKNOWLEDGEMENTS………………………………………………………… v
TABLE OF CONTENTS…………………………………………………………… vi
LIST OF TABLES………………………………………………………………….. viii
LIST OF FIGURES………………………………………………………………… ix
CHAPTER
I INTRODUCTION…………………………………………………….. 1
II EXPERIMENTAL CHARACTERIZATION OF REACTIVE
HAZARDS…………………………………………………………….
4
1. Experimental Techniques…………………………………………... 4 1.1 Thermal Analysis…………………………………………… 4 1.2 Sensitivity Tests……………………………………………. 11
2. Classifying Reactive Hazards………………………………………. 16 2.1 Classification Based on Sensitivity Tests…………………... 17 2.2 Classification Based on Calorimetric Data…………………. 17 2.3 Proposed Classification……………………………………. 21
3. Further Investigation of DSC Parameters to Quantify Reactivity…. 27 3.1 Experimental Data…………………………………………... 29 3.2 Results and Discussion……………………………………… 31
4. Conclusions………………………………………………………… 35
III STRUCTURE BASED PREDICTION OF REACTIVITY
HAZARDS ……………………………………………………………
38 1. Review of the Available Methods…………………………………. 39
1.1 Rules of Thumb……………………………………………. 39 1.2 Oxygen Balance Method………………………………….. 42 1.3 CHETAH…………………………………………………… 43
vii
CHAPTER Page
1.4 CART……………………………………………………… 46 2. Advanced Prediction Techniques…………………………………… 48 3. Application of Transition State Theory for Thermal Stability
Prediction…………………………………………………………… 49
3.1 Model Development……………………………………….. 50 3.2 Experimental Details……………………………………….. 58 3.3 Results and Discussion…………………………………….. 59
4. Correlating Calorimetric Data with Molecular Descriptors……….. 64 4.1 Data Set Selection………………………………………….. 65 4.2 Discussion of a Few Descriptors…………………………… 66 4.3 Correlations………………………………………………… 69 4.4 Correlations Using the Semi-empirical Method, AM1……. 73
5. Conclusions and Future Work……………………………………….. 76
IV DETAILED INVESTIGATION OF A REACTIVE SYSTEM……… 81
1. Background………………………………………………………… 81 2. Ab initio Heat of Formation for HA………………………………. 82
2.1 Computational Methods…………………………………… 84 2.2 Results and Discussion…………………………………….. 87 2.3 Choice of Best Values……………………………………… 91
3. Investigation of Hydroxylamine Runaway Behavior ……………... 95 3.1 Experimental Observations……………………………….. 95 3.2 Theoretical Calculations…………………………………… 96
4. Integrating Reactivity Data and Risk Analysis for Improved Process Design……………………………………………………... 100
5. Conclusions………………………………………………………… 104
V CONCLUSIONS..…………………………………………………….. 105
LITERATURE CITED……………………………………………………………... 107
APPENDIX A……………………………………………………………………... 117
APPENDIX B……………………………………………………………………... 119
APPENDIX C……………………………………………………………………... 120
APPENDIX D……………………………………………………………………... 121
VITA………………………………………………………………………………... 123
viii
LIST OF TABLES
TABLE
Page
1.1 Energies Associated with Typical Reactions…………………………… 2
2.1 Comparison of Available Calorimeters………………………………… 5
2.2 Explosivity Rank ……………………………………………………….. 18
2.3 Instability Rating Based on IPD………………………………………... 20
2.4 Summary of RSST Data for 30 wt % DTBP in Various Solvents……… 25
2.5 Summary of DSC and Sensitivity Data………………………………… 30
2.6 Explosion Propagation vs. Actual Rank………………………………... 36
2.7 Summary of Sensitivity Tests Predictions……………………………… 37
3.1 Functional Groups Indicative of Reactive Hazards…………………… 40
3.2 Oxygen Balance and Hazard Rank……………………………………... 42
3.3 Summary of Heat of Formation and Maximum Heat of Decomposition. 53
3.4 Summary of Experimental and Predicted Values for To (Tonset)………... 60
3.5 Comparison of Onset Temperatures……………………………………. 63
3.6 Onset Temperatures (observed and predicted)………………………... 71
3.7 Experimental Energy of Reaction .…………………………………….. 74
3.8 Summary of Energy of Reaction Values……………………………… 75
3.9 Decomposition Energies for Typical Functional Groups………………. 77
3.10 Typical Values for Energetic Polymerization…………………………... 78
3.11 -∆H, To Values Based on Functional Groups…………………………... 79
4.1 Experimental Heats of Formation (1atm and 298.17 K)……………….. 86
4.2 Summary of Calculated Heats of Formation (∆Hf)…………………….. 88
4.3 Accurate Values for HA Heat of Formation……………………………. 92
ix
LIST OF FIGURES
FIGURES
Page
2.1 A typical DSC run………………………………………………………. 7
2.2 RSST…………………………………………………………………….. 8
2.3 RSST run on 50-wt% hydrogen peroxide………………………………. 8
2.4 APTAC………………………………………………………………….. 9
2.5 APTAC run on 50-wt% hydroxylamine/water system………………… 10
2.6 Gap test………………………………………………………………….. 12
2.7 BAM impact sensitivity apparatus……………………………………… 13
2.8 Koenen test……………………………………………………………… 15
2.9 Time/pressure test assembly…………………………………………….. 16
2.10 Proposed classification for reactive chemicals………………………….. 23
2.11 Heat of reaction and onset temperature for DTBP in various solvents… 26
2.12 Schematic of DSC curves for two energetic materials………………….. 28
2.13 Correlation between UN Gap test and DSC data……………………….. 32
2.14 Relationship between the Koenen test and DSC data…………………... 33
2.15 Relationship between the Time/Pressure test and DSC data…………… 34
3.1 Hazard evaluation output from CHETAH 7.2…………………………... 45
3.2 Hypothesized potential energy surface (PES) for a runaway reaction….. 54
3.3 Comparison of onset temperatures …………………………………… 61
3.4 Predicted onset temperatures……………………………………………. 72
4.1 Systematic approach for assessing reactive hazards……………………. 82
4.2 Deviations from the average heat of formation values for the methods
employed in Table 4.3…………………………………………………...
93
x
Page
4.3 APTAC temperature-time profile for 50 wt% HA……………………… 95
4.4 Probable elementary reactions of HA in presence of Fe2+ …...………… 99
4.5 Fe2+ interacting with the nitrogen atom of HA ………………………… 99
4.6 Fe2+ interacting with the oxygen atom of HA …………………………. 100
4.7 Hydroxylamine production……………………………………………… 102
4.8 Quantitative risk analysis scheme………………………………………. 103
1
CHAPTER I
INTRODUCTION
Hazards posed by chemical reactions have historically received considerable
attention from industries, government agencies, and communities. There have been
numerous publicized incidents related to reactive chemicals.1,2
A typical chemical plant routinely produces, stores, and transports a number of
highly energetic chemicals. However, a few of these chemicals may pose toxic, fire, or
explosion hazards. This work focuses on evaluation of energetic hazards due to chemical
reactions. The release of energy stored within substances can be triggered by
temperature, mechanical impact, shock, or electrostatic energy. Therefore, it is important
to understand the conditions and scenarios leading to rapid release of energy and
consequently explosion.
Based on investigations of past incidents, the U.S. Chemical Safety and Hazard
Investigation Board (CSB) has concluded that reactive hazards are a significant problem3
in the Chemical Process Industry (CPI) and has recommended regulation of reactive
hazards. The state of New Jersey has broadened its Toxic Catastrophe Prevention Act
(TCPA)4 to include reactive chemicals. Also, the Center for Chemical Process Safety
(CCPS) has recently published a book dealing with reactive hazard management.5 Thus
there is increased impetus on managing reactivity within a manufacturing unit and
understanding reactive behavior of chemicals to prevent incidents.
This dissertation follows the style and format of Industrial & Engineering Chemistry Research.
2
The main aim of reactive chemicals legislation is to enforce reactive hazard
assessment. In an informal proposal, CSB has proposed a heat of reaction (-∆H) value of
100 cal/g as a threshold for performing reactive hazard assessment. This is an extremely
conservative criterion. For example, according to this criterion all the substances in
Table 1.1 would be subjected to reactive hazard assessment.
Table 1.1. Energies Associated with Typical Reactions 6
Chemical Reaction Associated Energy (-∆H, cal/g)
Methanol combustion 5430 Rusting of iron 1200
TNT decomposition 1100 Hydrogen peroxide decomposition 700 Ammonium nitrate decomposition 382
Sucrose (table sugar) decomposition 114
The reactive chemical section of the TCPA rule utilizes lists of chemicals and certain
functional groups, along with threshold values, as a trigger to perform reactive hazard
assessment. But neither the New Jersey regulation nor the CSB proposal consider
reaction kinetics.
It is important to point out the extreme difficulty to list properties characterizing
reactivity hazards. For example, commercial explosives are typically characterized by
2000 cal/g or more of energy; however, most of the chemicals leading to incidents in the
chemical industries have energies between 500 and 1500 cal/g. Thus, there are a variety
of reasons, besides the energy content, that can pose chemical reactivity hazards, and
recognizing chemicals and hazardous conditions is an area of considerable research. The
3
objectives of this work are to study the characteristics of reactivity hazards, expedite
hazard assessment, develop guidance for recognizing, and evaluating more hazardous
compositions and thus enable better utilization of resources.
Chapter II discusses experimental characterization of reactive hazards and
proposes a classification to rank reactive hazards. Chapter III highlights the role of
molecular modeling to predict reactive hazards and presents results of molecular
modeling. Chapter IV discusses the hydroxylamine system, as an example of a highly
reactive system.
4
CHAPTER II
EXPERIMENTAL CHARACTERIZATION OF REACTIVE HAZARDS
1. Experimental Techniques
There are a variety of experimental techniques to characterize and quantify
hazards due to chemical reactions. Experimentation provides a better understanding of
the energy content of a substance and its behavior under various conditions. Such
information is extremely useful for assessing reactive hazards and managing risks.
Several popular experimental techniques are discussed in Sections 1.1 and 1.2.
1.1 Thermal Analysis
A reactivity hazard involves conversion of stored chemical energy of the
components into mechanical or heat energy, and it is the uncontrolled release of this
stored energy that causes the damage in a reactive chemical incident. The reactivity of a
substance is normally assessed by performing calorimetric measurements.6 Information
about the amount of energy released and the rate of energy released for a process
chemical can be obtained by performing calorimetric tests. A small amount of the
sample is heated over a range of temperature (usually within 30 oC – 400 oC), and
temperature, pressure, and time data are recorded. This information is then used for
alarm settings, relief sizing, and process modeling. Overall thermodynamics and kinetics
of a reaction can be estimated from temperature-time data obtained from a calorimeter,
and this information is used to identify the material hazards posed by a composition and
risk of potential runaway reactions.
5
1.11Types of Calorimeters
There are various calorimeters available for performing reactive hazard
assessments. Prior to detailed testing, screening tests are performed7 using calorimeters
such as a Differential Scanning Calorimeter (DSC) or the Reactive System Screening
Tool (RSST) from Fauske and Associates (http://www.fauske.com). Such screening tests
are relatively inexpensive and can be performed quickly. Detailed testing can be
performed using other calorimeters such as the Automated Pressure Tracking Adiabatic
Calorimeter (APTAC) from TIAX (http://www.tiax.biz) or the Vent Sizing Package
(VSP) from Fauske and Associates. A comparison of three available calorimeters is
presented in Table 2.1 and a brief discussion of the various calorimeters is provided in
the following paragraphs.
Table 2.1. Comparison of Available Calorimeters
Calori- meter
Capital Cost
Time for a run
Sample size
Scanning Rate
(oC/min)
Data obtained
Comments
DSC 1 $ 1 hr 1-10 mg 10 T vs. time
Popular method to screen
reactive hazards
RSST 1.5/2 $ 6 hrs Up to 10 ml 1-5 T,P vs.
time
Open cell; data can be used for
relief sizing
APTAC / VSP 5 $
12-16 hrs
Up to 130 ml 1-2
T,P vs. time
Maintains adiabatic
conditions; maintenance
intensive
6
DSC
A DSC run can provide an overall indication of exothermic activity of the
composition being tested and can help assess potential reactive hazards. In a DSC, a
sample and a reference are subjected to a continuously increasing temperature and heat
is added to the reference to maintain it at the same temperature as the sample. This added
heat compensates for the heat lost or gained as a consequence of an overall endothermic
or exothermic reaction. When the rate of heat generation (Watts) in the sample exceeds a
particular value, the heat supply to the sample is cut off and this additional heat gain is
attributed to exothermic activity within the sample. This cut-off value depends on the
sensitivity of the particular instrument. For an exothermic reaction, a heat vs. time curve
exhibits a peak as shown in Figure 2.1. A base line is constructed from the initial heating
mode, and another line is drawn to coincide with the initial rise due to the exotherm. The
temperature, at the intersection of the two lines is called the onset temperature and
corresponds to a detectable level of heat due to a chemical reaction. The detected onset
temperature is thus a measure of the reaction kinetics and serves as a guideline for
selecting process or storage temperature. The energy released (-∆H) during the process is
calculated as the area under the heat-supplied (Watts) and time curve. DSC is a popular
screening tool because it is safer, since it involves a small amount of sample (1-10 mg),
and is faster, since with 10 oC/min scanning rate, a DSC run can be completed in an
hour. Normally, during a DSC experiment, pressure data are not recorded.
7
Figure 2.1. A typical DSC run.
RSST
The RSST uses a 10-ml sample cell contained in an open, well-insulated glass
test cell. A cross-section of the RSST is shown in Figure 2.2. The RSST is a ramping
calorimeter and ramps the temperature of the sample at a fixed rate using an electric
heater. It allows scanning rates up to 2 oC/min and can generate temperature, pressure,
and time profiles. Output from the RSST for 50 wt% hydrogen peroxide-water system is
illustrated in Figure 2.3. The RSST is used for screening reactive hazards, since it
provides temperature, pressure vs. time data at a moderate cost compared to the APTAC
or VSP.
Baseline Onset temperature (To)
Temperature
Hea
t sup
plie
d (W
)
8
Figure 2.2. RSST.
0
50
100
150
200
250
300
Time (min)
0
50
100
150
200
250
300
350
400
450
500
Figure 2.3. RSST run on 50 wt% hydrogen peroxide.
Sample cell
Container vessel
Temperature
Pressure
9
APTAC
The DSC and the RSST, discussed earlier, are quasi-adiabatic calorimeters, since
the sample cell losses heat to the surroundings. Adiabatic calorimeter minimizes the heat
loss to the surrounding by maintaining the surrounding temperature as close to the
sample temperature, and has proven to be an extremely useful tool to assess thermal
hazards. Following the screening tests, detailed measurements are generally performed
for more hazardous compositions using an adiabatic calorimeter such as the Automated
Pressure Tracking Adiabatic Calorimeter (APTAC). A cross-section of the APTAC is
shown in Figure 2.4 and a typical output is illustrated in Figure 2.5.
Figure 2.4. APTAC.
Reaction vessel Side
Stirrer Pressure
vessel
Top
Bottom
heater
Tube heater
10
The APTAC can be operated in a variety of test modes, such as heat-wait-search,
heat-ramping, and isothermal. If the self-heat rate of the sample is greater than a preset
threshold (0.1 °C/min), the apparatus tracks the reaction adiabatically until the reaction
is over or if one of the shutdown criteria is met. If no exotherm is detected, the sample is
heated to the next search temperature and the steps are repeated until one of the shut-
down criteria is met. Besides the temperature, the pressure outside the sample cell is
controlled to match the pressure inside the sample cell.
Figure 2.5. APTAC run on 50 wt.% hydroxylamine-water system
Hydroxylamine decomposition test
0
50
100
150
200
250
300
400 600 800 1000 1200 1400 1600
Time (min)
Onset TemperatureTo
Maximum TemperatureTmaxStep Heating
Wait
Search
Adiabatic Mode Begins
Adiabatic Mode Ends
11
1.2 Sensitivity Tests
Calorimetric tests capture temperature-time response of a substance and are
performed to detect thermal instability. However, the energy stored within a substance
can be released by a variety of stimuli. Sensitivity is defined as the ease with which a
substance subjected to external stimuli, such as shock, impact or heat, can undergo
detonation.8 A few of the techniques used to determine sensitivity9 of a material are
discussed below.
1.21 Shock Sensitivity10
The Gap test determines initiation of an explosion of a substance due to
detonation in the vicinity. Two cartridges of the smallest commercially manufactured
diameter are coaxially attached on a rod made of soft iron, wood, or plastic, as illustrated
in Figure 2.6. The gap value is the distance between the two cartridges. The gap medium
is such that it stops flying particles and direct heat transmission completely, thus serving
as a heat filter. Consequently, the shock wave is the only energy transmitted to the
substance being tested. The donor charge is a well-characterized explosive, for example
50 g RDX, that generates a known pressure wave (shock wave), and is set off during the
test. The resulting shock wave, generated during this explosion, is transmitted to the
testing material and may trigger a detonation.
12
Figure 2.6. Gap test.10
Detonation in the test sample is verified on the basis of observed mechanical effects. The
test results, based on degree of fragmentation observed, are typically reported as follows:
‘Yes’ or ‘+’ Tube completely fragmented or fragmented at both ends
‘Partial’ Tube only fragmented at booster end but fragmented length is more
than 1.5 times the average fragmented length found with an inert
material.
‘No’ or ‘−’ Fragmented length is less than 1.5 times the fragmented length with
an inert substance.
1.22 Impact Sensitivity11
During impact tests, the impact of a drop-weight on a substance is assessed. The
sample, placed between two flat, parallel, hardened steel surfaces, is subjected to an
impact by dropping a weight. The impact may result in initiation depending on
sensitivity of the material, weight mass, and its drop height (impact energy). Initiation is
13
observed by sound, light effects, or smoke, or by inspection. The BAM impact
apparatus, known to give fairly reproducible results, is shown in Figure 2.7. Typically
drop weights having a mass of 1, 2, 5, or 10 kg are used and the lowest impact energy
required to create a detonation is recorded. Thus drop-weight and drop-height at which
the initiation of the sample occurs are the main parameters determined from impact
testing. The drop height at which detonation is observed is thus a measure of impact
sensitivity of an explosive.
Figure 2.7. BAM impact sensitivity apparatus.11
1. Guiding rods 2. Locking and unlocking devices 3. Drop weight 4. Calibrated scale 5. Indented rod 6. Piston device 7. Anvil 8. Steel block 9. Steel Base
14
1.23 Heat Sensitivity10
Heat sensitivity tests, such as Koenen and time/pressure, are performed to assess
the role of heat in initiation of explosives.
Koenen test
The Koenen test measures the effect of strong heating under confinement. The
test sample is contained in a drawn steel tube (27 ml) equipped with a closure, which
allows orifice plates with various apertures of diameter 1.0, 1.5, 2.0, 2.5, 3.0, 5.0, 8.0,
12.0, or 20.0 mm. The tube is heated with four calibrated propane burners. The result
reported from such a test is the largest size orifice at which the tube is fragmented, and
the following guidelines are used for reporting:
‘Violent’ Limiting diameter greater than or equal to 2.0 mm.
‘Medium’ Limiting diameter is 1.5 mm.
‘Low’ Limiting diameter is equal to or less than 1 mm but an effect is observed on
the tube.
‘No’ Limiting diameter is less than 1 mm and in all tests the tube is unchanged.
A schematic of the apparatus used for performing Koenen tests is shown in Figure 2.8.
15
Figure 2.8. Koenen Test.
Time/Pressure test
This test measures the ability of a material to deflagrate under confinement. A 5
g sample is subjected to a flame in a pressure vessel (20 ml) fitted with a pressure
recording device and a bursting disc (2200 kPa). Based on the shortest time in three runs
for the pressure to rise from 690 to 2070 kPa, test results are classified as follows:
‘Rapid’ Time is less than 30 ms.
‘Slow’ Time is 30 ms or more.
‘No’ A gauge pressure of 2070 kPa is not achieved.
A schematic of assembly used for the time/pressure test is shown in Figure 2.9.
Nozzle
Burner
Sample test tube
16
Figure 2.9. Time/Pressure test assembly.
Sensitivity tests typically require more sample, elaborate testing facilities, and
are more expensive than calorimetric tests. The next section discusses hazard
classification of substances based on sensitivity tests, calorimetric tests, and
interrelationship between the two.
2. Classifying Reactive Hazards
Based on tests discussed in the earlier section, researchers have attempted to
develop a classification to enable ranking of chemicals based on material hazards. Such
a ranking can help can help to develop guidelines for handling, storage, and
transportation of materials.
Burst Disc
Sample (5 g.)
Pressure Transducer
Ignition system
17
2.1 Classification Based on Sensitivity Tests
Table 2.2 provides an explosivity-ranking scheme based on the three
recommended UN sensitivity tests, namely Gap, Koenen, and time/pressure. It is
identical to that used by Whitmore12, except this scheme gives precedence to the UN
Gap result over the BAM 50/60. Ranks A and B identify potential Class 1 substances:
“A” indicates substances that detonated, and “B” indicates those substances that did not
detonate but were strongly positive in the Koenen and/or Time/Pressure tests. Rank C
substances, which had milder results in the Koenen and Time/Pressure tests, are not
Class 1 but are candidates for classification as Self-Reactives or Organic Peroxides.
Rank D substances exhibited no positive results but may still be Self-Reactives or
Organic Peroxides, based on the results of the other recommended tests. This
classification is popular for categorizing substances for transportation.
2.2 Classification Based on Calorimetric Data
Unlike sensitivity tests, hazard classification based on calorimetry is not
well-established. There is disagreement among researchers regarding parameters
characterizing reactive chemicals. A part of the problem is that results from calorimetric
studies are highly dependent on the calorimeter and other conditions during the
experiment. The remainder of this chapter discusses approaches for developing a hazard
classification and associated issues.
18
Table 2.2. Explosivity Rank
Explosivity Rank
Severest Class 1 Property Correspondence to UN Classification
A Detonates (positive result in UN Gap, or BAM 50/60 or TNO 50/70 if UN Gap unavailable)
Potentially Class 1
B Heating under confinement: Violent (Koenen limiting diameter >2 mm), and/or Deflagration: Rapidly (pressure in Time/Pressure >2070 kPa in <30 ms)
Potentially Class 1, but does not detonate
C Heating under confinement: Medium or Low (Koenen limiting diameter <1.5 mm), and/or Deflagration: Slowly (pressure in Time/Pressure >2070 kPa in >30 ms)
Not Class 1
D No effect of heating under confinement, and does not deflagrate (pressure rise in Time/Pressure <2070 kPa)
No explosive properties with respect to transport classification
As discussed in Section 1, calorimetry or thermal analysis techniques represent
temperature, pressure vs. time behavior of a substance. From the temperature-time data,
the energy released (-∆H) during the process is calculated using the following formula:
)( max op TTmCH −Φ=∆−
where
p
ppss
mC
mCCm +=Φ – Phi factor
ms – Mass of the sample cell
19
Cps – Heat capacity of the sample cell
m – Mass of the sample
Cp – Heat capacity of the sample
Tmax – Maximum temperature attained by the sample during the reaction
From the temperature-time data, the rate constant for the reaction is obtained using the
following formula13:
( )o
n
o
TTTTTT
dtdT
k
−
−−
=
maxmax
max
where
n – order of the reaction
Thus, the overall thermodynamics and kinetics of a reaction can be estimated from
temperature-time calorimetric data.
The National Fire Protection Association (NFPA) recommends a classification
for intrinsic thermal instability14 of a substance based on Instantaneous Power Density
(IPD), which is defined as
RateHIPD *∆−=
RTEordero AeACHIPD /*** −∆−=
where
-∆H – enthalpy of reaction (cal/g)
Rate – Rate of reaction = A*exp(-EA/RT)*Coorder (g/ml s)
A – Arrhenius pre-exponential factor
20
EA – Activation energy
Co – Initial concentration of the material
R – Gas constant
Therefore IPD has units of W/ml, and the rate of reaction can be obtained from
calorimetric data. Based on the IPD, the classification illustrated in Table 2.3 is applied
for rating thermally unstable compounds.14
Table 2.3. Instability Rating Based on IPD
Instability Rating IPD at 250 oC
W/ml
Decomposition
initiation temperature (oC)
4 IPD ≥1000
3 100 ≤ IPD < 1000
2 10 ≤ IPD < 100 < 200
1 0.01 ≤ IPD < 10 200 ≤ IPD < 500
0 < 0.01 < 500
As an example, the IPD is calculated for the following system14:
Enthalpy of decomposition (-∆H) : -80.5 cal/gm
Arrhenius activation energy (EA) : 36.4 kcal/mol
Arrhenius pre-exponential (A) : 1.6 * 1015 /s
Reaction order : 1
Initial concentration or density of pure material: 0.8 g/ml
IPD = 0.8 * 1.6 * 1015*e {-36400/1.987*(250+273)}* 4.184 (W/ml)
= 270 W/ml
21
Thus this material is given an instability rating of 3.
The calculation of IPD is sensitive to the activation energy (EA) values. For
example, if the EA value were to differ by 5 % and be 34.6 kcal/ml instead of 36.4
kcal/mol, the IPD value would increase to 1813 W/ml and the instability rating of the
material would be 4.
2.3 Proposed Classification15
Although the calculation of IPD appears intuitive, it is difficult to obtain accurate
kinetic parameters based on calorimetric data. Because the calculation of kinetic
parameters requires additional work for the user and can be time consuming; a goal of
this work is to provide an easy method for classification.
2.31 Thermodynamic Parameter
The net energy released during reaction is a measure of stored potential energy of
the system. Therefore heat of reaction (-∆H) is recommended as one of the parameters
for characterizing energetic materials. The lower this energy the less energy that is
available for detonation.
2.32 Kinetic Parameter
The temperature at which a system first exhibits exothermic activity is called the
onset temperature (To) and denotes a rate of a chemical reaction significant enough to be
measured by the calorimeter. The detected onset temperature is thus a measure of the
reaction kinetics. Although there is considerable argument over its interpretation16 for
selecting appropriate process temperatures, the onset temperature is an important
parameter at the screening level of testing. In this regard, Ando et al. have proposed that
22
onset temperature be used as a parameter to classify reactive chemicals.17 Heat of
reaction is representative of the energy release potential of a substance and the onset
temperature is a measure of the rate of energy release, therefore these two parameters
can be combined to develop a hazard index. The onset temperature (To) and heat of
reaction (-∆H) can be easily determined from the temperature-time data.
Based on the above discussion, the reactive chemicals can be divided into the
following four classes, as shown in Figure 2.10:
1. Class I: These compounds react at low temperatures liberating a large amount of
heat.
2. Class II: Compounds react with significant heat release at higher temperatures.
3. Class III: Compounds react at low temperatures, similar to compounds in Class I, but
are more exothermic than chemicals in Class I.
4. Class IV: Chemicals react at higher temperatures and are mildly exothermic.
Thus, reactive hazards decrease from Class I to IV. The most hazardous chemicals are in
Class I, since they decompose at lower temperatures and release large amounts of heat.
These are also the chemicals that are more likely to decompose violently and should be
carefully handled and thoroughly tested. Chemicals in Class II lie in the high hazard
category since they release large amounts of energy, but chemicals in Classes III and IV
pose medium and low risk, respectively. It should be noted that by neglecting pressure
effects, this classification scheme could miss mildly exothermic but pressure generating
reactions.
23
Figure 2.10. Proposed classification for reactive chemicals.
2.33 Choice of Critical Values
The classification places rigid boundaries based on values for onset temperature
and heats of reaction. These rigid boundaries can be avoided by the use of fuzzy logic to
define the bounds, however our aim is to demonstrate a basis for reactive chemical
classification. With the static limits choices of threshold values are subject to judgment,
and choices of these values are discussed below.
A value of 200 oC is recommended for the critical onset temperature To,critical.
This value is in agreement with the NFPA intrinsic thermal stability rating, which
Hea
t of r
eact
ion
(-∆
H)
Onset temperature (To)
High -∆H, Low To
Low -∆H, Low To
Low -∆H, High To
High -∆H, High To
To,critical
-∆Hcritical
I
III IV
II
Very High Hazard High Hazard
Medium Hazard Low Hazard
Curve distinguishing detonating or deflagrating compounds (Explosion Potential line)
24
classifies materials that exhibit adiabatic exothermic initiation temperatures below 200 oC as more hazardous and specifies a hazard rank of 2.
The ASTM CHETAH program18 calculates the maximum heat of decomposition
based on the heat of formation, and if the maximum heat of decomposition is more
exothermic than -2.929 kJ/g it classifies the material as hazardous. Thus – 3 kJ/g (~ 700
cal/g) can be selected as a critical threshold value for the heat of reaction, ?Hcritical.
It is important to realize that DSC data are not explicitly indicative of possible
detonation or deflagration hazards. Previous research has shown that the boundary
between explosion propagation can be represented by the following equation 19:
log(QDSC) = 0.38 log(TDSC – 25) + 1.67
Rearranging the above equation, one can define a variable EP such that,
Explosion Potential (EP) = log(QDSC) - 0.38 log(TDSC – 25) - 1.67
where
QDSC – Heat of reaction, -∆H, (cal/g)
TDSC – Extrapolated onset temperature, (oC)
Substances with EP > 0, are considered to have potential to explode, either by detonation
or deflagration. The above equation for EP further strengthens the argument that onset
temperature (To) and heat of reaction (-∆H) are key parameters for hazard classification.
The EP equation can be used to define a boundary to separate compounds or
compositions that can undergo detonation or deflagration as indicated by the dotted line
in Figure 2.10. This is a more natural classification, than the classification based on rigid
boundaries and one can envision a family of curves, similar to the ones shown in Figure
25
2.10 for categorizing reactive hazards. An application of this classification is discussed
in the next section.
2.34 Application of Proposed Classification for Screening Reactive Hazards20
It is commonly emphasized to perform detailed analyses on the more reactive
systems. However there is no common consensus among researchers on the attributes of
a system that qualify it for a more sophisticated testing. The classification proposed
earlier can be used as a screen for recognizing more hazardous compositions. For
example, if a compound is categorized as Class I or II, further testing is entailed. This
approach is illustrated based on RSST data obtained for 30 wt % di-tert-butyl peroxide
(DTBP) in the nine organic solvents summarized in Table 2.4.
Table 2.4. Summary of RSST Data for 30 wt % DTBP in Various Solvents
Sr. no. Solvent Tonset Tmax (dT/dt)max (dP/dt)max Heat of reaction BDE
oC oC oC/min psi/min cal/g kcal/mol
1 methanol 117 180 10 7 126 33.7 2 chlorobenzene 120 260 1000 1000 117 33.8 3 n-butylamine 125 230 220 400 167 33.8 4 t-butanol 130 200 15 18 163 33.8 5 n-butanol 130 210 43 33 160 33.8 6 cyclohexane 133 240 300 633 113 37.2 7 toluene 135 250 700 900 153 37.4 8 tetrahydrofuran 135 243 425 1000 170 36.3 9 acetone 138 205 35 65 185 36.1
26
A plot of heat of reaction vs. Tonset for DTBP in the nine solvents, Figure 2.11,
indicates that all the compositions lie in Class III, according to the proposed
classification. These results suggest that significant decomposition of 30 wt % DTBP in
organic solvent can be initiated at temperatures lower than 200 oC, but the heat released
during the reaction is much less than the heat released during TNT decomposition.
Based on the tests carried out at the screening level, detailed testing of these mixtures
may not be necessary unless the operating temperature is greater than ~100 oC.
0
20
40
60
80
100
120
140
160
180
200
115 120 125 130 135 140
Tonset (oC)
Figure 2.11. Heat of reaction and onset temperature for DTBP in various solvents.
Thus the proposed classification, based on To and -∆H provides a powerful tool to
recognize the hazardous compositions. The next section presents results of our study
aimed at improving prediction of sensitivity tests from calorimetry data and thereby
identify parameters to refine the existing classification.
27
3. Further Investigation of DSC Parameters to Quantify Reactivity21
Domestic and international requirements mandate classification of hazardous
chemicals as a prerequisite for their transport. The interrelationship of DSC and shock
sensitivity data, represented by the Explosion Potential (EP) equation, suggests that there
may be an intrinsic correspondence of mechanism for detonation of energetic materials
initiated by different stimuli. Because DSC experiments are non-destructive, relatively
inexpensive, and utilize a small amount of sample, it is worthwhile to develop
correlations to predict sensitivity information from DSC data. These correlations can
also be used to predict energy release potential of substances and eventually serve as a
guide for development of a better classification.
Bodman22 recently investigated the interrelationship between To ,-∆H and
sensitivity tests with the aim of improving the EP Equation and proposed the following
correlation:
Explosion Potential (EP’) = log (-∆H) - 0.44 log(DSC To-25) – 2.11.
It is worth noting that the proposed relationships fail to identify all of the
detonating compounds, and further research is needed to develop more robust
correlations.
Onset temperature is a single point on a DSC curve and by including more
information from the thermal analysis curve a better correlation can be obtained. A
schematic of DSC runs on two energetic materials is illustrated in Figure 2.12. The DSC
peak for an energetic material that decomposes violently, in this case compound 2, is
much narrower than for a less energetic material, compound 1. In principle, the two
energetic materials can have comparable heats of reaction, calculated as area under the
28
curve but different peak shapes depending on the rate of energy release. For example, an
extremely narrow peak indicates a rapid release of energy and consequently possible
explosive behavior. From a safety viewpoint, the rate of release is extremely important
and therefore heat of reaction alone is not a sufficient measure for a realistic reactive
hazard assessment. Other parameters such as peak height, peak width, and aspect ratio
obtained from DSC curve are utilized to investigate relationship between the thermal
data and explosion behavior of a substance.
Figure 2.12. Schematic of DSC curves for two energetic materials.
When other parameters were included from peak shape analysis, our results
indicate that DSC parameters correlate effectively with the UN tests. The methodology
of this research is discussed below.
Temperature
Hea
t sup
plie
d )
Onset temperature
Compound 1
Compound 2
29
3.1 Experimental Data
DSC data on various compounds listed in Table 2.5 was obtained from Eastman
Kodak Company, Rochester, NY. Standard DSC experiments were conducted using a
TA Instruments Model 2920 calorimeter. A sample of ∼1 mg was sealed under nitrogen
in a glass capillary23, placed in a silver cradle, and heated in scanning mode at 10°C/min
from 25 to 420°C. The instrument was calibrated using a dedicated 1 mg indium
standard in a glass capillary at 10°C/min. The TA2920 DSC computer automatically
updated the cell constant, onset slope, and temperature correction factors. One DSC
scan was conducted for each of the 22 substances that are candidates for Class 1 testing
based on the UN Recommendations.
The test results from the three recommended UN Class 1 methods, listed in
Table 2.5, were acquired for the 22 substances from a number of sources and, therefore,
were generally run on different samples than those used for the DSC experiments, which
were conducted over a substantial period of time. The methods used were the UN Gap
Series 1(a) for detonation, Koenen for heating under confinement, and Time/Pressure for
deflagration. Results of the BAM 50/60 Steel Tube and TNO 50/70 Steel Tube tests,
which are considered to be reliable Class 1 detonation methods24, were used as
surrogates for the UN Gap test when the UN Gap results were not available.
30
Table 2.5. Summary of DSC and Sensitivity Data
Sr. no. Material
DSC, To
DSC, -∆H
Aspect ratio -∆H/To -∆H /To0.5 UN Gap Koenen
Time/ Pressure
oC J/g W/g oC
1 2,4-Dinitrophenyhydrazine
275 3381 3.38 12.3 203.9 Yes+ Violent NA
2 2,4-Dinitrotoluene 345 3529 75.15 10.2 190.0 Yes+ Medium Slow
3 4-Nitrophenylhydrazine 100%
255 2377 0.34 9.3 149.0 Yes Violent Rapid
4 3,5-Dinitrobenzoic acid 383 2909 4.48 7.6 148.6 Yes Low NA
5 2-Bromo-2-nitropropane-1,3-diol
209 2154 3.25 10.3 149.0 Yes+ Low No
6 2,2’-Dithiobis(4-methyl-5-nitrothiazole)
223 2221 0.89 10.0 148.7 Yes Medium Slow
7 Benzoyl peroxide 100% 107 1211 0.50 11.3 117.1 Yes+ Violent Rapid
8 Benzoyl peroxide 70% with H2O
104 908 0.21 8.7 89.0 Yes (No+)
Violent Rapid
9 2-Chloro-5-nitrobenzoic acid
366 1722 1.16 4.7 90.0 Yes Medium No
10 t-Butyl peroxybenzoate 124 1333 0.15 10.8 119.7 No+ Violent Slow
11 2-Diazo-1-napthol-5-sulphochloride
133 859 0.30 6.5 74.5 No+ Violent NA
12 4-Nitrophenylhydrazine 76% with H2O
244 2224 0.18 9.1 142.5 No Medium No
13 2-Amino-4-chloro-5-nitrophenol
225 1685 10.39 7.5 112.3 No Low Slow
14 Di-t-butyl peroxide 161 1253 0.63 7.8 98.8 No+ No Slow
15 1-Phenyl-5-mercapto tetrazole
159 1235 5.83 7.8 97.9 No++ Low Slow
16 Organic perchlorate # 1 224 1240 0.09 5.5 82.9 No Low No
17
Benzenediazonium, 2-methoxy -4-(phenylamino)-, sulfate (1:1)
178 832 2.43 4.7 62.4 No Low No
18 3-Nitrobenzenesulfonic acid sodium salt
368 1099 2.99 3.0 57.3 No No Slow
19 Malononitrile 276 1848 4.43 6.7 111.2 No No No 20 Organic perchlorate # 2 229 1465 0.07 6.4 96.8 No No No 21 Dilauroyl peroxide 88 721 0.13 8.2 76.9 No+ No No 22 3-Thiosemicarbazide 176 908 0.24 5.2 68.4 No No No
+BAM 50/60, ++TNO 50/70 instead of UN Gap
31
3.2 Results and Discussion
Earlier correlations failed to recognize a few of the Class A compounds. As
suggested above, additional information from calorimetric data, besides the onset
temperature and decomposition energy, should correlate more effectively with the UN-
recommended tests. The following parameters were obtained for each compound from
DSC experiments:
1. Decomposition energy (∆H or E, J/g)
2. Extrapolated onset temperature, (To, oC)
3. Peak height (W/g)
4. Peak width, at half the peak height (oC)
5. Aspect ratio (peak height/peak width at half peak height)
6. Initial slope (W/g/oC)
7. Maximum slope (W/g/oC)
Various combinations of the above set of variables were used to investigate the
correlation among DSC data and UN tests (Gap, Koenen, and Time/Pressure)
individually. A possible relationship was investigated by employing one of the above
parameters in combination with decomposition energy, which was employed for all the
trials. No more than two parameters were used during a trial, except for the proposed
correlation for UN Gap test. A visually satisfactory separation of data points on the
graphs was considered an acceptable solution. An energy threshold of 500 J/g is
employed for all the correlations, and any composition with energy less than 500 J/g is
not considered to be in Class 1.
Correlations among UN tests and DSC data, based on this analysis, are discussed
below:
32
3.21 Gap Test
For the Gap test, it was found that ∆H/To0.5 and the aspect ratio, obtained from
the DSC data, separated the detonating compounds (“Yes” on the Gap test), as shown in
Figure 2.13. The decomposition energy is a measure of the heat content of a system and,
therefore, the energy available for detonation. A lesser onset temperature is indicative of
faster kinetics and, consequently, a more rapid energy release for high energetic
materials.
The aspect ratio (peak height/peak width) represents the decomposition behavior
of a substance. For an ideal explosive, the peak height would be infinite and the peak
width would be zero, and therefore the higher the aspect ratio, the higher the tendency
for a violent decomposition. Compounds having ∆H/To0.5 > 88 J/g oC0.5 and aspect ratio
> 0.2 W/g oC are expected to exhibit a positive Gap test.
10
100
1000
0 0 1 10 100
Aspect ratio (W/g oC)
∆
Yes
No
y = 88
x = 0.2
Figure 2.13. Correlation between UN Gap test and DSC data
33
3.22 Koenen test
The onset temperature and heat of reaction, as shown in Figure 2.14, yielded
optimum separation for compounds exhibiting “Violent” behavior on the Koenen test.
Based on limited data set, it is proposed that compounds above the line, ∆H = 12.4 To –
796, are expected to exhibit a violent behavior on the Koenen test. Thus a Koenen
potential (KP) can be defined,
KP = ∆H – (12.4 To – 796)
such that if KP > 0, then the compound will display a violent behavior on the Koenen
test.
0
500
1000
1500
2000
2500
3000
3500
4000
0 50 100 150 200 250 300 350 400 450
To(oC)
∆
Violent
Medium
Low
No
y = 12.4 x - 796
Figure 2.14. Relationship between the Koenen test and DSC data.
34
3.23 Time-pressure
As seen from Figure 2.15, a ∆H/To ratio of 8 (J/g oC) separates the compounds
exhibiting rapid time-pressure behavior.
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Serial no. of compounds listed in Table 2.5
∆
Rapid
Slow
No
y = 8
Figure 2.15. Relationship between the Time/Pressure test and DSC data.
Based on the above recommendations, the predicted class are listed in Table 2.6. It is
apparent that by applying the proposed correlations, unlike previous correlations, all of
the Class A and B compounds can be identified. The correlations proposed in this work
screen out 5 of the 11 Class C and D compounds and all of the Class A and B
35
compounds. A summary of the predictions using earlier correlations and this work is
summarized in Table 2.7.
UN-recommended tests for transportation are time consuming and expensive.
Earlier researchers have proposed correlations to predict UN test outcomes using
parameters from DSC data, such as onset temperature and heat of reaction. Based on the
above correlations, DSC data can be used effectively to recognize Class 1 compounds.
Therefore, these correlations can be employed as a screening tool to reduce testing and
focus resources on more hazardous chemicals.
4. Conclusions
Various experimental techniques are available for characterizing reactive
hazards, such as sensitivity tests and thermal analysis. A classification, based on To and
-∆H obtained from calorimetric data is proposed to facilitate ranking of reactive
chemicals. Although it is true that criteria utilizing multiple parameters, such as
pressure change and rate of heat generation, obtained from calorimetric data would lead
to a better classification scheme, but the main aim was to establish a basis for
classification. By neglecting pressure effects, the classification scheme could miss
mildly exothermic but pressure generating reactions. The pressure criterion was not
included because DSC is often employed to gather data and it does not gather pressure
vs. time data. The correlations discussed in Section 3 of this Chapter guide the selection
of parameters for classification. For example, the aspect ratio correlates well with the
Gap test, a measure of explosive tendency of a material and is therefore a potential
candidate for refining the proposed classification. Since the sensitivity tests are
typically more resource consuming, correlations among DSC and sensitivity tests, can
serve as an effective tool for screening compounds for sensitivity testing.
36
Table 2.6. Explosion Propagation vs. Actual Rank
Sr. no.
Material Predicted Class
Explosion Propagation
Actual Class
UN Gap
Koenen Time/ Pressure
EP19 EP’22
1 2,4-Dinitrophenyhydrazine A 0.33 0.36 A Yes+ Violent NA 2 2,4-Dinitrotoluene A 0.30 0.33 A Yes+ Medium Slow 3 4-Nitrophenylhydrazine 100% A 0.20 0.24 A Yes Violent Rapid 4 3,5-Dinitrobenzoic acid A 0.20 0.23 A Yes Low NA
5 2-Bromo-2-nitropropane-1,3-diol A
0.18 0.22 A Yes+ Low No
6 2,2’-Dithiobis(4-methyl-5-nitrothiazole) A
0.18 0.22 A Yes Medium Slow
7 Benzoyl peroxide 100% A 0.06 0.13 A Yes+ Violent Rapid
8 Benzoyl peroxide 70% with H2O A
-0.05 0.01 A Yes (No+) Violent Rapid
9 2-Chloro-5-nitrobenzoic acid A -0.02 0.01 A Yes Medium No 10 t-Butyl peroxybenzoate B 0.07 0.13 B No+ Violent Slow
11 2-Diazo-1-napthol-5-sulphochloride B
-0.13 -0.07B No+ Violent NA
12 4-Nitrophenylhydrazine 76% with H2O B 0.18 0.23 C No Medium No
13 2-Amino-4-chloro-5-nitrophenol A 0.06
0.10 C No Low Slow
14 Di-t-butyl peroxide A -0.01 0.05 C No+ No Slow 15 1-Phenyl-5-mercapto tetrazole A -0.01 0.04 C No++ Low Slow 16 Organic perchlorate # 1 C/D -0.07 -0.03 C No Low No
17 Benzenediazonium, 2-methoxy-4-(phenylamino)-, sulfate (1:1)
C/D -0.20 -0.15 C No Low No
18 3-Nitrobenzenesulfonic acid sodium salt C/D -0.21
-0.19 D No No Slow
19 Malononitrile A 0.06 0.10 D No No No 20 Organic perchlorate # 2 C/D 0.00 0.04 D No No No
21 Dilauroyl peroxide B -0.12 -0.05 D No+ No No
22 3-Thiosemicarbazide C/D -0.16 -0.11 D No No No
+BAM 50/60, ++TNO 50/70 instead of UN Gap, Bold EP and EP’ values indicate incorrectly categorized Class A and B compounds
37
Table 2.7. Summary of Sensitivity Tests Predictions
A further advancement to reduce experimentation and expedite hazard evaluation
is prediction of experimental data using computational techniques, which is discussed
in the next chapter.
Yoshida19 Bodman22 This work
Number of Class A and B compounds successfully categorized
8/11 10/11 11/11
Number of Class C and D compounds successfully screened 7/11 5/11 5/11
38
CHAPTER III
STRCUTURE BASED PREDICITION OF REACTIVITY HAZARDS
As discussed earlier, a reliable experimental technique for assessing reactivity is
calorimetric analysis, which can be resource consuming and thus possible only for a
limited set of compounds. A computational screening tool can reduce experimentation
and screen out benign compounds. This chapter provides a brief review of computational
methods that can be employed quickly to estimate reactive hazards and a description of
efforts to develop methods for predicting calorimetric data. A goal of this research is to
develop a computerized program for screening reactive hazards.
Generally, rules of thumb based on prior experience and chemical knowledge are
used for screening and estimating reactive hazards of compounds. For example, the
presence of a ‘nitro’ group is regarded as an indicator of potential energy, as in
trinitrotoluene (TNT). Attempts have been made to develop a generalized framework for
estimating reactive hazards based on molecular structure, such as the oxygen balance
method25, Chemical Thermodynamic and Energy Release Evaluation (CHETAH)18, and
Calculated Adiabatic Reaction Temperature (CART).26 A brief description of these
methods is provided in Section 1 of this chapter. The above methodologies have
limitations, and considerable chemical intuition and experience are required for their
effective use. Also, the reliability of estimations for a range of compounds and process
conditions varies significantly.27 Sections 2 through 5 of this chapter discuss
Part of this chapter is reprinted with permission from, “Prediction of reactive hazards based on molecular structure”, by S.R. Saraf, W.J. Rogers, and M. Sam Mannan, 2003, J. Hazardous Materials, A98, 15-29. Copyright 2003 by the name of Elsevier. Part of this chapter is reprinted with permission from “Application of transition state theory for thermal stability prediction”, by S.R. Saraf, W.J. Rogers, and M. Sam Mannan, 2003, I & EC Res., 42, 1341. Copyright 2003 by the name of American Chemical Society (ACS).
39
improvements and advancements in predictive techniques for reactive hazard
assessment.
1. Review of Available Methods
This section reviews some popular methods for reactivity hazard evaluation,
including their strengths and limitations, and it attempts to provide the reader with
enough information to choose a method for a particular application. Some of these
methods have been reviewed previously.26
1.1 Rules of Thumb
The presence of certain functional groups is considered an indicator of reactivity.
This is the simplest possible reactivity screening method and serves as a guideline for
further analysis. For example, chemicals containing the following functional groups can
be considered potentially reactive:
-NO2 : organic nitro compounds
-O-O-, -O-OH : organic/inorganic peroxide and hydroperoxide compounds
-C C- : triple bonded carbon atoms as in acetylene and acetylenic compounds
A comprehensive summary of reactive groups can be found in Bretherick’s handbook28,
and a few of the reactive groups are summarized in Table 3.1.
40
Table 3.1. Functional Groups Indicative of Reactive Hazards 4
Groups containing Carbon -C≡C- Acetylenic compounds -C≡C-M Metal acetylides -C≡C-X N=N C
Haloacetylene derivatives Diazirines
-CN2 Diazo compounds -C-N=O, -N-N=O Nitroso compounds -C-NO2 Ar-NO2, Ar(NO2)n C(NO2)n O2NC-CNO2 HC[OCH2C(NO2)3]3, C[OCH2(NO2)3]4
Nitroalkanes, C-nitro and Nitroaryl and Polynitroaryl compounds Polynitroalkyl compounds Trinitroethyl orthoesters
-C-O-N=O Acyl or alkyl nitrites -C-O-NO2 Acyl or alkyl nitrates >CC< O
1,2-Epoxides
MC=N→O C=N-O-M
Metal fulminates or aci-nitro salts, oximates
-(CH-CH-)n- olymerization alkene monomers
Groups containing Oxygen -C-O-O-H, R-CO-OOH Alkylhydroperoxides,
Peroxyacids -C-O-O-C-, -CO-OOR Peroxides (cyclic, diacyl,
dialkyl,), peroxyesters -O-O-M, EOO-, MOO- Metal peroxides, peroxoacid
salts -O-O-E Peroxoacids, peroxyesters H3N.Cr-OO- Amminechromium
peroxocomplexes -O-X XOn -Cl-O3 ClO2
- R-O-Cl-O3 RN+H3ClO4
Hypohalites Halogen oxides Perchloryl compounds Chlorite salts Alkyl perchlorates Aminium perchlorates
S2O4 Dithionites -(C-C-O-)n O
Polymerization ester monomers
-(C-C-N-)n O
Polymerization amide monomers
41
Groups Containing Nitrogen F-C- (NO2)2 Fluorodinitromethyl
compounds -N-M N-metal derivatives -N=Hg+=N- Poly(dimercuryimmonium
salts) -N-NO2 N-nitro compounds =N+-N-NO2 N-Azolium nitroimidates -C-N=N-C- Azo compounds Ar-N=N-O-R Arenediazoates ArN=N-S-Ar Arenediazo aryl sulfides Ar-N=N-O-N=N-Ar Bis(arenediazo) oxides Ar-N=N-S-N=N-Ar Bis(arenediazo) sulfides -C-N=N-N-C- R (R=H, CN, OH, NO)
Trizenes
-N=N-N=N- -N=N-N=C-
High-nitrogen compounds Tetrazoles
-N3 Azides (acyl, halogen, nonmetal, organic)
C-N2±O- Arenediazonium oxides -C-N2 +S- Diazonium sulfides and
derivatives, .Xanthates N+-HZ-, N+EOn
- Hydrazinium salts, Oxosalts of nitrogenous bases
-N+-OH Z- Hydroxylaminium salts -C-N2+Z- Diazonium carboxylates or
salts [N→Metal]+ Z- Amminemetal oxosalts Ar-Metal-X X-Ar-Metal
Halo-arylmetals, Haloarenemetal p-complexes
-N-X XN3 -C-N-C- O X O
Halogen azides N-halogen compounds N-haloamides
-N-F2 -C(NF)NF2
Difluoroamino compounds N,N,N-trifluoroalkylamidines
N-O- N-O compounds
Abbreviations: Ar = aromatic (benzene); M = metal; R = organic chain; X = halogen; E = nonmetal; Z = anion; n = integer variable; all other abbreviations are for the element symbols from the periodic table of elements Note: Not all chemical bond symbols are shown .
Table 3.1. (Contd.)
42
1.2 Oxygen Balance Method
A quantitative correlation has been demonstrated between oxygen balance and
various measures of explosive effectiveness for several classes of more than 300
compounds organic explosives25, and the following formula was recommended for
calculating oxygen balance for a compound:
where
X – Number of atoms of carbon
Y – Number of atoms of hydrogen
Z – Number of atoms of oxygen
MW – Molecular weight
The above formula yields a value of zero for oxygen-balanced compounds, negative for
oxygen-poor, and positive for oxygen-rich compositions. This method is a criterion for
evaluating self-reactivity in the CHETAH program, and the classification indicated in
Table 3.2 is recommended for estimating hazard potential based on oxygen balance.29
Table 3.2. Oxygen Balance and Hazard Rank
Oxygen Balance Hazard Rank
More positive than +160 Low
+160 to +80 Medium
+80 to –120 High
–120 to –240 Medium
More negative than –240 Low
MWZYX
BalanceOxygen)2/2(1600 −+−
=
43
1.21 Strengths
The oxygen balance method is useful for estimating hazards of organic nitro
compounds and is universally employed in the explosive industry. In general, this
method is applicable to compounds containing C, H, N, and O.29
1.22 Weaknesses
However, it has been shown that there is no necessary connection between
oxygen balance and self-reactivity29. For example, water (H2O) has an oxygen-balance
value of 0 and is given a ‘high’ hazard ranking by this criterion. Also, the method cannot
be applied to oxygen free but hazardous compounds such as acetylene. Application of
the above oxygen balance equation to low-oxygen content or oxygen-free compounds
produces a highly negative, non-hazardous ranking regardless of the actual hazard
potential.
1.3 CHETAH18
CHETAH is a popular program available from the American Society for Testing
and Materials (ASTM) for prediction of reactivity hazards. The software uses the
‘Benson group contribution method’ 30 to estimate heat capacity, heat of formation, and
heat of combustion for a multitude of compounds. Also, the program includes a database
of thermo-chemical properties for selected organic and inorganic compounds. CHETAH
classifies chemicals based on their potential for violent explosion and includes the
following hazard evaluation criteria:
§ Maximum heat of decomposition
§ Oxygen balance
44
According to the first criterion, compositions with heats of reaction more
negative and therefore more exothermic than – 2.929 kJ/g are placed in a ‘high’ hazard
category. A detailed explanation of the above evaluation criteria and three additional
ones can be found in the CHETAH reference manual, and a critical review of CHETAH
for predicting reactivity hazards is available.31 The first criterion has proved to be a
reliable indicator of potential reactive hazards. The other criteria, however, are not
effective for all chemicals and compositions.31
1.31 Input to the Program
The molecular formula of a compound is the only input to the program. From the
included database, the thermodynamic properties are estimated and the hazard criteria
are determined from these values. An energy release evaluation sheet from
CHETAH 7.2 is shown in Figure 3.1. Based on its maximum heat of decomposition,
H2O2 is given a “high” hazard classification. However, it should be noted that the
estimated product spectrum might be incorrect. Thus, one problem is the thermodynamic
feasibility of a proposed stoichiometry under process conditions. Further, the program
gives no indication about the sensitivity to reaction initiation or process conditions to be
avoided. It is difficult to determine conditions under which H2O2 may pose reactive
hazards based only on such an analysis. Thus, the problem of reactivity is not just a
combinatorial problem (stoichiometric analysis) as implicitly suggested by this method.
It is important to realize that CHETAH provides an estimate of a material hazard but not
an estimate of the process risk in using the material.
1.32 Strengths
The software is user friendly and offers the flexibility to include user-defined
group values. It is computationally inexpensive and can be installed on a standard PC.
45
ENERGY RELEASE EVALUATION
Compound Name: Hydrogen Peroxide Formula: H2O2 Molecular weight: 34.015 Amount: 1 Mole(s) Heat of formation at 25 oC: -32.530 kcal/mol
PLOSIVE HAZARD CLASSIFICATION: Over-all Energy Release Potential is HIGH Value: -1.375
Contributing Details: Criterion Value Units Hazard Classification Maximum Heat of Decomposition (#2) -0.743 kcal/g HIGH Fuel Value – Heat of Decomposition 0.000 kcal/g HIGH Oxygen Balance (#3) 47.037 percent HIGH CHETAH ERE Criterion 4 46.934 kcal2/mol MEDIUM Total Number of Peroxide Bonds 1.000 Net Plosive Density (#4) 0.435 PLOSIVE Warning: These ratings only apply to hazards associated with strong mechanical shock. This does not
imply the absence of other hazards. Notes #1 This evaluation was developed to classify a composition as able or not able to decompose with
violence, if subjected to the proper conditions. Information on the interpretation of hazard classification criteria used by CHETAH may be found in the CHETAH documentation. (ASTM publication DS-51A) and in J. Chem. Ed., v66, A137 (1989).
#2 For decomposition products shown. #3 Experience has shown that the oxygen balance criterion is useful only for compounds composed
of the elements C, H, N, and O. #4 Sum of auxoplosive and plosphoric weights per gram of mixture.
Decomposition Products (chosen to maximize heat of decomposition) Moles State Species 0.500 ref-gas O2 Oxygen 1.000 gas H2O Water
HEAT OF COMBUSTION SECTION Fuel Value (Net Heat of Combustion)
MASS BASIS MOLE BASIS -0.743 kcal/g - 25.270 kcal/mol -3.108 kJ/g -105.730 kJ/mol -1337.246 Btu/lb
Combustion Products (Chosen for Fuel Value and Net Heat of Combustion)
MOLES STATE SPECIES 1.000 gas H2O Water
Figure 3.1. Hazard evaluation output from CHETAH 7.2.
46
1.33 Weaknesses
The Benson method can fail for group values that are not available in the
database or are incorrect. In the evaluation criteria, the program classifies compounds or
compositions into specific hazard categories. Thus the program places a boundary based
on a threshold value and thereby blurs the distinction between hazardous and non-
hazardous chemicals. Also, the program provides no insight into process conditions to be
avoided or information about the sensitivity of compounds to initiation of a reaction.
1.4 CART26
Adiabatic temperature rise due to a reaction is defined as:
CpH
Tadiabatic∆−
=∆
where
∆H – heat of reaction
Cp – average heat capacity of the reacting mixture
∆Tadiabatic – adiabatic temperature rise
The code developed for CART performs multiphase Gibbs free energy minimization and
adiabatic reaction temperature calculations. Based on the calculated ∆Tadiabatic, the
substance is classified as26:
E - Can explode when unconfined
N- No known explosion hazard when unconfined
47
An adiabatic temperature rise of 1400 K is considered a cut-off value for the above
classification. Thus, substances with an adiabatic temperature rise of more than 1400 K
are classified as E and lower than 1400 K as N. This value is based on the fact that most
combustion reactions leading to formation of CO2 and H2O have a threshold temperature
value near 1400 K, which is the minimum temperature required for carbon monoxide to
propagate a self-sustaining flame. A cut-off value of 1200 K for conservative estimates
is recommended.26 The heat of reaction can be approximated by the maximum heat of
decomposition that is calculated by CHETAH. For H2O2, CHETAH estimates a
maximum heat of decomposition of -25.27 kcal/mol and Cp as 10.31 cal/mol K, yielding
an adiabatic temperature rise of 2450 K. Based on the above discussion, H2O2 would be
classified as E. Again, this value is useful but it does not provide information about
process conditions to be avoided. It is worth noting that for H2O2, the CHETAH criteria
and the CART adiabatic temperature value indicate a potential reactive hazard.
1.41 Input to the CART Method
The heat of reaction, heat capacity of the reaction mixture, and other system
thermo-chemical values are required program inputs. All of these values can be obtained
from the literature or estimated using the CHETAH program.
1.42 Strengths
The CART criterion takes into account the heat capacity of the reaction mixture
and is therefore more effective than employing only the reaction energy of the first
CHETAH criterion. Higher CART values are associated with greater sensitivities to
initiation and higher propagation rates. CHETAH programmers should include
‘adiabatic temperature rise’ as one of the hazard evaluation criteria.
48
1.43 Weaknesses
Thermo-physical values, such as ∆H and Cp, must be used to estimate the
adiabatic rise in temperature. The heat of reaction can be approximated by the maximum
heat of decomposition calculated by CHETAH, and CHETAH can also be used to
estimate the average Cp value. If the CHETAH program is employed to calculate
thermo-physical values, limitations similar to the group contribution method are
encountered, as discussed above. The classification based on adiabatic temperature rise
works well for hazard estimation of compounds undergoing combustion reactions. For
compounds that do not undergo combustion type reactions, determining a threshold
value of ∆Tadiabatic is difficult. As pointed out in the same reference 26, the CART
classification and heats of reaction values fail for hazard ranking of organic peroxides.
Also, like CHETAH, this classification places a distinct boundary based on a threshold
value. It is also worth noting that for a realistic calculation of ∆Tadiabatic , an average value
of heat capacity for the reaction mixture is required, and accurate heat capacity values
are difficult to estimate.
2. Advanced Prediction Techniques
None of the available theoretical methods address the issue of chemical kinetics,
which can significantly affect the rate of energy release and consequently the hazards
posed by the substance. Therefore, future work is focused on developing theoretical
methods to quantify both kinetics and thermodynamics based on molecular structure
alone.
The calorimetric experiments are designed to gather temperature, pressure, and
time data and typically very little or nothing is known about the reaction mechanism and
species involved. It is difficult to extract exact kinetics from calorimetric data, since the
calorimetric data on a substance reflects temperature vs. time behavior. This limitation
49
of calorimetric information demonstrates the need for property predictions that can be
compared to experimental temperature-time data.
It is well known that the structure of a substance affects its reactivity6 and this
reactive nature of a compound is reflected in the calorimetric data. With advances in
computation speed and associated growth in computational chemistry algorithms,
molecular modeling has evolved into a popular resource for predicting material
properties. A brief overview of molecular modeling techniques, computational methods,
and available softwares is provided in Appendix A. Molecular modeling techniques,
principally quantum chemical calculations, were employed to gain information at
molecular (microscopic) level and develop predict observed data (macroscopic level).
Two different approaches, employing computational chemistry calculations were probed
to predict calorimetric data:
§ Applying Transition State Theory (TST) to the rate-limiting step.
§ Developing correlations using the Quantitative Structure Property Relationship
(QSPR) technique.
These two approaches are discussed in the following sections.
3. Application of Transition State Theory for Thermal Stability Prediction
Prediction of potential hazards requires the knowledge of both the kinetics and
thermodynamics. In this work, computational chemistry techniques are combined with
Transition State Theory32 (TST) for predicting calorimetric data for aromatic nitro
compounds. The heat of reaction (- ∆Hrxn) is based on the heat of formation data and is
approximated by the enthalpy of maximum decomposition as calculated by the
CHETAH18 program. The C−NO2 bond fission is proposed to be the rate-limiting step
for decomposition of aromatic nitro compounds (R−NO2), and TST is applied to
approximate the kinetics of this single step. The activation energy is estimated from the
bond strength values obtained at the density functional level of theory, B3P8633, and
50
cc-pVDZ34 basis set. The resulting predictions are compared with DSC data.
3.1 Model Development
To predict calorimetric data, the thermodynamic and kinetic parameters for a
reacting system must be combined with an unsteady state model for an adiabatic batch
reactor35. It has been shown that such a model for a batch reactor can fairly well
reproduce calorimetric data36 and is based on the following assumptions:
a. The reacting environment is adiabatic and therefore heat losses are negligible.
b. The mass and the volume of the liquid or solid phase remain constant (i.e.,
evaporation losses can be neglected).
c. The specific heat of the material is assumed constant during the reaction.
d. The reacting phase is assumed to be at uniform temperature.
With the above approximations, the appropriate mass and energy balance equations for a
first-order reaction are:
AA kC
dtdC
=−
(3.1)
V
Arxn
CkCH
dtdT
φρ∆−
=− (3.2)
where
CA - Concentration of the reactant (gmol/m3)
-∆Hrxn - Heat of reaction (cal/mol)
k - Rate constant for a first-order reaction (/s)
V
VVss
mCmCCm +
=φ - Phi factor ( ≥ 1 for a typical industrial vessel)
CV - Heat capacity of the reacting mixture (cal/mol K)
CVs - Heat capacity of the sample cell (cal/mol K)
51
ρ - Density of the reacting mixture (kg/m3)
ms - Mass of the sample cell
m - Mass of the test sample
Simulation of the temperature-time curve requires the prediction of kinetic (k) and
thermodynamic (-∆Hrxn) parameters, and the ρ, Cv data for the system. The choice of the
values for these parameters is discussed in the next section.
3.11 Recommended Parameters
Thermodynamic parameter estimation
The heat of reaction or the energy of reaction can be theoretically estimated using
the thermodynamic identity:
∆Hrxn = ∆Hf,Products - ∆Hf,Reactants
where
∆Hf,Products - Heat of formation of products
∆Hf,Reactants - Heat of formation of reactants
However, during the calorimetric analysis the end products are not determined, and the
multitudes of reactions and products within the reacting system are difficult to predict.
For a given chemical formula, the CHETAH18 program calculates the enthalpy of
reaction or enthalpy of maximum decomposition from the heat of formation (∆Hf). This
value is thus an upper bound on the energy of reaction and will be used in the
simulations discussed in this paper to approximate -∆Hrxn. Heat of formation values can
be easily obtained from the literature37,38 or can be calculated by employing
52
computational techniques39. The heat of formation and heat of maximum reaction values
used in these simulations are tabulated in Table 3.3. The variation of heat of reaction
with temperature is neglected. For compounds with available heat of formation values
for the gas, liquid, and solid phases, the numerically largest heat of reaction value was
used in each case.
Kinetic parameter estimation
A possible set of elementary steps is required to estimate the kinetics for a
reaction pathway. In this case, we assume that the nitro compounds undergo
unimolecular decomposition as shown below and potential energy for the reaction
pathway is depicted qualitatively in Figure 3.2.
R – NO2 R• + NO2• ………………. Product
This reaction is assumed to follow a radical mechanism. The first step is the rupture of
the weakest bond. We assume that the remaining steps are relatively fast, therefore the
bond scission is the rate-limiting step.
53
Table 3.3. Summary of Heat of Formation and Maximum Heat of Decomposition
Sr. no. Compound Standard heat of
formation* kcal/mol
Maximum heat of decomposition†
kcal/mol
gas liq. solid gas liq. solid
1 nitrobenzene 16.38 2.98 - -136.4 -123.0 -
2 2 nitrotoluene - - - - -127.1‡ -
3 3 nitrotoluene - -11.0 - - -117.9 -
4 4 nitrotoluene 7.38 - - -136.3 - -
5 1,2 dinitrobenzene - - -0.4 - - -209.3
6 1,3 dinitrobenzene - - -6.5 - - -203.1
7 1,4 dinitrobenzene - - -9.2 - - -200.4
8 2,6 dinitrotolueme - - -13.2 - - -207.3
9 3,4 dinitrotoluene - - - - -214.4§ -
10 2,4 dinitrotoluene 7.93 - -15.87 -228.4 - -204.5
11 2 nitroaniline - - -6.3 - - -118.2
12 3 nitroaniline 14.9 - - -139.4 - -
13 4 nitroaniline 13.2 - - -137.7 - -
14 2 nitrobenzoic acid - - -95.3 - - -119.6
15 3 nitrobenzoic acid - - -98.9 - - -116.1
16 4 nitrobenzoic acid - - -102.1 - - -112.9
17 2 nitrophenol -31.62 - - -136.3 - -
18 3 nitrophenol -26.12 - - -141.9 - -
19 4 nitrophenol -27.41 - - -140.6 - -
* Standard heat of formation values at 1 atm and 298.15 K are from the NIST Chemistry WebBook. † Calculated by CHETAH. ‡ Because the heat of formation value for 2 nitrotoluene was not available, an average of decomposition
values for 3 nitrotoluene and 4 nitrotoluene was used. § Because the heat of formation value for 3,4 dinitrotoluene was not available, an average of
decomposition values for 2,4 and 2,6 dinitrotoluene was used.
54
Figure 3.2. Hypothesized potential energy surface (PES) for a runaway reaction.
Reaction co-ordinate
Ene
rgy
EA
1st step
55
The rate constant for an unimolecular reactions under high pressure conditions is given
by the equation40:
RTEB A
A
TS eqq
hTk
k /*
−= (3.3)
where
kB - Boltzmann constant (J/K) = 1.38 x 10-23
h - Planck constant (Js) = 6.63 x 10-34
R - Gas constant (cal/mol K) = 1.987
T - Temperature (K)
qTS* - Partition function for the transition state (with 1 degree of freedom, along the
reaction coordinate, removed)
qA - Partition function for the reactant
EA - Activation energy (cal/mol)
In all further equations, the activation enthalpy is represented by EA and its
approximated value is based on bond dissociation energy. Each partition function is a
product of translational, vibrational, rotational, and electronic partition functions. For
unimolecular decomposition, the ratio of qTS and qA differs by one degree of vibrational
freedom - the one along which reaction occurs, and this ratio can vary between ~ 0.1 and
~1. For the simulations discussed here, this ratio is approximated by 1 to obtain a
conservative estimate for k. Substituting the values for kB and h, the rate constant can be
written as:
min)(/10*25.1)(/10*08.2 1210 RTE
RTE
RTE
BAAA
eTseTehTk
k−−−
=== (3.4)
Thus, EA is the only missing parameter and is estimated as discussed below.
Following the Polanyi type equation41,
56
EA = EA0 + γP?Hrxn
where
EA - Activation enthalpy for an elementary step
EA0 - Intrinsic activation enthalpy for a reaction class
γP - Proportionality constant, called the transfer coefficient, for a reaction class
?Hrxn - Heat of reaction for the elementary step
For a bond scission reaction the above equation reduces to42:
EA = γP * BDE (3.5)
where EA0 ~ 0
We further assume that the overall kinetics can be approximated by applying the
TST to evaluate the kinetic parameters for the rate-limiting first step. The activation
energy is therefore a fraction of the bond dissociation energy (BDE) of the weakest
bond, C−NO243. Computational chemistry calculations were performed to calculate the
BDE at the B3P8633 level of theory with the cc-pVDZ34 basis set, and the quantum
mechanical calculations were performed using the Gaussian 9844 suite of programs on
the Texas A&M supercomputer. The Gaussian software calculates energies, optimized
molecular structures, and vibrational frequencies, together with molecular properties that
are derived from these three basic computation types for a chemical formula. Optimized
geometries were obtained for the reactant (R−NO2) and the two fragments
(R• and NO2• ). The BDE is then calculated as
BDE = ENO2• + ER• - ER-NO2 (3.6)
BDE values can be calculated if the experimental heats of reaction are available.
Equation (3.4) reduces to
57
min)(/10*25.1 12 RTBDEP
eTkγ
−= (3.7)
Although the above TST equations apply for reactions in the gas phase, it is assumed
that the rate in the gas phase approximates the rate in a condensed phase. With the
current reaction-solvation theories, this is the best working assumption at this level of
analysis.
3.12 Physico-chemical Properties
The concerned physical properties, density (ρ) and heat capacity (Cv) are
available in the open literature37,38 or can be estimated with reasonable accuracy. For the
compounds considered in this research the Cv varied between 0.25 – 0.35 cal/gm K, and
the density varied between 800 – 1200 kg/m3.
Equations (3.1) and (3.2) can be further simplified to calculate onset temperature.
We assume that the concentration of the reactant (CA) is equal to the initial concentration
(CA0) until the temperature equals the onset temperature. This assumption decouples
Equation (3.1) and (3.2), and Equation (3.2) reduces to
MWCkH
CkCH
CkCH
dtdT
V
rxn
V
Arxn
V
Arxn3
0 10∆−=
∆−≈
∆−=
ρφρ (3.8)
MWC A
3
010*ρ
=Q
Substituting the expression for k from Equation (3.7) in Equation (3.8), we obtain
MWCeTH
dtdT
V
RTBDErxn
3/12 10***10*25.1* γ−∆−= (3.9)
58
Thus, γP is the only undetermined variable, and it serves as an adjustable parameter for
the simulations. When the rate of temperature increase exceeds a particular amount (ε),
the calorimeter detects the exothermic reaction. Thus, when dT/dt ≥ ε, T = To, and the
value of ε depends on the sensitivity of the calorimeter. For a given compound the above
equation has the form
TBeTAdt
dT /** −= (3.10)
where A and B are constants. Therefore at higher temperatures the exponential term
dominates, and values of dT / dt from Equation (3.9) are sensitive to the BDE values.
3.2 Experimental Details
For this work, we used available DSC data on aromatic nitro compounds. Pure
organic nitro compounds, aliphatic and aromatic, decompose at high temperatures and
exhibit large exotherms45. These compounds are identified as energetic materials, and
trinitrotoluene (TNT) is used as an explosive. Since a graphical detection procedure is
employed to obtain To, a variation of 5-30 oC is possible in the reported To values for the
same compound. The energy of reaction (-∆Hrxn) is the net heat released during the
reaction and is not the thermodynamic heat of reaction but includes other effects such as
sublimation, evaporation, adsorption, and enthalpy of mixing. Therefore, the
experimentally determined parameters, To and -∆Hrxn, depend on the type of calorimeter,
sample size, sample phase, and scanning rate. To compare the theoretically predicted
values, we chose experimental data from a single reference46 to maintain consistency the
experimental procedure. In this reference46, authors employed a Mettler TA4000 DSC
(0.2 W/gm sensitivity) with DSC25 measuring cell, scanning rate of 4 oC/min to
determine the To and -∆Hrxn values for 19 nitro compounds.
59
3.3 Results and Discussion
3.31 Choice of γp
Assuming a sensitivity of 0.1 oC/min and substituting the experimental onset
temperature for T and BDE for the 19 compounds listed in Table 3.4, we can determine
γp for each compound from Equation (3.9). The average of the γp values calculated for
mono-nitro compounds is 0.67 ± 0.06 and for di-nitro compounds is 0.71 ± 0.06. For a
sensitivity of 0.01 oC/min at To, the average γp value is 0.70 ± 0.06 for mono-nitro and
0.76 ± 0.06 for di-nitro compounds, respectively. Note that increasing the sensitivity of
the apparatus to detect a lower onset temperature increases the γp but the variation in γp
remains the same. Therefore, there is a correlation between the calculated BDE and the
activation energy required to predict the experimentally determined onset temperature,
and irrespective of the sensitivity of the DSC, the γp parameter can be adjusted to
reproduce the experimental data.
3.32 Results
Based on the above discussion we assumed a value of 0.70 and 0.76 for γp for
mono and dinitro compounds, respectively. A FORTRAN program was written to
calculate dT/dt, as given by Equation (3.9), for temperatures starting with 30 oC. The
temperature was increased by 1 oC if the rate of increase of temperature was less than
0.01 oC/min. The temperature at which the gradient of temperature with time increased
at the specified rate of 0.01 oC/min was taken as the onset temperature. The predicted
onset temperatures for 19 different compounds are presented in Table 3.4 with an
average aggregate error of 11% and a bias of -2%. Typical errors associated with the
DSC detected onset temperatures are within ± 5%.
60
B3P86 AM1
Sr. Structure To (oC) BDE To (oC) ? To (oC) error BDE To (oC) * ? To (oC) error
no. Expt.46 (kcal/mol) predicted exp - pre % (kcal/mol) predicted exp- pre %
1 nitrobenzene 380 75.6 297 83 22 27.6 302 78 21
2 2 nitrotoluene 290 73.4 282 8 3 26.2 290 0 0
3 3 nitrotoluene 310 75.9 301 9 3 27.6 304 6 2
4 4 nitrotoluene 320 76.7 305 15 5 28.5 312 8 3
5 2 nitroaniline 280 80.1 330 -50 -18 30.4 329 -49 -17
6 3 nitroaniline 300 76.5 303 -3 -1 26.8 294 6 2
7 4 nitroaniline 310 80.9 335 -25 -8 30.8 332 -22 -7
8 2 nitrobenzoic acid 270 66.4 231 39 14 22.9 259 11 4
9 3 nitrobenzoic acid 300 74.7 292 8 3 26.4 293 7 2
10 4 nitrobenzoic acid 310 76.5 306 4 1 27.3 302 8 3
11 2 nitrophenol 250 82.7 346 -96 -38 30.3 324 -74 -30
12 3 nitrophenol 310 75.77 294 16 5 26.5 288 22 7
13 4 nitrophenol 270 78.3 313 -43 -16 28.3 305 -35 -13
14 1,2 dinitrobenzene 280 64.5 251 29 10 18.1 246 34 12
15 1,3 dinitrobenzene 270 73.2 320 -50 -19 26.9 338 -68 -25
16 1,4 dinitrobenzene 350 72.9 319 31 9 26.8 338 12 3
17 2,6 dinitrotoluene 290 68.2 282 8 3 21.2 280 10 3
18 3,4 dinitrotoluene 280 64.7 254 26 9 18.0 247 33 12 19 2,4 dintitrotoluene 250 74.1 322 -72 -29 23.3 302 -52 -21
* Using scaled AM1 BDE values
Table 3.4. Summary of Experimental and Predicted Values for To (Tonset)
61
200
220
240
260
280
300
320
340
360
380
400
8 14 18 2 17 9 12 1 3 6 4 10 13 16 15 19 5 7 11
Serial number of the compound as in Table 3.4
Ref 45
Ref 17
Ref 6
Predicted
Figure 3.3. Comparison of onset temperatures.
62
The predictions are compared with experimental values from three different
sources6, 17,46 in Table 3.5 and are plotted in Figure 3.3. To data in Table 3.5, column 3,
were measured with a DSC at a scanning rate of 4°C/min46, and in column 4 with a DSC
at 10°C/min10, where the higher scanning rate, with other conditions constant,
consistently results in higher detected onset temperatures. Tonset data in Table 3.5,
column 5, are from a variety of sources.6 As seen from Figure 3.3, the experimental data
for each compound are scattered and the predictions appear to be reasonable. One reason
for the scatter in the experimental data is the graphical detection method for the onset
temperatures. Predictions from this model should better match measured values if data
from a more sensitive calorimeter such as an APTAC (Automated Pressure Tracking
Adiabatic Calorimeter) with larger sample sizes were used.
BDE values calculated with B3P86//cc-pVDZ were used for obtaining the γp. We
chose a density functional theory, B3P86, to determine the BDE values within
experimental accuracy but a typical optimization calculation can take about an hour on a
supercomputer. We also calculated BDE values using the quicker and less expensive
semi-empirical AM1 method47, and BDE values using each method are displayed in
Table 3.4. A typical optimization calculation using the AM1 method takes few seconds.
Although the AM1 calculated values of BDE are significantly lower than the
experimental values, they show a similar trend as exhibited by the higher level theory.
Consequently, the AM1 and B3P86//cc-pVDZ bond dissociation values were correlated
at a confidence level of ~ 0.9 and were related by the following equation:
BDE B3P86 = 1.3* BDEAM1 + 40.2
Thus the AM1 BDE values were scaled to be consistent with the higher level density
functional values, and the predicted onset temperatures exhibit a similar average
aggregate error of 10 % and a bias of -2%. The predicted onset temperature values from
the density functional method and from the scaled AM1 method are shown in Table 3.4.
63
In some cases where the offset is large between predicted and experimental Tonset,
thermal effects other than the reaction heat, especially heat of vaporization or
sublimation, as discussed earlier, could significantly affect the predictions. Measured
data for a range of compounds employing a more sensitive calorimeter at slower
scanning rates with larger sample sizes should provide a good test of this prediction
method because thermal effects other than heat of reaction should be less significant.
Table 3.5. Comparison of Onset Temperatures
Sr. no.
Compound
To46
oC To
17 oC
To6
oC Predicted
oC 8 2 nitrobenzoic acid 270 305 230 231 14 1,2 dinitrobenzene 280 - - 251 18 3,4 dinitrotoluene 280 322 - 254 2 2 nitrotoluene 290 338 280 282 17 2,6 dinitrotoluene 290 - - 282 9 3 nitrobenzoic acid 300 375 320 292 12 3 nitrophenol 310 353 320 294 1 nitrobenzene 380 400 360 297 3 3 nitrotoluene 310 361 300 301 6 3 nitroaniline 300 347 280 303 4 4 nitrotoluene 320 329 - 305 10 4 nitrobenzoic acid 310 379 - 306 13 4 nitrophenol 270 302 250 313 16 1,4 dinitrobenzene 350 - - 319 15 1,3 dinitrobenzene 270 - 380 320 19 2,4 dintitrotoluene 250 312 312 322 5 2 nitroaniline 280 341 280 330 7 4 nitroaniline 310 345 280 335 11 2 nitrophenol 250 300 250 346
64
4. Correlating Calorimetric Data with Molecular Descriptors
To predict reactivity of a substance it is necessary to deduce probable reaction
pathways, but it is difficult to predict the reaction pathways for a compound, especially
at high temperatures. The exothermic behavior of a substance is influenced by the
presence of functional groups 6,17,48, which also form a basis for reactivity classification.
This approach suggests that there is an inherent structure-property relationship between
the observed calorimetric properties and molecular structure. For example, as mentioned
earlier, the presence of the nitro group (NO2) can be a potential source of significant
reactivity. The reactive nature is manifested in calorimetric data, but this dependence of
observed behavior and molecular structure has not yet been quantified.
The Quantitative Structure-Property Relationship (QSPR) is a popular tool for
correlating observed values based on molecular properties. QSPR techniques have been
successfully employed for drug design49 and for correlating physical properties such as
boiling point50, autoignition temperature51, and molecular properties. In addition to
providing a means of predicting properties, a QSPR study may also lead to better
understanding of structural features affecting the observed data. The objective is to
correlate and predict DSC calorimetric data, namely onset temperature and energy of
reaction.
As discussed earlier, Tonset is indeed a ‘detected’ onset temperature because the
value depends on the sensitivity of the instrument and experimental technique.
Depending on the type of calorimeter, sample size, and scanning rate, Tonset can vary
within 5-50 oC for the same compound. For DSC data there is further distinction
between To (first deviation from base-line) and extrapolated To (intersection of base line
and tangent to the peak).
65
The energy of reaction, often due to decomposition or polymerization, is the net
heat released during a reaction. As discussed, this energy is not the thermodynamic heat
of reaction, because it includes other effects such as evaporation and enthalpy of mixing,
and heat absorbed by the sample cell.
We built a Quantitative Property Structure Relationship (QSPR) study table to
investigate correlations between calorimetric data and molecular descriptors. The first
column of the study table is either Tonset or energy of reaction obtained from calorimetric
experiments and is called the dependent variable. The remaining columns are the
independent variables (characteristic of the molecules) called descriptors, which are
characteristics of a molecule and account for the electronic and chemical structure of the
molecule. A descriptor value can be obtained by experimental measurement or
calculated based on molecular structure. Theoretical descriptors were used to facilitate
property predictions for unknown molecules.
4.1 Data Set Selection
We chose compounds belonging to the organic nitro family since a better
correlation of properties is expected within a family of similar compounds. This set of
compounds that was used to develop the correlation is called a ‘training set’. The choice
of data is critical for an effective correlation, and we chose data from a single reference46
to maintain consistency in experimental procedure and calorimetric sensitivity. With a
larger data set a predictive model could be developed, but we could not find a large set
of consistent data in the open literature was not found.
66
4.2 Discussion of a Few Descriptors
The choice of descriptors depends on the property to be correlated. Here
descriptors were selected that were expected to correlate with the detected onset
temperature or determined energy of reaction.
4.21 Highest occupied molecular orbitals (HOMO)
HOMO (highest occupied molecular orbital) is the highest energy level in the
molecule that contains electrons. It is crucially important in governing molecular
reactivity and properties. When a molecule acts as a Lewis base (an electron-pair donor)
in bond formation, the electrons are supplied from the HOMO. The ease of donation is
reflected in the energy of the HOMO. Molecules with high HOMOs are more able to
donate their electrons and are hence relatively reactive compared to molecules with low-
lying HOMOs.
4.22 Lowest unoccupied molecular orbitals (LUMO)
LUMO (lowest unoccupied molecular orbital) is the lowest energy level in the
molecule that contains no electrons. It is important in governing molecular reactivity and
properties.When a molecule acts as a Lewis acid (an electron-pair acceptor) in bond
formation, incoming electron pairs are received in its LUMO. Molecules with low-lying
LUMOs are more able to accept electrons than those with high LUMO.
HOMO and LUMO, collectively called as frontier orbitals, have been regarded as
major determinants of chemical reactivity.52 It has been shown that the electron
delocalization between HOMO and LUMO is generally indicative of easiness of
chemical reaction and the stereo-selective path, irrespective of intra and intermolecular
processes. For two approaching molecules larger the orbital overlapping for HOMO and
67
LUMO and smaller the level of separation of two overlapping orbitals the larger the
contribution of the orbital pair to the stabilization of an interacting system. Thus a likely
explanation of the importance of chemical reactions would be the fact that molecular
orbital perturbation theory requires that interactions between molecules, leading to some
form of reaction, have to possess the appropriate frontier orbital energy values for
electron transfer.53
4.23 Highest positive charge (HPC) and highest negative charge (HNC)
These descriptors are probable indicators of electrophillic or nucleophillic attacks
and are expected to correlate with the Tonset, which is a measure of kinetics.
4.24 Weakest bond (WB)
The weakest bond, here the C-NO2 bond, in a molecule is a kinetic descriptor,
since it represents the minimum activation energy required for initiating the reaction.
4.25 Mid-point potential (Vmid)
Previous work54 has shown that the electrostatic potential produced by carbon
and nitrogen charges at the C-NO2 bond mid-point correlates with the impact sensitivity.
RQ
RQ
Vmid NC
5.05.0+=
where
QC – Atomic charge on carbon
QN – Atomic charge on nitrogen
R – C-NO2 bond distance
68
It is believed that the buildup of positive electrostatic potential above the C-N bond is
responsible for destabilizing the bond.
4.26 Delocalizability index (Sr)
Here the descriptor (Sr) is defined as
∑=
=HOMO
i i
Sr1
1ε
where
ε i– Eigenvalue for the molecular orbital
The Sr index is similar to Fukui’s superdelocalizability index55. In the summation, the
eigenvalues for higher molecular orbitals (which are numerically smaller) will dominate,
and Sr is therefore a measure of delocalizability of electrons and a probable measure of
reactivity.
4.27 Dipole moment
The degree of polarity of a molecule is expressed in terms of dipole moment. The
electric dipole moment for a pair of opposite charges is defined as the magnitude of the
charge times the distance between them, and the defined direction is toward the positive
charge. It is useful in atoms and molecules where the effects of charge separation are
measurable, but the distances between the charges are too small to be easily measured.
The dipole moment of the molecule was also included as one of the descriptors.
4.28 Charge – bond strength descriptor (x)
This descriptor was calculated as follows
WBHNCHPC
x*5.0+
=
69
and is an indicator of charge to bond strength ratio in a molecule.
The descriptors discussed above are aimed at capturing reactivity characteristics
of substances. Most of the reactions involving reactive chemicals follow radical
mechanism; these descriptors are suitable for elucidating reactivity since radical
reactions are less influenced by the environment of reactions than ionic reactions. The
reactivity indices, frontier electron density, superdelocalizability, and delocalizability are
defined to discuss the reactivities of unsaturated and saturated molecules.56 It can be
argued, based on electronic theory, that behavior of molecules, especially reactivity, can
be explained based on distribution of electrons in a molecule.
Values of these descriptors were obtained using the Gaussian44 suite of programs
with the B3P8633 density functional model and the cc-pVDZ34 basis set and are
summarized in Appendix B. To develop a computationally inexpensive method, more
sophisticated models were not tested at this stage of the project. Further statistical
calculations were performed using the Statistical Analysis System (SAS).57
4.3 Correlations
The correlations were obtained by performing least square regression analysis on
the training set of molecules. The developed correlation has the form
Y = A1X1 + A2X2 + A3X3 + ….+ AnXn
where
Y – Dependent variable
X – Independent variable (descriptor)
A – Regression constant
70
4.31 Tonset
The details of the experimental onset temperatures and predicted values used are
summarized in Table 3.6. A statistical analysis was performed on the all descriptors and
their combinations, and the chosen descriptors were the ones that maximized the R2
value and minimized the error square terms58. As a result of this analysis the variables
that exhibited significant correlation with the dependent variable (Tonset) were retained,
and the statistically insignificant ones were discarded.
The following correlation based on the training set of 19 nitro compounds is
recommended:
Tonset (deg C) = 827.0 – 1035.79 * HPC – 4.4275 * Sr – 5.0654 * Dipole
A standard overall F-test (α = 0.05) indicates that the fitted correlation is significant and
not a chance correlation. The predicted onset temperature values with an absolute
average aggregate error of 6% and a bias of -0.5 % are listed in Table 3.6 and are plotted
against the experimental values in Figure 3.4. A correlation of 0.6 is obtained between
the predicted and the observed values. This level of correlation is reasonable given
significant variations in the experimentally determined onset temperatures due to the use
of a graphical detection procedure, as discussed above, and associated errors.
71
Table 3.6. Onset Temperatures (observed and predicted)
Structure To (oC) Residual % error
Expt Predicted (Expt-Predicted)
1 nitrobenzene 380 348 32 8 2 1,2 dinitrobenzene 280 297 -17 -6 3 1,3 dinitrobenzene 270 304 -34 -12 4 1,4 dinitrobenzene 350 328 22 6 5 2 nitrotoluene 290 309 -19 -7 6 3 nitrotoluene 310 315 -5 -2 7 4 nitrotoluene 320 311 9 3 8 2,6 dinitrotoluene 290 280 10 3 9 3,4 dinitrotoluene 280 261 19 7 10 2,4 dintitrotoluene 250 260 -10 -4 11 2 nitroaniline 280 256 24 9 12 3 nitroaniline 300 302 -2 -1 13 4 nitroaniline 310 279 31 10 14 2 nitrobenzoic acid 270 281 -11 -4 15 3 nitrobenzoic acid 300 296 4 1 16 4 nitrobenzoic acid 310 295 15 5 17 2 nitrophenol 250 274 -24 -10 18 3 nitrophenol 310 316 -6 -2 19 4 nitrophenol 270 309 -39 -14
72
240
260
280
300
320
340
360
380
400
240 260 280 300 320 340 360 380 400
Experimental (oC)
Predicted Agreement
Figure 3.4. Predicted onset temperatures.
73
4.32 Energy of reaction
It is observed that the energy of reaction values correlate strongly with the count
of –NO2 group in the nitro compounds59, which is consistent with NO2 as an indicator of
reactivity. The experimental heat of reaction values for all the 19 compounds are listed
in Table 3.7 and summarized for the nitro and dinitro compounds in Table 3.8. The
correlation for the energy of reaction is:
Energy of reaction [-∆H] (kcal/gmol) = 75 * Number of nitro groups
Thus for TNT (3 nitro groups) the predicted energy of reaction is 225 kcal/mol, which is
consistent with the experimentally determined value of 2396 kcal/mol.
4.4 Correlations Using the Semi-empirical Method, AM1
The descriptors for the above study were generated using the B3P86/cc-pVDZ
model. Typically an optimization for an aromatic nitro molecule using this model
requires about an hour of CPU time on the supercomputer. Therefore, for the descriptors
to be easily calculable it is important that predictions be possible using a
computationally inexpensive semi-empirical theory, such as AM1.47
An optimization using AM1 can be performed in few seconds. To use the
correlations generated earlier we must scale the AM1 descriptor values to the
B3P86/cc-pVDZ values. The Sr and dipole descriptors calculated using the AM1 model
correlated with the B3P86/cc-pVDZ values to yield R2 values of 0.98 and 0.82,
respectively. However the HPC values calculated using the two models did not show a
good correlation. We recommend the following equations to scale the Sr and dipole
74
Table 3.7. Experimental Energy of Reaction
Structure Energy of reaction (- ∆H) J/g kcal/mol
1 nitrobenzene 2757 81.1 2 1,2 dinitrobenzene 3310 133.0 3 1,3 dinitrobenzene 3488 140.1 4 1,4 dinitrobenzene 3701 148.7 5 2 nitrotoluene 2404 78.8 6 3 nitrotoluene 2070 67.9 7 4 nitrotoluene 2322 76.1 8 2,6 dinitrotoluene 3451 150.2 9 3,4 dinitrotoluene 3574 155.6 10 2,4 dintitrotoluene 3987 173.6 11 2 nitroaniline 2225 73.5 12 3 nitroaniline 2269 74.9 13 4 nitroaniline 2026 66.9 14 2 nitrobenzoic acid 1894 75.6 15 3 nitrobenzoic acid 1899 75.8 16 4 nitrobenzoic acid 1934 77.2 17 2 nitrophenol 2481 82.5 18 3 nitrophenol 2269 75.4 19 4 nitrophenol 2155 71.7
75
Table 3.8. Summary of Energy of Reaction Values
Compounds Energy of reaction (- ∆H) (kcal/mol)
Average Mononitro* 75 ± 5
Dinitro† 150 ± 14
moment:
SrB3P86 = 1.3093 SrAM1 - 0.1105
DipoleB3P86 = 0.9329 DipoleAM1- 0.2047
With the scaled descriptors, the following three-parameter correlation can be employed
for calculating Tonset:
Tonset (deg C) = 828.5 – 5.7969 * SrAM1 – 4.7255*DipoleAM1
Using the AM1 scaled descriptors and the above two-parameter correlation, predictions
for onset temperatures for the 19 compounds yielded an average absolute aggregate error
of 7% and a bias of -1%, which is in good agreement with the predictions obtained using
the more expensive B3P86 descriptors. Values of descriptors and predicted onset
temperatures using AM1 are summarized in Appendix C.
* Statistical analysis was performed on 1,5,6,7,11,12,13,14,15,16,17,18,19 compounds in Table 3.7. † Statistical analysis was performed on 2,3,4,8,9,10 compounds in Table 3.7.
76
5. Conclusions and Future Work
Computational screening to reactive hazards presents fundamental challenges in
predicting material properties and is of great interest to industry personnel. The QSPR
approach was also successfully used to correlate impact sensitivities to molecular
descriptors in our research group.60 Such correlations can be refined into a computerized
predictive tool to be run on a desktop computer.
Mary Kay O’Connor Process Safety Center (MKOPSC) is collaborating with
Dow Chemical Company, Midland, MI, and Eastman Kodak Company, Rochester, NY
to access their reactivity databases and develop correlations for a variety of families of
compounds. An initial analysis of available data indicates lack of data on pure
compounds, and computationally amenable compositions. A data set of 48 mono nitro
molecules, with average molecular weight of 234±85 g/mol was used to investigate
possible correlations with molecular descriptors. The energy of reaction yielded an
average value of 85±14 kcal/mol, consistent with results discussed earlier. However, the
onset temperatures did not yield satisfactory correlations with the descriptors discussed
earlier and lack of data on other families of compounds prevents testing of QSPR
descriptors. It is worth pointing out that calorimetric properties can be grouped
according to the functional groups, and values from different sources are summarized in
Table 3.9, 3.10, and 3.11. Based on values in the tables and the earlier classification, it is
possible to perform an easy screening of reactive hazards. For example, if the process
under consideration is ethylene (CH2=CH2) polymerization to form polyethylene, the
expected amount of heat released 20 kcal/mol, as indicated in Table 3.10. Since the
molecular weight of ethylene is 28 g/mol, the energy released per gram is ~ 700 cal,
indicative of a potential reactive hazard. If a molecule has a combination of functional
groups, the total energy released can be assumed to be sum of energy released by
individual functional groups, and the lowest of the onset temperatures among individual
groups can be taken as onset temperature for the combination.
77
Table 3.9. Decomposition Energies for Typical Functional Groups 48
Sr. no.
Functional group Decomposition energy* (-∆H)
(kcal/mol) Formula Name
1. >C=C< 12 – 22 2. -C≡C- 29 – 36 3. -CC-
O
17 – 24
4. -COOH 55 – 67 5. -C=O
OOH
57 – 69
6. -C-O-O-C
81 – 86
7. >S=O 10 – 17 8. SO2Cl 12 – 17 9. -NH-NH- 17 – 22 10. -N=N- 24 – 43 11. -N≡N+- 38 – 43 12. >C=N≡N 41 – 45 13. -N=N≡N 48 – 57 14. -N=N-N< 60 – 65 15. >C=NOH Oxime 26 – 33 16. >N-OH N-hydroxide 43 – 57 17. >N:O N-oxide 24 – 31 18. >C-N=O Nitroso 36 – 69 19. -N=C=O Isocyanate 12 – 18 20. >C-NO2 Nitro 74 – 86 21. >N-NO2 N-Nitro 96 – 103 22. -O-NO2 Acyl nitrate 96 – 115 23. NH2.HNO3 Amine nitrate 72 – 84
*. To convert to cal/g multiply the heat of decomposition by 1000/MW
O O
78
Table 3.10 Typical Values for Energetic Polymerization61
Monomer functional
group
Polymer bond
Polymerization Energy (-∆H)
kcal/mol 1. -C=C- -C-C- 20 2. -C=O- -C-O- 5 3. -C=N- -C-N- 1.4 4. -C≡N- -C=N- 7.2 5. -C=S- -C-S- 2 6. -S=O- -S-O- 7
79
Table 3.11 -∆H, To Values Based on Functional Groups 59
Chemical Class
Unstable Group
Decomposition Energy (-∆H)
kcal/mol
DSC (To)
°C
Mean Standard dev. Mean Standa
rd dev. 1. Perchlorate -ClO4 830 60 200 20 2. Nitro -NO2 340 60 240 60 3. Polynitro 350* 40 240 60 4. Nitroso -N=O 200 30 120 30
5. N-oxide
N O
140 40 210 30
6. Hydroxylamine, Oxime >N-OH 140 50 160 40
7. Tetrazole
N
N N
N
210 40 160 10
8. Triazene, triazole -N=N-N< 210 50 230 60
9. Diazo
N+
N
N+
N
220 60 110 20
10. Azo -N=N- 200 60 230 40
11. Hydrazine -NH-NH2 >N-NH2
100 30 210 40
12. Substituted Hydrazine
-NH-NH- >N-N< 100 30 220 50
13. -N-N- in a ring 100 60 250 50
14. 2 -N-N- in a ring 190 90 210 50
15. Imidazole N-C-N (ring) 130 60 270 50 16. Oxazole N-C-O (ring) 80 40 260 50 17. Thiazole N-C-S (ring) 80 50 260 40
18. Tetrazole + nitro 540 120 160 20
19. Substituted Hydrazine+ nitro
430 50 180 20
80
Future experimental work in our research group will focus on building libraries
of data for compounds, which would then be used to develop correlations based on
molecular level descriptors, and development of robust correlations to enable structure-
based predictions. Based on this analysis one can also envision descriptors (or imprints
of energetic materials) that can be developed into a qualitative hazard index.
The discussion so far has focused on characterizing and screening reactive
hazards. But systems where hazards are identified additional considerations and
resources are required. The next chapter focuses on a detailed investigation of
hydroxylamine (HA), as an example of a hazardous system.
81
CHAPTER IV
DETAILED INVESTIGATION OF A REACTIVE SYSTEM
Almost all mid-size and large companies have a reactive hazard management
program to assess potential reactive hazards during storage, transport, and processing of
reactants, intermediates, and products. For evaluating reactive hazards, it is rational to
develop a systematic protocol with a screening step, utilizing available information,
computations and experiments, as discussed earlier, followed by detailed testing. The
classification discussed above can be used as a screen to select the more hazardous
compositions for detailed testing. An overall assessment approach is shown in the
Figure 4.1. Earlier chapters focused on development of tools that can expedite reactive
hazard assessment. This chapter focuses on an investigation of hydroxylamine system, as
an example of highly reactive system.
1. Background
Hydroxylamine (HA), NH2OH, has recently been involved in two major
industrial incidents with disastrous consequences.62,63 Calorimetric studies on aqueous
solutions of HA indicate that it is a highly reactive compound64, but its properties are
Part of this chapter is reprinted with permission from, “Theoretical thermochemistry: ab initio heat of formation for hydroxylamine”, by S.R. Saraf, W.J. Rogers, M. Sam Mannan, M.B. Hall, and L.M. Thomson, J. Phys. Chem., Vol. 107, No. 8, 2003. Copyright 2003 by the name of American Chemical Society (ACS). Part of this chapter is reprinted with permission from “Hydroxylamine production: Will a QRA help you decide?”, by K. Krishna, S.R. Saraf, Y.J. Wang, J.T. Baldwin, W.J. Rogers, J.P. Gupta, and M. Sam Mannan, Reliability Engineering & System Safety, 2003, 81, 215-224,. Copyright 2003 by the name of Elsevier.
82
Figure 4.1. Systematic approach for assessing reactive hazards.
poorly characterized. Pure HA is known to explode at room temperature, and the
decomposition of HA is extremely sensitive to metal contamination.64
2. Ab initio Heat of Formation for HA
For chemicals with validated experimental data, estimations may not be
necessary, but for reactive substances with insufficient experimental data, such as
hydroxylamine, estimation methods are of prime importance.
Screening (Literature, Experimental and/or computational)
Selection of more hazardous compositions for further investigation
(Criteria based on classification discussed earlier)
Detailed testing (Sophisticated calorimetric tests and
detailed quantum calculations)
83
The reported experimental value for the heat of formation of gaseous HA is
-12.0 ± 2.4 kcal/mol65, which was derived by an indirect calculation from the
experimentally determined heat of formation of solid HA and the heat of
sublimation66,67,68. Data from measurements of solid HA should be more reliable than
data from liquid HA, because pure HA decomposes as it melts near 32 °C.66 However,
the reliability of the listed heat of formation for solid HA could not be assessed, because
the experimental procedure used to determine it was not found in the original
reference.68
Previous calculations by Sana, et al. 69 yielded -11.7 kcal/mol for the heat of
formation of gaseous HA using an isodesmic reaction at the MP4 level of theory.
Anderson70 determined a value of -10.6 kcal/mol by combining the calculated H2N–OH
bond energy71 by the G1 method with the experimental heats of formation for NH2 and
OH. Also, a heat of formation70 of -7.9 ± 1.5 kcal/mol was derived from the appearance
potential for NH2OH72 and heat of formation of HNO. Based on a statistical average of
the reported theoretical and experimental values for HA, Anderson70 recommended -9.6
± 2.2 kcal/mol for the gaseous HA heat of formation at 1 atm and 298.17 K.
The purpose of this work is to compare theoretical methods combined with
isodesmic reactions to obtain a reliable heat of formation for gaseous HA. For
comparison with an estimation approach often used by industry, the HA heat of
formation is calculated by the traditional Benson group contribution method. These
methods together with the details of the calculations are discussed in the next section and
are followed by a discussion of the results. The heat of formation values reported from
this work are for gaseous species at 1 atm and 298.17 K.
84
2.1 Computational Methods
2.11 Benson Group Contribution Method
Benson and Buss proposed a hierarchy of additivity methods for molecular
property estimations and established a theoretical framework to estimate heats of
formation based on ‘molecular groups’73. Employing the commercially available
CHETAH18 software, which includes the Benson group contribution method. Because
the H2N-(O) and HO-(N) groups were not available, the group values for NH2-(N), 11.4
kcal/mol, and OH-(O), -16.27 kcal/mol, were used as substitutes for the missing ones, as
recommended in the CHETAH18 manual. This procedure yielded -4.87 kcal/mol for the
gaseous HA heat of formation. However, substitutions for missing group values often
leads to deviations from the experimental values.
2.12 Theoretical Methods
A variety of theoretical methods, semi-empirical (AM147), density functional
theory (B3P8633 and B3LYP74), composite (G2,75 G3,76 G2MP2,77 G2MP2B3,78 G3B3,78
and CBS-Q79), and ab initio (MP2,80 MP3,81 MP4(SDTQ),82 CCSD,83 CCSD(T),84 and
QCISD(T)85) as implemented in the Gaussian 98 suite of programs44, were used for
geometry optimizations and frequency calculations. These calculations were performed
with Dunning correlation consistent polarized valence basis sets (cc-pVDZ34,
cc-pVTZ86, cc-pVQZ87, and cc-pV5Z88, where D, T, Q, and 5 refer to the number of
contracted functions in each valence sub-shell), and Dunning correlation consistent
polarized valence basis sets with diffuse functions for radial flexibility to represent
electron density far from the nuclei (AUG-cc-pVDZ and AUG-cc-pVTZ). Pople-style
basis sets 89,90 (6-31G, 6-31+G(d), 6-31G(d,p), 6-31+G(2df,p), 6-311G(d), 6-
311+G(2df,p), 6-31+G(3df,2p), 6-311+G(3df,2p), 6-311++G(3df,2p)) including
diffuse91,87 (denoted by “+” for Pople-style) and polarization functions92 (denoted by
85
“d”, “p”, ‘f”, for angular flexibility to represent regions of high electron density among
bonded atoms) were also employed. Finally, the Bond Additivity Correction (BAC)-
MP4 methodology was employed using the parameters listed by Melius and Zachariah93.
Errors in absolute quantities from quantum chemical calculations are often systematic.
To compensate for some of the systematic errors, isodesmic reactions, which conserve
the number of each type of bond in reactants and products, are used to obtain more
accurate heats of formation94. Here, the following isodesmic reactions were employed
for HA:
H2 + NH2OH ? H2O + NH3 (4.1)
H2O + NH2OH ? H2O2 + NH3 (4.2)
To benchmark the computed HA values, the heat of formation for hydrogen peroxide, a
similar species for which reliable experimental data are available, was calculated by the
same methods and with the following isodesmic reaction:
H2 + H2O2 ? 2 H2O (4.3)
The usual procedure for calculating the heat of formation value of an unknown
compound is to combine the heat of reaction obtained from an isodesmic reaction with
the experimental heat of formation values for the known compounds94. The HA heat of
formation using Reactions (4.1), (4.2), and (4.3) were determined from the equations
(4.4), (4.5), and (4.6) respectively using the calculated heat of reaction, ∆HCalcRxn, and
the experimental heats of formation values at 1 atm and 298.17 K for ammonia37,
water37, and hydrogen peroxide38 listed in Table 4.1.
∆Hf, NH2OH = ∆HExptf, NH3 + ∆HExpt
f, H2O - ∆HExptf, H2 - ∆HCalc
Rxn (1) (4.4)
∆Hf, NH2OH = ∆HExptf, NH3 + ∆HExpt
f, H2O2 - ∆HExptf, H2O - ∆HCalc
Rxn (2) (4.5)
86
∆Hf, H2O2 = 2 ∆HExptf, H2O - ∆HExpt
f, H2 - ∆HCalcRxn (3) (4.6)
The choice of isodesmic reaction is important to obtain accurate values. Although there
are 5 single bonds on the reactant side (1 H-H, 1 O-H, 1 N-O, 2 N-H) and on the product
side (3 N-H, 2 O-H) in Reaction (4.1), the N-O bond on the reactant side is not balanced
by a similar σ bond on the product side. Reaction (4.3) is similar to (4.1) in terms of
bond balance with the O-O bond unbalanced on the reactant side. In Reaction (4.2), there
are 6 single bonds on the reactant side (3 O-H, 1 N-O,2 N-H) and on the product side (3
N-H, 2 O-H, 1 O-O), but here the N-O bond is balanced better by the O-O bond on the
product side. A better bond balance should result in a more effective cancellation of
errors, therefore, Reaction (4.2) should yield a more accurate value for ∆HCalcrxn than
Reaction (4.1) at the same level of theory. Thus similar errors are expected in the heat of
formation values calculated using Reactions (4.1) and (4.3), and faster convergence with
increasing level of theory for Reaction (4.2). In addition, agreement between values
obtained from Reactions (4.1) and (4.2) can serve as an indicator that the theory is
adequate to model the system.
Table 4.1: Experimental Heats of Formation (1atm and 298.17 K)
Compound Molecular Formula Heat of Formation (kcal /mol)
Ammoniaa NH3 – 10.98 ± 0.084
Watera H2O – 57.7978 ± 0.0096
Hydrogen Peroxideb H2O2 – 32.58 ± 0.05c
a. Ref. 37. b. Ref. 38. c. Based on the listed experimental errors.
87
2.2 Results and Discussion
Values for the HA heat of formation calculated using the various levels of theory
and basis sets are presented in Table 4.2, and computed N-O bond lengths (HA) and O-O
bond lengths (hydrogen peroxide) are listed in Appendix D.
The Austin Model 1 (AM1) yielded a good prediction for the hydrogen peroxide
heat of formation, but the heat of formation value obtained for HA differed significantly
from the values obtained via ab initio, density functional, or the composite methods.
Semi-empirical methods, like AM1, perform equally well for similar compounds for
which parameters are available. However, in this case, AM1 models the O-O bond in
hydrogen peroxide but does not appear to work well for the N-O bond in HA.
Hartree-Fock (HF) is the lowest level ab initio theory employed in this work. The HF
theory is expected to yield fair to good results, despite the fact that it does not include a
full treatment of electron correlation, because errors are partially cancelled with the use
of isodesmic reactions. Heats of formation calculated with the Hartree-Fock model did
not exhibit consistent improvement with increasing basis sets, but they generally yielded
more consistent results for Reaction (4.2).
The density functional methods, although not truly ab initio, include electron
correlation at only a moderate increase in computing cost, as compared to HF, by using
functionals of electron density. Among the density functional methods, B3P86 yielded
slightly better results for hydrogen peroxide than B3LYP for identical basis sets.
However, even B3P86 with a 5Z basis set has an error of nearly 2 kcal/mol, as compared
to the experimental value, for hydrogen peroxide with Reaction (4.3). Unlike HF theory,
increasing basis functions (cc-pVDZ, cc-pVTZ, cc-pVQZ, and cc-pV5Z) and adding
diffuse functions in the density functional methods leads toward consistent values of the
heat of formation. Similar values were obtained using the 6-311+G (3df, 2p) and 6-31+G
(3df, 2p) basis sets. At the density functional level of theory, there was a significant
88
Table 4.2. Summary of Calculated Heats of Formation (∆Hf)
Hydroxylamine Hydrogen Peroxide
Method Basis Set Heat of formation (kcal/mol)
Difference between rxn (1) and (2)
Heat of formation (kcal/mol)
Reaction (1) Reaction (2) Reaction (3)
AM1 -32.34 -31.31 1.0 -33.61
HF cc-pVDZ -12.14 -12.02 0.1 -32.69
cc-pVTZ -9.76 -12.48 2.7 -29.85
cc-pVQZ -8.83 -13.06 4.3 -28.34
6-31G -10.65a -7.14 3.5 -35.59a
6-31G(d) -16.10 -10.69 5.4 -37.98
6-31+G(d) -17.47 -8.07 9.4 -33.11
6-31G (d,p) -11.81a -12.06 0.3 -32.42a
6-31+G (2df,p) -7.65a -11.71 4.1 -24.93a
B3P86 cc-pVDZ -18.67 -7.79 10.9 -43.45
cc-pVTZ -13.99 -9.31 4.7 -37.57
cc-pVQZ -12.73 -10.08 2.7 -35.03
cc-pV5Z -12.01 -10.39 1.6 -34.20
AUG-cc-pVDZ -10.62 -10.23 0.4 -33.00
AUG-cc-pVTZ -11.83 -10.39 1.4 -34.02
6-311G (d) -21.70 -7.12 14.5 -47.16
6-31+G (3df,2p) -12.63 -10.88 1.8 -34.32
6-311+G (3df,2p) -12.14 -10.89 1.3 -33.83
6-311++G (3df,2p) -12.12 -10.89 1.2 -33.81
B3LYP cc-pVDZ -18.76 -5.24 13.5 -46.10
cc-pVTZ -14.92 -8.38 6.5 -39.12
AUG-cc-pVDZ -10.48 -9.26 1.2 -33.80
AUG-cc-pVTZ -12.18 -9.69 2.5 -35.07
6-311+G(3df,2p) -8.59 -6.17 2.4 -34.99
MP2 cc-pVDZ -14.39 -9.76 4.6 -37.21
cc-pVTZ -10.24 -11.01 0.8 -31.81
89
Table 4.2. (Contd.)
Hydroxylamine Hydrogen Peroxide
Method Basis Set Heat of formation (kcal/mol)
Difference between rxn (1) and (2)
Heat of formation (kcal/mol
Reaction (1) Reaction (2) Reaction (3)
cc-pVQZ -8.61 -12.09 3.5 -29.10
MP3 6-31+G(2df,p) -8.76a - - -28.38a
cc-pVDZ -14.44b -9.82 b 4.6 -37.20 b
cc-pVTZ -10.46 b -10.77 b 0.3 -32.27 b
MP4 6-31+G(2df,p) -11.26 -11.89 0.6 -31.96
MP4(SDT
Q) cc-pVDZ -16.80 b -8.21 b 8.6 -41.17 b
CCSD(T) cc-pVDZ -17.05 -8.11 8.9 -41.52
cc-pVTZ -13.02 c -9.52 c 3.5 -36.07 c
cc-pVQZ -11.56 c -10.61 c 1.0 -33.52 c
QCISD(T) cc-pVDZ -17.08d -8.12d 9.0 -41.54d
BAC-MP4 MP4//HF -12.98 -11.09 1.9 -34.46
G2 -11.78 -11.53 0.3 -32.83
G2MP2 -11.69 -11.67 0.0 -32.60
G3 -11.15 -11.28 0.13 -32.46
G3MP2B3 -11.88 -11.45 0.4 -33.01
G3B3 -11.51 -11.35 0.2 -32.74
CBS-Q -12.18 -11.16 1.0 -33.60
GAe - 4.87 - - -32.50
Experiment
al
-12.0f
-7.9h - - -32.58g
a. Ref. 69 b. Single point energies and thermal corrections for the enthalpies for MP3 (SDTQ) and MP4 (SDTQ) were
calculated at MP2/cc-pVDZ geometry. c. Single point energies and thermal correction for the enthalpy for the CCSD(T)/cc-pVTZ and CCSD(T)/cc-pVQZ
were calculated at CCSD(T)/cc-pVDZ geometry. d. Single point energy and thermal correction for the enthalpy for the QCISD(T)/cc-pVTZ were calculated at
CCSD(T)/cc-pVDZ geometry. e. Group Additvity
f. Based on an indirect calculation as discussed in the text (Ref. 65, 66). g. Ref.37. h. Ref. 70 .
90
change in the calculated heat of formation from the cc-pVDZ to cc-pVTZ basis set. The
magnitudes of the calculated values decreased with Reaction (4.1) as the quality of the
basis set was increased, but they increased for Reaction (4.2). Thus, Reaction (4.1) and
(4.2) approached the basis set limit for the heat of formation from opposite directions.
The composite theories (G2, G3, G2MP2, G3MP2B3, G3B3 and CBS-Q) are
expected to yield the best results since they have been developed to model accurately
thermochemical quantities for small, light-atom, main group molecules. The mean
absolute deviations (MAD) associated with heat of formation value obtained using G2
and G2MP2 theories (with the G2 test set) are 1.2 and 1.6 kcal/mol, respectively95. The
G3 theory is a further improvement over G2 and reduces the MAD to 1.0 kcal/mol76.
The CBS-Q accounts for errors due to basis set truncation by an extrapolation, and the
MAD associated with the method is 1.0 kcal/mol95. The MAD associated for G3,
G3MP2B3, and G3B3, based on heat of formation values for 148 different molecules,
are 0.94, 1.13, and 0.93 kcal/mol, respectively78. All of these composite theories
performed well and predicted accurate energies for hydrogen peroxide.
The MP3 (SDTQ) and MP4 (SDTQ) results were poor for cc-pVDZ, but the
MP3 prediction improved with the cc-pVTZ basis set. CCSD(T)/cc-pVDZ and
QCISD(T)/cc-pVDZ geometries agree well with the experimental values, but realistic
energy predictions were obtained only with the cc-pVQZ basis set.
For Reactions (4.1) and (4.3), as expected, the heat of formation values obtained
for HA and hydrogen peroxide respectively exhibited trends in similar direction for the
various levels of theory and basis sets. For the HA heat of formation values using
Reaction (4.2), there was faster convergence with the basis sets for the same level of
theory. As can be seen from the heat of formation values from Reaction (4.2), accurate
values were obtained at lower levels of theory and with smaller basis sets.
91
2.3 Choice of Best Values
The difference between the values calculated using Reaction (4.1) and (4.2) can
be taken as a guide for selecting theories performing well for the system. The calculated
values, in Table 4.2, that exhibited a difference of 1 kcal/mol or less are shown in bold.
It is worth noting that these theories also predict a reasonable value for hydrogen
peroxide heat of formation (within 1 kcal/mol). However, not all of these methods are
reliable in other respects. Omitted from the final values to be averaged were the less
reliable semi-empirical AM1 predictions, since the predicted value for ∆Hf, NH2OH were
significantly different from the values obtained by other methods. The values obtained
using theories (HF, B3P86, B3LYP) that did not demonstrate an improvement in the
prediction with increasing basis set were also left out. The MP values were also left out
since these values did not exhibit convergence with increases in the basis set or the
perturbation level.
Table 4.3 summarizes the 7 best-predicted heat of formation values and their
averages, where the calculated values using Reactions (4.1) and (4.2) differed by no
more than 1 kcal/mol. The average calculated heat of formation for hydrogen peroxide
was -32.9 kcal/mol with a standard deviation of 0.4 kcal/mol. With Reaction (4.1), an
average value of -11.7 kcal/mol with a standard deviation of 0.3 kcal/mol was
calculated. With the more balanced Reaction (4.2), the average value was -11.4 kcal/mol
with a standard deviation of 0.3 kcal/mol.
92
Table 4.3. Accurate Values for HA Heat of Formation
NH2OH H2O2
Heat of formation (kcal/mol)
Theory Basis set
Mean
Average
Deviation
Rxn (1) Rxn (2) Rxn (3)
G2 1.295 -11.78 -11.53 -32.83
G2MP2 1.695 -11.69 -11.67 -32.60
G3 1.078 -11.15 -11.28 -32.46
G3MP2B3 1.1378 -11.88 -11.45 -33.01
G3B3 0.9378 -11.51 -11.35 -32.74
CBS-Q 1.095 -12.18 -11.16 -33.60
CCSD(T) cc-pVQZ - -11.56 -10.61 -33.52
Average 1.1 -11.7 -11.4 -32.9
St. dev. 0.3 0.3 0.3 0.4
Experimental -12.065 -32.5837
-7.970
The deviations from the average heat of formation for the various methods in
Table 4.3 are shown in Figure 4.2. From this pattern, it is apparent that the deviations
from average for heat of formation values from Reaction (4.1) and (4.3) track each other,
whereas the deviations for Reaction (4.2) do not follow the same trend. The average
calculated value of ∆Hf value for hydrogen peroxide is greater than the experimental
value by 0.3 kcal/mol. Since Reaction (4.1) and (4.3) are expected to yield similar errors,
93
we believe that ∆Hf value obtained using Reaction (4.1) will differ from the true value in
a similar manner and therefore recommend -11.4 kcal/mol for the ∆Hf of NH2OH as the
best estimate from both Reaction (4.1) and (4.2). The mean absolute deviation (MAD)
for each of the methods employed is listed in Table 4.3 and the average MAD value is
approximately 1.1 kcal/mol. However, the HA ∆Hf values are computed from isodesmic
reactions which should yield values with smaller errors, perhaps down to twice the
standard deviation of the various method. Thus the recommended ∆Hf value for HA,
including our precision, judgment of methodology, and accuracy is -11.4 ± 0.6 kcal/mol.
Furthurmore, the agreement and the consistency of the calculated hydrogen peroxide
average value with the experimental value suggests that our calculated average value for
∆Hf of HA is more reliable than the available experimental values, which as discussed in
the introduction, cannot be properly assessed.
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
G2 G2MP2 G3 G3MP2B3 G3B3 CBS-Q CCSD(T)
Method
Dev
iati
ons
from
ave
rage
hea
t of
fo
rmat
ion
(kca
l/mol
)
Rxn (1)
Rxn (2)
Rxn (3)
Figure 4.2. Deviations from the average heat of formation values for the
methods employed in Table 4.3.
94
Also, we have illustrated the importance of well-balanced isodesmic reactions for
determining accurate heats of formation, especially at lower levels of theory. Depending
on the level of theory, triple-ζ (6-311G or cc-pVTZ) or larger basis sets are necessary to
predict accurate HA heat of formation values. At all levels of theory the double-ζ (6-31G
or cc-pVDZ ) basis set yielded poor energies, but CCSD(T) and QCISD(T) predicted
accurate geometries in this basis set. The methods employed in obtaining the average
heat of formation value have an absolute accuracy of approximately 1.1 kcal/mol, but the
value obtained using isodesmic reactions is expected to have a smaller error and
therefore 1.1 kcal/mol represents the maximum absolute error in the calculation. As
expected the highly parameterized composite methods (G2, G3, G2MP2, G3MP2B3,
G3B3, CBS-Q) yielded the most accurate values. However, the unparametrized ab intio
CCSD(T)/cc-pVQZ yielded nearly as accurate values and in some cases, depending on
the accuracy needed, density functional methods, MP3, and MP4 may be adequate.
Heat of formation values can also be used for estimating decomposition energies.
If we use the value of –11.4 kcal/mol, CHETAH calculates the maximum heat of
decomposition as –1515 cal/g; thereby indicating a potential reactive hazard. According
to the program HA should decompose with the following stoichiometry:
NH2OH (g) → 0.33 N2 (g) + H2O (g) + 0.33 NH3 (g)
The experimentally observed heat of reaction is around 850 cal/g64, which includes all
thermal effects discussed above. The next section discusses a plausible decomposition
pathway for HA.
95
3. Investigation of Hydroxylamine Runaway Behavior
3.1 Experimental Observations
Pure HA is known to explode at room temperature. Calorimetric studies on
aqueous solutions of HA indicate that it is a highly reactive compound and the
decomposition of HA is extremely sensitive to metal contamination.64 Thermal
instability of hydroxylamine is clear from the APTAC results illustrated in Figure 4.3.
Figure 4.3. APTAC temperature-time profile for 50 wt% HA.
As shown in the above figure a significant reaction for 50 wt% HA is detected at around
120 oC. But when a small quantity of Fe2SO4 solution (8 ppm Fe2+) is added, HA reacts
rapidly at room temperature. Also, the contaminated sample shows a larger exotherm, as
seen from the red curve in the graph. The mechanism of Ha decomposition was
0
50
100
150
200
250
0 500 1000 1500
Time (min)
50 wt% HA + 0.8 ppm Fe2+
50 wt% HA
96
investigated, in presence and absence of metals. The aim of studying elementary
reactions is to understand initiation steps leading to the HA runaway reactions. Such
understanding of elementary reactions will aid in understanding the fundamental
behavior of HA, development of better inhibitors to prevent metal catalysis, and
consequently thermal runaway reactions. The results of our calculations are discussed in
the following section.
3.2 Theoretical Calculations
Runaway reactions, leading to explosion, generally follow a radical mechanism
and the mechanism can be categorized into initiation, propagation, and termination steps.
A key component of such explosive reactions are branching reactions, wherein two or
more radicals are created from a single radical, that accelerate the reaction.40 With the
above considerations, the following rules were observed to generate reaction network for
hydroxylamine decomposition reactions:
1. The first step is cleaving of bonds in the HA molecule. The dimerization of
hydroxylamine was not considered because experimental results do not suggest a
polymerization reaction.
2. There are no ionic reactions.
3. Every specie reacts with every other specie, but for any elementary reaction,
there are no more than two reactants. This is a reasonable assumption since three
or more species coming together is a much rarer event.
4. Experimentally observed products96 or stable species, such as NH3, H2O, N2O do
not participate in the chain propagation step.
5. Solvation effects have been neglected.
The following elementary reactions of hydroxylamine decomposition calculated
using the B3P86/cc-PVDZ level of theory, since good energy values were obtained for
the heat of formation calculations using this theory. Based on earlier discussion, the
97
proposed reactions are divided into three classes – initiation, propagation, and
termination, and the favorable reactions are summarized below. Associated enthalpies in
kcal/mol are indicated by ‘∆’ and products (stable species) are underlined.
Initiation
NH2OH → •NH2 + •OH ∆ = 61.6 kcal/mol
NH2OH → NH2O• + •H ∆ = 66.1
NH2OH → •NHOH + •H ∆ = 75.2
Propagation •NH2 + NH2OH → NH3 + NH2O• ∆ = -38.0 •OH + NH2OH → H2O + NH2O• ∆ = -47.2 •H + NH2O → •NH2 + H2O ∆ = -51.7 •H + NH2OH → •OH + NH3 ∆ = -42.2 •OH + NH2O• → HNO + H2O ∆ = -46.3 •NH2 + NH2O• → NH3 + HNO ∆ = -37.0 •H + NH2O• → HNO + H2 ∆ = -34.4 •H + NH2O• → NH + H2O ∆ = -26.1 •H + NH2O• → NH3 + O• ∆ = -8.6
HNO + NH2OH → NH2O• + NH2O• ∆ = -0.9 (Branching reaction)
NH + NH2OH → •NH2 + NH2O• ∆ = -25.6 (Branching reaction)
•O + NH2OH → NH2O• + •OH ∆ = -33.8
HNO + •NH2 → NH3 + •NO ∆ = -58.2
HNO + •OH → •NO + H2O ∆ = -67.5 •NO + NH → N2 + •OH ∆ = -87.6
98
Termination •NH2 + •H → NH3 ∆= -104.0 •OH + •H → H2O ∆= -114.0 •NH + NHO → N2O + H2 ∆= -26.0
NHO + NHO → N2O + H2O ∆= -87.7 •NO + •NH2 → N2 + H2O ∆= -109.2
During the initiation of a reaction, the newly formed radicals have a higher probability of
reacting with the reactant since the concentration of reactants is significantly higher. So
for the propagation steps the reactions involving NH2OH would be responsible for
accelerating the rate initially. The product spectrum, N2, N2O, H2O, NH3, H2, agrees
with experimentally observed products. However, from a safety viewpoint, it is
important to understand the initiation steps leading to the HA runaway reactions. Such
understanding of elementary reactions will aid in understanding the fundamental
behavior of HA, development of better inhibitors to prevent metal catalysis, and
consequently thermal runaway reactions. The catalytic behavior of HA was investigated
by probing potential reaction pathways in the presence of ferrous (Fe2+) ions. The
Stuttgart basis set97 was employed for modeling the Fe2+ ion. A few of the possible
reactions are shown in Figures 4.4, 4.5, and 4.6.
99
N
Fe
O
Fe
NO
Figure4.4. Probable elementary reactions of HA in the presence of Fe2+.
N
FeFe
O
Fe
N
N
O
Figure 4.5. Fe2+ interacting with the nitrogen atom of HA.
16 kcal/mol
- 2 H2O
- 2 kcal/mol
- H2O
63 kcal/mol
- OH
100
Fe
N
Fe
O
Fe
O
NO
Figure 4.6. Fe2+ interacting with the oxygen atom of HA.
Theoretical studies have provided insight into the HA - metal interactions, an
area of considerable interest in the field of catalysis modeling. Future experimental work
is aimed at gathering species-time data for developing better kinetic models and
validate some of the proposed elementary reactions.
4. Integrating Reactivity Data and Risk Analysis for Improved Process Design98
From the earlier sections of this chapter, it is evident that HA poses reactive
hazards. Although studies have characterized some of the hazards, risk involved from an
operational perspective is not obvious. The aim of this work is to integrate the available
knowledge on HA stability and perform a quantitative risk assessment on a generic HA
production plant as shown in Figure 4.7. Quantitative risk analysis aids decision-making
in two ways: it identifies the dominant contributors to the total risk, and it quantifies the
benefits of possible changes. These findings lead naturally to the specification of
- 6 kcal/mol
- H2O
59 kcal/mol
- NH2
101
possible measures to improve reliability or reduce the damage potential. Figure 4.8
depicts the procedure involved in quantitative risk analysis.
Based on available knowledge, major risks lie in the CSTR and distillation tower
besides the design fault, construction error, and other external factors. Fault tree
techniques are used to estimate the probability of these events with the existing
safeguards. The results of the fault tree are analyzed and conclusions and
recommendations are determined. The benefit of design changes and safeguards, such as
a temperature interlock on the CSTR and quench valve on the distillation column, can be
easily verified and compared by the fault tree results. These guidelines are also
applicable to the production of other hazardous chemicals.
102
Figure 4.7. Hydroxylamine production.
103
Figure 4.8. Quantitative risk analysis scheme.
104
5. Conclusions
Earlier chapters discussed the challenges in characterizing energetic materials.
This chapter focuses on hydroxylamine (HA) system, since HA was involved in two of
major industrial incidents, it has received considerable attention from researchers in last
few years. A systematic protocol for reactive hazard assessment would have recognized
the thermal hazards involved in the HA production unit. Based on calculations, the
recommended heat of formation for HA is -11.4 ± 0.6 kcal/mol. This is especially
important since experimentation on pure HA is not possible due to explosive hazards,
and demonstrates the importance of predictive techniques. A summary of plausible
reaction steps is proposed for HA decomposition in agreement with experimentally
observed products and heat of reaction. Continuing work focuses on interaction of HA
with metal atoms. The main objective is to understand the initiation and critical reactions
involved in HA runaway and use this information to develop inhibitors, radical
scavengers or chelating agents, to restrain progress of the reaction. Further, a risk
assessment study was performed to utilize the available knowledge of HA reactivity for
designing a safer production unit.
It should be noted that HA is an example of extremely reactive system and such
detailed analysis cannot be performed on all chemicals. Therefore development of a
systematic approach, as shown in Figure 4.1, is emphasized.
105
CHAPTER V
CONCLUSIONS
The field of reactive chemicals has attracted attention of researchers and industry
in the last few years in anticipation of possible regulations. This work is intended to
resolve some of the current issues and advance reactive hazard assessment.
A classification based on To and -∆H, obtained from calorimetric data, is
proposed to help recognize the more hazardous compositions. Previous researchers have
published correlations to predict explosive properties from calorimetric parameters
namely, To and -∆H. Using an additional parameter aspect ratio as an indicator of rate of
energy released, these correlations were refined. This has significantly improved
screening potential of DSC data for identifying explosion hazards.
A further advancement would be a computerized program for predicting DSC
properties, which can be developed into a screening tool. Based on experimental data on
aromatic mono nitro compounds, it was shown that calorimetrically determined
parameters can be predicted based on properties calculated at molecular level. A simple
potential energy surface with the first step of bond breaking as rate limiting was
proposed and onset temperatures for 19 mono nitro compounds were predicted with an
average error of 11%. A reduction in the predicted error to 6% was achieved by
correlating observed onset temperatures to molecular descriptors, similar to Quantitative
Structure Property Relationships (QSPR). Mary Kay O’Connor Process Safety Center
(MKOPSC) is currently collaborating with Dow Chemical Company and Eastman
Kodak to extend QSPR methodology to different families of compounds.
106
These correlations can be effectively developed into an automated computerized
screening tool to screen out the compositions. However the more hazardous compounds
necessitate additional testing and resources. Detailed investigation of HA system, as an
example of highly hazardous system, is provided. Pure HA is reported to explode at
room temperature and is therefore not well characterized. Based on theoretical
calculations, HA heat of formation is estimated as –11.4 kcal/mol and is believed to be
within 1 kcal/mol of experimental value. Further a mechanism for HA decomposition is
proposed with the aim of understanding the instability with respect temperature and
contamination, and propose effective inhibitors for the runaway reaction. Finally, a QRA
study was performed to integrate available reactivity and manufacturing information for
risk assessment.
The area of reactive chemicals presents unique challenges and this work has
demonstrated the significance of molecular characterization of energetic materials.
107
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117
APPENDIX A. DISCUSSION OF MOLECULAR MODELING METHODS
Molecular modeling techniques can be broadly classified into electronic structure
theories and force-field based methods. Electronic structure methods use the laws of
quantum mechanics to calculate geometries, energies, and other related properties of a
molecule. For the work in this dissertation, electronic structure or quantum chemistry
calculations were employed for obtaining information at molecular level. The
application of quantum mechanical laws to a system involves approximate numerical
solution to Schrödinger equation. Thus the effectiveness of the calculations depends on
the approximation involved and is a balance between computational resources and
desired accuracy. Generally, a theoretical calculation requires specification of level of
theory (approximations involved in solving Schrödinger equation) and
basis set (mathematical representation of molecular orbitals). It can also be argued that a
combination of level of theory and basis set represents approximation to Schrödinger
equation. The chart below illustrates various methods:
118
Table 1. Various theoretical methods
HF MP2
MP3 MP4 QCISD(T) .. .. Full CI
Minimal STO-3G
Split valence 3-21 G
Polarized 6-31 G
6-311 G (d,p) Diffuse 6-311+G (d,p)
6-311+G(2d,p) 6-311++G(3df,3pd) .. …
Bas
is s
et
∞ HF limit
Schrödinger Equation
The columns correspond to various theoretical methods and the rows to different basis
sets. With increasing basis set and level of theory, one approaches the exact solution to
Schrödinger equation and is accompanied by an increase in computational time. In
general, computational cost and accuracy increases as you move to the right or below in
the above chart.
There are commercial programs available for theoretical calculations and a few
of them are listed below:
§ Gaussian Inc. (http://www.gaussian.com)
§ Schrödinger Inc. (http://www.schrodinger.com/)
§ Accelrys (http://www.accelrys.com/)
119
APPENDIX B. DESCRIPTORS CALCULATED WITH B3P86/cc-pVDZ
HOMO LUMO HPC HNC WB Vmid Sr Dipole (HPC+HNC)/WB
a.u a.u kcal /mol 1/Ao 1/hartree mol/kcal
1 nitrobenzene -0.38818 -0.03931 0.519787 -0.35166 27.63 0.5249 -35.9097 5.2426 0.0061
2 1,2 dinitrobenzene -0.41432 -0.07306 0.515704 -0.35836 18.09 0.6140 -46.078 7.5324 0.0087
3 1,3 dinitrobenzene -0.41999 -0.07024 0.525467 -0.33995 26.93 0.5235 -45.5774 4.8378 0.0069
4 1,4 dinitrobenzene -0.41691 -0.08116 0.518757 -0.33439 26.80 0.5629 -45.5071 0.0014 0.0069
5 2 nitrotoluene -0.37379 -0.03716 0.520176 -0.3279 26.22 0.5247 -41.1747 5.0368 0.0073
6 3 nitrotoluene -0.37486 -0.03736 0.51954 -0.35262 27.60 0.5380 -41.0261 5.4371 0.0060
7 4 nitrotoluene -0.37868 -0.0384 0.521164 -0.3537 28.54 0.5118 -41.0197 5.7281 0.0059
8 2,6 dinitrotoluene -0.40231 -0.06426 0.522868 -0.35192 21.21 0.5094 -50.7843 3.6738 0.0081
9 3,4 dinitrotoluene -0.40235 -0.07084 0.517086 -0.36083 18.03 0.6272 -51.1144 7.8496 0.0087
10 2,4dinitrotluene -0.40535 -0.06766 0.526903 -0.34472 23.29 0.5102 -50.7286 5.4311 0.0078
11 2 nitroaniline -0.33332 -0.02919 0.533234 -0.53735 30.41 0.6039 -41.038 5.2902 -0.0001
12 3 nitroaniline -0.33065 -0.03154 0.51562 -0.56357 26.77 0.5118 -41.0257 5.4371 -0.0018
13 4 nitroaniline -0.3366 -0.0259 0.530443 -0.55023 30.78 0.4469 -41.0743 5.7281 -0.0006
14 2 nitrobenzoic acid -0.40089 -0.05264 0.524503 -0.36507 22.90 0.5965 -46.87 5.31 0.0070
15 3 nitrobenzoic acid -0.39561 -0.05653 0.480229 -0.33915 26.39 0.4975 -46.6519 3.318 0.0053
16 4 nitrobenzoic acid -0.40046 -0.0636 0.517231 -0.37614 27.31 0.5636 -46.5918 3.4293 0.0052
17 2nitrophenol -0.36422 -0.04351 0.531201 -0.39326 30.26 0.4201 -39.7609 4.3342 0.0046
18 3nitrophenol -0.36623 -0.04285 0.51869 -0.35112 26.48 0.5776 -39.8012 4.0073 0.0063
19 4nitrophenol -0.37015 -0.03914 0.526489 -0.35643 28.29 0.4857 -39.8302 5.2641 0.0060
120
APPENDIX C. AM1 DESCRIPTORS AND PREDICTED ONSET
TEMPERATURES
HOMO LUMO HPC HNC WB Vmid Sr Dipole AM1
predicted To
a.u a.u kcal /mol 1/Ao 1/hartree oC
1 nitrobenzene -0.30771 -0.11325 0.162701 -0.24179 75.63 0.3398 46.6603 4.3264 317
2 1,2 dinitrobenzene -0.31636 -0.13446 0.167717 -0.22571 64.50 0.3941 59.6145 6.3759 271
3 1,3 dinitrobenzene -0.3354 -0.13839 0.162783 -0.23217 73.15 0.3661 59.2751 4.0095 291
4 1,4 dinitrobenzene -0.33376 -0.15103 0.162391 -0.22926 72.92 0.3793 59.1759 0.0002 324
5 2 nitrotoluene -0.2949 -0.10907 0.152932 -0.25153 73.41 0.3259 53.4679 4.0731 303
6 3 nitrotoluene -0.29441 -0.11029 0.161248 -0.24312 75.86 0.3533 53.3280 4.6931 300
7 4 nitrotoluene -0.29757 -0.10866 0.159664 -0.24536 76.68 0.3545 53.3267 5.0266 298
8 2,6 dinitrotoluene -0.31534 -0.12849 0.146081 -0.23224 68.25 0.3515 66.0496 2.7574 283
9 3,4 dinitrotoluene -0.30856 -0.1297 0.164868 -0.22902 64.69 0.3926 66.2135 7.0637 253
10 2,4dinitrotluene -0.32353 -0.13239 0.158883 -0.24237 74.13 0.3671 65.9801 4.6759 271
11 2 nitroaniline -0.24817 -0.10364 0.162259 -0.30019 80.09 0.4423 53.6182 4.4874 301
12 3 nitroaniline -0.24378 -0.10277 0.159222 -0.24785 76.50 0.3530 53.8718 5.9096 300
13 4 nitroaniline -0.25054 -0.09118 0.109142 -0.26109 80.86 0.3305 54.0180 7.4857 298
14 2 nitrobenzoic
acid -0.31702 -0.13099 0.18627 -0.2355 66.41 0.3670 63.9692 3.7116 284
15 3 nitrobenzoic
acid -0.3187 -0.12183 0.229646 -0.23905 74.65 0.3530 61.0638 2.5373 298
16 4 nitrobenzoic
acid -0.31553 -0.13874 0.228782 -0.2358 74.12 0.3663 60.9865 3.5715 297
17 2nitrophenol -0.27598 -0.12394 0.180617 -0.29723 82.74 0.4017 51.5800 3.3382 312
18 3nitrophenol -0.25239 -0.11173 0.15679 -0.25364 75.75 0.3532 52.1654 3.4879 314
19 4nitrophenol -0.28044 -0.10407 0.163891 -0.25138 78.33 0.3422 52.2803 5.2343 305
121
APPENDIX D. SUMMARY OF BOND LENGTHS
NH2OH H2O2
Method Basis Set N-O (Å) O-O (Å)
AM1 1.342 1.303
HF cc-pVDZ 1.400 1.393
cc-pVTZ 1.398 1.387
cc-pVQZ 1.396 1.384
B3P86 6-311+G(3df,2p) 1.426 1.430
6-31+G(3df,2p) 1.428 1.431
6-311++G(3df,2p) 1.426 1.430
6-311G* 1.430 1.436
cc-pVDZ 1.441 1.437
cc-pVTZ 1.432 1.435
cc-pVQZ 1.428 1.432
cc-pV5Z 1.427 1.432
Aug-cc-pVDZ 1.415 1.435
Aug-cc-pVTZ 1.430 1.435
B3LYP 6-311+G(3df,2p) 1.441 1.446
cc-pVDZ 1.415 1.453
cc-pVTZ 1.447 1.452
Aug-cc-pVDZ 1.415 1.451
122
Aug-cc-pVTZ 1.445 1.451
MP2 cc-pVDZ 1.444 1.457
cc-pVTZ 1.442 1.451
cc-pVQZ 1.437 1.457
MP4 6-31+G(3df,2p) 1.449 1.465
CCSD(T) cc-pVDZ 1.454 1.470
CCSD(T) cc-pVDZ 1.454 1.470
G2 1.451 1.468
G2MP2 1.451 1.468
CBS-Q 1.438 1.453
G3 1.451 1.468
G3MP2B3 1.448 1.456
G3B3 1.448 1.456
BAC-MP4 1.404 1.396
Experimental 1.45338 1.47538
123
VITA
Sanjeev R. Saraf was born on 6th Feb. 1977 in Nagpur, India. He received his
Bachelor of Science degree in chemical engineering from University Department of
Chemical Technology (U.D.C.T), Mumbai in May 1999. He joined the Chemical
Engineering Department at Texas A&M University to pursue his Ph.D. in Aug. ’99. His
permanent address is 3 Savarkar Nagar, Khamla Road, Nagpur - 440015, India.