Key Takeaways & Executive Findings
- •• • NDGP EOS improves TATB detonation velocity prediction by 1.5%-2.5% and detonation pressure by 1.5%-4% compared to Fried and Cowan-Fickett EOS, enabling more reliable performance evaluation for TATB-based formulations. • • NOCP EOS enhances BTF detonation pressure prediction by 3%-5% relative to legacy EOS, with velocity accuracy comparable to Fried EOS but superior to Cowan-Fickett, critical for high-detonation-temperature explosives. • • Danilenko EOS for disordered low-density carbon improves LTNR detonation velocity prediction by 3%-7% across loading densities from 0.93 to 3.1 g·cm⁻³, addressing the weak initiation regime where conventional models fail. • • The new EOS are derived from molecular dynamics-based physical models, eliminating reliance on empirical fitting to detonation data, thus providing a generalizable framework for predicting performance of novel energetic materials.
Abstract
To improve the description of complex nano-carbon clusters in explosives such as TATB and BTF under high temperature and pressure, and to enhance the prediction accuracy of the detonation thermodynamic code VPL, two new equations of state (EOS) were developed. Based on molecular dynamics simulations of carbon condensation, a phase-composition algorithm was introduced and combined with graphite/diamond single-phase EOS to establish NDGP (Nano-Diamond-Graphite-Peng) for diamond-graphite core-shell nano-carbon clusters. Separately, a modified graphite EOS was formulated as NOCP (Nano-Onion-Carbon-Peng) for onion-like nano-carbon clusters at high detonation temperatures. These EOS were applied to calculate detonation velocity, pressure, overdriven Hugoniot, and work capacity for TATB (including TATB-based explosives) and BTF. Compared with Fried and Cowan-Fickett EOS, the new EOS improved prediction accuracy for TATB detonation velocity by 1.5%-2.5% and for BTF detonation pressure by 3%-5%. Additionally, an EOS for disordered low-density carbon was introduced to compute the detonation velocity of lead trinitroresorcinate (LTNR) as a function of loading density, achieving 3%-7% improvement over existing models. The results demonstrate that the new EOS provide more accurate predictions for explosives with complex carbon products, offering a robust tool for detonation performance evaluation.
1. Introduction
Detonation thermodynamic calculations are essential for predicting the performance of energetic materials, yet their accuracy hinges on the fidelity of equations of state (EOS) for condensed carbon products. Traditional EOS, such as Cowan-Fickett and Fried, assume simple macroscopic carbon structures (graphite or diamond), which fail to capture the complex nano-carbon clusters observed in explosives like TATB and BTF. For instance, TATB detonation produces diamond-graphite core-shell nanoparticles, while BTF yields onion-like graphitic carbon. These nanostructures exhibit significantly different thermodynamic properties (density, bulk modulus, internal energy) compared to bulk phases, leading to prediction errors exceeding 5% in detonation velocity and pressure when using legacy EOS in codes like CHEETAH and BKWS. The VPL code, despite its advanced gas-phase EOS, also suffers from systematic biases: overpredicting TATB performance and underpredicting BTF velocity.
To address this bottleneck, the present study leverages molecular dynamics simulations of carbon condensation to construct physically grounded models of nano-carbon clusters. Two new EOS are developed: NDGP for core-shell structures and NOCP for onion-like structures, both integrated into the VPL code. Additionally, a Danilenko EOS for disordered low-density carbon is introduced to improve predictions for weak initiators like LTNR. These models incorporate size-dependent corrections to the cold pressure and lattice thermal pressure terms, enabling accurate description of nanoscale effects without empirical calibration against detonation data. The result is a significant enhancement in predictive accuracy across a range of explosives, offering a robust tool for designing and evaluating novel energetic formulations.
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PENG Yue, YUAN Xiao-xia, ZHANG Lei, XIE Ming-wei, MA Hong-liang, LI Fang (2026). Optimization and Application of Equations of State for Detonation Condensed Carbon Products. Chinese Journal of Energetic Materials (含能材料). https://doi.org/10.11943/CJEM2026061
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Frequently Asked Questions
How do the new NDGP and NOCP equations of state account for the size-dependent properties of nano-carbon clusters, and what specific parameters are modified?
The EOS are based on a three-term formulation: cold pressure (pC), lattice thermal pressure (pIon), and electronic thermal pressure (pEle). For NDGP, the cold pressure uses the VINET form with parameters corrected as a function of the number of carbon atoms in the cluster, reflecting surface energy and curvature effects. The lattice thermal pressure is derived from Debye theory with a modified Grüneisen parameter ratio, following Young and Corey's approach. For NOCP, the cold pressure is corrected using Viecelli's method, and the Grüneisen parameter Γ0 is set to 0.552. These modifications allow the EOS to reproduce the density, compressibility, and internal energy of nanoscale clusters, which differ significantly from bulk graphite or diamond.
What are the quantitative improvements in detonation velocity and pressure predictions for TATB and BTF using the new EOS compared to legacy models?
For TATB, the NDGP EOS improves detonation velocity prediction by 1.5%-2.5% and detonation pressure by 1.5%-4% relative to Fried and Cowan-Fickett EOS. For BTF, the NOCP EOS improves detonation pressure prediction by 3%-5%, while detonation velocity accuracy is comparable to Fried EOS but superior to Cowan-Fickett by over 1%. These improvements are critical for applications where precise performance prediction is needed, such as in warhead design or safety assessments.
How does the Danilenko EOS improve predictions for weak initiators like LTNR, and what is the range of loading densities validated?
The Danilenko EOS, designed for disordered low-density carbon (initial density 1.8 g·cm⁻³), was integrated into VPL and used to compute LTNR detonation velocity across loading densities from 0.93 to 3.1 g·cm⁻³. Compared to Fried and Cowan-Fickett EOS, the Danilenko EOS reduces prediction errors from 3%-10% down to 1.5%-2%, achieving a 3%-7% improvement. This is particularly important for weak initiators where carbon products are less ordered and legacy high-density graphite EOS overestimate performance.
Are the new EOS applicable to other explosives beyond TATB, BTF, and LTNR? What is the physical basis for their generality?
Yes, the EOS are built from molecular dynamics simulations of carbon condensation, which are not calibrated to specific explosives. This gives them a physical foundation that can be extended to any explosive producing nano-carbon clusters. The NDGP and NOCP models capture the two dominant nanostructures (core-shell and onion-like), while the Danilenko EOS addresses disordered low-density carbon. Therefore, they can be applied to a wide range of CHNO explosives, provided the carbon product structure is known or can be inferred from detonation conditions.
What are the limitations of the new EOS, and what future work is suggested by the authors?
The authors note that the new EOS improve predictions for TATB, BTF, and LTNR, but the exact relationship between molecular structure (e.g., symmetry, periodicity) and carbon cluster morphology remains unclear. They suggest that advanced experimental techniques (e.g., small-angle X-ray scattering) and theoretical methods are needed to further validate and refine the models. Additionally, the current EOS assume equilibrium conditions; extending them to non-equilibrium or time-dependent scenarios may require further development.
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