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Simulation of Organic Monolayers as Templates for the Nucleation of Calcite Crystals Dorothy M. Duffy and John H. Harding* Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, U.K. Received February 20, 2004. In Final Form: June 4, 2004 Living organisms can control the size, shape, and structure of minerals. Attempts to reproduce this biological control in the laboratory often use Langmuir monolayers of long-chain carboxylic acids. We use large-scale molecular dynamics simulations to calculate the interfacial energies of calcite crystals grown on stearic (octadecanoic) acid monolayers. In light of these simulations we discuss the argument that the orientation of the growing mineral is controlled by the organic substrate acting as a template which the mineral must fit in order to grow.
Introduction Living organisms control the size, shape, and crystallographic orientation of growing crystals to form minerals with unusual morphologies and functional properties.1-3 This process of biomineralization has inspired attempts to reproduce such control in the laboratory where ordered arrays of organic molecules are used to modify and control crystal growth. Early experiments used Langmuir monolayers,4,5 such as the long-chain carboxylic acids, which form ordered arrays on the surface of water under applied pressure. The calcite crystals grown from aqueous solution on these monolayers nucleate on the (10.0) face, whereas calcite crystals nucleate on the (10.4) face on the surface of pure water. Self-assembled monolayers have been used as substrates for calcium carbonate crystal growth, and it was found that different headgroups, and even different metal substrates, tended to nucleate different crystal faces.6-10 The common explanation for these effects is that the organic layer is acting as a “template” to control the growth of the mineral.1,11 Most forms of this argument point to the good geometrical matching between the arrangement of ions on a given face of the crystal and the ordering of the functional groups attached to the aliphatic chains, assuming that the aliphatic chains are closepacked. This argument has been used to explain the different orientation produced by carboxylates rather than sulfonates. The remarkable “odd-even” effect,12 where * To whom correspondence may be addressed. E-mail: j.harding@ ucl.ac.uk. (1) Mann, S. Biomineralization, Principles and Concepts in Bioinorganic Materials Chemistry; Oxford University Press: Oxford, 2001. (2) Weiner, S.; Addadi, L. J. Mater. Chem. 1997, 7, 689-702. (3) Addadi, L.; Weiner, S. Nature 1997, 389, 912-915. (4) Mann, S.; Heywood, B. R.; Rajam, S.; Walker, J. B. A. J. Phys. D 1991, 24, 154-164. (5) Heywood, B. R.; Mann, S. Chem. Mater. 1994, 6, 311-318. (6) Ku¨ther, J.; Seshadri, R.; Knoll, W.; Tremel, W. J. Mater. Chem. 1998, 8, 641-650. (7) Aizenberg, J.; Black, A. J.; Whitesides, G. M. Nature 1999, 398, 495-498. (8) Aizenberg, J.; Black, A. J.; Whitesides, G. M. J. Am. Chem. Soc. 1999, 121, 4500-4509. (9) Travaille, A. M.; Donners, J. J. J. M.; Geritsen, J. W.; Sommerdijk, N. A. J. M.; Nolte, R. J. M.; van Kempen, H. Adv. Mater. 2002, 14, 492. (10) Travaille, A. M.; Kaptijn, L.; Verwer, P.; Hulsken, B.; Elemans, J. A. A. W.; Nolte, R. J. M.; van Kempen, H. J. Am. Chem. Soc. 2003, 125, 11571. (11) van der Merwe, J. H. Discuss. Faraday Soc. 1949, 5, 201. (12) Han, Y.-J.; Aizenberg, J. Angew. Chem., Int. Ed. 2003, 42, 36683670.
self-assembled monolayers of carboxylate-terminated alkanethiols nucleate crystals with different orientation on monolayers with odd and even chain lengths, has also been attributed to templating. Various types of polymers have also been used as templates. Dendrimers of polyamidoamine induce the growth of spherical or disklike crystals13 and polypentacosadiynoic acid (PDA) promotes nucleation of the (01.2) face of calcite.14 Despite the apparent success of this model, there are several obvious questions concerning its validity. The templating argument compares the geometries of perfect, unrelaxed, crystal surfaces with a rigid arrangement of the functional groups. Yet it is clear that this is not a realistic picture of either surface. Even in a vacuum a ceramic surface will relax and may reconstruct. This point applies with still greater force to an array of functional groups attached to aliphatic chains and covered with water. Such systems are expected to exhibit considerable disorder.15 A further problem concerns the growth process itself. This takes place in the presence of water, and therefore an essential part of the crystal growth is the displacement of the water molecules attached to the organic layer by the ions of the crystal. This is entirely ignored by the templating argument. However, to go beyond the simple model of a template, it is necessary to consider the details of how these crystals nucleate and grow. Simulation is an obvious tool to attack such a problem but faces a major problem of time scales. There have been very few attempts at a direct simulation of nucleation,16 and these have only been performed on much simpler systems than the one proposed here. This perhaps explains why, despite the extensive experimental data now available, there have been no serious attempts to simulate the biomineralization process directly. There have been a number of previous simulation studies on calcium carbonate. These have obtained potential models that can describe the various crystal phases and the energies and structures of the crystal surfaces.17 More recent work has considered the effect of water on the surface structure calcite18 and the mechanisms of growth and dissolution.19 A few recent studies (13) Naka, K.; Chujo, Y. Chem. Mater. 2001, 13, 3245-3259. (14) Berman, A.; Charych, D. J. Cryst. Growth 1999, 198/199, 796801. (15) Schreiber, F. Prog. Surf. Sci. 2000, 65, 151-256. (16) Anwar, J.; Boateng, P. K. J. Am. Chem. Soc. 1998, 120, 96009604.
10.1021/la049552b CCC: $27.50 © 2004 American Chemical Society Published on Web 07/28/2004
Monolayers for the Nucleation of Calcite Crystals
have considered molecules on vacuum surfaces of calcite in an attempt to understand inhibition.20 The most recent has included the effect of water.21 No studies to our knowledge have considered the effect of arrays of organic functional groups in controlling growth which is the essence of the templating argument. We have chosen to study calcium carbonate growth on stearic acid monolayers because this is a simple model of a biomineralized system. Calcite crystals grown from supersaturated solution under Langmuir monolayers of stearic acid have a marked preference for nucleation on the (10.0) face.4,5,22 The aim of this work is to predict the preferred nucleation face (and hence the orientation of crystal growth) of calcite crystals on the monolayer from aqueous solution by calculating interfacial energies. From the Wulff-Kaishew23 theorem we calculate the relative change in thickness of the nucleating crystal and estimate the enhanced nucleation rate. This enables us to understand which factors are controlling nucleation without facing the task of a direct simulation of the nucleation process. In previous publications we presented results of models of interfaces between Langmuir monolayers of stearic (octadecanoic) acid and calcite surfaces. Both neutral (unionized)24 and fully dissociated (ionized)25 monolayers were considered. We found that there was very good matching between the calcite surface structure and the monolayers and that the magnitudes of the adhesion energies were comparable with the surface energies. The calculations suggested that the nucleation rate for all surfaces would be enhanced significantly on stearic acid monolayers and no particular face appeared to be favored. Such models can explain why calcite crystals should grow preferentially on organic layers but not why a specific morphology should be favored. These simulations are conceptually similar to template models where only the matching of the pattern of carboxylate groups in the template array to the structure of possible calcite surfaces is considered. Unlike arguments based on the simple matching of surface patterns of template and crystal, the simulation recognizes that an organic layer is highly flexible. The situation is not the same as a key trying to fit into a rigid lock. The organic layer can, and does, adapt to the growing crystal. However, these simulations are not realistic models of experiments where crystals are grown from aqueous solution. Realistic simulations must include liquid water for the calculations of the crystal/water interfacial energies and crystal/ monolayer interfacial energies.18 In this paper we present a set of results for the crystal/ water interfacial energies and the crystal/monolayer interfacial energies for a range of calcite surfaces. Both neutral and fully dissociated monolayers are considered. The interfacial energies obtained from these simulations (17) Pavese, A.; Catti, M.; Parker, S. C.; Wall, A. Phys. Chem. Miner. 1996, 23, 89-93. Archer, T. D.; Birse, S. E. A.; Dove, M. T.; Redfern, S. A. T.; Gale, J. D.; Cygan, R. T. Phys. Chem. Miner. 2003, 30, 416424. (18) de Leeuw, N. H.; Parker, S. C. J. Chem. Soc., Faraday Trans. 1997, 93, 467-475. (19) de Leeuw, N. H.; Parker, S. C.; Harding, J. H. Phys. Rev. B 1999, 60, 13792-13799. (20) Nygren, M. A.; Gay, D. H.; Catlow, C. R. A.; Rohl, A. L.; Wilson, M. P. J. Chem. Soc., Faraday Trans. 1998, 94, 3685-3691. (21) de Leeuw, N. H.; Cooper, T. G. Cryst. Growth Des. 2004, 4, 123133. (22) Loste, E.; Marti, E.; Zarbakhsh, A.; Meldrum, F. C. Langmuir 2003, 19, 2830-2837. (23) Mutaftschiev, B. In The atomistic nature of crystal growth; Springer: Berlin, 2001; Chapter 9. (24) Duffy, D. M.; Harding, J. H. J. Mater. Chem. 2002, 12, 34193425. (25) Harding, J. H.; Duffy, D. M. M. R. S. Symp. Proc. 2003, 735, C11-5.1-6.
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are used to predict the crystal faces most likely to nucleate on Langmuir monolayers. Methods The energies are calculated using the general-purpose molecular dynamics program DL•POLY.26 All simulations use a time step of 1 fs and the Nose´-Hoover thermostat to maintain a temperature of 300 K. The Ewald summation is employed to calculate the Coulomb interactions. All other nonbonding interactions employed a cutoff of 10.1 Å. The derivation and validation of the interatomic potentials used are discussed in detail in the next section. The simulation blocks are periodic in two dimensions, and periodicity in the third dimension is invoked using an array of blocks separated by vacuum slabs of thickness equal to that of the blocks. Crystal blocks are obtained by cutting the crystal in the required crystallographic orientation. There are two distinct types of orientation in ionic crystals, one in which the planes are electrically neutral and a second in which the planes are composed of ions of one type. Care must be taken when attempting to simulate systems with polar directions. We consider the problems of polar directions in more detail in a companion paper.27 For present purposes it is enough to recall two well-known results.28 First, the surface energy of a polar surface diverges linearly with the number of planes in the crystal. This is due to the presence of a macroscopic dipole in the crystal if a simple bulk termination is used. It follows that any real system must remove this dipole, whether by reconstruction, absorption of charged ions, or whatever. Simulations of surfaces and interfaces usually use (as here) a slab of crystal of sufficient thickness that the interfaces on either side do not interact. The dipole moment is eliminated by moving ions from the top of the slab to the bottom. In the simplest case (as here) half a plane of ions is moved to produce a slab that is symmetrical about a central plane. As we shall see later, if the monolayer array consists of charged functional groups, this can play a vital role in removing the dipole moment from polar directions. Monolayers are constructed by arranging a twodimensional array of stearic acid molecules with the long axes perpendicular to the layer. The density of the monolayer is chosen to match the surface density of the ions of the crystal with the required orientation. The initial configuration of the crystal/monolayer interface was created by relaxing the monolayer onto the frozen crystal surface from a position 4 Å above the surface using a low temperature (10 K) simulation. A number of different lateral displacements was required to ensure that the lowest energy interface was obtained. The initial conformation of the crystal/water interface was obtained by equilibrating an ordered array of water molecules above a frozen crystal surface during a 50 ps simulation at 300 K. The final interfacial configurations created by these simulations were used as starting configurations for 100 ps simulations at 300 K with all atoms mobile. The average energy of the simulation over the final 60 ps was used for the interfacial energy calculations. Careful examination of the drift of the simulation energy over the simulations performed shows that this is sufficient for these systems to reach equilibrium. The interfacial energies and adhesion energies are calculated from the difference between the energies of two-dimensional blocks of atoms. The blocks are formed (26) Smith, W.; Forester, T. R. J. Mol. Graphics 1996, 14, 136-141. (27) Duffy, D. M.; Harding, J. H. Langmuir 2004, 20, 7637. (28) Tasker, P. W. J. Phys. C 1979, 12, 4977.
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Figure 1. Schematic representation of (a) the adhesion energy, (b) the crystal/water interfacial energy, and (c) the crystal/ monolayer interfacial energy calculations. The checkerboard pattern represents a crystal block, the lines represent the monolayer, and the dots represent a water block.
of a slab of calcite crystal with the selected crystallographic orientation, liquid water, a monolayer of stearic acid, or a combination of these. The adhesion energy between a monolayer and a crystal 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. In an aqueous environment the adhesion energy (βcm) is calculated from the difference between the energy of a system with a monolayer, crystal, water combination and a monolayer, water, crystal, water combination, as illustrated in Figure 1a. The total number of atoms of each type is the same in both simulations, but the position of the crystal slab is moved from adjacent to the monolayer in the first simulation into the middle of the water layer in the second. The crystal/water interfacial energy (γcw) is calculated from the difference between the energy of a crystal/water block and half the sum of the energies of a pure crystal and a pure water block, as shown in Figure 1b. The crystal/monolayer interfacial energy (γcm) is calculated from the difference between the energy of the final state of a crystal/monolayer block and half a pure water block and an initial state of half a pure crystal block and a water monolayer block, as illustrated in Figure 1c. The adhesion energy is equal to the difference between the crystal/monolayer interfacial energy and the crystal/ water interfacial energy.
βcm ) γcm - γcw
of Moller et al.,29 and the CHARMM30 potentials were used for the headgroup. The flexible TIP3P31 potential was used for water. The potentials describing the interactions between the crystal and water and between the crystal and the monolayer can be derived in a number of different ways. To choose the most suitable potential model for the current simulations, we have compared results obtained using different potentials with ab initio calculations. The first potential we consider (Pot 1) uses the Ca parameters of the CHARMM potential and the Lorentz-Berthelot combination rules to obtain the Lennard-Jones interactions between the crystal and the water or stearic acid molecules. The second potential (Pot 2) uses the scheme introduced by Schroder et al.32 in which the crystal interatomic potentials are modified to obtain the molecule/ crystal interactions by scaling the repulsive part of the potential by the ratio of the charge of the two atoms. This method ensures the equilibrium separation between atoms remains unchanged by charge modification. It has had considerable success in modeling the properties of zeolites and the interactions between water and metal oxides. The third potential (Pot 3), investigated for the water case only, is that derived by de Leeuw and Parker.18 This interaction potential is also based on the Schroder method and it gives good agreement with the experimental structure of ikaite (CaCO3‚6H2O). The interaction energy between a small single layer cluster of CaCO3 ions, with an ionic arrangement corresponding to the (10.4) surface of calcite, and a water molecule was calculated using Gaussian98.33 A geometry optimization, with the ionic positions frozen and the shape of the H2O molecule fixed, was performed at the HartreeFock level and using a LAN2DZ basis set. Fixing the ionic positions and the molecule shape ensured that only the interactions between the molecule and the substrate affected the relaxations. The minimum energy position of the molecule and the interaction energy, defined as the difference between the energy of the molecule on the cluster and the energy of the isolated molecule, was noted. An equivalent calculation was carried out using DL•POLY, again with the ionic coordinates and the molecule shape fixed, and the interaction energy and equilibrium separations for the three sets of interatomic potentials were compared with the Hartree-Fock values. The results are summarized in Table 1 and the minimum energy configuration is shown in Figure 2a. We note that potential derived using the CHARMM parameters for Ca2+ and the Lorentz-Berthelot combination rules (Pot 1) severely overestimates the magnitude of the interaction energy and underestimates the equilibrium interatomic separations. The potential derived using the Schroder scheme (Pot 2) and the de Leeuw, Parker potential (Pot 3) both gave much better agreement with the HartreeFock calculations. We have chosen to employ the de Leeuw,
(1)
Interatomic Potentials The interaction potentials used for CaCO3 were those derived by Pavese et al.17 which have been used to calculate a range of properties of calcite and aragonite crystals. We used the rigid ion version of the potentials as this resulted in a considerable saving in computing time and it did not have any significant effect on the surface energies or other properties relevant to the current study. The tail of the monolayer was modeled using the united atom potentials
(29) Moller, M. A.; Tildesley, D. J.; Kim, K. S.; Quirke, N. J. Chem. Phys. 1991, 94, 8390-8401. (30) MacKerell, A. D.; Bashford, D.; Bellott, M.; Dunbrack, R. L.; Evanseck, J. D.; Field, M. J.; Fischer, S.; Gao, J.; Guo, H.; Ha, S.; JosephMcCarthy, D.; Kuchnir, L.; Kuczera, K.; Lau, F. T. K.; Mattos, C.; Michnick, S.; Ngo, T.; Nguyen, D. T.; Prodhom, B.; Reiher, W. E.; Roux, B.; Schlenkrich, M.; Smith, J. C.; Stote, R.; Straub, J.; Watanabe, M.; Wiorkiewicz-Kuczera, J.; Yin, D.; Karplus, M. J. Phys. Chem. B 1998, 102, 3586-3616. (31) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. J. Chem. Phys. 1983, 79, 926-935. (32) Schroder, K. P.; Sauer, J.; Leslie, M.; Catlow, C. R. A.; Thomas, J. M. Chem. Phys. Lett. 1992, 188, 320-325. (33) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B. et al. GAUSSIAN 98, Gaussian Inc, Pittsburgh PA, 1998.
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Figure 2. The minimum energy configuration of (a) a water molecule and (b) a formic acid molecule on a cluster of CaCO3 ions calculated using Gaussian98 (HF). Table 1. The Interaction Energy (Eint) between an H2O Molecule and a CaCO3 Cluster Calculated Using the HF Method with Gaussian98 and Using DL•POLY with Three Interaction Potentialsa
Table 3. The Interaction Energy (Eint) between an Array of H2O Molecules and a CaCO3 Substrate, Calculated Using Plane-Wave DFT (VASP) and Using DL•POLY with Three Interaction Potentialsa
DL•POLY Gaussian98 mol-1)
Eint (kJ ROC/HW (Å) RCa/OW (Å)
-106.42 1.93 2.42
Pot 1
DL•POLY
Pot 2
-142.0 1.74 2.23
Pot 3
-103.0 1.78 2.37
-99.5 1.91 2.33
mol-1)
Eint (kJ ROC/HW (Å) RCa/OW (Å)
VASP
Pot 1
Pot 2
Pot 3
-85.7 1.71 2.38
-135.9 1.66 2.21
-101.9 1.64 2.32
-86.9 1.87 2.33
a The equilibrium separations between the carbonate O and the water H (ROC/HW) and the Ca ion and the water O (RCa/OW) are also included in the table.
a The equilibrium separations between the carbonate O and the water H (ROC/HW) and the Ca ion and the water O (RCa/OW) are also included in the table.
Table 2. The Interaction Energy (Eint) between an HCOOH Molecule and a CaCO3 Cluster Calculated Using the HF Method with Gaussian98 and Using DL•POLY with Two Interaction Potentialsa
Table 4. The Interaction Energy (Eint) between an Array of HCOOH Molecules and a CaCO3 Substrate, Calculated Using Plane-Wave DFT (VASP) and Using DL•POLY with Two Interaction Potentialsa
DL•POLY Gaussian98 mol-1)
Eint (kJ ROC/H (Å) RCa/OD (Å)
-112.7 1.66 2.44
Pot 1 -146.9 1.58 2.18
DL•POLY
Pot 2 -114.4 1.63 2.27
mol-1)
Eint (kJ ROC/H (Å) RCa/OD (Å)
VASP
Pot 1
Pot 2
-97.16 1.48 2.35
-136.3 1.54 2.18
-101.7 1.59 2.26
a The equilibrium separations between the carbonate O and the formic acid H (ROC/H) and the Ca ion and the carbonyl O (RCa/OD) are also included in the table.
a The equilibrium separations between the carbonate O and the formic acid H (ROC/H) and the Ca ion and the carbonyl O (RCa/OD) are also included in the table.
Parker potential because of the agreement with the experimental structure of ikaite. An equivalent set of calculations was carried out for formic (methanoic) acid to provide a test for the stearic acid potentials. The energies and equilibrium separations are summarized in Table 2, and the equilibrium conformation is shown in Figure 2b. Again the potentials derived using the Schroder scheme gave much better results than the Lorentz-Berthelot method, and these were chosen for the simulations. A further test was carried out by comparing DL•POLY simulations with plane-wave density functional calculations using VASP.34 A five-layer slab of calcite oriented in the (104) direction was taken as the substrate, and geometry-optimized GGA calculations, in which all the atoms were relaxed, were carried out. We used a 3 × 3 × 1 Monkhorst-Pack K-mesh and a cutoff value for the plane wave basis set of 500 eV. The results, along with the results from equivalent DL•POLY simulations, are summarized in Table 3 for water and in Table 4 for formic acid. A
similar trend to the Hartree-Fock calculations is apparent, with Pot 1 overestimating the interaction energy and underestimating the interatomic separations for both molecules. The Schroder scheme (Pot 2) and the Parker interaction potentials (Pot 3) both gave much better agreement.
(34) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 48, 13115-13118.
Results The interatomic potentials validated using ab initio techniques were used to calculate interfacial energies between water and calcite and between stearic acid and calcite using the methods outlined above. Two distinct monolayer states were considered, one in which the monolayer was undissociated (neutral) and a second in which the monolayer was fully dissociated (ionized). The degree of ionization of the monolayer depends on the pKa value of the acid and the local pH at the interface. This has been estimated by solving the Poisson-Boltzmann equation and the self-consistent Grahame equation for CaCO3 solution. At the experimental bulk pH of 6 the fraction of molecules ionized was calculated to be 60%.
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Table 5. The Crystal/Water Interfacial Energies (γcw), the Crystal/Monolayer Interfacial Energies (γcm), and the Adhesion Energies (β) for Interfaces between Calcite Crystals and Neutral Monolayers of Stearic Acida (10.4) (10.0) (11.0) (00.1)Ca (00.1)CO3 (01.2)Ca (01.2)CO3 (10.1)Ca (10.1)CO3
γcw (J m-2)
γcm (J m-2)
β ) γcm - γcw
1 + β/2γcw
area/molecule (Å2)
0.14 0.22 0.27 0.31 0.25 0.37 0.44 0.28 0.27
0.09 0.42 0.59 0.57 0.57 0.63 0.61 0.66 0.62
-0.05 0.20 0.32 0.26 0.32 0.26 0.17 0.38 0.35
0.83 1.45 1.59 1.42 1.64 1.35 1.38 1.68 1.65
19.28 20.96 24.21 19.93 19.93 20.63 20.63 28.73 28.73
a The ratio of the nucleation barrier on the monolayer to that in bulk solution (1 + β/2γ ) is included in the table, along with the surface cw area per monolayer molecule.
The calculations also show that Ca2+ ions condense onto the monolayer, neutralizing the charge.25,35 The calculated interfacial and adhesion energies for a range of calcite surfaces on neutral monolayers are summarized in Table 5. We can predict the crystal morphology from these energies using the Wulff-Kaishew theorem,23 which is an extension of the Wulff theorem for predicting the morphology of crystals growing on a substrate. The theorem states that the crystal will be truncated in the direction of the substrate by an amount that depends on the interfacial adhesion energy between the crystal and the substrate (βks) and the surface energy of the crystal in that direction (γk).
βks hks )1+ hk γk
(2)
Here hk is the perpendicular distance between the center of the crystal and face k. hks is the perpendicular distance between the center of the crystal and the substrate. Equation 2 implies that a negative adhesion energy will reduce the thickness of crystals in the direction perpendicular to the substrate. Since our calculations found that only the (10.4) face of calcite has a negative adhesion energy on neutral stearic acid monolayers in an aqueous environment only this (10.4) face will have enhanced nucleation. The (10.4) face also dominates the morphology of crystals nucleating from bulk aqueous solution; therefore crystals nucleating on a neutral monolayer should have similar morphology to the bulk crystals but they would be thinner in the direction perpendicular to the monolayer. At the level of classical nucleation theory the nucleation barrier (∆G*) is proportional to the volume of the critical nucleus; therefore the reduced volume of the crystal on the substrate leads to a reduced nucleation barrier (∆G*s). For a centrosymmetric crystal the ratio of the crystal volume on the interface to the crystal volume in free space is given by
βks ∆Gs* ∆Vs ) )1+ ∆G* ∆V 2γk
(3)
Applying this result to the (10.4) morphology, the volume of the crystal nucleated on the monolayer is decreased by a factor of 0.8 with respect to the bulk nucleated crystal. Therefore the nucleation barrier would be reduced by the same factor. The type of calcite surface that can adhere to ionized monolayers is restricted by the conditions of charge (35) The simpler case of CaCl2 solutions in contact with a Langmuir monolayer has been considered: Lockhead, M. J.; Letellier, S. R.; Vogel, V. J. Phys. Chem. B 1997, 101, 10821-10827.
Figure 3. An interface between a calcium terminated (00.1) surface of calcite and an ionized monolayer of stearic acid. The gray spheres represent C, red represents O, and green represents Ca.
neutrality and zero dipole moment. The charge of the ionized molecule is -1e; therefore a polar crystal block terminated on the lower surface by a half layer of carbonate ions and on the upper surface by a full layer of Ca2+ ions and a full layer of stearate molecules will have zero net charge and zero dipole moment. The case of the (00.1) interface is shown in Figure 3. For this type of interface there is very good matching between the carboxylate groups of the monolayer and the carbonate ions of the crystal. On neutral crystal surfaces charge neutrality is maintained by replacing one carbonate ion in the surface plane with two stearate molecules. In practice this is only possible when the spacing between the surface carbonate ions is large enough to accommodate two monolayer molecules, that is for surfaces with large surface unit cells. The surface area per carbonate ion in the (10.4) face is 19.3 Å2; therefore replacing the surface carbonate ions with two monolayer molecules would require a monolayer area per molecule of 9.6 Å2. The minimum area per molecule attainable for long chain carboxylic acids on the surface of water is about 19 Å2; therefore the surface density necessary to match the (10.4) surface is well beyond the experimental range. The surface area per carbonate ion of the (11.0) face is also too small to be experimentally accessible by the monolayer. The (10.0) face, on the other hand, has a surface area per carbonate ion of 41.2 Å2, and the area per monolayer molecule of 20.6 Å2 required to replace the surface carbonate ions is readily accessible experimentally. A snapshot of the 300 K simulation of the (10.0) calcite/monolayer interface is shown in Figure 4a. We note there is excellent matching between the mono-
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Figure 4. Snapshots of the 300 K simulations of (a) a (10.0) calcite/stearic acid monolayer, (b) a water block, (c) a stearic acid/water interface, (d) a (10.0) calcite block, and (e) a (10.0) calcite/water interface. The crystal/monolayer interfacial energy was calculated from simulations (a), (b), (c), and (d) and the crystal/water interfacial energy was calculated from simulations (b), (d), and (e).
layer and the crystal structure, with the carboxylate groups of the monolayer occupying the positions of the missing carbonate ions on the crystal surface. Also shown in Figure 4 are snapshots of the other simulations required to calculate both the crystal/water interfacial energy and
the crystal/monolayer interfacial energy. The monolayer charge at the monolayer/water interface is neutralized by a half layer of Ca2+ ions (Figure 4c). The calculated interfacial energies for the charged monolayers are summarized in Table 6. Two of the four
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Table 6. The Crystal/Water Interfacial Energies (γcw), the Crystal/Monolayer Interfacial Energies (γcm), and the Adhesion Energies (β) for Interfaces between Calcite Crystals and Ionized Monolayers of Stearic Acida (00.1) (01.2) (10.1) (10.0)
γcw (J m-2)
γcm (J m-2)
β ) γcm - γcw
1 + β/2γcw
area/molecule (Å2)
0.25 0.37 0.27 0.22
0.13 -0.01 0.37 0.25
-0.12 -0.38 0.10 0.03
0.76 0.49 1.18 1.07
19.93 15.47 28.73 20.96
a The ratio of the nucleation barrier on the monolayer to that in bulk solution (1 + β/2γ ) is included in the table, along with the surface cw area per monolayer molecule.
interfaces (the (00.1) and the (01.2) interfaces) have negative adhesion energies, and the (10.0) interface has a very small positive adhesion energy. However the simulation of the monolayer on an aqueous substrate at the density corresponding to the (01.2) face was unstable, with a group of molecules moving out of the monolayer and into the water. Indeed the monolayer density is higher than the experimentally attainable value. Polymers of PDA, which resemble carboxylic acid monolayers with the monomers polymerized to form a rigid raft, have been shown to nucleate the (01.2) face. The rigidity introduced by the polymerization may stabilize the raft sufficiently to permit nucleation of the (01.2) face. The question of the stabilization of this face is discussed in detail in the following paper.27 Our calculations show that the interfacial energy of the (00.1) face is less than that for the (10.0) face on ionized monolayers. This does not of itself demonstrate that the (00.1) interface should nucleate. An essential difference between the (00.1) and (10.0) directions is that the former is polar whereas the latter is not. Both crystallites would be expected to terminate with (10.4) surfaces at the water/ calcite interface since this is the lowest energy calcite/ water interface. For the (10.0) direction this is easy; there are no electrostatic constraints on how this direction grows, and (10.4) surfaces can readily be produced. For the (00.1) face this is difficult, since the dipole moment must also be quenched. This can be done either by the presence of (high-energy) polar surfaces or by the adsorption of ions onto the (10.4) facets formed at the outer surface of the crystal. Both of these processes are likely to be of high energy. This probably explains why the (00.1) growth direction is not seen. Further details are given in the following paper.27 Conclusions Our results establish that nucleation of calcite crystals on organic substrates is influenced by a range of factors, notably the degree of ionization and competition between the interactions of the crystal and water with the substrate. The simple model of an organic template controlling the growth of minerals by a lock-and-key mechanism must be modified to take account of this. The competition between the interaction of water and the interaction of the substrate with the crystal plays a crucial role in limiting the number of crystal faces that are nucleated on a given substrate. The degree of ionization of the substrate is also significant.
Fully ionized substrates have stronger adhesion to the crystal surfaces than neutral substrates and therefore they should be better at promoting nucleation. Hence the pH of the solution is an important factor in promoting nucleation. This also controls crystal shape since the ionized and neutral monolayers stabilize different surfaces, (10.4) for the neutral case and (10.0) or (00.1) for the ionized case. A further factor controlling the nucleation of neutral surfaces on ionized substrates is the density of the surface carbonate ions. This must be low enough to permit the substitution of each ion by charge groups of the substrate to create a neutral interface. The question of stereochemical matching only comes into play after these factors have been taken into account. Perhaps the best way to consider the template is in the context of a selfassembly process. The organic template is not a preexisting rigid structure onto which the mineral must fit, rather the interface between organic substrate and mineral assembles as the mineral grows. The constraint of stereochemical matching is then, other things being equal, likely to pick out a stable interface structure. Even so, the flexibility of the template may complicate this simple argument. In living systems, for example, thermal fluctuations and entanglement of biomolecules may disrupt the ideal substrate.36 If the template were made more rigid, by cross-linking the organic molecules into lines or sheets, stereochemical matching might be more important. We are investigating this possibility. However, one should not forget a basic point made throughout this paper: growing minerals on organic layers is a displacement process. Persuading the water to leave the surface is as important as persuading a mineral to grow there. Acknowledgment. The authors acknowledge funding from EPSRC under Grant GR/R25484/01. They also acknowledge computing facilities on the Mott machine at Rutherford-Appleton Laboratory funded under JREI Grant JR99BAP and also on the HP(x) machine under the Materials Chemistry Consortium headed by Professor Richard Catlow. The authors also wish to acknowledge many useful discussions on the derivation of potentials with Professor Steve Parker and thank Professor A. M. Stoneham for a critical reading of the manuscript. LA049552B (36) Stoneham, A. M. Mat. Sci. Eng. C 2003, 23, 235.
