Structure and Stability of Hydrolysis Reaction ... - ACS Publications

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Structure and Stability of Hydrolysis Reaction Products of MgO Nanoparticles Leading to the Formation of Brucite Mingyang Chen*,† and David A. Dixon*,‡ †

Beijing Computational Science Research Center, Beijing 100193, China Department of Chemistry, The University of Alabama, Tuscaloosa, Alabama 35487-0336, United States

‡

S Supporting Information *

ABSTRACT: The bottom-up formation of MgxOy(OH)z nanoparticles leading to Mg(OH)2 nanoparticles was modeled in two steps by using an evolutionary global optimization approach: (1) the formation of small MgnOm+nH2m clusters via the hydrolysis of (MgO)n and (2) the formation of multilayered (Mg(OH)2)n clusters via monolayer stacking. The sheet-like (Mg(OH)2)n structures were predicted as the energetically favorable reaction products for the (MgO)n + nH2O reaction, whereas more compact structures were found to dominate for the products of (MgO)n + mH2O, m < n. The stepwise hydrolysis reactions most likely follow the compact reaction path until the crossover point is reached. Multistep structural rearrangements are required for the conversion between the compact products and the sheet-like products even after the crossover point. The protective shell formed by the hydroxyl groups may inhibit the further hydrolysis reaction of the compact products, even though the hydrolysis reactions are both exothermic and exergonic; such an effect is less significant in the smaller structures. The hydrolysis of (MgO)n is not suitable for the preparation of the large sized (Mg(OH)2)n nanoparticles but may be used to synthesize the ultrasmall (Mg(OH)2)n nanoparticles. A fragment-based model was used to determine the structure-energy relationship for the monolayered (sheet-like) and multilayered (Mg(OH)2)n nanoparticles. The normalized clustering energy as a function of the size n was obtained for the raw particles and for the particles including solvent effects. The thermodynamically favored (Mg(OH)2)n nanoparticle types are (1) rhombic monolayers for n < 40, (2) hexagonal monolayers for 40 < n < 53, (3) rhombic multilayers for 53 < n < 78, and (4) hexagonal multilayers for n > 78 in vacuum at 0 K. In the presence of solvent, the critical sizes for the transition of the dominating particle shapes are shifted, and the growth rates in each dimension also change. This work provides a basis for controlling nanoparticle morphologies in the selective bottom-up synthesis of brucite-like (Mg(OH)2)n-related nanoparticles.

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INTRODUCTION Magnesium hydroxide (Mg(OH)2) is of broad interest in many scientific and industrial areas. Many applications of magnesium hydroxide are due to it being the simplest layered double hydroxide (LDH). Magnesium hydroxide can be used as the precursor for diverse types of LDHs. Monolayered and multilayered magnesium hydroxide LDHs have been used as carriers for small molecular systems such as metal ions and biomolecules and thus have applications in catalysis, energy storage, semiconductor device fabrication, drug delivery, and so on.1−3 Magnesium hydroxide monolayers can also stack with other 2D semiconductor monolayers, potentially giving rise to new heterolayered structures with interesting semiconducting properties.4 Magnesium hydroxide has been typically used as the precursor to magnesium oxide via dehydration reactions.5 The reverse process (hydrolysis of magnesium oxide), in general, is rarely used for the preparation of magnesium hydroxide.6 Nevertheless, it has been reported that MgO nanocubes (10, but dissolution of regularsized MgO nanocubes is essentially inhibited.7 Crystals and © XXXX American Chemical Society

nanoparticles of magnesium hydroxide with different sizes and morphologies (plate, needle, rod, etc.)8−11 can be prepared using different synthesis methods, including hydrothermal processing,12,13 water-in-oil microemulsion processing,14 and high-gravity reactive precipitation.15 A hexagonal lamellar plate was found the be the primary shape for Mg(OH)2 nanoparticles.16 Despite being studied experimentally and theoretically studied on various scales,17−19 the fundamental processes of magnesium hydroxide that are related to its bottom-up synthesis, such as formation, crystallization, growth, and delamination, have not been fully understood, much less for ultrasmall Mg(OH)2 nanoparticles at the atomistic level. We use our fragment-based structure-energy relationship model20 to elucidate the structure-energy-related phenomena for Mg(OH)2 nanoparticles, especially for ultrasmall nanoparticles whose properties differ from those of the molecules and the bulk. Received: July 29, 2017 Revised: September 11, 2017 Published: September 12, 2017 A

DOI: 10.1021/acs.jpcc.7b07507 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

Figure 1. Optimized geometries for the selected low-energy hydrolysis products of (MgO)n nanoclusters up to n = 18 at the B3LYP/DZVP level.

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COMPUTATIONAL DETAILS The global energy minima structures of the MgnOm+nH2m clusters were searched for using a docking-HGA (hybrid genetic algorithm) composite approach21 with energies calculated at the semiempirical molecular orbital theory (SEMO) level with the MNDO/MNDO/d parameters.22−24 The docking-HGA performs a global geometry optimization following the H2O docking on a magnesium oxide or magnesium oxide hydroxide cluster and can be used to model the thermodynamics of the stepwise hydrolysis reactions. The initial geometries for the docking-HGA calculation, the global energy minima for (MgO)n, were taken from our previous work.25 The details of the HGA can be found in our previous work26 building on that of Johnston.27 The resulting low-energy structures from the HGA calculations were optimized using density functional theory (DFT)28−30 with the B3LYP31,32 functional and the DZVP33 basis set. The DZVP basis set is chosen to study a large number of structures with a reasonable computational cost. In addition, for the small (MgO)n clusters, n < 10, the calculated normalized clustering energies using the combination of the B3LYP functional and DZVP basis set are within 0.6 kcal mol−1 of the CCSD(T)/CBS limits.25 The low-energy (Mg(OH)2)n layered structures were initially predicted using the bottomup-HGA method.20 Geometry patterns were identified in the gallery of structures resulting from the bottom-up-HGA calculations, and larger structures were then built based on the identified geometry patterns. For larger clusters, including the single- and multiple-layered (Mg(OH)2)n nanoparticles, the geometry optimization calculations were performed using the DFT B3LYP functional with the DZVP basis sets in conjunction with the empirical dispersion corrections using the D3 version of Grimme’s dispersion34 (denoted as B3LYP/ DZVP+GD3), as dispersion forces could play an important role in the stacking interactions. The docking-HGA and bottom-up-HGA calculations were performed using our own codes. The local geometry optimization steps were done using in the MOPAC201235

program suite. All of the DFT calculations were performed using the Gaussian 09 suite of programs.36

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RESULTS AND DISCUSSION Hydrolysis of Small (MgO)n Clusters, n = 1−10, 16, and 18. The lowest energy structures for the hydrolysis products of (MgO)n clusters,25 n= 1−10, 16 and 18 (eq 1) (MgO)n + mH 2O → Mg nOm + nH 2m

(1)

are shown in Figure 1. The optimized structures for additional low-energy hydrolysis products with their energies (enthalpies at 0 K) relative to the lowest energy isomers at the B3LYP/ DZVP level (including zero-point energy corrections) are given in Figure S1 (Supporting Information (SI)). The low-energy products for the hydrolysis reaction (eq 1) are denoted as structure n−mα (α = a, b, c, ...), where α indicates the ordering of relative stabilities of the isomer products. Among these (MgO)n clusters, (MgO)2 is the smallest part of a cubic cluster (a single face), (MgO)10 is a member of a 1-D cubic nanoparticle series (i.e., a set of particles sharing the same types of geometry fragments and local geometries), (MgO)16 is a member of a 2-D cubic nanoparticle series, and (MgO)18 is a member of the 3-D cubic nanoparticle series (Figure S2, SI). Low-dimensional structures (1-D and 2-D structures) were found to be dominant for the hydrolysis products for (MgO)n, n = 1−4, mainly due to the low-dimensional geometries of the (MgO)n precursors (Figure S2, SI). A high coordination number (CN) oxygen center starts to appear in most of the lowest energy hydrolysis products of (MgO)5, where CN is the number of atoms directly bonded to an O or Mg. As additional H2O molecules are added to the (MgO)5 precursor, the O−Mg CN of the highest coordinate O center of the product increases with CN = 3 for the reaction products with zero to one H2O, CN = 4 for the product with two to four H2O molecules, and CN = 5 for the product with five H2O molecules. Similar trends were found for larger clusters, where O can be bonded to up to six Mg atoms, as found in bulk MgO. However, as more H2O molecules react with (MgO)n to form MgnOm+nH2m, when m ≈ n, the 2-D sheet-like structures that resemble a single-layer of B


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The Journal of Physical Chemistry C the bulk brucite crystal dominate the hydrolysis products as the O atoms bond to up to three Mg atoms and the Mg atoms bond to up to six O atoms in octahedral coordination positions. Structures 6−6a, 7−7a, 8−8a, 9−9a, 10−10a, 16−15a, 16− 16a, 18−17a, and 18−18a are examples of the energetically favorable sheet-like MgnOm+nH2m clusters. During the stepwise hydrolysis of (MgO)16 and (MgO)18, the compact structures with m < n (in contrast with the sheet-like structures) have the high coordinate Mg and O centers surrounded by a protective shell consisting of the hydrolyzed surface sites. The protective shell may inhibit the further hydrolysis reaction of the compact products, despite the fact that the hydrolysis reactions are both exothermic and exergonic. Such an effect is less significant in the smaller structures. This suggests that the hydrolysis of regular-sized (MgO)n nanoparticles is not viable for synthesizing regular (Mg(OH)2)n nanoparticles, but the hydrolysis of the ultrasmall (MgO)n nanoparticles may lead to the formation of the ultrasmall (Mg(OH)2)n nanoparticles with a nonlayered structure. Subsequent hydrolysis reactions of such compact structures (such as 16−14a) lead to either direct compact products with molecularly adsorbed H2O molecules or the thermodynamically favorable sheet-like products. To form the latter, a significant amount of structural rearrangement is required, and a complex reaction mechanism is involved. To better understand the formation of the small MgnOm+nH2m clusters via hydrolysis reactions, the energetics for the forward reaction path, from the (MgO)n precursor to the lowest energy compact (Mg(OH)2)n product, and the reverse reaction path, from the sheet-like (Mg(OH)2)n to a low-energy MgnOm+nH2m, m < n, were calculated at the B3LYP/ DZVP level, as shown in the energy level diagrams in Figure 2 and Figure S3 (SI). For (MgO)6, the crossover between the two paths occurs at m = 6; at this point, the sheet-like structure 6−6a is only ∼0.5 kcal mol−1 lower in energy than the compact structure 6−6b. Before the crossover, the sheet-like structure 6−5d is ∼40 kcal mol−1 less stable than the lowest energy compact structure 6−5a. For the larger (MgO)n clusters, the energy difference between the sheet-like and the compact (Mg(OH)2)n clusters is found to increase (for example, ΔH(0K) = 12 and 54 kcal mol−1 for (Mg(OH)2)10 and (Mg(OH)2)18). For the hydrolysis of (MgO)16, the crossover between the reaction paths of the compact clusters and the sheet-like clusters occurs at m = 15, and for the hydrolysis of (MgO)18, the crossover occurs at m = 17. The compact structures resulting from further reactions of (MgO)16 and (MgO)18 with water become less stable due to the surface protective shell of hydroxyl groups. The energetics for the reaction path involving the sheet-like structures has a much steeper slope than the energetics for the reaction path involving the compact structures, which implies that the stepwise hydrolysis reactions will most likely follow the compact reaction path before the crossover point. It also implies that in the bottom-up synthesis of sheet-like (Mg(OH)2)n nanoclusters from (MgO)n leading to brucite, if there exist high coordinate Mg and O centers in the (MgO)n precursor, then the total reaction is thermodynamically favorable but probably not kinetically favorable. High reaction temperatures may help the formation of the sheet-like product. An alternative approach would be to form the extremely small sheet-like (Mg(OH)2)n from the low dimensional (MgO)n and then to form larger sheet-like (Mg(OH)2)n via self-assembly.

Figure 2. Calculated reaction energy level diagrams for (a) (MgO)6 + mH2O, m = 1−6 and (b) (MgO)18 + mH2O, m = 1−18 at the B3LYP/ DZVP level. The red values are the calculated reaction energies for the stepwise hydrolysis reactions to form the compact MgnOm+nH2m clusters, and the blue values are for the stepwise hydrolysis reactions to form the sheet-like MgnOm+nH2m clusters.

The influence of the GD3 dispersion correction on the calculated reaction energies was examined for the (MgO)9 hydrolysis reactions (Figure S4, SI). We found that the inclusion of GD3 dispersion corrections increases the exothermicity of hydrolysis reaction by approximately −5 kcal mol−1 per H2O, which accounts for ∼10% of the reaction energy. The GD3 corrections to the formation energies for a sheet-like isomer hydrolysis product and a compact isomer product are comparable (with the difference f5 > f4 ≈ ft5 ≈ ft4> f 3. According to the fragment-based model, the NCEs for all of the monolayered nanoparticle series that resulted from the E


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Figure 5. NCE as a function of n−1/2 for the monolayered (Mg(OH) 2 )n nanoparticles at the B3LYP/DZVP+GD3 level. NCErhombus = −30.866 × n−1 − 60.612 × n−1/2 + 95.986. NCEhexagon = −81.569 × n−1 − 52.635 × n−1/2 + 95.986. NCEequilateral‑triangle = −50.522 × n−1 − 64.088 × n−1/2 + 95.986.

We found that the NCE for the equilateral triangle is always smaller than the NCEs for the rhombus and hexagon at any n. The NCE for the rhombus is greater than the NCE for the hexagon for n < ∼40, and the opposite for n > ∼40. The energetic preference at small n for the rhombic nanoparticle series over the hexagonal nanoparticle series is due to the lower corner/bulk ratio in terms of the fragment counts of the rhombus. As n increases, the contribution to the NCE by the corner fragments becomes less significant. Therefore, the surface/bulk ratio starts to dominate the NCE, and hence the crossover occurs. At the thermodynamic limit (n → ∞), only the bulk fragment types contribute to the NCE, and thus all of the monolayer structures in different shapes that share the same bulk fragment type are equally thermodynamically favorable. Multilayered (Mg(OH)2)n structures can be formed by stacking several monolayers with no displacement along the a and b directions. Each fragment type in the (Mg(OH)2)n monolayer structures therefore diverges as two new fragment types in the multilayer structures are introduced. One type belongs to the two surface layers, indicated by the subscript “s”, and one type belongs to the bulk layers, indicated by the subscript “b” (Figure 6). As shown in Figure 6, the bulk fragment f6 of the monolayer structure splits into the bulk fragment f6b and the face-c (i.e., the horizontal faces with its normal in the c direction) fragment f6s in the parallelogrammatic and hexagonal multilayer structures. The fragments without dangling Mg−OH groups in the monolayer structure (f6, f5, and f4) have mostly retained their geometries when the monolayers stack to form the multilayer structure, and the interlayer stacking is similar to the stacking in brucite.38,39 The fragments with the dangling Mg−OH groups (ft4s, ft4b, ft5s, and ft5b) form the interlayer bonds via weak interactions. In the parallelogrammatic multilayer structures, ft4sand ft4b form the Mg−OH−Mg bridge bonds between the layers as part of the two chain-like edges, with a Lewis acid− base bonding nature, whereas in the rhombic multilayer structures ft5s and ft5s form interlayer hydrogen bonds. The strength of the interlayer interactions in the (Mg(OH)2)n multilayer structures is affected by the distance between the two involved fragments (indicated by the Mg−Mg distance between the two fragments). In both the hexagonal and parallelogrammatic (Mg(OH)2)n multilayer structures, the

Figure 6. Description of fragments of the (a) parallelogrammatic and (b) hexagonal multilayer nanoparticles series.

Mg−Mg distances for most of the interlayer fragment pairs are predicted to be ∼4.4 Å, with only a few exceptions. In the multilayered parallelogram structures, the Mg−Mg distances of the ft4s−ft4s, ft4s−ft4, and ft4b−ft4 fragment pairs along the vertical edges range from 3.4 to 3.8 Å due to the formation of the interlayer Lewis acid−base Mg−OH−Mg bonds and slightly increase as the number of the stacked layer increases. Lewis acid−base Mg−OH−Mg edges were found in all of the lowest energy parallelogrammatic multilayers structures but are less common in the hexagonal multilayers, which is presumably because the four-coordinate f4t corner fragment of the parallelogrammatic monolayer is more active than the fivecoordinate ft5 corner fragment of the hexagonal monolayer. The full edges of Mg−OH−Mg chains were only found in the lamellar parallelogrammatic multilayers. Because the Mg−Mg equilibrium distances in the loosely stacked bulk fragment pairs are longer than the Mg−Mg equilibrium distances in Mg− OH−Mg bonded edge fragment pairs, the stability of the multilayer nanoparticle decreases as it grows thicker with a greater difference between the thicknesses at the principle axis and at the Mg−OH−Mg chained edges. When the difference in the local thicknesses becomes too large, the Mg−OH−Mg bonds will break. In the hexagonal multilayer structures, the interlayer Mg−Mg distances of the f6−f6, f5−f5, f4−f4, and ft4b−ft4b fragment pairs are predicted to be ∼4.4 Å, and the d(ft4b−ft4s) ranges from 4.1 to 4.4 Å depending on whether hydrogen bonds are being formed. No Lewis acid−base Mg−OH−Mg bonds were found in the hexagonal multilayered (Mg(OH)2)n nanoparticles, with the exception of the overstacked multilayered hexagonal (7H)z (z > 2) nanoparticles (Figure S7, SI). This is in part because the corners of the hexagonal multilayers are more rigid than the acute corners of the rhombic multilayers. The d( ft5b−ft5s) distances in the hexagonal multilayer structures are significantly longer than the d( ft4b−ft4s) distances in the parallelogrammatic multilayer structures, suggesting that the interlayer hydrogen bonds cause much less strain than do the Lewis acid−base bonds. F


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fitting will make NCE6b converge toward NCE(∞), but this is not currently computationally feasible. The use of the approximate B3LYP/DZVP method may cause errors in the calculated energies, but since NCE6b is essentially the energy difference between the monomer and the monomer bulk fragment f6b in equilibrium (eq 5), the majority of the DFT error is expected to cancel. The predicted SEDi’s are expected to be reliable and universal for USNPs and much larger nanoparticles as SEDi’ is the energy difference between two fragments of equal size in the same nanoparticle at the equilibrium, so that any errors in the geometry or the level of DFT are expected to cancel. The relative stability of the fragment types is on the order from high to low: f6b (bulk) > f6s (horizontal faces) > f5b (vertical faces) > f5s (horizontal edges) > f45t b (vertical edges of the hexagonal multilayers, see the footnotes of Table 2 and SI) > f45t s (corners of the hexagonal multilayers) ≈ f44ts (corners of the parallelogrammatic multilayers) ≈ f44tb (vertical edges of the parallelogrammatic multilayers). The energy differences between bulk f6b fragments of the multilayer and f6 of the monolayer are predicted to be ∼13 kcal mol−1, which is approximately twice the energy difference between f6b and f6s. Therefore, the interlayer interaction per Mg(OH)2 site in the multilayered (Mg(OH)2)n is estimated to be ∼13 kcal mol−1 for the majority of sites. The above discussion highlights the importance of the interlayer energies in determining the energy of the bulk. We have shown previously20 that the ideal aspect ratio for the (la,lb,lc)-mer of the nanoparticle series with the shape of a parallelepiped, la/lb/lc, is approximately equal to the ratio between the surface energies of the face fragment types on the faces perpendicular to the a, b, and c directions, SED5b/SED5b/ SED 6s ≈ 5:5:2 for the parallelogrammatic (Mg(OH)2) n multilayers. This shows that the parallelogrammatic (Mg(OH)2)n multilayer nanoparticles with the ideal aspect ratios are lamellar rhombic prisms. The NCEs for the rhombic and hexagonal multilayered (Mg(OH)2)n are given in eqs 10 and 11

The fragment energy Fix for each fragment type f ix (i = 6, 5, 4, 4t, and 5t; x = “b” or “s”) was solved for using a least-squares fitting procedure, with the details given in the SI and the values given in Table 2. The surface energy density (SEDix) and Table 2. Predicted Energetics for the Fragment Types of the Multilayer (Mg(OH)2)n Nanoparticles at the B3LYP/DZVP +GD3 Level Fixa

SEDixb

NCEixc

f44tb d

−351.9997 −351.9886 −351.9718 −351.9629 −351.9296

0.0 7.0 17.5 23.1 44.0

108.7 101.7 91.2 85.7 64.7

f44ts d

−351.9311

43.0

65.7

f45t b d

−351.9346

40.9

67.9

42.9

65.8

quantity f6b f6s f5b f5s

f45t s a

−351.9314

d

−1 c

−1

In hartree. In kcal mol . In kcal mol . Eelectronic(1) = −351.826436 b

hartree.

f45t s =

d

f44tb =

2f4s + f 5t s 3

f4b + f 4t b 2

; f44ts =

f4s + f 4t s 2

; f45t b =

2f4b + f 5t b 3

; and

.

normalized clustering energy (NCEix) for each fragment type of the multilayered (Mg(OH)2)n were predicted using eqs 5 and 6. If the geometries of f6b in the fit structures have converged to the bulk geometry, then NCE6b is equivalent to NCE(∞), the extrapolated value for the NCE at the thermodynamic limit for (Mg(OH)2)n nanoparticles that contains the six-coordinate f6b fragment type only in the bulk region, which includes almost every large (Mg(OH)2)n particle under normal conditions. NCE6b is predicted to be 108.7 kcal mol−1, ∼20 kcal mol−1 higher than the experimental NCE(∞) of 88.2 kcal mol−1 derived from the gas-phase and solid-phase heats of formation (calculated40 ΔfH°gas = −132.8 kcal mol−1 using Feller− Peterson−Dixon method41−43 and the experimental44 ΔfH°solid = −221.0 kcal mol−1). The reason for this difference is that the geometry of the f6b fragment in the USNPs has not yet converged to the bulk limit, even though the largest multilayer USNP ((37H)3) we studied contains over 500 atoms. Although the overall geometry of the (Mg(OH)2)n is very similar to the bulk crystal, the geometry parameters have not yet fully converged to the bulk. The lamellar multilayer USNPs we studied have an average interlayer Mg−Mg distance of ∼4.4 Å, which is much shorter than the distance of 4.66 Å in the bulk. Most likely, the edges and corners of the monolayer have stronger stacking interactions (when forming the multilayers) than the bulk of the monolayer due to the lower Mg−O coordination numbers in the USNPs. The shorter, unconverged interlayer distances (than the interlayer distance in the bulk) in all of the studied USNPs lead to an overestimation of NCE(∞). Our prior studies have shown that, for some metal and metal oxide clusters, both the overall geometry and the geometry parameters converge quickly to the geometry of the bulk crystal at very small cluster sizes (for (Ag)n45 and (MgO)n,25 convergence is at n = ∼20), but that other clusters with a larger formula unit and a more complex bulk geometry such as (MgCO3)n,46 are not converged either in terms of the overall geometry or geometry parameters. The structural evolution for (Mg(OH)2)n lies somewhere between these two cases. Increasing the size of the clusters used in the least-squares

2l 2 SED6s n 8 − SED 44ts n

NCEmulti ‐ rhombus(la = lb = l , lc) = NCE6b − −

4llc 4l 8l SED5b − SED5s − c SED 44tb n n n

(10)

NCEmulti ‐ hexagon(r , h) (6r − 6)h 6r 2 − 6r + 2 SED5b SED6s − n n 12r − 12 6h 12 SED5s − SED 45t b − SED 45t s − (11) n n n

= NCE6b −

Minimizing Equation 11 against r and h under the constraint given in equation S10 in the SI by using the Lagrange multiplier method, we obtained the ideal aspect ratio for the hexagonal multilayer (Mg(OH)2)n when r and h are not too small by neglecting the low-order terms related to the edge fragment types in the resulting eq 12 SE SED5b r ≈ 5b = h SE6s SED6s G

(12) DOI: 10.1021/acs.jpcc.7b07507 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 7. (a) NCE as a function of (a) n−1/3 and (b) n for the multilayered and monolayered (Mg(OH)2)n at the B3LYP/DZVP+GD3 level. The solid curves are for the raw nanoparticles in the vacuum and the dashed curves are for the nanoparticles under the fictitious solvent effects that lower each Mg(OH)2 fragment with exposed OH molecules by 5 kcal mol−1. The fit NCE(n−1/3) functions and the intersections can be found in the SI.

where SE5b and SE6s are the total surface energies for f5b and f6s, which are equal to SED5b and SED6s in this case because both f5b

and f6s contain 1 Mg(OH)2 unit. Equation 12 can also apply to general hexagonal prismatic nanoparticles with similar local H


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bond energy in the water dimer47). The critical size between the rhombic and the hexagonal monolayered (Mg(OH)2)n is found to be invariant to the strength of the solvent effect. Neglecting the variation in ideal aspect ratios of the multilayers, the critical size (in terms of number of formula units) between the hexagonal monolayer and the rhombic multilayer is increased by 13 in the presence of a solvent effect with ΔE = −5 kcal mol−1, as compared with the critical size for the isolated nanoparticles. The critical size (in terms of number of formula units) between the rhombic multilayer and the hexagonal multilayer is upshifted by four by applying the solvent effect with ΔE = −5 kcal mol−1. The different behaviors of the critical sizes under the effect of solvent may allow control of the particle morphologies in the synthesis of the nanoparticles. The solvent can also affect the energy difference between the isomers with different shapes, which can be potentially useful for the selection and separation of selected isomers. Because the NCE is approximately a cubic function of n−1/3 for the multilayered (Mg(OH)2)n, the perturbation on NCE caused by the solvent effects is also approximately a cubic function of n−1/3, as shown in eq 13

symmetries. The ideal aspect ratio is predicted to be 5:2 for r/h, or approximately 10:2 for the ratio between the base diameter and height. This suggests that the hexagonal multilayer structures with the ideal aspect ratio are approximately twice as flat as the rhombic multilayer structures with the ideal aspect ratio. For the hexagonal and rhombic multilayer structures with the ideal aspect ratios, the values of la, lb, lc, r, and h are on the order of n1/3 (eqs S8 and S10 in the SI). Equations 10 and 11 can then be further simplified, and the NCE equations are now cubic functions of n−1/3 (solid curves in Figure 7a). The intersection between two NCE curves (Figure 7b) indicates the critical size at which two types of (Mg(OH)2)n nanoparticles are equally stable. The thermodynamically favored nanoparticle types are rhombic monolayers for n < 40, hexagonal monolayers for 40 < n < 53, rhombic multilayers for 53 < n < 78, and hexagonal multilayers for n > 78 in the vacuum at 0 K. In the case where the aspect ratio of the multilayered (Mg(OH)2)n is far from ideal, geometry rearrangements may occur. For some overly stacked rhombic and hexagonal multilayer nanoparticles, the vertical edges are mixtures of Mg−OH−Mg Lewis acid−base bonds and regularly stacked fragment pairs. The monolayer planes in these multilayers become tilted (Figure S7, SI). For example, structures (12P)5 and (16R)5 (see Figure S7, SI) have the monolayer planes slightly titled in a zigzag geometry. Partial delamination can also occur for the overly stacked rhombic and hexagonal multilayers, and the multilayer can break into several lamellar multilayered nanoparticles with the Mg−OH−Mg edge chains that stack on top of each other (e.g., structure (16R)6 and structure (7H)8 in Figure S7 in SI). For the hexagonal multilayers for which the Hbonding edges are dominant in the lamellar particles, the Mg− OH−Mg Lewis acid−base bonds are mostly found as part of the edges that connect two partially delaminated parts of the nanoparticles. Thermodynamic Control of the Particle Morphology. With the energetics for the dominant fragment types in (Mg(OH)2)n nanoparticles having been determined, we can predict the response of particle stability versus the variations in the fragment energies. Such variations can be caused by temperature, solvent effects, ligand binding, and so on, presumably by half of the interaction energy between the exposed fragment and the external molecule (solvent, ligand, and so on). Here we consider a simple case, where the variations in the fragment energies are caused by a fictitious solvent. We hypothesize that the solvent alters the fragment energies by interacting with the exposed hydroxyl groups and evenly applies an energy shift ΔE to each affected fragment. For the monolayered (Mg(OH)2)n, the energies of all of fragment types (Fi) are shifted by ΔE, which leads to no changes in the SEDi’s but to a −ΔE shift in NCE(∞) (NCE(∞)  NCE6). The NCE curves for the monolayered (Mg(OH)2)n are hence only vertically translated by −ΔE. For the multilayered (Mg(OH)2)n, all of the fragment types are affected by the solvent, except for the bulk fragment type (f6b). In contrast with the case of monolayered (Mg(OH)2)n, all of the SEDix’s will be shifted by ΔE, but NCE(∞) (NCE(∞)  NCE6b) remains the same. The presence of the solvent will rotate the NCE curves (as a function of n−1/3) around the intercept (at the n−1/3 = 0). The dashed lines in Figure 7a,b indicate the NCEs under the predicted solvent effect with ΔE = −5 kcal mol−1 (which is in the range of weak interactions, for example, the hydrogen

ΔNCEmultilayer(ΔE , n) = NCEΔE(n) − NCE 0(n) = an−1 + bn−2/3 + cn−1/3

(13)

The zeroth-order term of the cubic function is the perturbation on NCE(∞) and is determined to be zero as NCE(∞) only depends on F6b and is invariant to ΔE. The cubic NCE0 functions for the rhombic and hexagonal multilayered (Mg(OH)2)n with the ideal aspect ratios have been obtained by using the method of least-squares (Figure 7) and are given in eqs 14 and 15, respectively 0 −1 NCEmulti − 5.445n−2/3 − 77.367n−1/3 ‐ rhombus = − 27.507n

(14)

+ 108.734

0 −1 NCEmulti + 29.450n−2/3 − 74.108n−1/3 ‐ hexgon = − 236.260n

(15)

+ 108.734

Further numerical analysis shows that all of the coefficients in eq 13 can be given by the product of a constant and ΔE (Figure S8 in the SI). Substitution with the determined values of the coefficients into eq 13 gives the NCE for the rhombic (la/lc = 5:2) and hexagonal (r/h = 5:2) multilayers in the presence of solvent 0 ΔE NCEmulti ‐ rhombus = NCEmulti ‐ rhombus

+ ΔE × ( −14.276n−1 + 15.777n−2/3 − 6.617n−1/3)

(16)

and ΔE 0 NCEmulti ‐ rhombus = NCEmulti ‐ rhombus

+ ΔE × ( −23.030n−1 + 25.442n−2/3 − 7.375n−1/3)

(17)

Altering the fragment energies can also affect the ideal aspect ratios for the (Mg(OH)2)n multilayer nanoparticles. Figure 8 shows the variation in ideal aspect ratio for the rhombic (la/lc) and hexagonal (r/h) multilayer (Mg(OH)2)n under the effect of the solvent with ΔE ∈ (−7, 7] kcal mol−1. The ideal aspect I


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The “conduction bands” and “valence bands” arising from the surface fragments are well separated from the “bands” arising from the bulk fragments in the ultrasmall (Mg(OH)2)n nanoparticles, in which the surfaces are not negligible. This results in a much smaller HOMO−LUMO gap for the (Mg(OH)2)n ultrasmall nanoparticles than the experimentally measured band gap for the bulk crystals and large nanoparticles (Figure S11, SI). The optical band gap for Mg(OH)2 was measured to be ∼5.17 eV for a thin film,48 ∼5.7 eV for a micrometer-sized hexagonal nanodisk,49 and ∼5.76 eV for a micrometer-sized nanosheet network11 using the optical absorption spectroscopy. The band gap for the bulk was predicted50 to be ∼7.6 eV at the density functional theory level with the HSE06 functional; there is no available experimental data for the band gap measurement of the bulk. On the basis of our computational results, the HOMO−LUMO gap of the hexagonal [(Mg(OH)2)37]3 is predicted to be 2.8 eV, but the gap between the highest occupied and lowest unoccupied levels that arise from f6b is >6 eV. Therefore, the (Mg(OH)2)n ultrasmall nanoparticles have unique electro-optical properties that differ from the properties of the larger particles and may be potentially utilized in areas such as photocatalysis, for example, water splitting.

Figure 8. Predicted ideal aspect ratio (IAR) for the rhombic (la/lc) and hexagonal (r/h) multilayer (Mg(OH)2)n under the effects of solvent with ΔE ∈ (−7, 7] kcal mol−1, IAR(ΔE) = (17.5 + ΔE)/(7.0 + ΔE).

ratio converges to ∼1 quickly for positive ΔE and is infinite as ΔE → −7 kcal mol−1. The monolayer structures are prone to form in a strong solvent that can significantly lower the energy of the surface fragments. If ΔE < −7 kcal mol−1, full delamination is predicted and separated monolayers will be formed. The ratio between the thermodynamic growth rates in different dimensions is equal to the ideal aspect ratio, and such a ratio plays a key role in determining the shape of the nanoparticle. Electronic Properties. The total density of states (DOS) and partial density of states (PDOS) diagrams for the monolayer, double-layer, and triple-layer hexagonal [(Mg(OH)2)37]x (x = 1−3) nanoparticles are shown in Figure 9 with additional ones in Figure S9 (SI). The PDOS diagrams show that the high-lying occupied orbitals are dominated by the O 2p orbitals and the low-lying unoccupied orbitals are dominated by the Mg 3s orbitals, as would be expected from the formal charges. From the monolayer (Figure S9a) to double-layer (Figure S9b) to triple-layer (Figure S9a), the nanoparticle shows increasing bulk characteristics, indicated by the DOS “bands” with the increasing width and height. As the thickness of the nanoparticle increases, the HOMO shifts toward higher energy and the LUMO shifts toward lower energy, leading to a decrease in the HOMO−LUMO gap. Projecting onto each fragment type, the resulting PDOS for hexagonal [(Mg(OH)2)37]3 is shown in Figure 9b. We found a weak, broad “valence band” ranging from −5.0 to −3.8 eV in the high-lying occupied orbitals, which involves only the corners ( ft5s) and the vertical edges ( ft5b) and is thus determined to be local. In contrast, the two weak, sharp nonlocal “valence bands” centered at −6.2 and −5.8 eV involve all of the fragment types except for f4b and f4s, and can be mainly attributed to the horizontal edges ( f5s) and the vertical faces ( f5b). The strong, broad, nonlocal “valence band” with its edge at −6.8 eV is mainly attributed to the horizontal faces (f6s) and the bulk ( f6b). The four weak, sharp peaks that form the “conduction band minimum” are found to be nonlocal. The order for the contribution in the “conduction band minimum” by the fragment types, from high to low, is f4s > f4b > f5s > f5b > f6s, which suggests that the Mg sites with lower coordination numbers are better electron acceptors. The locality and nonlocality of the “valence bands” and the “conduction bands” are shown in the molecular orbital isodensity diagrams (Figure S10, SI)

■

CONCLUSIONS

The bottom-up formation of the brucite-like nanoparticles with different morphologies was modeled. The hydrolysis of (MgO)n nanoparticles was investigated by using the dockingHGA method. The results suggest that the hydrolysis of ultrasmall (MgO)n nanoparticles can potentially be used for the synthesis of ultrasmall (Mg(OH)2)n nanoparticles, whereas the formation of large (Mg(OH)2)n nanoparticles by hydrolysis of large (MgO)n, despite being exothermic and exergonic, may be kinetically inhibited. Monolayer stacking leads to the formation of brucite-like multilayer structures. We note that brucite-like layers form very early in the growth of these nanoparticles. We employed a fragment-based model to determine the structure-energy relationship for the mono- and multilayered (Mg(OH)2)n nanoparticles. Using an energy-decompositionbased fragmentation scheme, the total energy, normalized clustering energy, and surface energy density were obtained for all fragment types in the energetically dominant (Mg(OH)2)n multilayer nanoparticles. These parameters are energy fingerprints for layered (Mg(OH)2)n nanoparticles and are key to understanding the structure-energy relationships for a broad class of (Mg(OH)2)n nanoparticles. Using these parameters, we obtained the NCE as a function of n for several types of monoand multilayered (Mg(OH)2)n nanoparticles, and we were also able to predict the stabilities of selected layered (Mg(OH)2)n molecules with irregular shapes. The ideal aspect ratio (equivalent to the ratio between growth rates in different dimensions) was predicted as la/lc = 5:2 for the rhombic multilayers and r/h = 5:2 for hexagonal multilayers. The morphological phase diagram was predicted. A strength of the fragment-based model is its ability to predict properties for both large (up to bulk-sized) nanoparticles and ultrasmall nanoparticles. The predicted energetic parameters also allow us to predict perturbed properties under the effects of external influence (e.g., solvent and ligand). Our predictions provide a basis for better thermodynamic control in the bottom-up synthesis of the (Mg(OH)2)n and its related molecules, especially on the ultrasmall nanoscale. J


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Figure 9. (a) Density of states and partial density of states diagrams for [(Mg(OH)2)37]3 with the population projected to the atomic orbitals. (b) Density of states and partial density of states diagrams for [(Mg(OH)2)37]3 with the population projected to the fragment types. The total DOS is indicated by the red curve in the upper panel; the populations of the occupied (colored) and virtual (gray) molecular orbitals are indicated by the vertical lines in the lower panels.

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ASSOCIATED CONTENT

optimized (MgO)n nanoclusters up to n = 18; the calculated reaction energy level diagrams for (MgO)n + mH2O, 1 ⩽ m ⩽ n (n = 1−5, 7−10, and 16); comparison between the reaction energy levels calculated at the B3LYP/DZVP and B3LYP/DZVP+GD3 levels for the (MgO)9 + mH2O (1 ⩽ m ⩽9) hydrolysis reactions; the average numbers of O atoms around Mg as a function of the cutoff radius for the hydrolysis reaction products of (MgO)9, (MgO)16, and (MgO)18; the optimized geometries (full list) and calculated NCEs (kcal mol−1) for the layered (Mg(OH)2)n, n ⩽ 111 at the B3LYP/DZVP +GD3 level; the optimized geometries for the layered

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b07507. Reference 36 with full list of author names; fragmentbased energy decomposition for the (Mg(OH)2 ) n monolayer and multilayer clusters; the fit of the NCE(n−1/3) functions and intersection points for the layered (Mg(OH)2)n nanoparticles in Figure 7; the optimized geometries for the low energy hydrolysis products of (MgO)n nanoclusters up to n = 18; the K


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(8) Wang, S.-Y.; Li, G.-M.; Xu, W.; Liu, C.; Dai, L.; Zhu, H.-C. Facile Preparation and Application of Magnesium Hydroxide Assembly Spheres. Res. Chem. Intermed. 2016, 42, 2661−2668. (9) Chen, H.; Xu, C.; Liu, Y.; Zhao, G. Formation of Flower-like magnesium Hydroxide Microstructure via a Solvothermal Process. Electron. Mater. Lett. 2012, 8, 529−533. (10) An, D.; Ding, X.; Wang, Z.; Liu, Y. Synthesis of Ordered Arrays of Magnesium Hydroxide Nanoparticles via a Simple Method. Colloids Surf., A 2010, 356, 28−31. (11) Al-Hazmi, F.; Umar, A.; Dar, G. N.; Al-Ghamdi, A. A.; Al-Sayari, S. A.; Al-Hajry, A.; Kim, S. H.; Al-Tuwirqi, R. M.; Alnowaiserb, F.; ElTantawy, F. Microwave Assisted Rapid Growth of Mg(OH) 2 Nanosheet Networks for Ethanol Chemical Sensor Application. J. Alloys Compd. 2012, 519, 4−8. (12) Ding, Y.; Zhang, G.; Wu, H.; Hai, B.; Wang, L.; Qian, Y. Nanoscale Magnesium Hydroxide and Magnesium Oxide Powders: Control over Size, Shape, and Structure via Hydrothermal Synthesis. Chem. Mater. 2001, 13, 435−440. (13) Chen, Y.; Zhou, T.; Fang, H.; Li, S.; Yao, Y.; He, Y. A Novel Preparation of Nano-Sized Hexagonal Mg (OH)2. Procedia Eng. 2015, 102, 388−394. (14) Wu, J.; Yan, H.; Zhang, X.; Wei, L.; Liu, X.; Xu, B. Magnesium Hydroxide Nanoparticles Synthesized in Water-in-oil Microemulsions. J. Colloid Interface Sci. 2008, 324, 167−171. (15) Sun, Q.; Chen, B.; Wu, X.; Wang, M.; Zhang, C.; Zeng, X.; Wang, J.; Chen, J. Preparation of Transparent Suspension of Lamellar Magnesium Hydroxide Nanocrystals Using a High-Gravity Reactive Precipitation Combined with Surface Modification. Ind. Eng. Chem. Res. 2015, 54, 666−671. (16) Mullin, J. W.; Murphy, J. D.; Söhnel, O.; Spoors, G. Aging of Precipitated Magnesium Hydroxide. Ind. Eng. Chem. Res. 1989, 28, 1725−1730. (17) Karazhanov, S. Z.; Pishtshev, A.; Klopov, M. Electronic and Optical Properties of Magnesium and Calcium Hydroxides: The Role of Covalency and Many-Body Effects. Phys. Scr. 2015, 90, 094015. (18) Lv, J.; Qiu, L.; Qu, B. Controlled Growth of Three Morphological Structures of Magnesium Hydroxide Nanoparticles by Wet Precipitation Method. J. Cryst. Growth 2004, 267, 676−684. (19) Henrist, C.; Mathieu, J. P.; Vogels, C.; Rulmont, A.; Cloots, R. Morphological Study of Magnesium Hydroxide Nanoparticles Precipitated in Dilute Aqueous Solution. J. Cryst. Growth 2003, 249, 321−330. (20) Chen, M.; Dixon, D. A. Modeling the Formation of TiO2 UltraSmall Nanoparticles. Nanoscale 2017, 9, 7143−7162. (21) Chen, M.; Straatsma, T. P.; Dixon, D. A. Molecular and Dissociative Adsorption of Water on (TiO2)n Clusters, n = 1 to 4. J. Phys. Chem. A 2015, 119, 11406−11421. (22) Dewar, M. J. S.; Thiel, W. Ground States of Molecules. 38. The MNDO Method. Approximations and Parameters. J. Am. Chem. Soc. 1977, 99, 4899−4907. (23) Dewar, M. J. S.; Thiel, W. Ground States of Molecules. 39. MNDO Results for Molecules Containing Hydrogen, Carbon, Nitrogen, and Oxygen. J. Am. Chem. Soc. 1977, 99, 4907−4917. (24) Thiel, W.; Voityuk, A. A. Extension of MNDO to d Orbitals: Parameters and Results for the Second-row Elements and for the Zinc Group. J. Phys. Chem. 1996, 100, 616−626. (25) Chen, M.; Felmy, A. R.; Dixon, D. A. Structures and Stabilities of (MgO)n Nanoclusters. J. Phys. Chem. A 2014, 118, 3136−3146. (26) Chen, M.; Dixon, D. A. Tree GrowthHybrid Genetic Algorithm for Predicting the Structure of Small (TiO2)n, n = 2−13, Nanoclusters. J. Chem. Theory Comput. 2013, 9 (7), 3189−3200. (27) Johnston, R. L. Evolving Better Nanoparticles: Genetic Algorithms for Optimising Cluster Geometries. Dalton Transactions 2003, 22, 4193−4207. (28) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys. Rev. 1964, 136, B864−B871. (29) Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133− A1138.

(Mg(OH)2)n with tilted or partially delaminated layer planes; the coefficients (a, b, and c) in the perturbation polynomial ΔNCEmultilayer(ΔE,n)= ax−1 + bx−2/3 + c−1/3 as a function of ΔE for the (Mg(OH)2)n multilayers; DOS and PDOS for the double-layered and triple-layered [(Mg(OH)2) 37]x; the isodensity molecular orbital diagrams for the HOMO and LUMO of [(Mg(OH)2)37]3; the calculated HOMO−LUMO gap for the layered hexagonal and rhombic (Mg(OH)2)n nanoparticles at B3LYP/DZVP+GD3 level; the calculated reaction energies and thermal corrections for the Mg16O16+mH2m → (MgO)16 + mH2O reactions; and the Cartesian coordinates and total energy for the optimized magnesium hydroxides clusters and nanoparticles. (PDF)

AUTHOR INFORMATION

Corresponding Authors

*M.C.: E-mail: [email protected]. *D.A.D.: E-mail: [email protected]. ORCID

Mingyang Chen: 0000-0002-9866-8695 David A. Dixon: 0000-0002-9492-0056 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.C. gratefully acknowledges funding from the Beijing Computational Science Research Center and National Natural Science Foundation of China (Grant No. U1530401) and computational resources from the Beijing Computational Science Research Center. D.A.D. was supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energy (DOE) (Geosciences Program) on a subcontract from the Pacific Northwest National Laboratory. D.A.D. also thanks the Robert Ramsay Chair Fund of The University of Alabama for support.

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