New Micro-Method for Prediction of 

Vapor Pressure of Energetic Materials

by Rose A. Pesce-Rodriguez and Elizabeth Klier

ARL-TR-6887 July 2014

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Army Research Laboratory

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ARL-TR-6887 July 2014

New Micro-Method for Prediction of 

Vapor Pressure of Energetic Materials

Rose A. Pesce-Rodriguez

Weapons and Materials Research Directorate, ARL

Elizabeth Klier

Padua Academy, Wilmington, DE

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New Micro-Method for Prediction of Vapor Pressure of Energetic Materials

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Rose A. Pesce-Rodriguez and Elizabeth Klier

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14. ABSTRACT

A new indirect method for estimating vapor pressures of organic materials, including energetic materials, has been developed.

The method provides an estimate that appears to be good to within an order of magnitude. The method relies on the 

availability of reliable experimental vapor pressure measurements at the temperature of interest. These vapor pressure values 

are correlated against corresponding thermogravimetric analysis (TGA) weight-loss onset temperatures to yield a line whose 

slope and intercept may be used to calculate the vapor pressure of an organic material. While less accurate than direct methods 

to determine vapor pressure, the new predictor is useful for quickly obtaining estimates for new compounds that might be 

available in only milligram quantities. Since the method can be used to predict vapor pressure at elevated temperatures, it is 

useful for predicting behavior of energetic materials to be subjected to vacuum stability testing. The method has been applied 

to approximately 30 energetic high-nitrogen compounds whose vapor pressures have not previously been reported.

15. SUBJECT TERMS

Vapor Pressure prediction, energetic materials, thermogravimetric analysis

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Rose A. Pesce-Rodriguez

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iii

Contents

List of Figures iv

List of Tables iv

Acknowledgements v

1. Introduction 1

2. Experimental 4

3. Results and Discussion 6

4. Conclusions 10

5. References 12

List of Symbols, Abbreviations, and Acronyms 15

Distribution List 17
iv

List of Figures

Figure 1. Vapor pressure vs. molecular weight at eight temperatures for seven energetic 

materials, from reference 16 (left). Log vapor pressure (at 370 K, from left) vs. molecular 

weight (right). ............................................................................................................................2

Figure 2. Log vapor pressure at 100 °C (373 K) vs. molecular weight for six energetic 

materials.....................................................................................................................................3

Figure 3. TGA traces for nine energetic materials heated at 10 °C/min..........................................5

Figure 4. Log vapor pressure at 100 °C versus TGA weight-loss temperatures for 14 

compounds (mix of energetic and non-energetic materials). References for vapor 

pressures: TNT, urea nitrate, PETN, RDX, HMX, TATB, and HNS (20), caffeine (19, 21

both values used in linear regression), naphthalene (22), benzoic acid (23), adipic acid 

(24), anthraquinone (25, 26, 27), melamine (28).......................................................................6

Figure 5. Log vapor pressure at (a) 100, (b) 70, and (c) 25 °C vs. TGA weight-loss 

temperatures for several compounds (mix of energetic and non-energetic materials). .............7

Figure 6. Log vapor pressure at 100 °C vs. TGA weight-loss temperatures “limited” and 

“RDX/HMX” calibration sets....................................................................................................8

List of Tables

Table 1. Samples used in this work. ................................................................................................4

Table 2. Repeatability of TGA weight-loss onset determination. ...................................................6

Table 3. Comparison of predicted vapor pressures at 100 oC for CL-20 using 3 sets of 

correlation data with values calculated estimate by Boddu et al. (29).......................................8

Table 4. Comparison of predicted vapor pressures at 100 °C for several energetics with 

experimental data from the literature.........................................................................................9

Table 5. Predicted vapor pressures at 100 °C for 29 high-nitrogen energetic materials. ................9
v

Acknowledgments

The Office of Naval Research (ONR) is acknowledged for funding the compatibility work that 

started this investigation (Liaison: Heather Hayden).

Erik Hangeland, Kimberly Watts, and Noah Lieb of the Environmental Quality Technology –

Ordnance Environmental Program (EQT-OEP) are acknowledged for funding the bulk of this 

work.

Jennifer Gottfried, Kim Spangler, and Brian Roos (U.S. Army Research Laboratory [ARL]) are 

acknowledged for useful discussions.
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction

Knowledge of a substance’s vapor pressure is critical to calculations related to any material’s 

processing, use, long-term aging, and environmental fate/transport. Rigorous measurement of a 

substance’s vapor pressure may be obtained by several proven direct methods, including the 

following:

• Direct pressure measurement methods rely on sensitive pressure gauges that directly 

measure the pressure exerted by a material. These methods cannot distinguish impurities 

from test materials and require long equilibration times (1–3).

• Effusion methods require high vacuum and a micron-scale orifice that permits escape, but 

not re-entry, of volatilized material. Weight loss of a material held at a certain temperature 

is determined collecting vaporized material that has passed through the orifice on a cold 

trap. Mass loss is usually followed as a function of time. This method requires long 

equilibration times, cannot distinguish between impurities and test materials, and is subject 

to typical problems associated with high vacuum systems (4–6).

• Gas saturation (also known as transpiration) methods require establishing an equilibrium 

concentration of vapor in a carrier gas above a test material. The test material is then 

separated from the carrier gas and its mass determined. The method is subject to typical 

problems associated with high vacuum systems (6–8).

• Thermogravimetric methods measure mass loss and correlate to vapor pressure by use of 

Langmuir theory. The method requires a uniform surface area that is most easily obtained 

by melting/freezing a test material. While this approach may not be feasible for some 

energetic materials that decompose on melting, it has been successfully applied to a 

number of energetic materials (9–10).

• Differential scanning calorimetry (DSC) methods offer the advantage of observing phase 

changes, but require that the material exhibits a sharp melting point. Also required are the 

use of a pressure/vacuum chamber and samples in DSC pans with pin holes to allow 

material to escape as the material is heated. Pressure is recorded during observance of the 

boiling endotherm, and the boiling temperature is recorded as the extrapolated onset 

temperature (11–12).

• Gas chromatography (GC) headspace analysis requires the establishment of an equilibrium 

concentration of vapor in the headspace above a test material. Samples are then collected 

and analyzed by GC, which is calibrated in advance using known masses/volumes of 

standard test material (13–15).
2

There is no single direct vapor pressure measurement method that is applicable to the entire 

range of vapor pressures and temperatures. Several methods are therefore recommended for 

measuring vapor pressure. The reader is advised against accepting vapor pressure data quoted in 

non-primary sources because values are often extrapolated from data collected at higher 

temperatures and may not be accurate at the desired temperature. For this study, accurate values 

for vapor pressure at 25 °C were sought out for a number of energetic and non-energetic 

compounds. Very little data found on material data sheets for vapor pressure at 25 °C, for 

example, are reliable.

Indirect measures of vapor pressure involve the correlation of some property of a material with 

experimentally determined direct vapor pressure measurements. The correlation is then used to 

calculate the vapor pressure of a material whose vapor pressure is not known. An example of an 

indirect method is given in figure 1 (left) (16). Figure 1 (right) shows what appears to be an 

excellent correlation of data for four energetic materials at 370 K from the plot on the left. An 

attempt to extend the correlation to include additional energetic materials from the current study 

is shown in figure 2 and illustrates that molecular weight is actually not a good predictor for 

vapor pressure. 

Figure 1. Vapor pressure vs. molecular weight at eight temperatures for seven energetic materials, from 

reference 16 (left). Log vapor pressure (at 370 K, from left) vs. molecular weight (right).

GC can also be used for indirect prediction of vapor pressure. The method is based on the 

correlation of the inverse of GC retention time to vapor pressure and has been found to give 

reasonable results for non-polar organic compounds (17) and polychlorobiphenyl (18). No

references to the method’s use for predicting the vapor pressure of energetic materials was found 

in the literature. 
3

Figure 2. Log vapor pressure at 100 °C (373 K) vs. molecular weight for 

six energetic materials.

The vapor pressure of a material will vary with crystal form (19), as well as with temperature for 

a given crystal form. While results are often cited at specific temperatures, results may also be 

reported for a range of temperatures in the form of the Clausius–Clapeyron equation 

(equation 1), the slope of which may be used to calculate the heat of sublimation (for a solid) or 

vaporization (for a liquid).

 3log P = A - B/T (1)

where

P - pressure

T - temperature (K)

A - species-specific constant

B - ΔH(sublimation or vaporization)/2.303R 

R - gas constant [8.314 J/(mol-K)]

For a critical review of vapor pressures of energetic material, the reader is directed to a recent 

publication by Ostmark et al. (20), which presents data for 23 energetic materials. The reference 

includes coefficients for the Clausius–Clapeyron equation, the temperature range at which 

measurements were made, and vapor pressure values at 25 °C (usually extrapolated).

The subject of the current work is a new indirect method for prediction of the vapor pressure of 

organic materials (energetic or non-energetic) that is based on the correlation of reliable 

experimental vapor pressure measurements at the temperature of interest with the temperature at 

which weight-loss begins in a thermogravimetric analysis (TGA) at a fixed heating rate. The 

method has been found to be applicable across a wide range of temperatures and vapor pressures. 
4

While the method will not replace rigorous, direct measurements of vapor pressure, it is seen a 

potentially useful tool for those in the chemical propulsion community who need vapor pressure 

values for a variety of applications.

2. Experimental

Samples used in this work are listed in table 1 along with any available identifying information.

Table 1. Samples used in this work.

Material Available Identifying Information

Benzoic acid Sigma Aldrich (for calorimetric determination)

Adipic acid Mettler certified thermometric standard

Anthraquinone Mettler certified thermometric standard

Naphthalene Mettler certified thermometric standard

Caffeine Arthur R Thomas Co thermometric standard

Acetanilide Arthur R Thomas Co thermometric standard

Melamine Sigma Aldrich

Urea Nitrate Matt Sherrill (U.S. Army Research Laboratory [ARL])

RDX Class 5; Lot HOL88M675079

HMX Class 5; Lot BAE09D082-03J

HNS Class 1?; Lot 208130110D

PETN Class 5?; Lot 96-34

TATB Class 5?; Lot BAE06K298-002

TNT Flake; CIB91H003-090

CL-20 Class 5; EX-9405294

NTO BAE0713305-001

DNAN Provided by the U.S. Army Armaments Research and Development Engineering Center

(ARDEC)

Fox-7 Naval Surface Warfare Center, Indian Head Division (NSWC-IHD); LLFOX7000; 50L-02

Fox-12 NSWC-IHD; LL9440Q03; 20047012

TAGZT NSWC-IHD; IH23003M-0613

BTAT Synthesized by ARDEC

HAO-TAF Synthesized by ARDEC

ABTOX Synthesized by ARDEC

TKX-50 Synthesized by ARDEC

All other highnitrogen 

compounds

Synthesized by Klapötke’s group at the Ludwig-Maximilian University of Munich.

Stored at ARL since 2007.

Analyzed as received.

Note: All abbreviations of defined on the List of Symbols, Abberivations, and Acronyms at the end of the report.
5

All samples were subjected to TGA using a TA Systems Q500 TGA. Analyses were conducted 

by first allowing the sample to equilibrate at 40 °C for 5 min and then heating at 10 °C/min to 

400 °C. All analyses were run under an inert atmosphere (nitrogen flowing at 60 mL/min). 

Sample mass generally ranged from 1 to 2 mg. No effort was made to use a constant mass. All 

samples were powders or crystals, and were dispersed in disposable aluminum pans that were 

then placed on a standard platinum TGA hanging pan. No effort was made to control the 

distribution of the sample in the aluminum pan other than to gently tap the aluminum pan before 

placing on the platinum pan. Weight-loss onset temperatures were determined by identifying the 

temperature at which the starting mass-% has decreased by 0.3 wt.%. Given a sample that starts

out at 100.0 wt.%, the weight-loss onset temperature therefore corresponds to the temperature at 

which the mass decreased to 99.7 wt.%. There is no physical significance to this mass loss; the 

0.3% loss was arbitrarily selected and appears to result in a useful correlation with 

experimentally determined vapor pressures from the literature.

An example of TGA data and weight-loss onset temperatures for a number of energetic materials 

is given in figure 3. Table 2 presents data on the reproducibility of determining the TGA weightloss onset temperature for RDX. Reproducible values were readily obtained using the process 

described above despite the variation in sample size.

Figure 3. TGA traces for nine energetic materials heated at 10 °C/min.
6

Table 2. Repeatability of TGA weight-loss onset determination.

RDX – Trial # Sample Mass

(mg) 

TGA Weight-loss Onset 

Temperature (oC) 

1 0.838 149 

2 0.615 151 

3 0.481 149 

4 0.451 152 

5 0.536 151 

6 0.523 148 

average ----- 150 ± 1.4

3. Results and Discussion

Figure 4 shows a correlation of log vapor pressure at 100 °C versus TGA weight-loss 

temperatures for 14 materials (energetic and non-energetic). The two data points in red are both 

for caffeine; values for vapor pressures measured by two different groups differ by about two 

orders of magnitude. It is clear that any indirect prediction method can only be as good as the 

direct measurements used in establishing the correlation.

Figure 4. Log vapor pressure at 100 °C versus TGA weight-loss temperatures for 14 compounds (mix of 

energetic and non-energetic materials). References for vapor pressures: TNT, urea nitrate, PETN, 

RDX, HMX, TATB, and HNS (20), caffeine (19, 21 both values used in linear regression),

naphthalene (22), benzoic acid (23), adipic acid (24), anthraquinone (25, 26, 27), melamine (28).
7

Whereas the correlation shown in figure 4 includes vapor pressure data that were either obtained 

in the range of 100 °C or obtained outside that range and extrapolated to 100 °C, the plots shown 

in figure 5 are obtained using only data obtained in the range of the indicated temperatures (i.e., 

100, 70, and 25 °C). The correlation for 25 °C includes just 5 points. Despite the plethora of data 

for vapor pressures at 25 °C available on internet, reliable data (i.e., data obtained in a range that 

includes 25 °C) was very hard to come by for the materials on hand in our lab. For all three 

temperatures, correlation coefficients are a minimum of 0.9 and are expected to yield useful 

predictions for materials with unknown vapor pressures at those temperatures.

Figure 5. Log vapor pressure at (a) 100, (b) 70, and (c) 25 °C vs. TGA weight-loss temperatures for several 

compounds (mix of energetic and non-energetic materials).

Using the correlation plots shown in figure 5a and c, the vapor pressures of CL-20 at 100 and 

25 °C were determined, and then compared with values calculated by Boddu et al. (29). The 

results are shown in table 3. ARL predictions are approximately two orders of magnitude higher 

than the calculated estimates by Boddu et al. At 100 °C, the ARL prediction suggests that the 

vapor pressure of CL-20 (log VP = –7.2) is about an order of magnitude higher than HMX 

(log VP = –8.3), whereas the Boddu et al. calculation (log VP = –9.2) predicts it to be about an 

order of magnitude lower than HMX. In either case, it is clear that CL-20 has a relatively low 

vapor pressure. For calculations involving vapor pressure, an estimate between 10–7and 10–9torr 

(at 100 °C) is probably reasonable to use until an experimental value is determined.
8

Table 3. Comparison of predicted vapor pressures at 100 oC for CL-20 using 3 sets of 

correlation data with values calculated estimate by Boddu et al. (29).

Temperature

( °C)

Boddu et al. Estimate

log VP (torr)

ARL Prediction for CL-20 log VP 

(torr)

– – Full Limited RDX/HMX

25 –14.1 –12.5 – –

100 –9.15 –7.2 –7.1 –7.3

The correlation in figure 5a was generated with TGA weight-loss onset data for eight different 

compounds (the “full set,” which includes 2 data points for caffeine). What if those nine

compounds were not available, but common materials found in most energetic material labs were 

available? What if only RDX and HMX were available? Correlations with these limited 

calibration sets are given in figure 6. The correlation on the left was produced with four common 

energetic materials, i.e., TNT, PETN, RDX and HMX, which comprise the “limited set,” while 

RDX and HMX comprise the “RDX/HMX set” (figure 6, right). The slope and intercept of the

line from the “limited set” is nearly identical to that from the “full set” (figure 5a); the 

correlation coefficient of the former is better primarily because the discrepant data for caffeine 

are omitted. The slope of the line from the “RDX/HMX set” data is slightly higher, but as can be 

seen in table 3, gives nearly the same predicted values for CL-20 vapor pressure at 100 °C. These 

results suggest that reasonable vapor predictions can be made in any lab with a TGA and a 

couple of “standard” materials (energetic or not) with reliable, known vapor pressure values.

Figure 6. Log vapor pressure at 100 °C vs. TGA weight-loss temperatures “limited” and “RDX/HMX” 

calibration sets. 

Predicted values for the vapor pressure of NTO, DNAN, TATB, and HNS are compared with 

experimental values from the literature in table 4. Values generally agree to within an order of 

magnitude (i.e., value agrees within ± 1 log units).
9

Table 4. Comparison of predicted vapor pressures at 100 °C for several energetics with 

experimental data from the literature. 

Sample Experimental

log VP (torr)

Predicted Values (from 3 Correlation Sets)

log VP (torr)

Full Limited RDX/HMX

NTO –4.6 (30) –4.9 –5.2 –5.0

DNAN –1.5 (30) –1.5 –1.8 –1.0

TATB –8.8 (20) – –7.4 –7.6

HNS –11.0 (20) – –11.4 –12.1

Table 5 gives predicted vapor pressures for 29 high-nitrogen energetic materials using both the 

“full” and “RDX/HMX” correlation data sets. Most of the high-nitrogen samples were 

synthesized by Klapötke’s group at the Ludwig-Maximilian University of Munich and stored at 

ARL since 2007. Each was analyzed as received. There are some obvious questions about the 

data. For example, why do samples 2 and 3, 1-methyl-5-aminotetrazolium nitrate and 1,4-

dimethyl-5-aminotetrazolium nitrate, which differ by just a methyl group, have predicted vapor 

pressures that vary by four orders of magnitude? The difference may be real, or may be due to 

sample impurities. It is beyond the scope of the current work to resolve such differences. The 

predicted values listed in table 5 will be further investigated based on mission needs.

Table 5. Predicted vapor pressures at 100 °C for 29 high-nitrogen energetic materials.

Control

Number Nomenclature

TGA 

Wt-loss

Onset

(oC)

Predicted

log VP

at 100 °C

(torr)

(Full Cal)

Predicted

log VP

at 100 °C

(torr)

(RDX/HMX Cal)

1 HAT NO3 5-Aminotetrazolium nitrate 102 –1.5 –0.9

2 1-Methyl-5-aminotetrazolium nitrate 91 –0.8 –0.2

3 1,4-Dimethyl-5-aminotetrazolium nitrate 160 –4.8 –4.7

6 1,4-Dimethyl-5-aminotetrazolium dinitramide 150 –4.3 –4.0

7 Guanidinium-5-nitrotetrazolate 152 –4.4 –4.1

8 Aminoguanidinium-5-nitrotetrazole 82 –0.3 0.4

9 1,4-dimethyl-5-aminotetrazolium-5,5’-azotetrazolate 105 –1.6 –1.1

10 H2BTA Biz(tetrazolyl)amine; 

(N,N-bis (1(2)H-tetrazol-5-yl)amine 233 –9.1 –9.4

14 GNT Guanazinium nitrotetrazolate 149 –4.2 –3.9

16 NTNAP, 1-nitrotetrazolato-2-nitro-2-aza-propane 130 –3.1 –2.7

17 TNMM-oxamide

N,N'- Bis-(tris-(nitratomethyl)-methyl)-oxamide; 152 –4.4 –4.1

21 Ammonium-1-methyl-5-nitriminotetrazolate 125 –2.8 –2.4
10

Table 5. Predicted vapor pressures at 100 °C for 29 high-nitrogen energetic materials (continued).

Control

Number Nomenclature

TGA 

Wt-loss

Onset

(oC)

Predicted

log VP

at 100 °C

(torr)

(Full Cal)

Predicted

log VP

at 100 °C

(torr)

(RDX/HMX Cal)

22 Diammonium-5,5’-azotetrazolate 140 –3.7 –3.4

24 DMATNT

1,4-Dimethyl-5-aminotetrazolium 5-nitrotetrazolate 160 –4.8 –4.7

26 Triaminoguanidinium-1-methyl-5-nitriminotetrazolate 171 –5.5 –5.4

27 Hydrazinebistetrazole 206 –7.5 –7.6

29 TAGDN (Triaminoguanidinium-5-dinitrate) 81 –0.2 0.5

---- Fox-7 (1,1-Diamino-2,2-dinitroethene) 159 –4.8 –4.6

---- Fox-12 (N-guanylurea-dinitramide) 198 –7.0 –7.1

---- TAGZT (triaminoguanidinium azotetrazolate) 170 –5.4 –5.3

---- BTAT bis(2,2,2-trinitroethyl)-3,6- diaminotetrazine 143 –3.8 –3.5

---- DAUHAT NG

Diaminouronium 5-Nitriminotetrazolate 174 –5.6 –5.6

---- NGA2 1-Nitramino-2,3-dinitroxypropane 98 –1.2 –0.6

---- ANG 1-amino-3-nitroguanidine 165 –5.1 –5.0

---- AMBTT

ammonium bis (1-methyl tetrazolyl) triazenate 175 –5.7 –5.6

---- 1-NAP-5-AT

1-(2-Nitro-2-aza-propyl)-5-aminotetrazole 104 –1.6 –1.0

---- HAO-TAF 4-(1-hydroxylammoniumoxy)tetrazolyl-3-amino furazan 126 –2.9 –2.4

---- ABTOX Bis(1-ammoniumoxy)tetrazolate 140 –3.7 –3.4

---- TKX-50 Bis(1-hydroxylammo-niumoxy)tetrazolate 147 –4.1 –3.8

4. Conclusions

We drew the following conclusions from this work:

• A new micro-method for predicting vapor pressure has been developed.

• The method requires a TGA and several energetic and/or inert materials with reliable 

experimentally determined vapor pressures at the temperatures of interest.
11

• The new method gives predicted vapor pressures that seem to be within about an order of 

magnitude of experimentally determined vapor pressures (i.e., value agrees within ± 1 log 

units).

• It appears that the method can give reasonable values by calibrating with as few as two

standards (RDX and HMX).

• The method has been used to predict the vapor pressures of approximately 30 energetic 

materials whose vapor pressures have not previously been determined.

• Predicted values are expected to be close enough to true values to be useful for processing, 

use, and fate and transport calculations.

• The new micro-method does not replace more rigorous methods of vapor pressure

determination.
12

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and Heat of Sublimation of Crystal Polymorphs. Journal of Thermal Analysis and 

Calorimetry, 1999, 57, 45–60.

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List of Symbols, Abbreviations, and Acronyms

1-NAP-5-AT 1-(2-nitro-2-aza-propyl)-5-aminotetrazole

ABTOX bis(1-ammoniumoxy)tetrazolate 

AMBTT ammonium bis (1-methyl tetrazolyl) triazenate 

ANG 1-amino-3-nitroguanidine 

ARDEC U.S. Army Armaments Research and Development Engineering Center

ARL U.S. Army Research Laboratory

BTAT bis(2,2,2-trinitroethyl)-3,6- diaminotetrazine 

DAUHAT NG diaminouronium 5 nitriminotetrazolate 

DMATNT 1,4-Dimethyl-5-aminotetrazolium 5-nitrotetrazolate 

DNAN 2,4-dinitroanisole

DSC differential scanning calorimetry

EQT-OEP Environment Quality Technology-Ordnance Environmental Program

Fox-12 N-guanylurea-dinitramide

Fox-7 1,1-diamino-2,2-dinitroethene

GC gas chromatography 

GNT guanazinium nitrotetrazolate

H2BTA biz(tetrazolyl)amine (N,N-bis (1(2)H-tetrazol-5-yl)amine

HAO-TAF 4-(1-hydroxylammoniumoxy)tetrazolyl-3-amino furazan 

HAT NO 3 5-Aminotetrazolium nitrate

HMX cyclotetramethylenetetranitramine

HNS hexanitrostilbene

NGA2 1-nitramino-2,3-dinitroxypropane

NSWC-IHD Naval Surface Warfare Center, Indian Head Division 
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NTNAP 1-nitrotetrazolato-2-nitro-2-aza-propane 

NTO nitrotriazolone

ONR Office of Naval Research

PETN pentaerythrite tetranitrate

RDX cyclotrimethylenetrinitramine 

TAGDN triaminoguanidinium-5-dinitrate

TAGZT triaminoguanidinium azotetrazolate

TATB triaminotrinitrobenzene

TGA thermogravimetric analysis 

TKX-50 bis(1-hydroxylammo-niumoxy)tetrazolate

TNMM-oxamide N,N'- bis-(tris-(nitratomethyl)-methyl)-oxamide

TNT 2,4,6-trinitrotoluene
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