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Molecular dynamics simulations of shock waves in oriented nitromethane single crystals
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10.1063/1.3561397
/content/aip/journal/jcp/134/12/10.1063/1.3561397
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/12/10.1063/1.3561397

Figures

Image of FIG. 1.
FIG. 1.

Schematic diagram of the approach used to generate shock waves. The leftmost (tan) region is the stationary piston comprised of rigid molecules. A slab containing flexible molecules (blue and green regions) equilibrated to 200 K impacts with speed u p from the right onto the stationary piston. The interface between the postshock material (blue region) and the preshock material (green region) is the shock front position (solid red line) that advances at shock velocity u s from left to right.

Image of FIG. 2.
FIG. 2.

Nitromethane crystal structure and the definition of molecular layers used in the analysis of the MD results. (a) Initial configuration of the piston for the [100] shock simulation; the 96 molecules between the two dashed lines comprise one molecular layer. (b) Initial configuration of the piston for the [010] shock simulation; only one-half of the vertical size of the 20a × 65b × 12c system studied is shown; the 240 molecules between the two dashed lines comprise one molecular layer (480 molecules in the full-size sample). (c) Initial configuration of the piston for the [001] shock simulation; the 80 molecules between the two dashed lines comprise one molecular layer.

Image of FIG. 3.
FIG. 3.

(a) Center-of-mass position for each layer along the shock direction [010] (CMP y ) as a function of the time during shock propagation (solid lines). The dashed line connecting shock front positions as time evolves tracks the shock trajectory in the y–t plane; the CMP y velocity is u c . The numbers 21, 31, 51, 111, and 121 denote specific layer numbers. (b) Layers with the maximum gradient of kinetic energy [(K y )max] plotted as a function of time. The calculation of the maximum gradient of the kinetic energy for each layer is the same as described in Ref. 31.

Image of FIG. 4.
FIG. 4.

Schematic diagram of the approach used to define fixed-volume bins for trajectory analysis. In the laboratory frame the spatial origin for the bins translates linearly to the right with time, so as to remain stationary in the reference frame centered on the shock front. The width of the bins Δλ is constant. Bins for postshock and preshock materials are labeled by negative and positive integers, respectively; the bin that contains the shock front at any given instant in time is denoted bin 1. The number of postshock [N o (t)] and preshock [N r(t)] bins increases and decreases, respectively, with time t. The total number of bins N b (t) = N o (t) + N r (t) decreases linearly in time due to compression of the flexible slab as the shock wave advances through the material. Bins, or partial bins, at least 14 Å from either end of the flexible slab (denoted by crosses in the left-most and right-most bins in the figure) are excluded from the analysis of properties.

Image of FIG. 5.
FIG. 5.

Projections of snapshots of molecular centers of mass for the three shock simulations studied at the respective instants of maximum compression. Projections along (a) [010] for the [100] shock; (b) [001] for the [100] shock; (c) [001] for the [010] shock; (d) [100] for the [010] shock; (e) [100] for the [001] shock; and (f) [100] followed by a counterclockwise rotation of 50° around the direction [001] for the [001] shock. The bottom abscissa is the distance from the shock front and the top abscissa is the time since the passage of the shock front. The regions to the left of the yellow lines are the fixed pistons; the red solid lines denote the instantaneous shock front positions at the ends of the simulations. The black dashed lines mark the approximate postshock times at which the 2D RDFs shown in Fig. 9 converge to essentially stable values for the [100] and [001] shocks.

Image of FIG. 6.
FIG. 6.

The mass density as a function of distance from the shock front (bottom abscissa) and time since shock passage (top abscissa). (a) Results for bin widths Δλ set equal to the unit cell parameters (a, b, and c for the [100], [010] and [001] shock directions, respectively); and (b) as in (a) except that Δλ = 2.0 Å for all three cases. Shocked material is associated with negative values for the position and positive values for time; the time is calculated based on the shock velocity in the [100] case, which is only slightly different from those for the [010] and [001] cases since the shock velocities for all three cases are very similar (see Table II).

Image of FIG. 7.
FIG. 7.

The intermolecular (lattice), intramolecular (vibrational–rotational), and total temperatures as functions of distance (bottom abscissa) and time (top abscissa) from the shock front. (a) Dashed curves: [100] shock; solid curves: [001] shock. The postshock time in (a) is determined as described in the caption for Fig. 6. (b) [010] shock; the postshock time is determined using the [010] shock velocity.

Image of FIG. 8.
FIG. 8.

As in Fig. 7 except the Cartesian components of total kinetic energy are shown.

Image of FIG. 9.
FIG. 9.

2D center-of-mass RDFs for shocks along (a) [100], (b) [010], and (c) [001].

Image of FIG. 10.
FIG. 10.

2D MSDs of molecular centers of mass vs time.

Image of FIG. 11.
FIG. 11.

Orientational order parameter P 2(θ) for C–N bond vectors as functions of time.

Image of FIG. 12.
FIG. 12.

Molecular rotational distribution functions. (a) Angle distribution functions for five evenly spaced times between 0.2 and 1.0 ps behind the shock front. The results for the [001] shock are shown by the dashed curves and those for [100] by the solid curves. (b) Angle distribution function for five evenly spaced times between 1.0 and 5.0 ps behind the shock front. The results for the [001] shock are shown by the dashed curves and those for [100] by the solid curves. [(c) and (d)]: Same as (a) and (b) except the results are for the [010] shock.

Tables

Generic image for table
Table I.

Lattice parameters of nitromethane at T = 200 K and P = 1 atm.

Generic image for table
Table II.

Shock velocity, pressure, and temperature for shocks along [100], [010], and [001].a

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/content/aip/journal/jcp/134/12/10.1063/1.3561397
2011-03-25
2014-04-23
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Molecular dynamics simulations of shock waves in oriented nitromethane single crystals
http://aip.metastore.ingenta.com/content/aip/journal/jcp/134/12/10.1063/1.3561397
10.1063/1.3561397
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