Compact Clusters in Water

The minimum energy and most compact structures ofnCaCO₃ clusters (i.e. those with initial highest Ca–C coordination) for eachnin the range 1–40 were simulated for 10 ns in water, and the mean potential energy,U, taken from the latter regions of the trajectories are shown in Figure 4.1. The underlying trends in the data show a rapid monotonic decrease in potential energy with increasing cluster size for clusters up to around nine formula units. For larger clusters, Figure 4.1 shows some scatter superimposed on a general increase ofU with cluster size, up to a plateau around

0 10 20 30 40 -30.2 -30 -29.8 U (eV) 0 10 20 30 40 nCaCO₃ -29.0 -27.0 -25.0 0 10 20 30 40

Figure 4.1: Average potential energy, U, per formula unit of calcium carbonate calculated for clusters of initialnCaCO₃. Average values were calculated from the final 2 ns of a 10 ns MD trajectory of clusters simulated in water. The energy values are exclusive of bulk water energies in respective systems. Error bars indicate uncertainties relating to one standard error of the mean. The potential energy of the clusters in the gas phase are also provided and shown by the blue data points, with the shifted scale (in blue) on the right of the graph applicable to these data points only.

n= 30. The difference in U between the minimum around n= 9 and the largest cluster sizes is on the order of _∼0.1 eV per CaCO₃ ion pair, which is comparable in strength to a moderately strong hydrogen bond. The general trends observed here contrast with those seen from cluster optimisations in vacuum (shown by the blue curve in Figure 4.1), where extra stability was found from increasing ionic coordination in dense amorphous clusters, up to the largest cluster size considered in this study (_∼2 nm in diameter).

The increase in cluster energy as a function of size can be ascribed to ion hydration in solution, and can be explained by considering the time evolution ofnCa for the various system sizes. Figure 4.2 shows an example of the initial and final states of large and small clusters at the beginning and end of 10 ns simulations. In small clusters (1 _≤ n _≤ 10 for nCaCO₃) nearly every ion was in contact with the solvent, even for particles with maximum nCa. The presence of the cluster– solvent boundary introduced an energy penalty (i.e. the interfacial energy), and the clusters were too small to be stabilised by a favourable bulk energy contribution. Energetically, it was more favourable for the clusters to partially dissolve (see Figure

Figure 4.2: Initial and final snapshots of minimum energy calcium carbonate clusters (from vacuum optimisations) simulated in water for 10 ns. Top shows 5 CaCO₃ at the beginning of the simulation which partially dissolved to give the 4 CaCO₃, low density cluster shown on the right, plus one ion pair which has been omitted. Bottom shows a 32 CaCO₃ cluster, for which partial loss of surface ions occurred over the 10 ns simulation, but for which a well defined ionic core was retained. Ca, C and O atoms are shown as yellow, black and red, respectively, while green lines show distances between carbon and calcium below 3.825 ˚A, highlighting ions connected in the first coordination shell. Water has been omitted for clarity.

4.2 for 5 CaCO₃), allowing retention of limited ionic coordination, but also greatly increasing ion stabilisation through solvation. In the case of 9 CaCO₃, byt= 10 ns, the cluster dissociated and small clusters of ions dynamically dissolved and aggre- gated during the simulation. This dynamic (dis)ordering was found for all small clusters of initialnCaCO3, with cluster size distributions (CSDs) indicating a wide range of possible cluster sizes after relaxation in water. A particularly interesting case was observed for a six formula unit cluster; this dissolved into solution to form smaller clusters, which underwent dynamic aggregation and dissolution, before a six formula unit cluster was reformed, and a considerable volume of configuration space was explored on the time-scale of the experiment.

As cluster size increased, the stabilisation from high ionic coordination within the cluster was sufficient to avoid complete cluster dissolution over a 10 ns trajec- tory, as shown in Figure 4.2 for the in vacuo minimum energy 32 CaCO₃ cluster (CSDs showed little change over the course of the simulation for large clusters). The internal core sub-lattice structure of ions in the cluster over 10 ns was retained for clusters of initial high density with n larger than _∼ 20. Surface ions in larger particles coordinated strongly with solvent molecules, and this binding was suffi- cient to disassemble surface ions, creating dendritic arms and rings which protruded into solution and, on occasion, dissociated into small clusters. Ion pairs observed to dissociate from the cluster surface, yet this was insufficient to “break” the cluster on the time-scale of the simulations. This result appears to contrast from the find- ings of earlier simulation studies, reporting the structural stability of highly ordered nanoparticles of CaCO₃ in water, where calcite nanoparticles (of comparable size to the larger dense clusters in this study) were found to be stabilised by the effect of strongly coordinating surface water [Kerisit and Parker, 2004; Cooke and Elliott, 2007]. Although we have not considered calcite stability at this scale, the general differing result can most probably be ascribed to the choice of force field.

As small clusters partially dissolved in solution,nCawas observed to decrease over time, resulting in structures with coordination motifs that were found in higher energy clusters from gas phase optimisations. Oligomers of ions formed with solvent stabilisation of ions at the chain ends of dendritic arms. The coordination between monomeric ions in the chain was observed to be dynamic, with ion–ion separation reaching considerable distances, and ion pair loss and recombination prevalent over long time-scales. This behaviour is very much analogous to the that of Ca2+, CO₃2− and HCO₃− ions in aqueous solution, and is further evidence for the stability of dynamically ordered liquid-like oxyanion polymer (DOLLOP) over more ordered structures in solution [Demicheliset al., 2011].

The radial distribution functions (RDFs) for large clusters which retained high coordination during simulation are provided in Appendix A. These show that compact clusters were amorphous with no long range atomic order. It is not ex- pected that at the sizes studied there is likely to be crystalline order in clusters, but a study to investigate the bond ordering in the core of amorphous clusters would in- dicate whether atomic coordination environments were comparable to the crystalline phases of calcium carbonate. The RDFs show that for n > 10, atomic density is retained throughout the simulation at larger, which is indicative that clusters re- mained particulate over long simulation times (i.e. up to 50 ns). The doublet in the first peak in the Ca–C RDF (see Figure A.1) shows that both monodentate and bidentate binding of carbonate to calcium was apparent in the clusters. Bidentate binding tended to be more probable in compact clusters, which is not surprising as this maximises the electrostatic interaction between ions.