Temperature Effects

If one is to construct a phase diagram for calcium carbonate, then the effect of temperature on low density clusters can help to resolve the features of the diagram in the prenucleation regime. To this effect, a low density 20 CaCO₃ cluster was simulated in water for 20 ns in the temperature range 320–500 K. As temperature increased, the potential energies of the cluster per formula unit increased linearly (as shown in Figure C.6) from _∼ -30 – -18 eV. The linear scaling of energy with temperature is expected for a homogeneous bulk phase.

Figure 4.6 (a) shows the change in nCa and average cluster size as a func- tion of temperature. Both of these quantities increased as T increased, with the coordination increasing from a value comparable to that of DOLLOP, to one which approached the values expected for the most dense cluster when relaxed in water (see Figure 4.4 for 20 CaCO₃). The change in coordination was approximately linear, consistent with the change in potential energy. The average cluster size at 500 K is close toN = 100, which is the maximum possible value, suggesting that the cluster condensed in solution as the temperature increased.

(a)

(b)

Figure 4.6: (a) Coordination of carbon to calcium, nCa, and average cluster size, < N >(as a measure of number of cluster atoms), for simulations of a low density 20 CaCO₃ in water. Simulations were performed for 20 ns, with measurements taken from the final 10 ns of trajectories. Black circles shownCaand blue diamonds show < N >, withy axis scales shown on the left and right, respectively.

(b) Coordination probabilities of n carbons to a single calcium as a function of temperature, for the simulations described in (a). Coordination was measured using

clusters in solution. However, through consideration of the change in bonding prob- abilities,PCa−_nC, as a function of temperature, that was not the case. Coordination

of calcium to two and three carbons decreased as T increased, as shown in Figure 4.6 (b), and this was associated with an increase in calcium coordination to 4₋6 carbons. At T = 460 K, the probability of calcium binding to four carbons was higher thanPCa−3C, and there was also a small probability of six–fold coordination (PCa−_6C ∼0.05 atT = 500 K). These results suggest that as temperature increased,

clusters of calcium carbonate aggregate in solution, and at the same time, ions pack more closely. There was a relatively large increase in the average lifetime of bonds at the higher temperatures. Probability densities of 0.1 were found for bond lifetimes at 0.45 ns (measured over the final 5 ns of simulation) forT = 500 K; similar prob- ability densities were found at a maximum bond lifetime of 0.1 ns for T = 320 K. While these lifetimes are smaller than compact clusters at 300 K, they do indicate that dynamic ordering decreased as temperature increased, and that the cluster was behaving more like ACC than a dense liquid at the highest temperature. Higher temperature should favour high entropy states, which does not, at first sight, appear to be the case for calcium carbonate. However, increasing ion coordination results in the release of highly constrained water from ion solvation shells. The disruption of water order around ions will lead to a favourable increase in water entropy. This is likely to be the driving force for condensation at high temperature.

4.3.4 Surface Charge Bias

It is interesting to consider the effects of solvation on the strength of the charge bias of clusters which was found during optimisations, and is discussed in Chapter 3 (section 3.3.3). The charge bias which was observed for clusters (particularly those which were compact) in the gas phase was reduced when clusters were immersed and relaxed in water. This can be attributed to ion hydration and partial disso- lution of clusters. However, the nature of a charge distribution bias did persist in these systems, as shown in Figure 4.7, which provides the final configurations for an open and compact cluster of 27CaCO₃ when simulated in water. The cluster with maximum initial nCa remained relatively dense by the end of a 5 ns simula- tion, and the majority of positively charged species resided below the surface of the cluster. In contrast, ions in the sampled cluster with lowest initial nCa, became further exposed to solvent molecules over the course of the simulation, and density continued to reduce as the structure disassembled, resulting in charge distributions approaching uniformity. Although data are presented here for one size of cluster, similar behaviour was commonly found for all of the larger cluster sizes studied.

Figure 4.7: Configurations for clusters of 27CaCO₃after 5 ns of simulation in water. Top and bottom show clusters with nCa =2.5 (t0, nCa = 3.1) and nCa =3.8 (t0,

nCa = 4.7); the explicit structure is shown on the right (see the caption in Figure 4.2 for atom identities), while the image on the left is an electrostatic potential map, indicating the electrostatic charge distribution half way through the simulation cell zaxis for Ca, C and O atoms only [Aksimentiev and Schulten, 2005]. Here shading represents negative (red) and positive (blue) regions, ranging from -100 – 280 kBT