Investigations of the Intermolecular Forces between RDX and

Article pubs.acs.org/JPCA

Investigations of the Intermolecular Forces between RDX and Polyethylene by Force−Distance Spectroscopy and Molecular Dynamics Simulations D. E. Taylor,† K. E. Strawhecker,‡ E. R. Shanholtz,§,#,¶ D. C. Sorescu,∥,⊥ and R. C. Sausa*,† †

ARL-RDL-WML-B, ‡ARL-RDL-WMM-EG, and §ARL-RDL-WMM-EUS, Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, United States ∥ National Energy Technology Laboratory, U.S. Department of Energy, Pittsburgh, Pennsylvania 15236, United States ⊥ Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States ABSTRACT: The development of novel nanoenergetic materials with enhanced bulk properties requires an understanding of the intermolecular interactions occurring between molecular components. We investigate the surface interactions between 1,3,5-trinitro-1,3,5triazacyclohexane (RDX) and polyethylene (PE) crystals on the basis of combined use of molecular dynamics (MD) simulations and force−distance spectroscopy, in conjunction with Lifshitz macroscopic theory of van der Waals forces between continuous materials. The binding energy in the RDX−PE system depends both on the degree of PE crystallinity and on the RDX crystal face. Our MD simulations yield binding energies of approximately 132 and 120 mJ/m2 for 100% amorphous and 100% crystalline PE on RDX (210), respectively. The average value is about 36% greater than our experimental value of 81 ± 15 mJ/m2 for PE (∼48% amorphous) on RDX (210). By comparison, Liftshitz theory predicts a value of about 79 mJ/m2 for PE interacting with RDX. Our MD simulations also predict larger binding energies for both amorphous and crystalline PE on RDX (210) compared to the RDX (001) surface. Analysis of the interaction potential indicates that about 60% of the binding energy in the PE−RDX system is due to attractive interactions between HPE−ORDX and CPE−NRDX pairs of atoms. Further, amorphous PE shows a much longer interaction distance than crystalline PE with the (210) and (001) RDX surfaces due to the possibility of larger polymer elongations in the case of amorphous PE as strain is applied. Also, we report estimates of the binding energies of energetic materials RDX and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) with PE, propylene, polystyrene, and several fluorinecontaining polymers using Lifshitz theory and compare these with reported MD calculations.

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INTRODUCTION

understanding of the physical and chemical interactions occurring at energetic material−polymer interfaces. The adhesion properties of polymeric systems on surfaces of energetic molecular crystals can be characterized using force− distance (FD) spectroscopy. This technique employs an atomic force microscope (AFM) to measure the interaction force between two surfaces. FD spectroscopy offers direct measurements of the interfacial forces between two interacting materials, generally having magnitudes on the order of 10−6 to 10 −13 N and with sub-nanometer resolution. This information can be used to extract the binding strength of the interacting materials and the relative stiffness of the sample surface. Although this experimental technique has been applied to many systems, its application to energetic materials is extremely limited.14−20 Zakon and co-workers21 studied the adhesion of different energetic particles, including 1,3,5-trinitrotoluene (TNT), 1,3,5-trinitro-1,3,5-triazacyclohexane (RDX), and octahydro-

Intermolecular interactions govern many physical and chemical processes occurring on the surface of materials such as adsorption, adhesion, and catalysis. These interactions are particularly important for particles of nanometer to micrometer size in length having large surface areas. Such properties can lead to an increase in the contact with surrounding materials, thereby increasing the probability of chemical and physical interactions. Thus, understanding intermolecular interactions among different materials and integrating them into design strategies is paramount to develop novel structured materials or to enhance the performances of the existing ones. In the case of energetic materials with polymeric binders, understanding how these interact is particularly important in several areas, for example to develop new polymer-based sensors for explosives detection,1 to increase the collection efficiency of the explosive residues adsorbed on surfaces for enhanced detection sensitivity,2−4 or to formulate new, polymer-based explosives or munitions.5−13 Thus, tailoring the compatibility and binding properties of the particular constituents for enhanced performance requires a fundamental © 2014 American Chemical Society

Received: April 22, 2014 Revised: May 23, 2014 Published: June 12, 2014 5083

dx.doi.org/10.1021/jp5039317 | J. Phys. Chem. A 2014, 118, 5083−5097

The Journal of Physical Chemistry A

Article

In this work, we focus on analysis of the interaction properties of polyethylene (PE) with RDX surfaces. Figure 1

1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) and gold substrates coated with different self-assembled monolayers (SAM) by AFM and density functional theory (DFT). In one set of experiments, they deposited the SAMs on a gold-plated tip and glued the particles on a glass slide, whereas in another set of experiments they glued the explosive particles on the cantilever and deposited the SAMs on a glass substrate. They found that the SAMs with the hydroxyl (−OH) or the phenyl (−C6H5) end groups yielded higher adhesion forces relative to the methyl (−CH3) group or other groups studied. Their DFT calculations of a single, energetic molecule and a 5-atom hydrocarbon chain containing the selected functional groups substantiated qualitatively their experimental findings. No direct quantification of the measured forces was provided due to the difficulty to determine the contact area of the micro particles used with irregular shapes and roughness. More recently, Chaffee-Cipich and co-workers22 reported the adhesion forces of different energetic particles (including RDX) mounted on an AFM cantilever and several polymer-coated substrates. They reported an adhesion force normalized by the particle’s average radius of curvature of 45 ± 9 nN/μm for RDX and two, melanine-based coatings. Their experimental results compare very well with their Matlab-based simulations using an adhesion model based on van der Waals forces. Molecular dynamics (MD) complements FD spectroscopy and provides a useful means for determining molecular and surface structures and their time evolution together with the corresponding interfacial binding energies.7−13 Using this technique, Xiao and co-workers investigated the binding and mechanical properties of β-HMX and α-RDX interacting with a variety of fluorine-containing polymers.7,8 Among these, the largest binding energy found using force field calculations was for HMX interacting with polyvinylidene difluoride (PVDF). More recently, in a subsequent MD study focused on RDXbased plastic explosives, it was found that the binding energies of RDX with PVDF or polychlorotrifluoroethylene (PCTFE) depend on the specific polymer used and on the RDX crystal face on which adhesion of the polymer takes place. On the basis of the calculated elastic tensors and bulk mechanical properties, it was concluded8 that addition of small amounts of fluorine polymers to the energetic crystals improve their mechanical properties. Several other researchers performed MD simulations of RDX-based plastic explosives to determine the effect of the interface interactions between crystalline RDX and the polymer binder upon the mechanical properties of the hybrid systems. Li and co-workers9 investigated the interactions of RDX and 3(azidomethyl)-3-methyloxetane (AMMO), whereas Lan and co-workers10 studied those of RDX and hydroxyl terminated glycidyl azide polymer (GAP) or GAP grafted with dimethylhydantoin (DMH). Similarly, Abou-Rachid and coworkers11 studied the interfacial interactions of RDX and hydroxy terminated polybutadiene (HTPB) and dioctyl adipate (DOA), and more recently the interfacial interactions of RDX with HTPB−isophorone diisocyanate (IPDE)-DOA.12 These studies have demonstrated that for a given polymeric system the binding energies on different crystalline surfaces of RDX are different from each other. Also, the mechanical properties of RDX are generally improved by adding a specific polymer in formulation. Specifically, the addition of a small amount of polymer to RDX yields a system that is more ductile, yet less rigid and less brittle compared to neat RDX.

Figure 1. Molecular formulas and unit-cell structures of crystalline αRDX (left panels) and PE (right panels).

shows the molecular and crystal structures of both these two materials. Polyethylene consists of many repeating (−[ CH2− CH2]n−) units, where n typically ranges from 103 to 106. Its molecular weight, extent and type of side branching, and polydispersity control mostly its degree of crystallinity, and thus its density. PE crystals consist of macromolecules in the trans conformation, as this configuration possesses the lowest potential energy. X-ray crystallography reveals that PE crystals are orthorhombic cuboids with cell dimensions of a = 7.417 Å, b = 4.939 Å, and c = 2.534 Å.23,24 Each cell comprises two C2H4 units, one unit from one chain segment and four other shared with adjoining cells at the corners. A molecular weight of 56.0 g/mol for the unit cell, together with its unit-cell volume, yields a calculated density of 1.00 g/cm3 at 298 K. In contrast, the RDX molecule consists of three alternating N−NO2 and CH2 groups arranged in a six-membered C−N ring. RDX exists in a number of conformations. In the gas phase an axial AAA chair conformation with C3v symmetry was shown to be the most stable by electron diffraction experiments, whereas in condensed phase the EAA conformation with two nitrogen groups in the axial positions and the third one in the equatorial position was determined to be the most stable.25 In the condensed phase, RDX has three polymorphs, α, β, and γ, with the α polymorph existing at ambient pressure and temperature. X-ray and neutron scattering studies reveal that the α-RDX crystal structure is orthorhombic (space group Pbca) and has cell dimensions of a = 13.182 Å, b = 11.574 Å, and c = 10.709 Å.25,26 Each cell comprises eight RDX molecules, yielding a calculated density at ambient conditions of 1.806 g/cm3. In this paper, we report our combined experimental and modeling studies of the RDX−PE system by FD spectroscopy and MD simulations. We explore the role played by the degree of PE crystallinity and by the RDX crystallographic face on binding energy of the PE−RDX system, report the binding energies of the crystalline and amorphous PE on the RDX 5084



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Figure 2. (A) AFM image of RDX (210) recorded over an area of 5 μm × 5 μm with a resolution of 1024 × 1024 pixels. (B) Surface height distribution. (C) Roughness scan of the horizontal center line of the image in (A). (D) Surface topography of the PE colloid (inset) with details of the most prominent feature that makes contact with the RDX surface.

(210) and RDX (001) surfaces, and reveal and quantify key atomic interactions contributing to the total binding energy of these systems. Finally, we utilize Lifshitz theory to estimate the binding energies of RDX and HMX energetic crystals with PE and other polymers such as PVDC, PCTFE, and polytetrafluoroethylene (PTFE) and compare our results to those reported previously.

system can be obtained on the basis of the energy equipartition theorem as follows: 1 1 mωo 2⟨Zc 2⟩ = k bT 2 2

(1)

where m corresponds to the oscillating mass of the cantilever, ωo corresponds to the resonant frequency of the system, ⟨Zc2⟩ represents the mean-square deflection of the cantilever’s thermal vibrations, kb corresponds to the Boltzmann constant, and T is the absolute temperature.27−29 Because ωo2 = kc/m, the above equation reduces to kc = kbT/⟨Zc2⟩, where kc represents the cantilever’s spring constant. A spring constant of 25.6 N/m was obtained in our experiments from the thermal noise power spectrum by fitting the resonance peak determined at 288 kHz and using its area as a measure of the resonance energy. Such a stiff cantilever lessens the impact humidity has on the force measurements. Four sets of force measurements, each set recorded at a different surface location and consisting of four different measurements, were recorded for the RDX (210) surface at 24.1 °C and ∼36% relative humidity (RH), where capillary force effects are minimal. The MFP-3D AFM was used to ascertain the roughness of the RDX (210) crystal surface. Figure 2A shows a typical RDX surface image recorded in noncontact mode using a silicon cantilever (28 N/m, 188 Hz) at a rate of 0.25 Hz in air. The resolution is 1024 × 1024 pixels and the scan size is 5 μm × 5

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EXPERIMENTAL METHODS An AFM (MFP-3D, Asylum) equipped with a temperature controller and an enclosure for vibration and acoustic isolations was utilized for both FD spectroscopy and surface imaging. In the FD mode, a polyethylene sphere of about 50 μm in diameter was glued to the tip of a cantilever with the aid of micromanipulators and a stereoscope. We will discuss our preparation of the polyethylene microspheres later in this paper. The AFM records the cantilever deflection as a function of the distance between the sample and the cantilever rest position. The supplied Igor Pro Software converts the photodiode sensor output and piezoelectric position into the dependence of the force on the distance between PE−RDX and PE−PE samples, respectively. The spring constant of the PEcontaining cantilever was measured using the AFM’s built-in thermal noise method. This method models the cantilever as a simple harmonic oscillator relying on the thermal vibrations that occur at room temperature. The potential energy of this 5085



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Figure 3. Typical RDX−PE force−distance plot. The inset shows the force values obtained from 16 measurements.

μm. The surface roughness was evaluated as the root-meansquare value, Rq, of the distribution of heights in the AFM topographical image obtained using Igor Pro 6 software. The Rq has been determined on the basis of the equation n

Rq =

∑1 Yi 2 Vn

and 2-propanol (Fisher Scientific, ACS grade) and then dried with nitrogen gas (Matheson, 99.999%). After mounting the PE spheres on the cantilevers, both the spheres and cantilevers are rinsed with 2-propanol followed by nitrogen drying. We obtained the RDX crystals with (210) surface areas of ∼5 mm2 from Dr. K. Ramos of the Los Alamos National Laboratory. The resulting low density PE spheres are semicrystalline. Their percent crystallinity, Pc, can be related to their density via the equation Pc = 100(ρc/ρPE)[(ρPE − ρa)/(ρc − ρa)], if they are composed of both crystalline and amorphous phases.31 In the above equation, ρc represents the density of 100% crystalline PE, ρa represents the density of 100% amorphous PE, and ρPE represents the density of our PE sample. We estimated a Pc value of about 47% for our PE spheres using a ρc value of 1.00 g/cm3, ρa value of 0.853 g/cm3, and a sample ρPE value of 0.92 g/cm3 This value overestimates somewhat the degree of PE crystallinity of our samples because the above equation applies to a two-phase system. In the latter part of this paper, we show that our PE spheres contain a disordered anisotropic phase, in addition to the amorphous and orthorhombic, crystalline phases. The Raman analyses of the RDX (210) and PE surfaces were performed using a LabRAM Aramis Microscope (Horiba Jobin Yvon). The spectra were acquired in a backscattering geometry using the 532 nm radiation from a 20 mW laser and a 10× microscope objective. This objective both focused the laser radiation to a spot size of about 1 μm2 and collected the induced Raman signal. The spectra were collected in the spectral region from 50 to 4000 cm−1 with a resolution of ∼0.8 cm−1. Raman signals from a standard toluene/acetonitrile (1:1) mixture (786.5, 1003.6, 1211.4, 2253.2, 2291.8, 2940.9, and 3057.6 cm−1) and silicon (520 cm−1) were used for instrument calibration.32 The Raman spectrum of RDX (210) (not presented) is similar to RDX spectra previously reported in the literature.33−36 Briefly, the observed spectral features result from both intermolecular and intramolecular vibrations. The strongest peak near 100 cm−1 results from a lattice mode

1/2

(2)

where Yi is the height value and Vn is the number of points for the defined area. RDX roughness analyses of the 25 μm2 area and the 1 μm2 area at its center yield Rq values of 787.3 pm and 779.6 pm, respectively. Figure 2 (right) shows a 3-D image of the PE colloid captured with an Olympus confocal, scanning microscope (LEXT-OLS-3100/OLS v. 5.0.9 software) using a 408 nm laser and a bright-field, 50× objective (MPLFLN 50× BD). The vertical length resolution of the instrument is 10 nm. The inset reveals a number of micrometer size asperities present on the PE surface, whereas the main figure reveals the prominent feature that comes into contact with the RDX surface. We performed surface analysis of the images after invoking the software’s spike removal and first-order, flattening-fitting routine to remove the random spikes and the noise from the thermal drift. Our analysis of the prominent PE feature yields an effective radius, Reff, of 1.17 × 10−6 m. This value is an average of the particle's measured x, y, and z radii obtained from x-y contour plots, and x-z and y-z planes passing through the midpoints of the particle’s x and y lengths. Polyethylene (PE) spheres are prepared by spheroidization.30 Low-density polyethylene particles (Alpha Aesar) with a reported density of 0.92 g/cm3 at 20 °C and particle size of 500 μm were first placed in a beaker with silicon oil, which was stirred with a Teflon-coated magnet and then heated to about 110 °C for about 10 min. The mixture was then cooled slowly to room temperature to preserve the shape of the spherical particles, and the spheres were filtered from the oil. The mixtures were rinsed several times with 1,2-dichloroethane (Sigma-Aldrich, 99.8%), acetone (Fisher Scientific, ACS grade), 5086



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vibration. The peak near 850 cm−1 is attributed to C−N−C deformation and CH2 rocking, whereas the peak near 886 cm−1 results from symmetric ring stretching. Other noteworthy peaks occur near 1275 and 1600 cm−1 (NO2 symmetric and asymmetric stretches) and in the range 2950−3100 cm−1 (C−H symmetric and asymmetric modes of vibrations). The Raman spectrum of PE will be presented and discussed in the latter part of this paper. Figure 3 shows the typical force−distance traces for the RDX (210) surface and the PE colloid using a load of about 2.5 × 10−6 N and a scan rate of 1 Hz. The approach trace is shown in red, whereas the retraction trace is represented in black. A negative force implies attraction between the two material surfaces. There is no measurable interaction for separation distances larger than 200 nm (point A). As the PE sample approaches the RDX surface, we observe a decrease in the force and a jump into contact (point B). Thereafter, the PE surface is coupled to RDX surface as the force increases to ∼2.5 μN (point C). At this point, the PE sample is retracted from the RDX surface until the forces reach a minimum (point D) which we arbitrarily assign as the origin of the distance. Thereafter, the PE surface separates from the RDX surface. The retraction curve in Figure 3 shows three distinct features: a peak at 0 nm, a smooth, negative curvature extending from about 5 to 185 nm, and a small, abrupt force increase near 185 nm. These features reflect a number of PE− RDX surface interactions that depend both on physical properties and on chemical composition of the interacting materials. Lifshitz−van der Waals attractions, e.g., Debye, Keesom, and London forces, are the primary sources of interaction in this system.19 The smooth, negative curvature in the force trace is characteristic of polymer-based systems, stemming from the stretching of the polymer until it detaches from the surface. We describe and discuss this phenomenon for the RDX−PE(100% amorphous) system in the modeling section. We ruled out electrostatic forces resulting from macroscopic triboelectric charging while handling the samples because we did not observe any electrical charging of the two materials. RDX and PE may pick up a charge when they are in contact during the measurement; however, we did not observe this in our case. We performed the FD measurements several times at various RDX surface locations and did not observe an increase in the force values with repeated contact (Figure 3). Although capillary forces due to water condensation on the PE or RDX surface are not expected to dominate under our experimental conditions (∼36% RH and PE is hydrophobic), they may play a minor role because water molecules may condense on the RDX surface facilitated by the presence of N− NO2 functional groups. Zakon and co-workers measured the adhesion forces of irregular particles of TNT, HMX, RDX, and pentaerythritol tetranitrate (PETN) with various SAMs by FD spectroscopy and attributed the larger adhesion values of some of their measurements involving TNT and HMX to capillary forces contributions.21 Their RH ranged from 35 to 60% for their ambient condition measurements; however, they did not report the RH values for their specific measurements. Figure 3 shows that the maximum force for separating PE from RDX is about 230 nN. A statistical analysis of 16 different measurements (inset panel in Figure 3) using four different locations yields an average value of −275 ± 50 nN. This value is nearly independent of the scan rate, 0.1−1 Hz, and is not normalized to the particle size or to the contact area. The experiments were performed at low applied loads, ∼2.5 × 10−6

N, to minimize deformation of PE. Nevertheless, some hysteresis was observed due to the contact between PE sphere and RDX surface. We normalized the energies with the PE− RDX contact area to allow easy comparison with our Lifshitz and MD calculated values. For this purpose, we have used the following Johnson−Kendall−Roberts (JKR) expression to obtain an estimate of the PE−RDX contact area (Ac) from the contact radius, a, of the PE colloid using the experimental force−displacement curves.19,20,37,38 a=

⎛ R eff ⎞1/3 ⎜ ⎟ ( −FpJKR + ⎝ K ⎠

Fl − FpJKR )2/3

(3)

Here, Reff is the effective radius of the PE colloid, Fl is the maximum externally applied loading force, FJRK p is the measured force pull-off force to separate the colloid from the surface, and K represents the effective elastic modulus expressed as K=

4 [(1 − ν12)/E1 + (1 − ν2 2)/E2]−1 3

(4)

where E1 and E2 represent the Young’s modulii of RDX (210) and of the low density PE, respectively, and ν1 and ν2 represent their respective Poisson’s ratios. We obtained an a value of about 2.45 × 10−7 m (Ac ∼ 1.88 × 10−13 m2) using the E1 = 21.0 GPa [RDX (210)]39 and ν1 ≈ 0.2240 values for RDX and the E2 = 0.25 GPa and ν2 = 0.38 values for PE,41 together with an Reff value of ∼1.17 × 10−6 m, and Fl and Fp measured values of about 2.54 × 10−6 and −2.75 × 10−7 N, respectively. We note that the a value determined in this study is approximately 19% and 22% greater than the values obtained from Derjaguin−Muller−Toporov (DMT) and Hertz models, respectively.19 The JKR model is more applicable for interacting soft materials and large contact areas, whereas the DMT model is more appropriate for systems with hard materials and small contact.42−44 Here, the value of the contact area between the PE colloid and the RDX surface (∼10−13 m2) is much greater than those from typical AFM, sharp cantilever probes (∼10−16 m2).

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MODELING METHODS RDX−PE Potential Development. Atomistic modeling of a RDX-PE system requires a potential that accurately treats the intramolecular RDX−RDX and PE−PE interactions in addition to the intermolecular terms occurring between RDX and PE at their interface. To account for the RDX−RDX interactions, we selected the nitramine potential developed by Smith and Bharadwaj (SB), which was originally parametrized for condensed-phase simulations of HMX.45 Additional studies have shown that this potential predicts accurately the lattice parameters, the bulk modulus ,and the elastic constants of both α-RDX and γ-RDX phases.46 The PE−PE interactions are treated using the COMPASS force field.47 Both RDX−RDX and PE−PE potentials were selected on the basis of their accuracies for prediction of the structure of the individual components and their reliance on quantum mechanically derived reference data for parametrization. The RDX−PE cross terms are treated using Coulombic charge−charge interaction terms together with Buckingham exponential-6 (exp-6) potential terms of the form: qiqj C ij V (r )RDX − PE = + Aij exp( −Bij rij) − 66 ∑ r rij i ∈ RDX, j ∈ PE ij (5) 5087



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Figure 4. Sample configuration of a 43-oligomer (260 atoms) PE chain interacting with a 4200-atom RDX(001) surface used for fitting of the RDXPE intermolecular cross terms. The carbon atoms are colored in black, the oxygen atoms in red, the nitrogen atoms in blue, and the hydrogen atoms in white.

Figure 5. Comparison of the Coulomb+exponential-6 interaction energies (eq 5) for a set of 250 different configurations of a 43-oligomer (260 atoms) PE chain interacting with a 4200-atom RDX (001) slab to the corresponding DFT calculated values.

where the i index labels atoms of the RDX layer and j corresponds to those of PE. The set of atomic charges {qi}i∈RDX and {qj}j∈PE in eq 5 are fixed at the values defined in the individual SB and COMPASS potentials, respectively. The remaining parameters were fitted to 250 quantum mechanical interaction energies of a randomly configured, 43-oligomer (260 atoms) PE chain interacting with a 4200-atom, optimized RDX (001) slab (Figure 4). These configurations were selected to span both the attractive and repulsive regions of the potential energy surface of PE interacting with RDX surface. The QM energies were obtained on the basis of dispersion-corrected density functional theory (DFT) calculations using the Quickstep module of the CP2K program.48 DFT calculations used a mixed Gaussian and plane wave scheme with the Perdew−Becke−Ernzerhof49 (PBE) exchange−correlation functional and a triple-ζ valence plus polarization basis sets. The plane wave density cutoff was set to 400 Ry. The longrange, dispersion interactions were included using the D3 method of Grimme.50 All interaction energies were corrected

for basis set superposition error using the Counterpoise approach.51 The (Aij, Bij, Cij) parameters of eq 5 were fitted with the PIKAIA52 genetic algorithm with the fitness of each individual in the population determined by the magnitude of the rootmean-square (RMS) deviation between the reference DFT interaction energies and those obtained from eq 5. The final RMS deviation for the entire data set is 3.73 kcal/mol. A plot of the interaction energies predicted by the classical force field and those obtained using DFT is shown in Figure 5. To test the transferability of the potential, we computed both the DFT and classical interaction energies of several additional configurations that were not included in the original potential fit, some of which contained multiple PE chains interacting with the RDX surface. Comparisons of the DFT and fitted potential interaction energies for configurations with up to four PE chains on the RDX surface are shown in Figure 6. As shown, the potential shows good transferability to multichain configurations, which is critical for an accurate treatment of the condensed-phase, RDX−PE interface. 5088



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Figure 6. Comparison of the force field energies to the corresponding DFT values for various multichain PE configurations interacting with RDX(001) surface.

Construction of RDX-PE Simulation Cell. Using the developed RDX-PE potential, uniaxial tension molecular dynamics simulations of amorphous and crystalline polyethylene adsorbed on the RDX (001) and (210) surfaces were conducted. These data allow direct comparison to our experimental force−distance spectroscopy results. For brevity, the following discussion will detail the simulation protocol used to obtain the stress−strain curve of amorphous polyethylene on the RDX (001) surface. An analogous procedure was applied for the RDX (210) surface and crystalline PE simulations. All simulations described below were conducted with the LAMMPS software package.53 The RDX−PE simulation cells were constructed in three steps: (1) equilibration of the isolated RDX cell; (2) equilibration of the isolated amorphous PE cell; (3) combination of the two cells followed by equilibration of the composite supercell. The initial configuration of α-RDX corresponds to the experimental cell and was replicated to generate a 3 × 3 × 9 supercell (39.6 Å × 34.8 Å × 96.5 Å) containing 13 608 atoms. The equilibrium structure (300 K, 1 atm) was obtained using isothermal−isostress (NsT) molecular dynamics simulations for 1 ns with a 1 fs time step based on the aforementioned SB potential. The interaction potential cutoff was 15 Å and the long-range Coulombic interactions were included using Ewald summation. Velocity scaling was applied every 5 time steps during the first 50 ps of the simulation with system averages accumulated every 10 ps to ensure that the correct temperature and pressure were maintained during the

course of the simulation. The time-averaged, ambient-state (300 K, 1 atm), unit-cell parameters are a = 13.49 Å, b = 11.55 Å, and c = 10.56 Å, in good agreement with those obtained experimentally.25,26 Four different amorphous PE simulation cells were generated with each cell containing 60 randomly configured unbranched PE chains (15 600 atoms total) with each chain containing 43 ethylene units. The lateral dimensions (a- and b-cell axes) of each of the four PE cells are initially set equal to the lengths obtained for the equilibrated RDX layer (40.47 Å × 34.65 Å) and the c cell vector length (100.9 Å), which is normal to the RDX−PE interface, was chosen such that the density of each PE cell corresponded to the experimental published value (0.853 g/cm3). Each of these four cells are populated with 60 PE chains using a random walk algorithm with periodicity allowed along the a and b directions and a confined layer constraint enforced along the c axis. The atomic coordinates within each cell were then relaxed using conjugate gradient minimization to remove the excess configurational energy and then subjected to 1 ns of isothermal−isochoric (NVT) molecular dynamics at 800 K, followed by 1 ns at 300 K, to further randomize and equilibrate the chain orientations. During these simulations, the wall/reflect option available in LAMMPS was applied along the c direction to maintain the confined layer structure. Given the individual RDX slab and the amorphous PE cells, four combined RDX−PE supercells (29 208 atoms each) were constructed, where each of the four amorphous PE cells was 5089



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Figure 7. Composite RDX−PE supercell showing the RDX, PE, and the interface regions referenced in text together with the corresponding orientation of the cell vectors.

placed above the a−b plane of the equilibrated RDX slab (e.g., the RDX (001) surface), as shown in Figure 7. The cells were then subjected to 1 ns of NVT molecular dynamics at 500 K, with the RDX layer fixed, followed by 1 ns of NVT dynamics at 300 K with all RDX and PE atoms being allowed to move. These thermalized cells were then subjected to 1 ns of NsT dynamics at 300 K and 1 atm, resulting in a fully relaxed cell. Time averages of the six unique components of the stress tensor were monitored during the NsT simulations to ensure that the cells correspond to a zero-stress state, an absolute requirement for the impending stress−strain analysis. For the crystalline PE simulations, the RDX 001 surface was placed in contact with the 001 surface of a 14 × 8 × 14 crystalline PE cell. This cell size was chosen on the basis of the lateral dimensions of the RDX layer and the long axes of the crystalline PE chains were parallel to the RDX b axis. The orientation where the long axes of the chains were parallel to the RDX a axis (effectively a 90° rotation of the PE layer) were found to be higher in energy and were not used. Given this orientation, the supercell was subjected to 1 ns of NVT dynamics at 800 K and then fully relaxed using an NPT ensemble at 300 K and ambient pressure. Stress−Strain Curves. The stress−strain curves for each of the four relaxed RDX−PE cells were obtained by means of uniaxial strain (compression and tension), MD simulations. During the simulations, all atoms residing in the lower 70 Å part of the RDX layer (Figure 7, Region 1) and the upper 70 Å of the PE layer (Figure 7, Region 3) were frozen, whereas the atomic positions within the central 60 Å layer (Figure 7, Region

2), which contains the interface, were integrated during the trajectory. At each time step, all atoms in the central, upper, and lower layers above and below the interface are displaced by a distance of ±0.0003 Å along the c-axis. This value corresponds to a strain rate of 1013/s when the displacements of the upper and lower boundaries of Region 2 of Figure 7 are used to define the strain. We tested smaller strain rates and found that a rate of 1013/s yields the best balance between computational cost and the number of time steps required to obtain the full stress− strain curve. During the simulation, the strain was applied continuously at 1% intervals with the stress at each strain given by the time average of the σzz component of the local stress for the atoms in Region 2.

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RESULTS AND DISCUSSION Polyethylene Crystallinity. We employ Raman spectroscopy to characterize the PE surface as well as to determine the degree of crystallinity of PE samples. We recorded Raman spectra of PE as received and PE processed in the spectral region 100−4000 cm−1. The spectral PE features, which correspond to Δυ = +1 or Stokes transitions, are clustered in four distinct regions: (1) 1000−1200 cm−1 (C−C stretching vibrations); (2) 1220−1390 cm−1 (CH2 twisting vibrations); (3) 1380−1540 cm−1(CH2 bending vibrations), and (4) 2800− 3000 cm−1 (C−H symmetric and asymmetric vibrations).54−59 The first three spectral regions are presented in Figure 8. For comparison purposes, the most intense peak near 1285 cm−1 is approximately a factor of 10 less intense than the peaks near 5090



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41.9% was obtained when we used the average value of I(1415)nor = 0.144 for 38.9% crystallinity calculated from the data reported by Cherukupalli and Ogale.57 Thus, our sample is about 48% amorphous, 34−42% crystalline, and 10−18% disordered. The disorderd phase may be related in part to the degree of polyethylene branching. Rabiej and co-workers studied this polyethylene phase with wide-angle X-ray scattering and Raman spectroscopy, and they found that the density of crystalline polyethylene decreased with degree of branching to a value typical of amorphous polyethylene.59 Force Spectroscopy and Lifshitz Theory. We normalized the force-distance curves with respect to the contact area to allow comparison with Lifshitz theory calculations and MD simulations. Figure 9 shows a typical energy per unit area-

Figure 8. Observed and fitted Raman spectra of PE in the 1000−1500 cm−1 region.

2900 cm−1 (not shown). The spectra of both the as-received and the processed samples are nearly identical, suggesting that PE did not undergo any chemical transformations or pick up any impurities in the spheroidization and cleaning processes. We utilize the PE Raman spectral range 1000−1500 cm−1 to determine the amorphous, crystalline, and disordered components of our sample (Figure 8). The band near 1060 cm−1 is a superposition of two peaks, a C−C crystalline peak (main) and a C−C amorphous peak (shoulder), and the peak at 1130 cm−1 is attributed mostly to the C−C crystalline band. The band near 1300 cm−1 comprises two peaks. The sharp peak centered near 1295 cm−1 (main) is attributed to PE in its orthorhombic, crystalline phase, whereas the broad peak near 1305 cm−1 (shoulder) is attributed to PE in its amorphous phase. The peaks near 1415, 1440, and 1460 cm−1 arise from CH2 bending vibrations. The features near 1415 and 1460 cm−1 reflect mostly PE in its crystalline state, whereas the peak near 1440 cm−1 is due to PE in both its crystalline and amorphous states.54 The weak peaks near 1170 and 1370 cm−1 result from CH2 rocking and wagging vibrations, respectively.57 The total integrated intensity of the 1415 cm−1 peak is independent of temperature and is nearly free from CH2 vibrations from amorphous PE, yet it is sensitive to changes in PE crystallinity; the stronger the intensity the higher the crystallinity. Thus, it serves as a measure of PE crystallinity when normalized to the integral intensity of the CH2-twisting band, ITW = I1295 + I1305, proposed as an internal standard.54 I1305 normalized to ITW yields the fraction component of the amorphous phase, a-PE, I(1415)nor normalized to ITW yields the fraction component of the crystalline phase, c-PE, and 1 − (aPE + c-PE) yields the fraction component of the disordered, anisotropic phase, d-PE. We obtained these values by fitting all the peaks in the spectral region from 1000 to 1500 cm−1 with Lorentzian functions, except for the 1440 cm−1 peak for which we used both a Lorentzian and a Gaussian functions to approximate the contribution of the CH2-bending vibrations resulting from the crystalline and amorphous phases, respectively.55 On the basis of a previously reported value of 0.46 for I(1415)nor‑100% for 100% PE crystallinity54 and with our measured result of I(1415)nor = 0.155, we obtained the c-PE value of 34% and an a-PE value of 48.4% . However, a c-PE value of

Figure 9. Experimental dependence of the energy per unit area on separation distance for the interaction of RDX (210) with a-PE (∼48% amorphous). The indicated curve was obtained by integrating the corresponding force−distance dependence from about −40 to +250 nm, and using a contact area of 1.88 × 10−13 m2.

distance curve for the interaction of RDX (210) and a-PE (∼48% amorphous). This curve was obtained by integrating the corresponding force−distance plot under retraction from about −40 nm to about +250 nm. The difference between the maximum energy value and the value where RDX and PE are separated (baseline) yields the separation energy for the system, 70.7 mJ/m2. A statistical analysis of our data yields an average Es per unit area of about 81 ± 15 mJ/m2 (see also Table 1), which was obtained using an average energy of 1.52 × 10−14 J and a contact area of 1.88 × 10−13 m2. The macroscopic theory of van der Waals forces developed by Lifshitz provides a useful continuum approach to calculate the interaction energy between materials in terms of their dielectric susceptibilities and indices of refraction. The following expression yields the Hamaker constant based on Table 1. Experimental and Calculated Separation Energies (mJ/m2) of Different Crystallographic RDX Surfaces Interacting with Amorphous and Crystalline Polyethylene material RDX (001) RDX (210)

a-PE (∼48%)a

a-PE (100%)

c-PE (100%)

81 ± 15

129 132

115 120

a

PE sample is 48% amorphous, 34−42% crystalline, and 10−18% disordered. 5091



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Table 2. Separation Energies of RDX- and HMX-Based Polymer Systems Obtained Using Liftshitz Theory of van der Waals Forces Using a Contact D0 Value of 0.165 nma medium (air) material (1)b

material (2)b

RDX

PE PP PS PVDF PCTFE PTFE RDX PE

RDX PE

10−20AHam

medium (air) Es (mJ/m2)

material (1)b

material (2)

10−20AHam

Es (mJ/m2)

8.11 7.65 9.22 6.95 6.45 5.86 9.06 7.27 medium (H2O)b

79 74 90 68 63 57 88 71

HMX

PE PP PS PVDF PCTFE PTFE HMX

8.30 7.82 9.43 7.11 6.60 5.99 9.47

81 76 92 69 64 58 92

HMX

medium (H2O)

material

polymer

10−20AHam

Es (mJ/m2)

material

polymer

10−20AHam

Es (mJ/m2)

RDX

PE PP PS PVDF PCTFE PTFE

1.41 1.20 1.91 0.797 0.663 0.404

14 12 19 7.7 6.5 3.9

HMX

PE pp PS PVDF PCTFE PTFE

1.48 1.25 2.01 0.833 0.687 0.413

14 12 20 8.1 6.7 4.0

a

The list of acronyms used is as follows: polyethylene (PE), polystyrene (PS), polypropylene (PP), polytetrafluoroethyene (PTFE), polyvinylidene fluoride (PVDF), and polychlorotrifluoroethylene (PCTFE). bThe list of material constants used to evaluate the Hamaker constant given by eq 6 are as follows: for α-RDX n = 1.578 as obtained from refs 67 and 68 and ε = 3.14 as given in ref 68; for β-HMX, values of n = 1.594 and ε = 3.08 were taken from refs 72 and 68; for H2O and air the respective values of n = 1.33 and ε = 80.4 and n = 1.00 and ε = 1.00 were taken from ref 73; for all polymers except PE the n values are from ref 60 and the ε data are from refs 61 and 71; for PE the n value was taken as the average of the data provided in refs 60 and 61.

27 to 36 mJ/m2 (see refs 62−66), which can be compared to our estimated value of ∼31 mJ/m2. In the case of the RDX− RDX interaction, we obtained an AHam value of about 9.1 × 10−20 J and an interaction energy E ≈ 88 mJ/m2 (γ ≈ 44 mJ/ m2) based on material constants indicated in the footnote of Table 2. Typical experimental surface energies for RDX at 298 K reported in the literature range from 24 to 42 mJ/m2.69,70 By applying eq 6 for the case when PE interacts with RDX in air and at room temperature, we obtained values of approximately 8.1 × 10−20 J and 79 mJ/m2 for APE−RDX and EPE−RDX, respectively. The latter value for interaction energy is in excellent agreement with the value of 81 mJ/m2 we measured experimentaly. Table 2 also indicates the Hamaker constants and the separation energies determined from Lifshitz theory for RDX and HMX crystals interacting with various polymers either in air or in water. In general, the data reveal several trends. First, the separation energies of all the systems are about an order of magnitude greater in air than in water. These results are expected because the ε and n values of water are greater than those of air. Second, the RDX-RDX separation energy is smaller than that of HMX−HMX in air (∼88 vs ∼92 mJ/m2). This trend applies also to RDX-based systems shown in Table 2 compared to their HMX-based counterparts. It can be seen that the results obtained are due primarily to the differences in the refractive indices of the corresponding materials. Indeed, by changing the value of ε for the RDX by a factor of 3 changes the RDX−RDX separation energy by about 1%, whereas changing the value of n by 10% changes the energy by about 50%. From the data in Table 2 it can be also seen that the separation energies of the fluorine-containing polymers are smaller than those containing hydrogen. For example, the separation energy of RDX−PTFE (−[CF2−CF2]n−) is about 57 mJ/m2 compared to that of RDX−PE, ∼79 mJ/m2.

Lifshitz theory for the interaction of two materials across a medium:19 A = Av=0 + Av>0 ≈ +

3hνe 8 2

⎛ ε − ε3 ⎞⎛ ε2 − ε3 ⎞ 3 k bT ⎜ 1 ⎟ ⎟⎜ 4 ⎝ ε1 + ε3 ⎠⎝ ε2 + ε3 ⎠ (n12 − n32)(n2 2 − n32)

(n12

2

2

+ n3 ) (n2 + n32) { (n12 + n32) +

(n2 2 + n32) }

(6)

In eq 6, kb represents the Boltzmann constant (1.38 × 10−23 J/ K), T represents the temperature (K), h represents Planck’s constant (6.63 × 10−34 J s), νe represents the absorption frequency (Hz), and ε and n represent the relative static dielectric constants and refractive indices of the materials, respectively. Subscripts 1 and 2 denote the two interacting materials located inside a medium indicated by subscript 3. The first term in the above expression corresponds to the zerofrequency energy of the van der Waals interaction and includes the Keesom and Debye dipolar contributions, whereas the second term corresponds to the dispersion energy and includes the London energy contribution. Starting from the Hamaker expression given in eq 6, we considered first the case of similar interacting materials in air, i.e., PE−PE and RDX−RDX, by taking n1 = n2 and ε1 = ε2. We obtained a value of AHam of about 7.3 × 10−20 J for polyethylene in air at 298 K using the parameter values indicated in the footnote of Table 2. The above expression is independent of the geometry of the material. Thus, for the simple case of two, similar materials in a planar configuration, the interaction energy corresponds to E(D) = −A/12πD2 per unit area, where D represents the separation distance. We obtained a value of E ≈ 71 mJ/m2 for the binding energy of two PE surfaces in contact, using a contact value Do = 0.165 × 10−9 m, which works remarkably well for many materials.19 For PE, the typical surface energies (γ = E/2) reported in the literature range from 5092



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yields a value of approximately 129 mJ/m2. The interaction energy is a function of the RDX and PE surface morphology, and on the basis of these values, amorphous PE is predicted to have the highest affinity for the RDX (210) surface whereas a slightly smaller interaction energy of 126 mJ/m2 was determined in the case of the RDX(001) surface. These values are in reasonable agreement with the experimental value of 81 mJ/m2 obtained for the interaction energy of PE (∼48% amorphous) with RDX (210). Furthermore, for both (210) and (001) RDX surfaces, the amorphous PE binding energies exceed the corresponding values for crystalline PE by about 10%. Table 1 lists all the MD computed interaction energy values. Figure 11 shows snapshots of the MD equilibrated interfaces for amorphous (left) and crystalline (right) PE adsorbed on the

Although both PTFE and PE are nonpolar molecules, the electron-rich, fluorine atoms in PTFE cause an unfavorable interaction with the electron-rich, oxygen atoms in RDX. In contrast, the hydrogen atoms in PE are attracted to the oxygen atoms in RDX, resulting in a larger RDX−PE binding energy compared to RDX−PTFE. Finally, the separation energies of both RDX and HMX with the fluorinated polymers follow the trend PVDF (−[CH2− CF2]n −) > PCTFE (−[CH(Cl)-CF2]n−) > PTFE. PVDF possesses a permanent dipole that augments its attraction to RDX, unlike PCTFE and PTFE. These findings agree to those of Xiao and co-workers7,8 who performed molecular mechanics and molecular orbital calculations and found that separation energy of HMX−PVDF is larger than that of HMX−PCTFE or HMX−PTFE, which have similar separation energies. Molecular Dynamics Simulations. Plots of the total interaction energy per unit area and of the corresponding force as a function of separation between amorphous PE and the RDX (210) surface are presented in Figure 10. The computed value for the interaction energy averaged over the four individual amorphous PE samples is about 132 mJ/m2. This value was obtained using a computed total energy of 2.59 × 10−21 J and an effective area of 1.96 × 10−17 m2. Similar calculations for the RDX (001) surface and amorphous PE

Figure 11. Snapshots of the RDX (210)−PE interfaces for cells containing amorphous (a-PE) and crystalline (c-PE) polyethylene. Layers are displaced to aid visualization of the individual components.

RDX (210) surface. Visual inspection of the displaced layer indicates that the RDX nitro groups appear to favor a more directed orientation, penetrating the amorphous PE layer, than observed when interacting with crystalline PE. On the basis of analysis of the atom pair contributions to the total interaction energy (discussed below), it was found that the dominant contribution to the RDX−PE binding energy arises from interactions between polyethylene hydrogen atoms with the RDX oxygen atoms. The increased directionality of the oxygen containing RDX nitro substituents at the amorphous PE−RDX interface maximizes the oxygen−hydrogen interactions, resulting in a larger binding energy relative to the crystalline layer. However, it should be kept in mind that these energy differences are quite small and definitive resolution of these closely spaced energies requires force fields developed using QM methods with larger basis sets than those considered in the current work, which are beyond the current computational capabilities for the system sizes used here. From the simulation data, the average energy per methylene (−CH2) unit was obtained by dividing the total RDX−PE interaction energy by the number of methylene units contained within region 2 (Figure 7) at the interface. Irrespective of the RDX surface or PE structure (crystalline or amorphous), the average interaction energy per methylene group remains essentially constant with a value of ∼1.07 × 10−21 J/CH2. Due to the pairwise form of the interaction potential used to compute the RDX−PE interaction in this work (eq 5), the pairwise contributions to the total interaction energy can be easily delineated. The pairwise contributions for crystalline PE and amorphous PE placed on the RDX (210) surface are shown in Figure 12. The separation energy between these two surfaces results from the interplay of all the pairwise

Figure 10. Plots of the total interaction energy per unit area (top panel) and of the corresponding force (bottom panel) as a function of separation distance obtained from MD simulations of the RDX (210)−PE (100% amorphous) system. The force results were obtained using an effective contact area of 1.96 × 10−17 m2 for the RDX−PE system. 5093



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Figure 12. Atom−atom pair contributions to the total interaction energy as a function of distance for amorphous (100%) and crystalline (100%) PE on the RDX (210) surface.

contact with the RDX (210) surface, yielding the long-range interaction apparent in the curves of Figure 13. The crystalline PE layer shows no appreciable elongation and as the separation increases, the RDX surface remains effectively free of any crystalline PE chains, resulting in the rapid falloff of the interaction energy as the separation increases.

contributions. Despite the difference in RDX surface morphology when in contact with the crystalline or amorphous PE layers, the attractive contribution to the total interaction energy, in both cases, is dominated by the HPE−O RDX interaction at all separations, followed closely by the CPE− NRDX interaction. Both of these interactions account for over 60% of the attractive energy. In contrast, the repulsion contributions are dominated by the HPE−NRDX and CPE− ORDX interactions, and account for over 60% of the repulsive energy. Further, as shown in Figure 12, the interaction energy for the RDX−crystalline PE interface goes to zero at approximately 0.6 nm, representing a much shorter range interaction than that observed for amorphous PE, which shows nonzero interaction even for boundaries separated by as much as 3.0 nm. The longer interaction range observed for amorphous PE results from elongation of the polymer layer as strain is applied to the sample; see Figure 13, which contains snapshots taken from the MD trajectory for the crystalline and amorphous PE under tensile loading simulations conditions. As indicated in this figure, as the surface separation increases, the amorphous PE layer shows extensive elongation, and at t = 50 ps (3.0 nm displacement), several PE chains are still in close

■

CONCLUSIONS We have studied the surface interactions of crystalline and amorphous PE with RDX using both force−distance spectroscopy and MD simulations and found that the binding energy of these materials depends on both the RDX crystal face and the degree of PE crystallinity. Our MD simulations predict a value of ∼132 mJ/m2 for binding of PE (100% amorphous) to the RDX (210) surface, which is approximately 10% greater than that obtained when PE (100% crystalline) interacts with the same surface. These values are in reasonable agreement with our measured value of 81 ± 15 mJ/m2 for RDX (210) and PE (∼48% amorphous). Also, the binding energies of PE (100% amorphous) or PE (100% crystalline) with RDX (210) surface exceed the corresponding binding energies to RDX (001) surface by about 3 and 4 mJ/m2, respectively. Irrespective of 5094



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ACKNOWLEDGMENTS

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REFERENCES

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We thank Drs. R. Pesce-Rodriquez of the Army Research Laboratory (ARL) and K. Behler of ARL-Bowhead Science & Technology for many helpful discussions, and Dr. K. Ramos of the Los Alamos National Laboratory for providing us with the RDX crystals. Support from the ARL Multiscale Response of Energetic Materials Program and the ARL-Oak Ridge Institute for Science and Education Program is gratefully acknowledged. We also acknowledge with thanks a supercomputing challenge grant at several DOD Supercomputing Resource Centers (DSRCs).

(1) Toal, S.; Trogler, W. Polymer Sensors for Nitroaromatic Explosives Detection. J. Mater. Chem. 2006, 16, 2871−2883 and references therin. (2) Chipuk, J.; Mazzitelli, C.; Kendall, J.; Straight, S.; Reaves, M.; Chamberlin, S. Tunable, Self-Curing Polymers for the Forensic Collection of Latent Signatures from Within Porous Materials. Homeland Security Affairs 2012, No. Supplement 5, 1−7. (3) Tam, M.; Pilon, P.; Zaknoun, H. Quantified Explosives Transfer on Surfaces for the Evaluation of Trace Detection Equipment. J. Forensic Sci. 2013, 58, 1336−1340. (4) Yinon, J.; Zitrin, S. Modern Methods and Applications in Analysis of Explosives; John Wiley and Sons, LTD: West Sussex, 1993. (5) Singh, A.; Kumar, M.; Sonu, P.; Singh, M.; Srivastava, A. Mechanical and Explosive Properties of Plastic Bonded Explosives Based on Mixture of HMX and TATB. Defense Sci. J. 2013, 63, 622− 639. (6) Kumar, A.; Rao, V. Evaluation of Plastic Bonded Explosive (PBX) Formualtions based on RDX, Aluminum, and HTPB for Underwater Applications. Propellants Explos. Pyrotech. 2012, 35, 359−364. (7) Xiao, J.; Fang, G.; Ji, G.; Xiao, H. Simulation Investigation in the Binding Energy and Mechanical Properties of HMX-Based PolymerBonded Explosives. Chinese Sci. Bull. 2005, 50, 21−26. (8) Zhu, W.; Xiao, J.; Zhu, W.; Xiao, H. Molecular Dynamics Simulations of RDX and RDX-Based Plastic-Bonded Explosives. J. Hazard. Mater. 2009, 164, 1082−1088. (9) Li, M.; Li, F.; Shen, R. Molecular Dynamics Study of RDX/ AMMO Propellant. Chin. J. Chem. Phys. 2011, 24, 199−205. (10) Lan, Y.; Zhai, J.; Li, D.; R. Yang, R. Multiscale Simulation on the Influence of Dimethyl Hydantion on Mechanical Properties of GAP/ RDX Propellants. Propellants Explos. Pyrotech. 2013, 35, 1−6. (11) Abou-Rachid, H.; Lussier, L.-S.; Ringuette, S.; Lafleur-Lambert, X.; Jaidann, M.; Brisson, J. On the Correlation between Miscibility and Solubility Properties of Energetic Plasticizers/Polymer Blends: Modeling and Simulation Studies. Propellants Explos. Pyrotech. 2008, 33, 301−310. (12) Jaidann, M.; Abou-Rachid, H.; Lafleur-Lambert, X.; Brisson, J. Atomistic Studies of RDX and FOX-7-Based Plastic-Bonded Explosives: Molecular Dynamics Simulation. Procedia Computer Sci. 2011, 4, 1177−1185. (13) Gee, R.; Maiti, A.; Bastea, S.; Fried, L. Molecular Dynamics Investigation of Adhesion between TATB Suefaces and Amorphous Fluoropolymers. Macromolecules 2007, 40, 3422−3428. (14) Leite, F.; Bueno, C.; Da Róz, A.; Ziemath, E.; Oliveira, O., Jr. Theoretical Models for Surface Forces and Adhesion and Their Measurement Using Atomic Force Microscopy. Int. J. Mol. Sci. 2012, 13, 12773−12856. (15) Drelich, J.; Tormoen, G.; Beach, E. Determination of Solid Surface Tension from Particle−Substrate Pull-Off Forces Measured with the Atomic Force Microscope. J. Colloid Interface Sci. 2004, 280, 484−497. (16) Butt, H.-B.; Cappella, B.; M. Kappl, M. Force Measurements with Atomic Force Microscope: Technique, Interpretation and Application. Surf. Sci. Rep. 2005, 59, 1−152.

Figure 13. Snapshots of RDX−PE configurations taken every 10 ps during the tensile loading MD simulations. (A) shows the amorphous PE data and (B) shows the crystalline PE data.

the RDX surface or the degree of PE crystallinity, the average interaction energy per polyethylene unit remains essentially constant with a value of ∼1 × 10−21 J/CH2. Our MD simulations reveal that the H PE −O RDX and C PE −N RDX interactions contribute mostly to the attractive interactions, whereas the HPE−NRDX and CPE−ORDX interactions dominate the repulsive interactions in these systems. The effective interaction of amorphous PE with either a (210) or (001) RDX surface extends over 5 times the interaction distance obtained in the case of crystalline PE, which we attribute to the elongation of the polymer surface layer under strain. Our Lifshitz theory calculations show that the binding energy values for RDX-based polymers are slightly less than those for HMXbased polymers and that they depend on the polymer type. For the set of polymers investigated interacting with RDX or HMX the following trend of the corresponding binding energies has been determined: PS > PE ≈ PP > PVDF > PCTFE > PTFE.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address #

Department of Physics, University of Maryland, Baltimore County, Baltimore, MD 21250. Notes

The authors declare no competing financial interest. ¶ ARL-ORISE Researcher. 5095



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