MD and Force Field Development for HMX

1
MD and Force Field Development for HMX

• Level 0 - Generic Force Field (Dreiding)
  calculations
• Density of States
• Pressure Loading
• Phase transitions
• Level 1 - Vibrationally accurate force field for
  DMN, HMX RDX
• DFT (B3LYP) calculations on isolated monomers
• QUEST calculations on condensed phase systems
• FFOPT parameterization
• Intra-, inter-molecular VET, phonon - phonon
  couplings
• H-bond effects

2
Crystallographic Forms of HMX
E 0.10 kg/cm2
E 0.20 kg/cm2
429 K - to melting point
r 1.58
r 1.78
r 1.894
r 1.839
E 0.20 kg/cm2
Impact Energy E 0.75 kg/cm2
Stable _at_ 300K
377 - 429 K
3
Correlation of Density of States (from MD) with
Sensitivity (h50 measurement)
b-HMX h50 0.33m
TATB h50 3.2m
g-HMX h50 0.14m
a-HMX h50 N/A
d-HMX h50 N/A most sensitive
4
Chair Form - a, Boat Form - b,g,d
Short intra-molecular HO contacts, responsible
for VET and energy localization in N-N bond?
QM B3LYP/6-31G E 0.0
QM B3LYP/6-31G E 2.218 Kcal/mol
5
Comparison of Molecular Cell Parameters for HMX
b and a forms
6
Dreiding Frequencies Comparable to DFT Calculation
7
Comparison of different van der Waals functions
for HO interaction

• Dreiding Exponential-6 has the softest inner wall
• Dreiding LJ 12-6 is too steep on the inner wall
• COMPASS force field (9-6) is a good approximation
  to the exp-6 form
• Dreiding 9-6 is not adequate

• Conclusion
• Accuracy - Exponential - 6
• Speed - COMPASS

8
Comparison of Crystallographic Cell Data with
Experimental Values from Cady Ollinger for b-HMX
9
Comparison of b-HMX Elastic Constants and Bulk
Modulus with Experimental Data (Joe Zaug, LANL)
10
HMX Cold Compression Curves for the 4 crystal
morphologies

• a form is the least compressible followed
  closely by the g form
• d form is the most compressible
• stable b form is intermediate in compressibility

a
d
b
11
Isothermal P-V curves for b-HMX

• P-V curves obtained from
• minimization for 0K
• 20ps NPT Molecular Dynamics at elevated
  temperatures
• evidence of melting above 600K?

Melting behavior?
12
Calculation of Shock Adiabat intersection with
P-V isotherms

• Proof-of-principle exercise to calculate
  temperatures from intersection points
• Volume needs to be converted to engineering units

13
b-HMX Cv from Phonon Dispersion Curves of Crystal

• Series converged at 222 directions in Brillouin
  zone
• 90 of asymptotic high T limit reached at 1400K

14
Convergence of Gruneisen Parameter from 50ps
(0.5fs step) MD of 4x3x2 supercell of b-HMX

• Gruneisen Parameter shows converged behavior by
  40ps of MD

15
Level 1 - Vibrationally Accurate Force Field
Development - Dimethylnitramine
16
Comparison of Vibrational Frequencies for DMN
17
Geometric Parameters for DMN Crystal
18
TATB

• Overview
• TATB (1,3,5-triamino-2,4,6-trinitrobenzene) has
  planar structure. This makes it easy to pack and
  can have high density. Experimental density at
  STP is 1.9374 g/cc.
• TATB crystal has low symmetry triclinic (P-1).

19
TATB

• Force Field Result
• Compare with
• Experiment
• Exp6-Dreiding Force Field uses Morse bond stretch
  and Exp6 van der Waals interaction. The 300K
  isothermal curve fits well with the experimental
  data.

20
TATB

• Isothermal Curves with Exp6-Dreiding Force Field

21
TATB

• Force Field Improvement
• and Ab initio calculations
• Lacking experimental data, we use ab initio
  calculations to improve and validate our force
  field. Optimization of the initial results is
  on-going.
• Specific Heat at constant pressure for gas phase
  TATB are calculated at different temperatures
  from vibrational frequencies.

22
TATB

• Ab initio calculations of
• Dimer Binding Energy
• Dimer binding Energy of two TATB molecules as a
  function of the separation distance is calculated
  to explore H-bond potential.
• At STP, the H2N-NO2 separation distance in TATB
  crystal is 3.400A in a direction, 3.421A in b
  direction.

23
TATB

• Ab initio Calculations of Dihedral Angle Torsion
  Energy

f2
f1
f3
f0
F0 is the O-N-C-C dihedral angle. F1 is the left
hand H-N-C-C dihedral angle. F2 is the right hand
H-N-C-C dihedral angle. F3 is the non-planarity
of C6 ring.
24
TATB

• Future Work
• Shock Hugoniot from isotherms
• Gruneisen Parameter
• Further Force Field Improvement
• Large scale calculations

25
Kel-F800

• Overview
• Kel-F 800 is a random copolymer of
  chlorotrifluoroethylene and vinylidene fluoride
  monomer units in a 31 ratio.
• The presence of the vinylidene fluoride disrupts
  the the crystallinity of the chlorotrifluroethylen
  e to form an essentially amorphous polymer
• Although amorphous, the polymer is very dense due
  to the presence of the Cl and F atoms
• It is used in composites and as a binder for many
  plastic-bonded explosive systems
• First atomistic/molecular study of Kel-F 800
  system.

26
Kel-F 800

• The packing dilemma
• Using 2 chains causes alignment within unit cell
  giving a crystalline type appearance.
• Using more chains in the unit cell overcomes this
  problem.
• The Cerius2 Amorphous builder initially builds to
  the correct density but minimizes to a much lower
  density than given from experimental.
• The MSC developed code for Cohesive Energy
  Density packs the molecules in such a way as to
  maintain the correct density.

24 monomers - 2 chains
24 monomers - 16 chains
The appearance of chain alignment is apparent
when only 2 chains are used however the relative
complexity of the 16 chain case should eliminate
this problem.
27
Kel-F800
Cohesive Energy Density
COMPASS
PCTFE
75

• Validation
• Due to the lack of experimental data for the pure
  Kel-F 800 polymer system, poly(chlorotrifluorethle
  ne-co-vinylidene fluoride) Some validation work
  was done by calculating Cohesive Energy Densities
  and Solubility parameters using a MSC in-house
  developed code.
• Initial studies and choice of force field were
  conducted on pure PCTFE, poly(chlorotrifluoroethyl
  ene) for which some experimental data is given.
• The Dreiding-EXP6 force field appears to be the
  force field of choice. It is, however, somewhat
  slower than the COMPASS force field.

70
65
Upper limit of Experiment
60
Dreiding-EXP6
CED (cal/cm3)
55
lower limit of Experiment
50
45
40
2
5
16
No of "Polymer" chains in cell
Cohesive Energy Density
Kel-F 800
100
80
60
Dreiding-EXP6
CED (cal/cm3)
COMPASS
40
20
0
2
5
16
No of "Polymer"chains in cell
28
Kel-F 800
Kel-F800

• Force Field Choice
• Initial work was done using the Dreiding force
  field. This uses Lennard-Jones (LJ) 12-6
  potential to calculate the van der Waals
  interactions.
• This forcefield gives a very steep inner wall
  slope for the pair potential between 2 non-bonded
  atoms.
• The Buckingham EXP6 potential gives a much a
  more gentle inner wall slope, however is
  computationally more demanding and substantially
  slower.
• The Compass force field from MSI uses LJ 9-6
  potential and is supposedly optimized for polymer
  simulations. It is also faster than the EXP6
  potential.

Cold Compression Curves
Force field comparisons
70
COMP
60
EXP6
LJ9-6
50
Dreiding-EXP6
LJ12-6
40
Pressure (GPa)
30
20
COMPASS
10
0
0.45
0.55
0.65
0.75
0.85
0.95
V/Vo
29
Kel-F800
Kel-F 800

• Isothermal Compression
• The Dreiding-EXP6 and Compass force fields have
  proven to be the best.
• Compass has the advantage of being
  computationally faster than EXP6.
• The disadvantage is that Compass is not
  parameterized for HE materials.
• Dreiding-EXP6, although slow, will be able to
  handle the inclusion of the HMX and TATB
  molecules for a more complete shock wave
  simulation on an atomistic level.

Isothermal Compression Curves
Dreiding-EXP6 force field
70
0K
100K
60
200K
300K
50
40
Pressure (GPa)
30
20
Cold Compression
10
0
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
Volume (cm3/g)
30
Kel-F800

• Future work
• Determining molecular weight dependence of chains
  used in cell
• finding the compromise between accuracy and
  speed.
• Calculating the GRUNEISEN parameter and other
  physical properties
• as a function of temperature and pressure
• longer Molecular Dynamics runs
• Repeating for various polymer binders
• eg Estane
• Huge simulations combining polymer binder and HE
  materials.