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Simulations of Calcite Crystallization on Self-Assembled Monolayers Colin L. Freeman,*,† John H. Harding,† and Dorothy M. Duffy‡ Department of Engineering Materials, UniVersity of Sheffield, Sir Robert Hadfield Building, Mappin Street, Sheffield, S1 3JD, U.K., and Department of Physics and Astronomy, UniVersity College London, Gower Street, London, WC1E 6BT, U.K. ReceiVed February 4, 2008. ReVised Manuscript ReceiVed May 2, 2008 This paper presents simulations of calcium carbonate ordering in contact with self-assembled monolayers. The calculations use potential-based molecular dynamics to model the crystallization of calcium carbonate to calcite expressing both the (00.1) and (01.2) surfaces. The effect of monolayer properties: ionization; epitaxial matching; charge density; and headgroup orientation on the crystallization process are examined in detail. The results demonstrate that highly charged surfaces are vital to stimulate ordering and crystallization. Template directed crystallization requires charge epitaxy between both the crystal surface and the monolayer. The orientation of the headgroup appears to make no contribution to the selection of the crystal surface.
Introduction Biomineralization processes exert a control and selectivity that produces complex crystal morphologies, often with high energy surfaces. It is therefore unsurprising that much effort is devoted to designing methods to duplicate these processes. One such method involves the use of self-assembled monolayers (SAMs). These present an organized array of head groups at which crystallization can occur. Control of crystal growth could arise from a combination of many effects: headgroup identity; solution pH; and temperature. However, how this control is achieved is still not fully understood. Much attention on crystal growth with SAMs has focused on the extremely common biomineral, calcium carbonate, CaCO3, which possesses several crystalline polymorphs: aragonite, vaterite and calcite (the most common). The growth of calcite generally produces the lowest energy (10.4) surface with the exception of the contact point between the calcite crystal and SAM. Here a depressed ”pyramid” is obtained, most commonly exhibiting the (00.1)1 and (01.2)2 calcite surfaces. Both these surfaces are polar implying that the SAM must stabilize their growth. Given that the SAMs used in ref 2 are terminated with carboxylic acid (COOH) head groups which will, at the right pH, ionize, there is the possibility of a Stern layer system developing which will encourage polar surfaces.3 The identity of the functional groups is clearly important. Aizenberg et al.4,5 found no control over the calcite crystals when terminating their monolayer chains with either methyl groups or phosphates. However, carboxylic acids, alcohols and sulfates modified the calcite orientation. The alcohols would be unaffected by the pH implying a headgroup influence beyond that of surface polarity. * To whom correspondence should be addressed. Phone: +44 (0)114 222 6021. Fax: +44 (0)114 222 5943. E-mail:
[email protected]. † University of Sheffield. ‡ University College London. (1) Lahiri, J.; Xu, G.; Dabbs, D. M.; Yao, N.; Aksay, I. A.; Groves, J. T. J. Am. Chem. Soc. 1997, 119, 5449–5450. (2) Champ, S.; Dickinson, J. A.; Fallon, P. S.; Heywood, B. R.; Mascal, M. Angew. Chem., Int. Ed. 2000, 39, 2716–2719. (3) Lurched, M. J.; Likelier, S. R.; Voile, V. J. Phys. Chem. B 1997, 101, 10821–10827. (4) Aizenberg, J.; Black, A. J.; Whitesides, G. M. J. Am. Chem. Soc. 1999, 121, 4500–4509. (5) Aizenberg, J.; Black, A. J.; Whitesides, G. M. Nature 1999, 398, 495–498.
Crystal growth is commonly linked to epitaxial matching to the substrate. For example, Lahiri et al.1 note that the spacing between the head groups in one axis was the same as the Ca-Ca separation (∼5 Å) in the (00.1) surface expressed. Some matching has been found between stepped calcite surfaces and complex, relatively large organic molecules.6 However, other studies, e.g., refs 7 and 8 have demonstrated that a surface can be grown despite possessing no epitaxial matching to the monolayer. Recent work suggests that some monolayers cannot provide epitaxial matching due their packing density9 and theoretical studies10 have found that lattice matching and adhesion energies are not enough to explain the surfaces seen experimentally. The SAM organization is a product of multiple factors: the underlying substrate (e.g., an Ag or Au sheet); the pH (degree of ionization) and the identity of the headgroup. It is therefore unlikely that the role of the substrate is limited to simple lattice matching. Matching between the orientation of the headgroup with the CO3 groups of the calcite may select particular surfaces [4,8,11]. SAMs on Ag substrate adopt an angle of ∼ 30° with the surface normal, compared to an angle of ∼ 40-45° on Au substrates. The Ag and Au substrates grow the (01.2) and (01.3) surfaces respectively,11 in which the angle of the CO3 groups closely match the headgroup angles. This orientation issue has also been linked to the so-called ”odd-even” effect12–14 whereby different calcite surfaces are selected depending on whether the SAM chains contain an odd or even number of carbon atoms. One result of varying the chain length is to alter the orientation of the head groups. These conclusions must be tempered by consideration of the growth conditions: room temperature and low surface pressures; under these conditions the SAM should (6) Estroff, L. A.; Incarvito, C. D.; Hamilton, A. D. J. Am. Chem. Soc. 2004, 126, 2–3. (7) Volkmer, D.; Fricke, M.; Agena, C.; Mattay, J. CrystEngComm 2002, 4, 288–295. (8) Donners, J.J.J.M.; Nolte, R. J. M.; Sommerdijk, N.A.J.M. J. Am. Chem. Soc. 2002, 124, 9700–9701. (9) Volkmer, D.; Mayr, N.; Fricke, M. J. Chem. Soc., Dalton Trans. 2006, 4889–4895. (10) Duffy, D. M.; Harding, J. H. Langmuir 2004, 20, 7630–7636. (11) Han, Y.-J.; Aizenberg, J. J. Am. Chem. Soc. 2003, 125, 4032–4033. (12) Gupta, V. K.; Abbott, N. L. Science 1997, 276, 1533–1536. (13) Edgar, R.; Huang, J. Y.; Popovitz-Biro, R.; Kiaer, K.; Bouwman, W. G.; Howes, P. B.; Als-Bielsen, J.; Shen, Y. R.; Lahav, M.; Leiserowitz, L. J. Phys. Chem. B 2000, 104, 6843–6850. (14) Popovitz-Biro, R.; Wang, J. L.; Majewski, J.; Shavit, E.; Leiserowitz, L.; Lahav, M. J. Am. Chem. Soc. 1994, 116, 1179–1191.
10.1021/la800389g CCC: $40.75 2008 American Chemical Society Published on Web 08/02/2008
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be extremely mobile15 and the organized array continually disrupted by thermal motion. Duffy and Harding16 modeled the structure of the SAMs and found that, although differences exist between the average orientation of head groups belonging to odd and even length chains, there are also large overlaps within the distributions. Analysis of SAM chain binding to substrates17 suggests that there are several potential sites for the SAM chains and that movement between these sites may be possible. This implies that the recognized packing of the SAM may be variable over the time scale of the crystallization. It has been demonstrated that odd and even length monolayer chains possess different dipole moments which may influence crystallization.18 Therefore the headgroup orientation may mask a separate issue. The importance of charge epitaxy cannot be neglected when considering calcite crystallization. The crystal surface may be selected to match the local charge density of the monolayer implying that the packing of the monolayer and its degree of ionization is important. The metastable polymorphs of CaCO3, aragonite and vaterite, can be stabilized by high charge densities,19 which can be used to selectively grow particular polymorphs.20 The possibility that a flexible monolayer may actually aid the selection has been considered by Popescu et al.21,22 By varying the size of an R group on their Langmuir monolayer chains they were able to disrupt the hydrogen bonding network at the surface, varying the flexibility. Their results found that the most flexible system also demonstrated the greatest control of the orientation of the calcite samplesssuggesting that the calcite and monolayer may “modify” each other to generate favourable growth conditions. It has long been suggested that organisms may make use of amorphous calcium carbonate (ACC) as a precursor to crystallization and this possibility is now being considered in synthetic crystallization as well, e.g., refs 23-25. Using the mobile template argument suggests that when initial contact occurs between the monolayer and nanoparticle, the ACC undergoes some degree of ordering which in turn influences the structure of the monolayer which then encourages further ordering of the ACC eventually leading to some degree of continuous feedback between the two systems.26 Therefore the ability of the monolayer to stabilize the ACC particle may also be important25,27,28 as this will control its crystallization rate. The chemistry of the monolayer and the local environment may control concentration gradients and diffusion rates which may make the issue of selectivity one of kinetics.29,30 (15) Volkmer, D.; Fricke, M.; Gleiche, M.; Chi, L. Mater. Sci. Eng. C 2005, 25, 161–167. (16) Duffy, D. M.; Harding, J. H. Langmuir 2005, 21, 3850–3857. (17) Yu, M.; Bovet, N.; Satterley, C. J.; Bengio´, S.; Lovelock, K. R. J.; Milligan, P.; Jones, R.; Woodruff, D.; Dhanak, V. Phys. ReV. Lett. 2006, 97, 166102. (18) Sushko, M. L.; Shluger, A. L. J. Phys. Chem. B 2007, 111, 4019–4025. (19) Volkmer, D.; Fricke, M.; Agena, C.; Mattay, J. J. Mater. Chem. 2004, 14, 2249–2259. (20) Fricke, M.; Volkmer, D.; Krill, I. I. I.; Kellermann, M.; Hirsch, A. Cryst. Growth Des. 2006, 6, 1120–1123. (21) Popescu, D. C.; van Leeuwen, E. N. M.; Rossi, N. A. A.; Holder, S. J.; Jansen, J. A.; Sommerdijk, N. A. J. M. Angew. Chem., Int. Ed. 2006, 45, 1762– 1767. (22) Popescu, D. C.; Smulders, M. J. M.; Pichon, B. P.; Chebotareva, N.; Kwak, S.-KY.; van Asselen, O. L. J.; Sijbesma, R. P.; DiMasi, E.; Sommerdijk, N. A. J. M. J. Am. Chem. Soc. 2007, 129, 14058–14067. (23) Addadi, L.; Raz, S.; Weiner, S. AdV. Mater. 2003, 12, 959–970. (24) Bolze, J.; Peng, B.; Dingenouts, N.; Panine, P.; Narayanan, T.; Ballauff, M. Langmuir 2002, 18, 8364–8369. (26) Lee, J. R. I.; Han, T.Y.-J.; Willey, T. M.; Wang, D.; Meulenberg, R. W.; Nilsson, J.; Dove, P. M.; Terminello, L. J.; van Buuren, T.; De Yoreo, J. J. J. Am. Chem. Soc. 2007, 23, 5449–5450. (25) Xu, X.; Han, J. T.; Cho, K. Chem. Mater. 2004, 16, 1740–1746. (27) Xu, X.; Han, J. T.; Cho, K. Langmuir 2005, 21, 4801–4804. (28) DiMasi, E.; Patel, V. M.; Sivakumar, M.; Olszta, M. J.; Yang, Y. P.; Gower, L. B. Langmuir 2002, 18, 8902–8909.
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Figure 1. Figure of setup for crystallization simulations. In this and subsequent figures, calcium is depicted in light gray, oxygen in white, carbon in black.
Clearly the crystallization on SAMs is a complex issue. Although much of the research on SAMs has been performed with experimental methods, computer simulations are a valuable tool to analyze the behavior of these systems. Many previous simulation studies have calculated adsorption energies of the calcite at SAM surfaces. An alternative method is to approximate the crystallization event.31 It has been considered that calcite crystallizes from an amorphous nanoparticle at the SAM surface, driven by the charge associated with the ionized monolayer. Nucleation events are too improbable under normal conditions to simulate with standard molecular dynamics (MD) but it is possible to approximate the process by using reduced cell sizes and elevated temperatures. In this paper we analyze crystallization of calcium carbonate nanoparticles at SAM interfaces. By separately varying the structure and ionization of the SAM we are able to isolate the effect these properties have with calcite crystallization and comment on their relationships.
Methods SAM surfaces were constructed from 16-mercaptohexadecanoic acid (MHA), which has been shown to induce crystallization in the (01.2) orientation. Once constructed the chains were frozen and cut so only the head groups remainedseffectively creating a single sheet of COOH groups (see Figure 1). This approximation prevented us from investigating mobility effects but was reasonable due to the very weak interactions between the organic chains and CaCO3. The calcite nanoparticle was obtained by cutting a spherical cluster of 166 CaCO3 formula units from a 3000 K simulation of molten CaCO3. Simulations considered a neutral SAM, where none of the head groups are ionized, a half-ionized SAM and a fully ionized SAM. Ionization of the SAM was performed by removing H atoms and the charge compensated for by the addition of Ca ions (half as many Ca as the number of H removed) to the SAM layer. Three different configurations of the half-ionized SAM were generated to account (29) DiMasi, E.; Olszta, M. J.; Patel, V. M.; Gower, L. B. CrystEngComm 2003, 5, 346–350. (30) DiMasi, E.; Kwak, S.-Y.; Amos, F. F.; Olszta, M. J.; Lush, D.; Gower, L. B. Phys. ReV. Lett. 2006, 97, 045503. (31) Duffy, D. M.; Harding, J. H. Surf. Sci. 2005, 595, 151–156.
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for the significance of arrangement effects. The CaCO 3 cluster was placed about 6 Å above the surface of the SAM. A control simulation with no SAM present was also performed. MD simulations were performed on the system using the DL_POLY32 program. The CaCO3 forcefield was that described by Pavese et al.33,34 although only rigid ions were used to permit larger simulations. This forcefield uses a Born description of the interactions. The carbonate ion is modeled as four individual atoms connected via bonding potentials and the angles maintained through harmonic terms. The organic atoms (i.e., the COOH head groups) were described with the AMBER forcefield.35 We use an all atom model from the general AMBER forcefield. There are no standard potentials for the interactions between the organic and mineral components of the system so we fit new ones using the methods described in ref 36. This method effectively fits the new crossterm potentials between the organic and mineral to a known structure with the relevant component parts. The atoms of this fitting structure are charged in an appropriate manner to mimic the charge interaction between the organic molecule and mineral. In order to increase the rate of ordering within the nanoparticle elevated temperatures of 500 and 800 K were used for the simulations. The temperature was cycled between these values to encourage the system to explore as much of the energy surface as possible. The elevated temperature meant that no water solvent could be used as this would have simply been vaporised. Similarly the organic molecules were kept frozen during the simulations. Such a model is clearly a considerable simplification of the real system. However, it does manage to retain basic features of an amorphous-crystalline transition in the presence of the monolayer while being simulated on a reasonable computational time scale. The slab model was used for the simulation cell, whereby the system is contained within a 3d periodic box (33.2 Å × 28.8 Å in the plane of the substrate) but separated from the other substrate layers by a substantial vacuum gap (∼40 Å). A Nose´-Hoover NVT thermostat with a 0.1 ps relaxation time was used to maintain a constant temperature. Coulombic forces were calculated with a periodic Ewald summation and the short-range potentials had a cutoff of 10.1 Å. Simulations were performed with 1 fs timesteps. The total simulation time scale was 20 ns but this was divided into a series of 0.5 ns simulations, which alternated between a temperature of 500 and 800 K (see ref 31 for details).
Results and Discussion Calcite Crystallization. Figure 2 shows the final structure in several of the simulations. In all three cases the nanoparticle moves into contact with the surface and undergoes some transformation. All three of the half-ionized configurations produced very similar results as described below. In order to quantify these observations we have generated a series of radial distribution functions (RDFs) of C-C for the CaCO3 as shown in Figure 3a. The RDF of the neutral SAM and the half-ionized SAM are not shown as they appear indistinguishable from the RDF of the CaCO3 with no SAM present. Despite some broad peaks and troughs none of these simulations demonstrate clear ordering. In contrast, the fully ionized SAM system produces a better defined RDF with clear peaks, that when compared to the calcite crystal, match well to the short-range separations. This implies, unlike the other cases, that the CaCO3 interacting with the fully ionized SAM has begun some kind of ordering into the calcite crystal structure during the simulation. (32) Smith, W.; Forester, T. R. J. Mol. Graphics 1996, 198/199, 796–781. (33) Pavese, A.; Catti, M.; Price, G. D.; Jackson, R. A. Phys. Chem. Miner. 1992, 19, 80–87. (34) Pavese, A.; Catti, M.; Parker, S. C.; Wall, A. Phys. Chem. Miner. 1996, 23, 89–93. (35) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. J. Am. Chem. Soc. 1995, 117, 5179–5197. (36) Freeman, C. L.; Harding, J. H.; Cooke, D. C.; Elliot, J. A.; Lardge, J. S.; Duffy, D. M. J. Phys. Chem. C 2007, 111, 11943–11951.
Figure 2. Snapshots of final configurations (after 20 ns) from the simulations of the nanoparticle interacting with (a) neutral SAM, (b) half-ionized SAM, (c) fully ionized SAM. Hydrogen atoms are depicted in dark gray.
The ordering can be further analyzed with a crystal order parameter;31 1/2[3cos2 θ - 1], where θ is the angle between the normal to the carbonate ion plane and the surface normal. The order parameter is calculated throughout the 20 ns simulations and shown in Figure 3b. Again the order parameters from the half-ionized and neutral system are very similar to that of the system with no SAM so are not shown for clarity. These systems all show little change over the course of the simulation while the fully ionized system sees a rapid ordering that plateaus after ∼3 ns at about 0.6. Due to the edge effects of the CaCO3 we would not expect it to adopt a fully crystallized form which would have an order parameter of unity. A final method of analyzing the nanoparticle is to calculate the angular frequency distribution of the carbonate groups. What angles do they most commonly adopt during the simulation? The angles are found by comparing the surface normal to that of the normal to the carbonate plane (as for the order parameter) and then counted over the course of the final 10 ns of the
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Figure 4. Arrangements of the monolayer head groups in (a) configuration (1), (b) configuration (2), (c) configuration (3).
Figure 3. (a) RDF of CaCO3 nanoparticle interacting with fully ionized SAM (black) and with no SAM present (light gray), also shown is the RDF of calcite (gray); (b) order parameter (see text) of CaCO3 nanoparticle interacting with fully ionized SAM (black) and with no SAM present (light gray); (c) Frequency of angles between CO3 plane normal and surface normal (see text) for fully ionized SAM (black), half-ionized SAM (dashed), neutral SAM (light gray).
simulations. For the nanoparticle with no SAM present (where we assume a surface normal parallel to that of the simulations with the SAM) the angular frequency results demonstrate the expected random frequency distribution. To remove any statistical weighting all the subsequent angle plots are constructed with respect to that of the nanoparticle with no SAM present. These plots (shown in Figure 3c) demonstrate similar results to the
order parameter and RDF. The half-ionized and neutral simulations show random distributions of the carbonate ions very similar to that of the isolated nanoparticle. The carbonate ions of the nanoparticle with a fully ionized SAM have a strong preference to be perpendicular to the surface normal (an angle of 0°/180°) demonstrating that the carbonates are stacking parallel to the surface. Analyzing the structure further we see that the nanoparticle at the interface is adopting a layer similar to that of the (00.1) calcite surface. This is a polar surface that is largely commensurate with the headgroup layout in the SAM. So it satisfies both an epitaxial argument and any polarization issues. The results demonstrate that without a significant ionization of the SAM the CaCO3 particle does not undergo any significant ordering at the interface agreeing with experimental conclusions that the pH level must be high enough to ionize the head groups. Surface Order. The standard SAM layout of the head groups is largely commensurate with the (00.1) calcite surface and it has been demonstrated that in purely energetic terms this surface is the most stable at the interface.10 Is this epitaxy actually selecting the crystal face and is it influencing the crystallization process? The significance of the epitaxy between the SAM and the CaCO3 was tested by disrupting the order of the SAM. Two new configurations of the SAM head groups were created from the fully ionized system (now referred to as configuration (1)) as shown in Figure 4. In configuration (2) alternate rows of head groups are displaced in the x direction generating a SAM surface with clusters of closely packed head groups, thus removing the epitaxy between the calcite crystal and the SAM although
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Table 1. Epitaxial Order Parameters for SAM and Calcite Surfaces SAM confuration confuration confuration confuration
(00.1)-Ca
(01.2)
0.983 0.320 0.602 0.628
0.326 0.147 0.241 0.978
(1) (2) (3) (01.2)
maintaining some level of order at the interface. In configuration (3) the head groups were randomly moved by varying degrees. This creates a disordered SAM but with small regions that still resemble the standard monolayer pattern. Note that the headgroup position only was adjusted to alter the epitaxy, the orientation, charge etc. of these groups has not been affected. The relationship between the order of the monolayer surfaces and the calcite surface can be described with an epitaxial order parameter that is dependent on the local atomic environment.37 We define a set of Nq surface wavevectors qi for atom i, which given a surface position vector, r, connecting any near neighbors, have the identity
exp(iq · r) ) 1
(1)
Therefore, the local order parameter, Ψi, is
Ψi ) [
1 1 Nq Z
∑ ∑ exp(iq · r)]2 r
(2)
q
where we average over all the vectors of Z surface neighbors within a set cutoff, rc, which is chosen to be between the second and third nearest neighbors of the Ca ions. A global order parameter for the surface is then calculated by averaging over all the atoms present. Note that we are only considering surface vectors and surface atoms in this order parameter as this is the region of interest. We can apply this order parameter to the interface between the monolayer and calcite surface by examining the local order of each of the monolayer surface carbons with the reciprocal surface vectors of the Ca ions in the calcite surface. This provides an epitaxial order parameter for the degree of epitaxy between the two surfaces. Values for the three monolayers with the polar (00.1)-Ca and (012)-Ca calcite surfaces have been calculated and are presented in Table 1. Given that the monolayer is ionized we would expect a polar calcite surface to grow so have only considered these in our order calculations. There is a very close match between the ordered monolayer and the (00.1) Ca terminated surface. Configuration (3) demonstrates a greater match than configuration (2) due to the regions of the monolayer that still closely resemble the original structure of configuration (1). The matching with the (01.2) polar calcite surface is worse for all three monolayers and, therefore, we would expect to see the (00.1) surface in preference to the (01.2) surface. The resulting RDFs, crystal order parameters and angular frequency plots can be seen in panels a, b and c of Figure 5, respectively. In both cases the level of order in the CaCO3 is reduced. Configuration (2) produces results very similar to that of the half-ionized/neutral systems, with no significant change in the order parameter over the length of the simulation, no alignment of the carbonates to the surface or any clear peaks in the RDF. The RDF of configuration (3) shows a small degree of order with three of the peaks visible but no appearance of the third peak. The order parameter shows that some ordering is taking place but at a far slower rate compared to the unmodified SAM, after 20 ns the CaCO 3 has an order parameter of 0.45. The angular distribution is similar to that of configuration (1) but the frequency of the 0°/180° peaks is reduced. Allowing the simulation to run for a further 10 ns resulted in an order parameter (37) Morris, J. R. Phys. ReV. B 2002, 66, 144104.
Figure 5. (a) RDF of CaCO3 nanoparticle interacting with fully ionized SAMs with different structures, configuration (1) (black), configuration (2) (dashed line) and configuration (3) (light gray), also shown is the RDF of calcite (gray); (b) order parameter (see text) of CaCO3 nanoparticle interacting with fully ionized SAMs with different structures, configuration (1) (black), configuration (2) (dashed line) and configuration (3) (light gray); (c) frequency of angles between CO3 plane normal and surface normal (see text) for fully ionized SAMs with different structures, configuration (1) (black), configuration (2) (dashed line) and configuration (3) (light gray).
of 0.55, still less than that of configuration (1) but the value is clearly increasing with time. The rate of crystallization has been inhibited by disruption of the SAM surface order demonstrating an effect due to the epitaxy between the monolayer and
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Figure 6. Snapshots of simulation for configuration (3) showing the regions of the nanoparticle where ordering is beginning (with whole of carbonate depicted in dark gray) at (a) 5.8 and (b) 6.8 ns.
nanoparticle. The position of the head groups dictates the positions of the Ca ions which in turn determine the calcite surface that will form. Therefore if the head groups are too closely or distantly spaced the resulting Ca patterning is unlikely to match a low energy face of the calcite crystal. Viewing Figure 4, we can see that although there is no long-range order in configuration (3) there are small regions that possess a similar arrangement to that of configuration (1) and this is why its epitaxial order parameter was 0.602san average of closely and poorly matching regions. Snapshots of the configuration (3) simulation demonstrate that these areas facilitate the ordering of the localized ions (see Figure 6). This effect then gradually spreads across the particle. Conversely configuration (2) generally has the head groups positioned in tighter groups (some 3-4 Å apart) than configuration (1). The arrangement clearly does not match the density required for the two polar calcite crystals. Crystallization only requires matching in a small region as the effect can readily pass through the particle despite the poor matching across the remainder of the interface. In the region of crystallization the matching as judged by our epitaxial order parameter may need to be close to unity but overall the value for the entire interface can be quite low, e.g., ∼0.6. This also implies that the monolayer cannot exert much control over the growing crystal once ordering has begun, it may only serve to impede or encourage the process. Charge Density. As the repositioning of the head groups will affect the charge density the epitaxial effect described above may not be epitaxial matching alone. None of the half-ionized SAMs stimulated crystallization but this could be linked to the localized charge density and whether this matches a crystal surface. The position of the hydrogen at the surface may disrupt the crystallization via either charge density issues or steric hindrance. We can examine the effect of this by removing all the hydrogen atoms from the surface of the half-ionized SAM but maintaining the same total surface charge by applying a reduced charge of -0.5e to all the ionized head groups (i.e., CO20.5-). Therefore, although the SAM surface is fully ionized it possesses a total charge of that equal to the half-ionized SAM. This was achieved by reducing the charge of the oxygens in the CO2 group to -0.4e compared to -0.65e for the standard ionized CO-2 group. Identical simulations to those described for the other SAMS were performed with the new SAM. The RDF showed no formation of a calcite-like structure within the CaCO 3 particle. However, the order parameter (shown in Figure 7) reaches a value of ∼ 0.35 after about 5 ns and maintains this for the remaining 15 ns of the simulation. Similarly the angular plot showed an increased frequency for the 0°/180° angles to about 75% of that of the fully ionized system. This result indicates that some ordering of the carbonates is taking place but the process is stalling and not reaching the level seen in the fully ionized
Figure 7. Order parameter (see text) of CaCO3 nanoparticle interacting with ionized SAMs, fully ionized SAM with varied charge (black), half-ionized SAM with uniform charge (light gray) and SAM with [012] charge density (dashed line).
system. By generating a homogeneous surface charge density (same arrangement but weaker than configuration (1)) some initial ordering of the nanoparticle in contact with the SAM takes place but the reduced overall charge is unable to spread the effect further into the nanoparticle so the order parameter remains low and the RDF demonstrates no clear calcite structure. No crystallization is seen in the standard half-ionized system reported in this section due to the localized epitaxial charge density as well as the reduced charge. Separating epitaxy and the localized charge density is difficult. One possible test is to vary the charge of the CO2- groups at the surface. These were divided into two equal groups; one with a charge of -0.5e and the other with a charge of -1.5e. This new SAM setup has the same total surface charge and atomic arrangement as the standard fully ionized SAM but the local charge density is adjusted as the functional groups have larger and smaller charges. Therefore this system is very similar to that of the half-ionized SAM except the total charge is doubled. The resulting order parameter of the MD simulations are shown in Figure 7. The RDF showed no ordering. The order parameter shows little order until 15 ns is reached when the CO3 groups in close contact with the SAM and within the nanoparticle begin to adopt a parallel orientation to the SAM. The angular frequency showed a small peak at 0°/180°. The simulation was allowed to continue for a further 10 ns. During this extra time the order parameter reaches ∼0.3 and fluctuates about this point while both the RDFs and angular frequency plots show little change. The inability of the fully ionized system with a varied charge
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Table 2. Charge Densities for SAM and Calcite Surfaces SAM/calcite
charge density [e/Å2]
(00.1) (01.2) fully ionized half-ionized neutral fully ionized with increased charge
0.086 0.126 0.100 0.050 0.0 0.126
density to induce further order after ∼15 ns implies that a local charge density too far from the desired value cannot stimulate further order in the nanoparticle despite a large surface charge. Crucially these results demonstrate that conclusions that could be drawn about surface epitaxy must always be considered in the context of charge density as well. It has been proposed that the charge density selects the particularly morphology of the CaCO3 crystal grown, e.g., refs 19 and 20. Table 2 lists the average surface charge density of two of the most common polar calcite surfaces and the SAMs used in the simulations. Crystallization on the fully ionized SAM produces a structure that resembles the (00.1) calcite surface (Ca terminated). The charge density of this surface is 0.014 e/Å2 less than that of the SAM. Experiments generally report the (01.2) calcite surface which has a charge density 0.026 e/Å2 greater than the fully ionized SAM. If charge density is selecting the growth surface then by increasing the charge density of the SAM to 0.126 e/Å2 the (01.2) surface should form instead of the (00.1) surface. The charges of the COO- head groups were increased to -1.25e to generate a surface charge density of 0.126 e/Å2, therefore 30 Ca ions were used instead of 24 to ensure the cell remained neutral. The simulations were performed under the same conditions as described previously. The RDF closely resembled that of the standard fully ionized monolayer indicating that the nanoparticle is adopting a calcite-like structure. The order parameter (shown in Figure 7) fluctuates far more over the course of the simulation but reaches a value of ∼0.5 which is in the region of an ordered particle. The angle variation showed that the carbonate groups are generally parallel to the monolayer surface and inspection shows that the structure closely resembles that of (00.1) calcite as has been seen in all the other crystallization attempts. Clearly, altering the charge density has failed to induce a different calcite surface. The extra Ca neutralizing the monolayer surface appear to disperse from the surface into the nanoparticle leaving the correct number to form the (00.1) surface. This demonstrates that the global charge density alone is not controlling the crystallization process. Clearly the level of commensuration between the head groups and the (00.1) surface is the dominating variable. If selectivity is to occur at the monolayer there must be some degree of epitaxy between the monolayer and that surface. This result should be tempered with the consideration that the monolayer is frozen. A mobile monolayer may adjust its layout to better match the (01.2) surface if the charge density were better suited to it. The results of configuration (3) tell us that only a small region of matching is required so a surface that demonstrates relatively poor epitaxy but close charge density could influence the crystallization event. One final test that can be considered for this possibility is to adjust the layout of the headgroups to match that of the (01.2) surface. The CO2H headgroups were moved such that the C atoms were at points near identical to those found in the (01.2) surface. The epitaxial order parameter for the interface is 0.978 (see Table 1 with the (01.2) surface and now only 0.628 for the (00.1) surface. The angle of the headgroup was set at that used in the previous calculations. The simulation was run with the
Figure 8. Snapshots of final configuration (after 20 ns) from the simulation of the nanoparticle interacting with the monolayer with a (01.2) surface epitaxy.
same parameters as described previously, all the head groups were ionized and the resulting charge neutralized with Ca2+ ions. A snapshot of the final configuration can be seen in Figure 8 and the order parameter, RDF and angle data can be viewed in panels a, b and c of Figure 9, respectively. The RDF, although not as clear as the standard fully ionized system, demonstrates there has been some ordering toward the calcite structure. The order parameter is now calculated by taking a normal to the head groups with an approximate angle of 30° to the surface normal as the carbonates of the nanoparticle order but do not align parallel with the surface. The order parameter follows all the signs of nanoparticle ordering reaching a value of ∼0.45, this implies that the carbonate groups are aligning at ∼60° to the surface. The angle frequency plot confirms this; the usually large peaks at 0° and 180° are significantly reduced while there are two clear humps at ∼65° and ∼115°. Viewing the snapshot of the simulation it can be seen that the carbonate groups are clearly ordering and aligning themselves at an angle of ∼60° to the surface. The increased frequency of angles between 60° and 120° appears to be due to the flipping of the carbonates between the two values. In the (01.2) surface the carbonates are all at 60° to the surface and the positions of the carbonates of the nanoparticle closely match those within the (01.2) surface. Unlike in the previous simulations the nanoparticle is producing a (01.2) calcite surface as opposed to the (00.1) surface. Interestingly the (01.2) surface is most commonly reported for experimental growth - particularly on MHA. These simulations agree with the energetic calculations of Duffy and Harding10 that show that the (00.1) surface would be expected to grow on this monolayer. They found that disruption of the surface through the use of bicarbonate ions38 did lead to energetic favoring of the (01.2) surface over the (00.1) surface. In addition they have demonstrated that growth factors to do with the stability of the whole nanoparticle may be a contributing factor.39 Clearly these results suggest that charge density alone cannot control the surface growth and some degree of epitaxy is needed. Head Group Orientation. As discussed in the introduction, the orientation of the headgroup may influence the crystal surface expressed. Effectively an epitaxy between the angles of the head groups and the carbonate ions in the CaCO3 is adopted. The resulting structure from the crystallization of the amorphous nanoparticle best matches the structure of the (00.1) calcite. In this surface the carbonate ions all orientate perpendicular to the monolayer surface normal. Given that the head groups of the monolayer adopt an angle of 30° to the surface normal the head groups and carbonate ions are clearly not entering an epitaxial arrangement. (38) Duffy, D. M.; Travaille, A. M.; vanKempen, H.; Harding, J. H. J. Phys. Chem. B 2005, 109, 5713–5718. (39) Duffy, D. M.; Harding, J. H. Symposium on Architecture and Application of Biomaterials and Biomolecular Materials held at the 2003 MRS Fall Meeting 2003, 257–259.
9614 Langmuir, Vol. 24, No. 17, 2008
Figure 9. (a) RDF of CaCO3 nanoparticle interacting with ionized SAMs, fully ionized SAM (configuration (1)) (black), fully ionized SAM with (01.2) organization (light gray), also shown is the RDF of calcite (gray); (b) order parameter (see text) of CaCO3 nanoparticle interacting with ionized SAMs, fully ionized SAM (configuration (1)) (black), fully ionized SAM with (01.2) organization (light gray); (c) Frequency of angles between CO3 plane normal and surface normal (see text) for fully ionized SAM (configuration (1)) (black), fully ionized SAM with (01.2) organization (light gray).
The orientation of the head groups were changed so that they were at 60° to the surface normal and simulations identical to that of the first fully ionized monolayer (configuration (1)) were run. Comparing the data for the new headgroup orientation to those of configuration (1) as shown in Figure 10 we see very
Freeman et al.
Figure 10. (a) RDF of CaCO3 nanoparticle interacting with ionized SAMs, fully ionized SAM (configuration (1)) (black), fully ionized SAM with head groups orientated to 30° (light gray), also shown is the RDF of calcite (gray); (b) order parameter (see text) of CaCO3 nanoparticle interacting with ionized SAMs, fully ionized SAM (configuration (1)) (black), fully ionized SAM with head groups orientated to 30° (light gray); (c) Frequency of angles between CO3 plane normal and surface normal (see text) for fully ionized SAM (configuration (1)) (black), fully ionized SAM with head groups orientated to 30° (light gray).
little difference. The CaCO3 crystallizes to a calcite-like structure with a surface similar to that of the (00.1). The only noticeable
Simulations of Calcite Crystallization on SAMs
effect is in the order parameter. The order parameter increases at a slower rate in the simulation with 60° head groups as compared to 30° in configuration (1). A similar result was observed by Duffy and Harding31 where the nanoparticle took longer to order in contact with an odd chain-length monolayer compared to an even chain-length monolayer. It is possible that the headgroup orientation exerts a kinetic influence on the crystallization process, which could affect the resulting crystal morphology. However, further comment will require more detailed calculations. Our simulations find that the Ca ions arrange themselves to best match the charge density and layout of the head groups. This arrangement of Ca ions is then determining the position of the subsequent layer of carbonate ions independently of the orientation of the headgroup. Our results suggest that a simple alignment model between headgroup and carbonate groups is unlikely to exist and the influence of headgroup orientation on the SAM selectivity is probably the result of a different effect (e.g., dipole variation due to headgroup orientation or some kinetic effect) masked by the orientation issue.
Conclusions We have performed a series of simulations which model crystallization of CaCO 3 nanoparticles at SAM interfaces. Our simulations have analyzed the effect of the pH (SAM ionization), epitaxy, charge density and headgroup orientation on the crystallization process. Ordering of the nanoparticle relies on the ionization of the SAM; without a fully ionized monolayer ordering is limited to the interface demonstrating the importance of pH to ensure crystallization. Our results suggest that surface epitaxy is linked to the headgroup charge and that there must be a close agreement between the local charge density of the monolayer and the growing crystal surface. Disruption of the global charge density by varying the ionization of groups or reordering of the SAM will limit the rate of ordering. Growth is also influenced by epitaxy and the growing surface will try to match the monolayer structure. We have successfully induced either (00.1) or (01.2) calcite growth by varying the epitaxial arrangement of the monolayer. The charge density and the surface epitaxy must be close to that of the growing crystal face (i.e., close to unity as calculated with our epitaxial order parameter). But, the overall global charge density and
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epitaxy match can be reasonably poor, e.g., 0.602, for configuration (3), as long as regions exist where the match is good at a local level. When the global epitaxy parameter falls as low as 0.32 our simulations indicate that crystallization does not occur. Adjusting the angle of the head groups resulted in no variation in the ordering of the nanoparticle particularly the angle of the carbonate ions: The orientation of the headgroup cannot alone be responsible for the selectivity of different SAMs. Our results demonstrate that at the point of contact between the monolayer and calcium carbonate there must be a close match between the epitaxy and charge density in order for crystallization to occur. However as the effect can easily spread through the nanoparticle (as seen in the case of the disordered monolayer in configuration (3)) this contact region can be small. When we consider a solvated, dynamic monolayer we can see that the formation of surface defects and rearrangement of the chains/ head groups will allow for the match to improve as the crystallization event occurs further stimulating the ordering of the calcium carbonate. If further understanding is to be gained about the interface between crystals and organic arrays a range of other methods need to be considered. Long-time, large scale models are required to remove edge-effects and temperature issues. As discussed, the presence of solvent may be important, especially if an ACC precursor (containing a H2O-CaCO3 mix) is forming. Simulations also need to account for the particulars of the local SAM structure and how this can vary at the contact point and during the crystallization process. Our simulations have explored the crystallization event of calcium carbonate in contact with SAMs. We have isolated ionization, charge density, epitaxial and headgroup orientation effects and explained their influence of the crystallization process. Acknowledgment. The authors acknowledge funding from EPSRC under Grant No. GR/S80103/01 (Sheffield). They also acknowledge computing facilities on the Mott2 machine at Rutherford-Appleton Laboratory funded under EPSRC Grant No. GR/S84415/01. The authors would also like to thank Dr Mingjun Yang for his advice on organic molecular modelling. LA800389G
