Chemistry Background¶

Scientific basis for PHOENIX calculations.

Oxygen Balance¶

Definition¶

Oxygen balance (OB%) indicates the excess or deficiency of oxygen in a compound for complete oxidation to CO₂, H₂O, SO₂, P₄O₁₀, etc.

Formula¶

\[ OB\% = \frac{-1600}{MW} \times \left( 2a + \frac{b}{2} + M - c - d \right) \]

Where for \(C_a H_b O_c X_d\) (with halogen X):

Symbol	Meaning
\(a\)	Carbon atoms
\(b\)	Hydrogen atoms
\(c\)	Oxygen atoms
\(d\)	Halogen atoms
\(M\)	Metal atoms (assumed monovalent)
\(MW\)	Molecular weight (g/mol)

Complete Formula (PHOENIX Implementation)¶

For compounds \(C_a H_b N_c O_d S_e P_f F_g Cl_h Br_i\):

\[ OB\% = \frac{-1600}{MW} \times \left( 2a + \frac{b}{2} + \frac{5f}{2} + 2e - \frac{g}{2} - \frac{h}{2} - \frac{i}{2} - d \right) \]

Interpretation¶

OB%	Condition	Example
OB% > 0	Oxygen excess (oxidizer)	NH₄NO₃ (+20%)
OB% ≈ 0	Balanced	RDX (-22%)
OB% < 0	Oxygen deficient	TNT (-74%)

Compounds with OB% close to zero release maximum energy on decomposition.

Maximum Heat of Decomposition¶

Definition¶

The maximum heat of decomposition (ΔHd) is the theoretical maximum energy release when a compound decomposes to its most thermodynamically stable products.

Calculation¶

\[ \Delta H_d = \sum_i n_i \cdot \Delta H_f^{\circ}(\text{product}_i) - \Delta H_f^{\circ}(\text{reactant}) \]

Where: - \(n_i\) = moles of product \(i\) - \(\Delta H_f^{\circ}\) = standard enthalpy of formation

Sign Convention¶

Sign	Meaning
ΔHd < 0	Exothermic (energy release)
ΔHd > 0	Endothermic (energy absorption)

Thermodynamic Hierarchy¶

PHOENIX uses a priority-based hierarchy to determine decomposition products:

Priority	Reaction	ΔHf° Product	Reason
1	F + H → HF	-273.3 kJ/mol	Most exothermic H-X bond
2	N → ½N₂	0.0 kJ/mol	Always forms N₂
3	P + O → ¼P₄O₁₀	-746.0 kJ/mol (per P)	Highly exothermic
4	H + O → ½H₂O	-241.8 kJ/mol	Water formation
5	C + O → ½CO₂	-393.5 kJ/mol	Full oxidation
6	S + O → SO₂	-296.8 kJ/mol	Sulfur oxidation
7	C + ½O → CO	-110.5 kJ/mol	Partial oxidation
8	Cl + H → HCl	-92.3 kJ/mol	After water
9	Br + H → HBr	-36.3 kJ/mol	After HCl
10	C → C(s)	0.0 kJ/mol	Graphite
11	H → ½H₂	0.0 kJ/mol	Hydrogen gas

Unit Conversion¶

\[ \Delta H_d \text{ (cal/g)} = \frac{\Delta H_d \text{ (kJ/mol)} \times 1000}{4.184 \times MW} \]

CHETAH Criteria¶

ASTM E659 defines four hazard screening criteria.

Criterion 1: High Instability¶

\[ \Delta H_d < -300 \text{ cal/g} \quad (-1255 \text{ kJ/kg}) \]

Indicates high potential for violent decomposition.

Criterion 2: Medium Instability¶

\[ -300 \text{ cal/g} \leq \Delta H_d < -100 \text{ cal/g} \]

Moderate decomposition energy.

Criterion 3: Oxygen Balance Concern¶

\[ -200\% < OB\% < +100\% \]

Compounds that can participate in self-oxidation reactions.

Criterion 4: Functional Group Alerts¶

Presence of functional groups associated with: - Explosive potential - Thermal instability - Shock sensitivity

Classification Logic¶

IF Criterion 1: HIGH
ELSE IF Criterion 2: MEDIUM
ELSE IF Criteria 3 AND 4: MEDIUM
ELSE IF ANY criterion: MEDIUM
ELSE: LOW

Benson Group Additivity¶

Theory¶

Benson GA estimates thermodynamic properties by summing contributions from molecular fragments (groups).

\[ \Delta H_f^{\circ} = \sum_j n_j \cdot h_j \]

Where: - \(n_j\) = occurrences of group \(j\) - \(h_j\) = enthalpy contribution of group \(j\)

Group Notation¶

Groups are defined by central atom and neighbors:

Notation	Meaning
C-(H)₃(C)	Carbon bonded to 3 H and 1 C
C-(H)₂(C)₂	Carbon bonded to 2 H and 2 C
Cb-H	Benzene carbon bonded to H
O-(H)(C)	Oxygen in alcohol

Accuracy¶

Property	Typical Uncertainty
ΔHf°	±5-10 kJ/mol
S°	±5-10 J/(mol·K)
Cp	±5-10 J/(mol·K)

Limitations¶

Strained ring corrections needed
Unusual bonding patterns may lack data
Large molecules (>100 atoms) less accurate

Gas Generation¶

Ideal Gas Law¶

Gas volume is calculated using:

\[ V = \frac{n \cdot R \cdot T}{P \cdot MW} \]

Where: - \(V\) = volume per gram (L/g) - \(n\) = moles of gas per mole of compound - \(R\) = 0.08206 L·atm/(mol·K) - \(T\) = temperature (K) - \(P\) = 1 atm - \(MW\) = molecular weight (g/mol)

At Standard Conditions (298.15 K)¶

\[ V_m = R \cdot T = 24.47 \text{ L/mol} \]

Gas Products¶

Product	Phase
N₂	Gas
H₂O	Gas
CO₂	Gas
CO	Gas
HF, HCl, HBr	Gas
H₂	Gas
SO₂	Gas
O₂, F₂, Cl₂, Br₂	Gas

Non-gas products: C (graphite), S (rhombic), P₄O₁₀

References¶

Primary Sources¶

ASTM E659 - Standard Test Method for Determining Thermodynamic Properties, Reactivities, and Initiation Hazards of Materials
Benson, S.W. - "Thermochemical Kinetics" 2nd Ed., Wiley, 1976
NIST-JANAF - Thermochemical Tables, 4th Ed., 1998

Additional References¶

Meyer et al. - "Explosives" 6th Ed., Wiley-VCH, 2007
Lide, D.R. - CRC Handbook of Chemistry and Physics
CalebBell/chemicals - Python library for thermodynamic data