Article pubs.acs.org/JPCC
Modeling Calcite Crystallization on Self-Assembled CarboxylateTerminated Alkanethiols Alexander S. Côté,* Robert Darkins, and Dorothy M. Duffy Department of Physics and Astronomy, University College London, Gower Street, London, WC1E 6BT U.K. ABSTRACT: We systematically investigate the crystallization of calcite on self-assembled monolayers (SAMs) composed of carboxylate-terminated alkanethiols of various lengths using molecular dynamics simulation and employing metadynamics to accelerate the process. The (012) calcite surface is found to nucleate on all SAMs, irrespective of the monolayer length. Our simulations provide insight into the growth and structure of the calcite/SAM interface. In particular, we identify point defects at the interface as playing a crucial role in quenching the net dipole moment and accommodating the poor epitaxial match. Step formation also readily occurs as a means of reducing the calcite-monolayer lattice mismatch. The (012)/SAM interface was shown to have a higher energy than the (001)/SAM interface, which had an excellent epitaxial match; therefore, (012) nucleation is assumed to be a kinetic effect.
1. INTRODUCTION The crystallization of calcite on highly ordered monolayer surfaces has attracted considerable interest in the past few decades. Such template surfaces include Langmuir monolayers, thin films, hydrogen-bonded ribbons and self-assembled monolayers (SAMs) with a variety of functionalized headgroups, all of which have been shown to exert great control over the mineral’s growth.1−3 When CaCO3 crystallizes on such monolayers, a commonly encountered calcite surface after nucleation is the polar (012) surface,4−10 and it has been established that its preferential growth is sensitive to the choice of monolayer and its ionization state. With their organized array of headgroups that can heterogeneously induce nucleation, ω-terminated alkanethiol SAMs [X(CH2)nS−] are a popular choice both in computational and experimental studies.11−14 One noteworthy experimental result for alkanethiol SAMs with carboxylic acid headgroups is the so-called odd−even effect. It was found that for SAMs with an even number of carbons in their individual molecules, the crystallization of CaCO3 gave rise to polar (01x) calcite surfaces, typically (012). SAMs with oddnumbered chains, on the other hand, exhibited no such orientation preference.8,15−19 Furthermore, the reported dominance of polar orientations such as (012) over the polar (001) orientation is unexpected from a thermodynamic point of view, since (001) provides a much better match to the charge density and epitaxy of the monolayers.18,20,21 Han and Aizenberg22 suggested that the odd−even effect was a consequence of the chain parity affecting the headgroup angle and thence the calcite orientation. This was recently elaborated on by Freeman et al.,23 who simulated water and disordered CaCO3 atop 15- and 16-C flexible alkanethiol SAMs and found that the carboxyl O−O vectors remained, on average, more parallel to the substrate in “even” monolayers. Nielsen et al. © 2014 American Chemical Society
measured the nucleation rate (J) of calcite crystals on 11- and 16-carbon alkanethiol SAMs24 and found that the dependence of J on supersaturation was consistent with classical nucleation theory. From their results they were able to demonstrate that crystallization on the 16-carbon SAM had a lower nucleation barrier than crystallization on the 11-C SAM, which implies that the calcite/16-carbon SAM has a lower interfacial energy. They found a preferential orientation of (013) and (012) calcite crystals on the 11- and 16-carbon SAMs, respectively. This work focuses on calcite growth for a range of SAMs composed of carboxylate (COO−)-terminated alkanethiols of different chain lengths supported on a gold film. Using metadynamics, we induce and then analyze the crystallization of disordered CaCO3.
2. METHODS Our model SAM consisted of 48 alkanethiol molecules in a periodic supercell with lateral dimensions of x = 28.78 Å and y = 33.23 Å. The unrelaxed structure of one of the SAMs is shown in Figure 1. A substantial vacuum gap of ∼65 Å was added in the z direction to separate the substrate from its periodic images. Molecules of seven different chain lengths were used, of the form HS-(CH2)n-COOH, where n = 9, 10, 14, 15, 16, 19, and 20. In all cases the headgroups were fully ionized and 24 Ca2+ cations were added to neutralize the surface charge. The SAMs were gradually equilibrated at 300 K by increasing the temperature in three steps from 0 to 300 K. Disordered CaCO3 (300 units), obtained by gradually melting and then cooling a slab of calcite, was deposited on the seven different length SAMs while they were held rigid. Received: June 3, 2014 Revised: July 27, 2014 Published: July 30, 2014 19188
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3.5kT and δh = 10σ, respectively, where σ is the standard deviation of each order parameter calculated from a 1 ns equilibration simulation in the disordered state. Such wide Gaussians were necessary in order to saturate the deep energy basins and achieve crystallization within a practical time frame. The deposition interval was 250 fs. The simulations were carried out using DL_POLY classic v.1.9.31 The electrostatics were handled by the Ewald summation method, and the short-range potentials had a cutoff of 9 Å. We used a united atom potential for the organic molecules, generated with CHARMM,32 and the interactions between the atoms of the monolayer were given by a LennardJones potential. Water, used only in the adhesion-energy calculations (section 3.5), was modeled with the TIP3P potential.33 The organic−calcium interaction was represented by a Buckingham potential. The interactions between the alkanethiols and calcium carbonate/water were fitted using the methods described in ref 34, which have already been used successfully in previous simulation studies. Finally, calcium carbonate was represented with the Raiteri et al. force field.35,36 The simulation time step was 0.5 fs, sampling the canonical ensemble at 300 K using the Nose-Hoover thermostat with a 20 fs relaxation time. After crystallization we further relaxed the cells for 1 ns with unbiased molecular dynamics. All cases were analyzed to examine the resulting surfaces as well as the evolution of the structure and charge density during crystallization.
Figure 1. Self-assembled monolayer of MHA (HS-(CH2)15-COOH) before relaxation. The headgroups are ionized, and the chargeneutralizing calcium ions (in green) are also shown.
This slab was thick enough for our simulations to model crystallization; larger configurations would only increase the computational time. The slab was placed 4 Å above each frozen SAM and allowed to relax on the surface. Following that, the SAMs were unfrozen and each system was equilibrated for another 1 ns. The metadynamics technique25,26 was used to enhance crystallization, allowing us to carry out the simulations at 300 K. Using this biased approach, we adiabatically drove the CaCO3 away from its initial phase and assumed it to take the minimum free-energy pathway to crystallization. As collective variables, we used the local potential energy plus five Steinhardt Q4 order parameters27 of the form Q 4αβ
⎡ 4π =⎢ ⎢ 9 ⎣
⎛ 1 ∑ ⎜⎜ NN m =−4 ⎝ c a 4
3. RESULTS 3.1. Crystal Orientation. In all cases, the disordered CaCO3 crystallized within 20 ns to surfaces very close to (012) (Figure 2).
⎞2 ⎤ f ( r ) Y ( , ) θ φ ∑ c b 4m b b ⎟⎟ ⎥⎥ ⎠⎦ b=1
1/2
Nb
where the tapering function ⎧1 if r ≤ r1 ⎪ ⎫ ⎪ 1 ⎧ ⎡ (r − r ) ⎤ 1 fc (r ) = ⎨ ⎨cos⎢ π ⎥ + 1⎬ if r1 < r ≤ r2 ⎪ 2 ⎩ ⎣ r2 − r1 ⎦ ⎭ ⎪ ⎪0 if r > r2 ⎩ ⎪
⎪
⎪
⎪
restricts the contributions of the spherical harmonic to shortrange.28,29 Within that range, index b runs over all Nb vectors connecting atoms of type α to those of type β, and r is the scalar distance between the two atom types. Nc is equal to the number of Nb atoms in a perfect crystal. Our values for r1, r2, and Nc are presented in Table 1 and were obtained via the procedure described by Quigley et al.30 The height (w) and width (δh) of the Gaussian augmentations of the bias potential were chosen as w =
Figure 2. Calcite crystallized on SAMs of (a) 11-C- and (b) 20-C-long chains, resulting in the (012) structure in both cases.
The (012) calcite surface, which invariably emerged, provides a relatively poor epitaxial match to the SAM and the surface vectors are incommensurate with those of the monolayer. Our simulations reveal how the crystallizing CaCO3 can overcome these incompatibilities: (a) In all cases, one of the calcite surface vectors aligned with the SAM supercell to within no more than 14°. Furthermore, in all cases the first layer above the monolayer had point defects that lowered the number of calcium ions in it with respect to the layers above, as can be seen in Figure 3. We explain the reason for this in the next section. (b) In cases where the structure failed to rotate enough during crystallization to become commensurate with the supercell, steps were formed, as illustrated in Figure 4. The monolayer chains subsequently adapted their lengths and orientations to conform to the steps. This demonstrates that
Table 1. Parameters Used in the Metadynamics Simulations for Calcite at 300 K α
β
Nc
r1 (Å)
r2 (Å)
Ca Ca Ca C C
Ca C O C O
12 12 12 8 3
5.1 3.5 2.6 5.1 1.7
5.6 4.0 3.1 5.5 2.3 19189
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Figure 3. Top-down view of the interfacial layers on SAMs of (a) 11C- and (b) 20-C-long chains (the first two charged layers of the formed calcite crystal). The dotted black lines show the calcite lattice at the interfacial layer. From top to bottom, carbonate ions are shown as red, calcium ions as green, and the monolayer headgroups as black.
Figure 5. Planes of an ionic crystal (a) exhibiting a net dipole moment μ and (b) a crystal block with no dipole moment, after transferring half the charge from one end of the block to the other.
The crystallized calcite layers resulting from the metadynamics simulations also quenched the dipole of the polar surfaces by introducing defects. The number of Ca ions in the first layer above the monolayer was reduced with respect to the perfect crystal, thus making the combined charge of that first layer with the ionized headgroups equal to half the charge of the individual layers above it (Figure 6). In some cases one or
Figure 4. Stepped (012) surfaces on the (a) 15-C and (b) 20-C (first attempt) SAMs. These are close to (013) and (034) crystal orientations, shown under each surface. The SAM headgroups are colored black, the carbonate ions red, and the calcium ions green.
the monolayer structure is not retained during growth. Instead, it adjusts to accommodate the emerging calcite structure. This complex interplay between substrate and adsorbate is well established in the context of soft-templating.21,37 No correlation was observed between the SAM chain length and the formation of steps, which instead appears to be a random occurrence. We confirmed this by repeating the crystallization on the 20-C SAM which initially crystallized as a stepped surface as seen in Figure 4; no steps were seen the second time (Figure 2). (c) Finally, in some cases a small number of carbonate ions were buried at the level of the headgroups. This also contributes to the necessary quenching of the slab’s dipole moment, described in the next section. 3.2. Dipole Quenching. The (012) surface is polar, meaning that it consists of a repeat unit with a net dipole moment perpendicular to the surface. As a result, in a periodic cell, the surface energy diverges to infinity and the crystal becomes unstable.38 In order for it to stabilize and grow, the dipole must be quenched. It has been shown39,40 that the energy of a finite crystal block will be lowered if charge is transferred from one face to the other. In this way, the electric field at the center planes is zero, and the surface energy becomes finite for any crystal block size (Figure 5). Duffy et al.20,21 suggested two possible mechanisms by which the dipole could be quenched for interfaces between monolayers of ionized stearate and polar calcite crystals. Depending on the density of the monolayer, they were able to artificially create stable crystal blocks by removing calcium ions that were in contact with the monolayer forming the first charged plane and an equal number from the opposite end, thus modifying the charge density of the outermost planes.
Figure 6. Charge layers in the resulting (012) crystal slab on the 16-C monolayer. As the monolayer has a lower density than the perfect (012) crystal planes, the dipole moment is quenched by reducing the ionic density of the two opposing ends of the crystal block, thus resulting in a stable structure. When necessary, carbonate ions (in red) modify the monolayer’s charge.
more carbonate ions were absorbed into the SAM, adding to the overall charge density of the ionized headgroup layer, with strong similarities to the bicarbonate ions in ref 21. Thus, in each case, the first charged layer of the resulting crystal contains defects and has a lower charge density than the layers above it. A similar reduction in charge density takes place in the uppermost layers, at the opposing end of the calcite block, resulting in an overall zero dipole moment and a stable crystal. Figure 6 shows the final configuration of the 16-C chain SAM, where one carbonate ion can be seen among the SAM headgroups, contributing to the dipole quenching. 3.3. Crystallization Details. In all cases, crystallization began with charge separation induced by the ionized SAM, whereby the calcium and carbonate ions were driven by electrostatics to form distinct layers. The ordering of the carbonate ions was then a secondary process. Figure 7 shows the z density of the calcium layers at different stages during crystallization on one of the monolayers. It is clear that the layers closer to the monolayer form first, and then they propagate to the rest of the structure. Moreover, the distance of the layers formed, even in the early stages, is close to the ideal (012) plane distance. The ionic ordering of the carbonates is the final stage. 19190
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rigidity of the monolayer which accelerates growth due to the strong epitaxial driving force. After crystallization, the monolayer under the (001) surface was also allowed to move, and we calculated the energy for both structures, which contain the same number of atoms, as an average after equilibration for 1 ns at 300 K. We found that the (001) surface is energetically more favorable by 0.34 J/m2. This suggests that the (001) structure is thermodynamically more stable, as expected given the excellent epitaxial match, and yet in all cases we observe the (012) structure forming. We conclude that nucleation kinetics are responsible for selecting the (012) surface. Darkins et al.43 showed that, of the two polar surfaces, the growth of (012) is indeed kinetically favored and crystallizes faster than (001) from disordered CaCO3 under the same conditions. The rate-limiting step was found to be the ionic ordering. This is believed to be because the random distribution of the carbonate angles in the disordered calcium carbonate more closely resembles the distribution in the (012) crystal than that in (001). This higher crystallization rate may explain the prevalence of the (012) surface in simulations involving carboxylate-terminated alkanethiols. 3.5. Adhesion Energies. We also calculated the adhesion energies in water for all monolayer/crystal structures using the method described in ref 44. Here the adhesion energy is defined as the difference between the energy of a crystal slab with an attached monolayer and the energy of an isolated crystal and an isolated monolayer, both in water. A lower adhesion energy would result in a lower interfacial energy and hence a lower nucleation barrier. The same amount of water was added in all configurations, and we equilibrated the structures for at least 5 ns. We excluded the 10-C case, where the crystal formed with a defect near the surface. The results are displayed in Figure 10. The adhesion energy of (001) on the 16-C SAM is considerably lower than in the the (012) case, as previously found.20 For the (012) cases, the energies range between −0.55 and −0.35 J/m2. It is important to note that when the crystal has defects or steps near the surface (e.g., 15C), the adhesion energy is higher. We notice that there is an energetic preference for longer SAMs, as well as even monolayers compared to their nearest odd ones, which could be related to the parity dependence seen experimentally. Our interfacial energy calculations are consistent with the experimental results of Nielsen et al. on 11-C and 16-C monolayers,24 where the 16-C SAM was associated with a lower nucleation barrier, suggesting a lower adhesion energy. Additionally, the stepped (012) obtained on our 15-C SAM is very close to a (013) surface, observed by Nielsen et al. on the 11-C SAM. It may be that the nucleation of stepped (012) surfaces is more common on odd SAMs than on even SAMs, but we were unable to carry out sufficient simulations to fully investigate this effect.
Figure 7. z-density plot of the calcium ions at different simulation intervals for the 16-C SAM. The layers closer to the monolayer form first. The vertical dotted lines denote the planes in the ideal (012) crystal.
3.4. SAM Flexibility and (012) vs (001). It has been shown experimentally2,41,42 that rigid monolayers exhibit a more limited selectivity than fully flexible monolayers. Earlier simulations by Freeman et al.11 have shown that rigid chains result in the (001) calcite surface. This is because, as mentioned above, the (001) surface exhibits a much greater epitaxial agreement with the headgroup structure of the monolayer. We reproduced this finding by repeating our metadynamics simulations on the 16-C SAM but keeping the SAM molecules rigid. As expected, the resulting surface after crystallization was the (001) surface, with both surface vectors perfectly aligned with the supercell (Figure 8).
Figure 8. Top-down view of the first two layers of the (001) calcite surface crystallized on a 16-C-long fixed SAM. The SAM molecules were allowed to relax after crystallization. The dotted black lines show the calcite lattice at the interfacial layer. From top to bottom, carbonate ions are shown as red, calcium ions as green, and the monolayer headgroups as black.
Comparing the charge density of this contrived (001) slab with that of the (0.12) slab previously grown on the same monolayer, we find that in both cases the dipole is quenched with the same procedure as described in section 3.2. A key difference is that, in the (001) case, the layers have almost identical charge densities since they match the headgroup arrangement very well; therefore, no defects are required in the first layer. The charge density evolution for both the flexible and rigid 16-C monolayers is shown in Figure 9 for the first three charged layers above the SAM. The much shorter crystallization time of the (001) surface is due to the artificial
4. CONCLUSIONS We have crystallized disordered CaCO3 on carboxylate SAMs, using metadynamics, and have found that in all cases the calcite crystal forms close to the (012) orientation. The initial stage of the crystallization process involves charge separation into layers oriented parallel to the surface of the SAM, with an interplanar spacing close to the spacing between (012) planes in calcite. The dipole moment of the polar surface is quenched during crystallization with metadynamics by the introduction of defects in the interfacial layer between the crystal and the monolayer, 19191
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Figure 9. Charge density evolution during calcite crystallization with metadynamics on a 16-C monolayer, where the chain is (a) flexible, resulting in a (012) surface and (b) kept rigid, resulting in a (001) surface.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge the use of the UCL Legion High Performance Computing Facility and associated support services in the completion of this work. The work was supported by the Engineering and Physical Sciences Research Council (grant no. EP/I001514/1). This programme grant funds the Materials Interface with Biology (MIB) consortium. R.D. acknowledges funding from the EPSRC under the Molecular Modelling and Materials Science Industrial Doctorate Centre and from Pacific Northwestern National Laboratory.
Figure 10. Adhesion energies between the formed crystal and the monolayer. The high energies of the 15-C case (in red) are due to the steps near the monolayer surface. We notice a dependence on parity and also length.
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REFERENCES
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which reduces the ionic density. The resulting interface is separated into regions that have a very close epitaxial match with the substrate and defective regions that have a low ionic density. An artificially frozen SAM induces crystallization in the (001) orientation, which has an almost perfect epitaxial match with the SAM. The (001) interfacial structure was found to have a much lower energy than the (012) interface. This result implies that the crystallization to the (012) orientation is dominated by kinetic factors. The flexible substrate does not offer a strong enough driving force to overcome the energy barriers associated with the rotation of the carbonate ions to the (001) orientation. Adhesion energies were calculated for all of the interfaces that were modeled by the metadynamics simulations. Interestingly, there appears to be a trend toward lower adhesion energies for long SAMs and for SAMs with even numbers of C atoms in the alkyl chains; however, due to the small number of simulations carried out, we cannot claim that this is a statistically significant result. Nevertheless, this result is consistent with experimental observations of the lower nucleation barriers associated with SAMs with long alkyl chains and even numbers of C atoms. 19192
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