Prediction of the Growth Habit of 7-Amino-4, 6-dinitrobenzofuroxan

DOI: 10.1021/cg901023s

Prediction of the Growth Habit of 7-Amino-4,6-dinitrobenzofuroxan Mediated by Cosolvents

2010, Vol. 10 618–625

Hye-Eun Lee,† Tae Bum Lee,‡ Hyoun-Soo Kim,§ and Kee-Kahb Koo*,† †

Department of Chemical and Biomolecular Engineering, Sogang University, Seoul 121-742, Korea, Department of Chemistry and Biochemistry, Auburn University, Alabama 36849, and Agency for Defense Development, Daejeon 305-600, Korea

‡ §

Received August 24, 2009; Revised Manuscript Received November 27, 2009

ABSTRACT: The morphology of 7-amino-4,6-dinitrobenzofuroxan (ADNBF) recrystallized from cosolvents was shown to evolve systematically from rod to plate as the mixing ratio of cosolvents (N-methyl-2-pyrrolidone (NMP)/acetonitrile, NMP/ chloroacetone, and NMP/methanol) varied from 1:1 to 1:4. In an attempt to explain the cosolvent effect on the shape evolution of ADNBF crystals, the characteristics of the ADNBF crystal surface were investigated by molecular modeling techniques. The morphology of ADNBF recrystallized from cosolvents was predicted by the modified attachment energy model with terms of binding site density, as well as interaction energy and fraction of cosolvents. Comparison of predicted morphologies with experimental results shows that the higher binding site density with solvents in the (001) surface of ADNBF is responsible for the strong inhibition of growth on the (001) plane even though interaction of individual solvent molecules on this surface is weaker than that on the other planes.

1. Introduction 7-Amino-4,6-dinitrobenzofuroxan (ADNBF) (C6H3N5O6, monoclinic, P21, a = 11.957 A˚, b = 9.863 A˚, c = 7.180 A˚, β = 98.131°, Z = 4) was synthesized and studied intensively as an insensitive molecular explosive.1-8 Norris and Weber6-8 reported the synthetic route of ADNBF by the conversion of TeNA (2,3,4,6-tetranitroaniline) into ADNBF under the azidation reaction in acetic acid through the addition of solid NaN3 or aqueous NaN3 solution. However, the acidity of ADNBF obtained by that route was found to be very high, which originated from the incorporation of acetic acid during precipitation of ADNBF. The high acidity of energetic materials was reported not acceptable for explosive formulation.9-11 Hence acetic acid included in ADNBF crystals should be removed before final formulation. The morphology and crystal size distribution of energetic materials are also crucial factors for explosive formulation in sensitivity and packing density because high sensitivity can cause unintended explosion and low packing density results in poor performance.12-15 Recrystallization would be a way to have adequate morphology and reduce acetic acid in ADNBF crystals. In practice, the amount of acetic acid in ADNBF recrystallized from solvents such as dimethylformamide (DMF), N-methyl-2-pyrrolidone (NMP), and dimethyl sulfoxide (DMSO) was reported to be reduced from 0.2 to 0.02 wt %. However, typical morphologies of ADNBF recrystallized from those solvents were shown to be still unsuitable for application.11 Therefore, in the present work, experiments on recrystallization of ADNBF from cosolvents was performed to produce ADNBF crystals with desired shape and size. In those experiments, systematic change of the growth habit of ADNBF was observed with the mass ratio of cosolvents. In an attempt to explain the cosolvent effect on the shape evolution of the ADNBF crystal, interactions between crystal surfaces and solute or solvent molecules were studied by means of molecular modeling. *To whom correspondence should be addressed. Phone: þ82-2-705-8680. E-mail: [email protected]. pubs.acs.org/crystal

Published on Web 12/18/2009

It has been known that solvents, additives, or impurities alter the growth rate of certain crystal faces during crystal growth by their strong adsorption on specific faces of the crystal.16-19 To understand the shape of crystals grown from solution, numerous growth models, such as attachment energy, two-dimensional nucleation, and the Burton-CabreraFrank (BCF) mechanism, and simulation techniques including molecular dynamics and Monte Carlo methods have been reported.20-31 Those reports show clearly that understanding the energetics of solvent molecules at crystal surfaces would provide a rational interpretation of morphological change mediated by solvent. The calculation of solvent-surface interaction energy based on molecular dynamics has been suggested as a way to predict the solvent-mediated growth habit.20-23,32-34 However, only using interaction energy is not sufficient for quantitative predictions of morphological change as Winn and Doherty35 mentioned. The relationship between surface characteristics and affinity of solvent has been discussed to elucidate solvent effect on crystal morphology.36-43 Some specific binding sites generated by surface characteristics have been also shown to become a main source of growth retardation.44 Therefore, for quantitative explanation of solvent effects on crystal growth, those different binding sites on each face should be considered with interaction energy. In the present work, the direct influence of solvent molecules on each surface of the crystal was considered. Binding site density was introduced into morphology prediction to quantify the solvent effect on the growth habit of ADNBF and the attachment energy model was modified by integrating with interaction energy, binding site density, and solubility. One thing that should be taken into account is that the morphologically important faces are radically changed by solvent incorporation. We suspected that even though the ADNBF interaction between growth layers (attachment energy) is strong, a surface would be retarded only if many solvent molecules specifically interact with that growth layer. The relatively different effects of solvent on various surfaces r 2009 American Chemical Society

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Crystal Growth & Design, Vol. 10, No. 2, 2010

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Table 1. Evaluation of Lattice Energy and Lattice Parameter of Disorder Models Lattice parameter variationb (%) model namea

Figure 1. (a) Molecular structure of ADNBF with possible 2-fold rotation axis by positional disorder of nitrogen atoms (green dashed circles). (b) A unit cell of ADNBF crystal3 showing different occupancy of nitrogen (green circles). Each disordered nitrogen atom has different occupancy (0.62 for N1, 0.38 for N6, 0.66 for N10 , and 0.34 for N60 ).

were accounted so that better elucidation can be possible for dramatic changes of crystal shape mediated by cosolvents. 2. Experimental Section ADNBF was supplied by Hanwha Co. and refined by recrystallization from NMP. All solvents used in the present experiments were purchased from Sigma-Aldrich (purity 99.5%). Three combinations of cosolvents, NMP/acetonitrile, NMP/chloroacetone, and NMP/ methanol, with mass ratios of 1:1 to 1:4 were used for the recrystallization of ADNBF. Rerystallization experiments were conducted in a 100 mL double-jacketed glass crystallizer equipped with an agitator, FBRM (focused beam reflective measurement; S400, LASENTEC) and a thermostat (model 9710, Polyscience). Saturated solutions of ADNBF prepared at 60 °C were cooled to 0 °C at cooling rate of 1 °C/ min. Solubilities of ADNBF with compositions of cosolvents were determined by a polythermal method at 60 °C. The morphology of ADNBF crystals was observed by a scanning electron microscope (Hitachi S-4300, Japan). The samples were attached to double-sided carbon tape and coated with gold under vacuum in an argon atmosphere prior to observation. Powder X-ray diffraction (PXRD) patterns were obtained using an X-ray diffractometer (MiniFlex, Rigaku, Japan) operated at 30 kV and 15 mA with graphite-monochromatized Cu KR radiation (λ = 1.5418 A˚). PXRD data were collected using a rotating flat-plate sample holder over the 2θ range from 5° to 50° with step size of 0.02° at ambient conditions and scanning rate of 1.0 deg/min. In order to investigate the preferred orientation of ADNBF crystals, PXRD data of powder samples prepared by crushing with a mortar and pestle were compared with those of noncrushed powder samples.

3. Computational Method The crystal structure of ADNBF is available from the Cambridge Structural Database (CSD ref code DOYCID). Various combinations of force fields and charge assigning methods45,46 were evaluated by the comparison of the lattice parameters and lattice energies of ADNBF obtained by geometry optimization. Among them, the Dreiding/Charge Equiolibration (QEq) set was found to give us the lowest deviation in the lattice parameters, and charge distribution for ADNBF was also qualitatively well matched with quantum-mechanically determined electrostatic potential.47 Therefore, the Dreiding Charge Equilibration (QEq) set was selected for further simulation of the ADNBF crystal. In Figure 1a, disorder positions of the nitrogen atoms in ADNBF are presented in green dashed circles, which can be envisioned by a 2-fold rotation axis. All positional disorders in

disorder 1 disorder 2 disorder 3 disorder 4 disorder 5 disorder 6 disorder 7 disorder 8 disorder 9 disorder 10 disorder 11 disorder 12

lattice energy (kcal/mol)

a

b

c

R

β

γ

-38.24 -37.29 -34.44 -33.32 -35.86 -36.47 -33.56 -33.42 -34.32 -34.78 -34.89 -34.46

12.11 1.90 1.92 2.13 4.31 13.62 1.98 1.99 4.43 1.93 1.90 4.39

4.53 0.87 0.87 0.73 1.42 6.46 0.80 0.77 2.17 0.83 0.85 2.11

18.41 0.78 0.80 0.83 1.50 20.04 0.92 0.90 0.83 0.64 0.68 0.84

0.00 0.00 0.00 0.00 1.89 0.09 0.26 0.24 2.13 0.02 0.01 2.13

7.59 2.16 2.12 3.00 0.87 6.89 2.39 2.38 0.95 1.92 1.92 1.01

0.00 0.00 0.00 0.00 2.23 1.69 0.42 0.47 3.10 0.01 0.03 3.02

a Disorder models are determined by nitrogen atom position: disorder 1 (N60 N6N6N60 ), disorder 2 (N10 N6N6N10 ), disorder 3 (N60 N1N1N60 ), disorder 4 (N10 N1N1N10 ), disorder 5 (N60 N6N6N10 ), disorder 6 (N10 N6N6N60 ), disorder 7 (N60 N1N1N10 ), disorder 8 (N10 N1N1N60 ), disorder 9 (N10 N6N1N60 ), disorder 10 (N10 N1N6N60 ), disorder 11 (N60 N6N1N10 ), and disorder 12 (N60 N1N6N10 ). b Lattice parameter variation was calculated by relative error (%), which is the differences between the simulated parameter and crystallographic data.3

the ADNBF crystal (N1, N6, N10 , N60 ) are presented in Figure 1b.3 Disordered molecules in the asymmetric unit can be understood through the alternative rotation of one [1,2,5]-oxadiazole ring satisfying a 21 screw operation. From Figure 1b, 12 systematic models of disordered ADNBF crystals can be made by alternative removal of nitrogen (N1, N6, N10 , and N60 ) as listed in Table 1. First of all, from those model structures, disorders 1, 2, 3, and 4 (Figure 2a) were selected by the comparison of lattice parameters obtained by geometry optimization. Among them, XRD patterns of disorders 2 and 3 were found to be in good accordance with that of the synthesized ADNBF crystal (Figure 2b). However, the lattice energy of disorder 2 was shown to be lower than that of disorder 3, and it had a smaller deviation in lattice parameters (Table 1). Hence disorder 2 was taken as a starting model unit of ADNBF in the present study. The attachment energy (Eatt) is the energy released by the addition of a growth slice onto the crystal face and is a useful tool for morphology prediction of crystals.48,49 However, the attachment energy model does not provide realistic prediction when external factors such as solvents and additives affect greatly the growth habit of crystals.35,50 Several studies showed that binding of additives or solvent molecules reduces the growth rate of certain crystal faces, and the interaction energy was incorporated into the conventional attachment energy model.20-23 Hartman and Bennema48 showed that attachment energy can be related to specific surface energy, γhkl, (eq 1), ZEatt dhkl γhkl ¼ ð1Þ 2Vcell NA Z is the number of molecules per unit cell, Vcell is the unit cell volume, NA is Avogadro’s number, and dhkl is the interplanar spacing of the lattice plane (hkl). The attachment energy in eq 1 can be substituted by interaction energy between the solvent adsorbed and crystal surface because the attachment energy is also interaction energy of the newly adsorbed layer on the crystal surface. From the analogy of calculation for attachment energy and solvent interaction, the

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Figure 2. (a) Unit cell structures of disorders 1-4. Green circles indicate the positions of disordered nitrogen. (b) Simulated powder X-ray diffraction patterns of disorders 1, 2, 3, and 4, reference structure,3 and experimental powder X-ray diffraction pattern of synthesized ADNBF.

solvent-specific surface energy equation, U hkl, was derived as eq 2.23,51 U hkl ¼

hkl ZR Uhkl hkl SR NA

ð2Þ

ZRhkl is the number of adsorbed solvent molecules per SRhkl, Uhkl is the interaction energy of each solvent, and SRhkl is the area of surface where the solvent molecule is docked. Here the interaction energy of each solvent (Uhkl) is calculated by eq 3. Uhkl ¼ Etotal -ðEdockedmolecule þ Esurface Þ

ð3Þ

Etotal, Edocked molecule, and Esurface are the energies of a surface with a docked molecule, of only a docked molecule, and of only a surface, respectively. Individual surfaces of a crystal have different packing orientations of molecules since the growth unit is asymmetric.52,53 The different arrangement of molecules on each face varies the surface geometry and complicates the interaction behavior of docking molecules onto surface. Therefore, diverse binding sites and interaction energies of docked molecules should be addressed to understand the effect of solvent on the growth of each surface.36,44,54 In the present work, relevant crystal surfaces were decided by the attachment energy model, and molecular dynamics was performed to have the energy histograms with various binding configurations between solvents and crystal surfaces. In the calculations by dynamics, each two-dimensional surface was larger than 20 A˚ 20 A˚. A solvent or solute molecule was located on the center of a given surface, and only a docked molecule was allowed to be movable. Dynamics of each surface at 310 K were performed with NVT ensemble, 1 fs time step, and 100 ps dynamics time (Materials Studio 4.2).55 Configurations of each molecule on a crystal surface were taken every 1 ps, and their geometries were optimized to

specify the binding site and binding energy. van der Waals energy was calculated with a cutoff distance of 12.5 A˚. Coulombic interaction of the present model system was calculated by the Ewald summation method with accuracy of 0.0001 kcal/mol. Finally, based on the energy histogram, interaction energy (Uhkl) of various configurations between surface and adsorbed single molecule was weight-averaged as Uhkl,avg. Interaction energy between a solvent molecule and a crystal surface is obviously an important factor that alters the growth habit of that plane. However, it is insufficient to explain solvent effects on the growth habit change by the interaction energy only because various solvent and solute molecules interact simultaneously with the crystal surface in reality. Therefore, in the present work, the fraction of binding sites for each surface and mole fractions of solvent and solute were considered based on the concept given by Hammond et al.23 To obtain the fraction of binding sites, the number of solvent and solute binding sites on each surface was counted from the geometry-optimized configuration and then the counted binding sites per unit area were normalized. The ratio of surface binding sites of each face was expressed as the binding site density, khkl. Equation 4 is the modified Hammond equation solution for the calculation of interaction energy of solution (Uhkl ) introduced in the present work. solution ¼ Uhkl

1 solvent1 ðks1 ns1 Uhkl , avg ns1 þ ns2 þ nh hkl

solvent2 h host þ ks2 hkl ns2 Uhkl, avg þ khkl nh Uhkl, avg Þ

ð4Þ

where ns1, ns2, and nh are the mole fractions of solvent 1, solvent 2, and solute, respectively, based on ADNBF solubisolvent1 solvent2 host , Uhkl,avg , and Uhkl,avg are the lity data at 60 °C, Uhkl,avg s1 , interaction energies of molecule on the (hkl) surface, and khkl s2 h khkl, and khkl are the binding site densities on each surface for

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Figure 3. (a) ADNBF morphology predicted by the attachment energy model and (b) SEM image of synthesized ADNBF crystals. Table 2. Interplanar Spacing (dhkl) and Calculated Attachment Energies of the ADNBF Crystal face

dhkl (A˚)

attachment energy (kcal/mol)

(100) (010) (001) (110) (101) (111)

11.55 9.95 7.01 7.54 6.53 5.46

-45.20 -53.71 -73.34 -73.92 -79.96 -91.05

solvent 1, solvent 2, and solute, respectively. With eq 2, solution was replaced with surface energy of solution, Uhkl solution solution . Finally, solution-mediated surface energy, γhkl , Uhkl was obtained from the difference between surface energy of vacuum , from eq 1) and surface energy of solution. vacuum (γhkl solution

¼ γvacuum -U hkl γsolution hkl hkl

ð5Þ

4. Results and Discussion 4.1. Morphology Prediction of ADNBF by the Attachment Energy Model. Morphology of ADNBF predicted by the attachment energy model is shown in Figure 3a and interplanar spacings (dhkl) and attachment energies of ADNBF crystal are listed in Table 2. From those results, the morphologically important faces can be written in the order: (100) > (010) > (001). In those three planes, the (001) surface is expected to grow faster than the other main surfaces since this surface has the largest attachment energy and the shortest unit cell dimension (d001 = 7.01 A˚). It can be said that the predicted morphology of ADNBF by the attachment energy model agrees qualitatively with that of the synthesized ADNBF crystal, which is cubic shape as can be seen from Figure 3b. 4.2. Morphology of Recrystallized ADNBF. Unlike the morphology of synthesized ADNBF, crystals grown from cosolvents were observed to have characteristic morphologies with the composition of the cosolvents. SEM images in Figure 4 show that the morphologies of ADNBF crystals are systematically changed from needle to plate-like with cosolvent compositions. In all cases of 1:1 mixing ratio of cosolvents, morphologies of ADNBF are rod-like, and this suggests that NMP has a strong effect on the crystal shape. When ADNBF crystallized from NMP/acetonitirle (mixing ratio = 1:4), the crystal shape was rectangular plate-like, and in cases of NMP/methanol or NMP/chloroacetone, morphologies were shown to be hexagonal plate-like. To identify those large planes, PXRD patterns were obtained

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for samples prepared by grinding and as described in ref 56. Figure 5a is the PXRD of synthesized ADNBF and Figure 5b-d are PXRDs of samples grown from cosolvents with mixing ratio of 1:4. The diffraction patterns from the recrystallized ADNBF (red, green, and orange lines) exhibit one strong reflection at the (001) plane, whereas the diffraction patterns of ground crystals (black filled areas) have different intensities that are similar to that of synthesized ADNBF. Since the intensity of diffraction peaks is directly affected by crystal morphology, one strong reflection at the (001) plane implies that ADNBF crystals have a large basal plane that is morphologically the most important surface for all solvents with ratio of 1:4. 4.3. Interaction Energy of Solvent with Crystal Surface. From the present experimental results, the (001) surface was demonstrated to be the slowest growing face, suggesting that solvents interfere intensively with the growth of this plane. In an attempt to comprehend the strong inhibition of growth of a specific surface, interaction energies between surface and adsorbed single molecules (Uhkl) were calculated by molecular dynamics and weight-averaged as listed in Table 3. All the solvent molecules are shown to be strongly bound on the (010) surface, while (001) surface binding is generally weak. On the other hand, interaction energy of the ADNBF molecule to the crystal surface is the strongest on the (100) plane, while it is the weakest on the (001) plane. The interaction energies of ADNBF molecules on ADNBF crystal surfaces surpass those of the solvents on all surfaces. Hence it seems that solvent interaction with the crystal surface would not be a main factor in morphological change of ADNBF crystal. However, it is obvious that solvents affect greatly the ADNBF morphology (Figure 4), and PXRD data indicate that the (001) surface is the most solvent-affected plane. The growth retardation by solvent is significant on the (001) plane, but surprisingly, the interaction energy of the solvent (Uhkl,avg) on the (001) plane is shown to be the weakest. These results imply that there should be additional consideration to elucidate the solvent effect on the growth habit of ADNBF crystals. 4.4. Possible Binding Sites Calculation. In order to understand the prominent inhibition on the (001) plane, configurations of solvent molecules on the surface of the ADNBF crystal were explored. The ADNBF molecule has a carbon ring substituted by several functional groups such as NO2, NH2, and NO as can be seen from Figure 1. The carbon ring, which is surrounded by electron-withdrawing groups, has positive charge because its electron density is moved to the substituents.57-61 Therefore, the polynitro arene structure in ADNBF makes it possible to have noncovalent π interactions between lone pair electrons of electronegative atoms and the polynitro arene. All solvent molecules used in the present experiments have at least one atom with high electronegativity. Therefore, ADNBF crystal packing would be disturbed by electrostatic interactions of solvents on the polynitro arene.37,62,63 Also, solvent molecules can interrupt the crystal packing by making a hydrogen bond with -NH2 and -CH in ADNBF. The packing orientations of ADNBF molecules on (001), (010), and (100) faces are shown in Figure 6. It is easily perceptible that the outmost layer for each surface possess various functional groups and arrangement of ADNBF molecules. Thus the solvent molecules act differently at each crystal surface. Figure 7 is the view of (001), (010), and (100) surfaces represented by the Connolly surface with the

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Figure 4. SEM images of ADNBF recrystallized from cosolvents and their predicted morphologies with solvent effect: (a) NMP/acetonitrile, (b) NMP/chloroacetone, and (c) NMP/methanol. Mass ratio of cosolvents is 1:1 to 1:4. Table 3. Interaction Energies (Uhkl,avg., kcal/mol) of ADNBF, NMP, Acetonitrile, Chloroacetone, and Methanol Molecules on the ADNBF Crystal Plane crystal plane ADNBF NMP acetonitrile chloroacetone methanol (100) (010) (001) (110) (101) (111)

-47.42 -33.77 -31.78 -32.43 -38.89 -34.20

-20.64 -26.48 -18.72 -19.59 -22.51 -20.78

-12.67 -13.67 -7.94 -10.12 -10.68 -11.68

-21.41 -24.76 -15.75 -18.97 -22.58 -22.2

-17.88 -22.48 -16.7 -16.55 -16.62 -14.59

Figure 6. Packing arrangement of ADNBF molecules on each crystal plane. Figure 5. Powder X-ray diffraction (PXRD) patterns of (a) ADNBF as-synthesized, (b) ADNBF recrystallized from NMP/ acetonitrile, (c) ADNBF recrystallized from NMP/chloroacetone, and (d) ADNBF recrystallized from NMP/methanol. Mixing ratio of all cosolvents was 1:4. Colored lines are PXRD patterns of recrystallized ADNBF and black filled area peaks are PXRD patterns of recrystallized ADNBF after grinding.

observable binding sites (dashed circles) for better recognition of surface geometry and functional groups. On the (001) plane, ADNBF molecules are vertically arranged on the surface, and many hydrogen atoms of NH2 and CH groups jut out toward the interface (Figure 7a). Therefore, the (001) surface would be the most frequent contact and susceptible surface for solvent molecules leading to higher binding site density. On the other hand, the (010) surface has a wedge of two ring planes, and only π interactions with the polynitro arene are possible (Figure 7b). On the (100) surface, ADNBF

molecules almost lay down on the surface offering the polynitro arene and a few hydrogens as binding sites (Figure 7c). Therefore, those distinctive surface geometries and functional groups lead to dissimilarity of binding site densities for each surface of ADNBF as shown in Table 4. The (001) surface has the highest binding site density for all molecules, and the (010) surface has generally the fewest binding sites that can interact with solvents. It is also shown also that the binding site densities are diverse depending on the type of molecules. The difference between methanol and acetonitrile is that methanol has a hydroxyl group while acetonitrile molecules have nitrogen atoms. The hydroxyl group acts as a donor as well as an acceptor; hence it is easy for it to make hydrogen bonds with ADNBF. Consequently, binding site density for methanol is high for all faces of the ADNBF crystal.

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Figure 7. The (a) (001), (b) (010), and (c) (100) planes covered by Connolly surface. Red circles show the binding sites of solvents on each surface. Table 4. Binding Site Densities of Each Surface of the ADNBF Crystala surface ADNBF (100) (010) (001) (110) (101) (111)

0.607 (6) 0.587 (6) 1.000 (10) 0.606 (6) 0.590 (6) 0.884 (6)

NMP 0.337 (6) 0.326 (6) 1.000 (18) 0.337 (6) 0.328 (6) 0.655 (8)

acetonitrile chloroacetone methanol 0.202 (6) 0.196 (6) 1.000 (30) 0.404 (12) 0.492 (15) 0.295 (6)

0.405 (12) 0.196 (6) 1.000 (30) 0.606 (18) 0.197 (6) 0.393 (8)

0.379 (9) 0.489 (12) 1.000 (24) 0.926 (22) 0.738 (18) 0.246 (4)

a Each binding site density is normalized by surface area of (001). The numbers in parentheses represent the number of binding sites on each 2D surface model.

Therefore, methanol can more effectively inhibit the growth of a specific surface than acetonitrile. On the other hand, both acetonitrile and chloroacetone have no hydroxyl group. However, unlike the acetonitrile, the chloroacetone molecule has two electronegative atoms that are oriented in different directions. It has been suggested that approaching molecules with effective orientation at the interface can easily participate in crystal growth.52 Therefore chloroacetone, which has more chance to offer an effective orientation at the interface, can more easily interact with the interface than acetonitrile. In order to reflect the effective orientations that chloroacetone has, its binding site is regarded as two, when one binding site interacts with two different configurations: for example, because oxygen or chlorine atoms of chloroacetone can bind to hydrogen of ADNBF, the hydrogen position is counted as two binding sites. Therefore, binding site density for chloroacetone is higher than that for acetonitrile. Chloroacetone and methanol show different binding site densities on some surfaces because of their different functional groups compared with those of acetonitrile. This may be a reason for two different shapes of ADNBF appearing in the cosolvents with mixing ratio of 1:4, rectangular plate-like morphology from NMP/acetonitrile and hexagonal platelike morphology from NMP/methanol and NMP/chloroacetone. 4.5. Interaction Energy of Solution. Combining the factors that we have considered so far gives a more reasonable explanation for solvent effects. Various configurations of solvent molecules on the (010) and (001) planes are shown in Figure 8. Locations that molecules can reside are decisive because the (010) surface has deep pocket-like grooves that can serve as good sites for the approaching molecules (Figure 8a). As a result, inside the groove, molecules strongly interact with peripheral surface molecules, and thus this is a reason for the highest interaction energy for single molecule (Uhkl,avg) at the (010) plane (Table 3). However, the adsorbed

molecules on the (010) plane have limited configurations because they are placed inside the pocket, and (010) surface itself has relatively smaller binding site as can be seen from Figure 7. Therefore, the (010) surface has the smallest binding site density (khkl), while interaction energies with solvents are strong. Docked molecules on the (001) plane can have numerous configurations because the (001) surface contains many binding sites. Also, the smoother surface geometry of the (001) plane than the (010) plane gives more accessibility to solvent molecules with various approaching angles. Figure 8b illustrates various configurations of acetonitrile and chloroacetone on the (001) surface showing the highest density of binding sites (khkl) (Table 4). On the (001) surface, various configurations of solvent molecule can be bound due to the many protruding functional groups and the surface geometry. This means that a large amount of solvent molecules can interact simultaneously on the same surface of crystal. Although interaction energy of a single solvent solvent ) is low, many molemolecule on the (001) surface (U001,avg solvent cules can concurrently affect the (001) surface (high k001 value). Therefore, the overall effect of solvent on the (001) plane becomes substantial. Conversely, in case of the (010) solvent solvent is large, but binding site density (k010 ) is surface, U010,avg low. As a result, the influence of solvent on the (010) surface becomes weaker than that on the (001) plane. It was shown that integrating binding site density (khkl) with interaction energy (Uhkl,avg) gives rational prediction and elucidates the solvent effect on the growth habit of ADNBF (Figure 4). When we take both of those into consideration, suppression of growth of ADNBF in the [001] direction can be explained, and also other surfaces are adequately predicted. Therefore, by combining the interaction energy and binding sites with the attachment energy model, the limitation of the attachment energy on the solution-mediated habit of ADNBF can be overcome, and thus simple morphology prediction can be possible. However, in cases of solvent ratios of 1:1, all the morphologies of ADNBF exhibit rod-like shape, while the predicted morphology shows that the (001) plane is still prominent. One reason for this discordance may be attributed to the variation of fraction of solute during crystallization, which was not possible to consider in the present work. During the crystallization, the amount of dissolved ADNBF in solution is decreased and thus the relative mole fraction of ADNBF also is varied. The degree of variation would be large for the solution with a mole fraction of 1:1, in which ADNBF is

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Figure 8. (a) Some solvent configurations of acetonitrile (right), chloroacetone (middle), and methanol (left) on the (010) surface of ADNBF and (b) various optimized binding sites for acetonitrile (right) and chloroacetone (left) on the (001) surface of ADNBF. The pink grid on the ADNBF surface is the solvent-accessible area.

highly soluble. Another reason for discrepancy in morphology prediction may be that binding site density for one kind of solvent or solute was considered in the calculation of solution , but in reality, three kinds of molecules would Uhkl competitively interact with the surface of the crystal. Therefore, this may be another reason for overestimation at the (001) surface in cosolvents with mixing ratio of 1:1 because competitive interaction of molecules in solution cannot be explained by simple addition of binding site densities. For better morphology prediction of crystals from cosolvents, these problems should be resolved. 5. Conclusions In the present work, the growth habit of ADNBF from cosolvents was predicted using the modified attachment energy model with the additional term of solvent incorporation. We attempted to explore the solvent influence on the growth habit of ADNBF crystal by making the connection between interaction energy of the solvent molecule and the binding sites on the crystal surfaces that can interact with solvents. Morphologies of ADNBF recrystallized from cosolvents (NMP/acetonitrile, NMP/chloroacetone, and NMP/methanol) with mixing ratios of 1:4 were observed to be plate-like due to the strong inhibition of growth of the (001) surfaces. The interaction energy of a single solvent molecule with the crystal surface was not able to explain retardation of the (001) plane, whereas the interaction energy combined with the binding site density of each surface was shown to rationalize the inhibition of growth of the (001) plane. When surfaces of the ADNBF crystal were explored, ADNBF molecules in the (001) plane were found to be vertically packed and offer many hydrogen atoms at the solid-liquid interface as binding sites.

Therefore, high binding site density on the (001) plane increases interaction frequency of solvent molecules and thus the (001) surface becomes strongly affected by solvent molecules albeit interaction energy of individual solvent molecules is weak. Even though there is some discrepancy between predicted and experimental morphologies of ADNBF from cosolvents with mixing ratio of 1:1, it is noteworthy that binding site density on the specific crystal surface should be an important factor to characterize the morphological change of crystals grown from solution. Acknowledgment. This work was supported by the Defense Acquisition Program Administration and Agency for Defense Development, the Special Research Grant of Sogang University, and a grant (M2009010025) from the Fundamental R&D Program for Core Technology of Materials funded by the Ministry of Knowledge Economy (MKE), Republic of Korea.

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Prediction of the Growth Habit of 7-Amino-4, 6-dinitrobenzofuroxan

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