Conclusiones del capítulo

To understand the equilibrium between ion pairs and a dense liquid phase, a number of simulations were conducted in the concentration range 20–51 mM (see Table 6.2). Liquid clusters have been shown to be prevalent in solution close to the upper limit of this concentration range at high pH [Demicheliset al., 2011]. The C20−20 system

was set up for this purpose. In this system, no bicarbonate ions were included, as carbonates lead to a more stable, long-lived cluster, and so simulations in the absence of bicarbonate should overestimate the equilibrium sizes and lifetimes of any dense liquid clusters. Furthermore, as the formation of a dense liquid phase is diffusion limited, simulations initiated where there is a high local concentration of ions should allow an equilibrium to be established relatively quickly.

While a low density cluster was sampled for the current study, this had been optimised in vacuum (see Chapter 3), and so the coordination of ions was relatively large compared with those suggested for dense liquid clusters [Demicheliset al., 2011; Wallace et al., 2013]. The cluster was therefore relaxed at 20 mM for 15 ns. After this period, the coordination probabilities showed (see Figure E.3) a preference for Ca–2C binding, along with coordination of calcium to three and four anions. Partial dissociation was observed with a small cluster (2 CaCO₃) dissolving into solution. The largest cluster contained 36 ions, for which a snapshot is provided in Figure E.3. Subsequently, water was removed from the final configuration to produce systems with concentrations 20-51 mM. A short 300 ps simulation was performed to relax water with ion coordinates frozen. This was taken to bet= 0, from which 27–50 ns simulations, with all atoms mobile, were performed.

The mass weighted average cluster size,S, was calculated: S =P

sWs/PWs where sand Ws are the number of atoms and weight fraction of clusters, and the sum is over all clusters in each configuration. The time dependence of lnS as a function of concentration is presented in Figure 6.5 (a). It is clear from the plot that S decreases exponentially with time at all concentrations. The simulations did not reach an equilibrium by the end of up to 50 ns simulations, and further dissolution of associates is likely to be observed in longer simulations. The general trends in the data show that as the concentration increased, the dissolution rate for clusters decreased. Dissolution at [C]=30 mM was observed to deviate from the general trend. It was observed that for this simulation, there was a retention of rel- atively high probability of calcium binding to three anions late into the trajectory. Dissolution rates are readily calculated from the slope of the semi–log plots, giving

(a)

(b)

Figure 6.5: Simulations of system C20−₂₀ at [C]=20, 30, 40 and 51 mM. (a) ln(S)

as a function of time; the data has been shifted for clarity as follows, ln(S)₋1, ln(S), ln(S) + 2, ln(S) + 3 for [C]=20, 30, 40 and 51 mM, respectively. (b) The average cluster size in units of number of atoms, and average largest cluster size in units of number of ions, for all concentrations studied for system C20−20 by the end

values shown in Table 6.4.

Table 6.4: Dissolution rates measured as ln(S)/t(see Figure 6.5 (a)), of a 20 CaCO₃ cluster at varying concentrations.

[C]/mM ln(S)/t/ns−1

20 0.100±0.010 30 0.032±0.003 40 0.056±0.004 51 0.029±0.004

Average and maximum cluster sizes at the end of simulation are shown in Figure 6.5 (b). At 20 and 40 mM these values are, within statistical uncertainties, consistent with ion pairs. Larger clusters are seen at 30 and 51 mM, though we note that from the ln(S(t)) plots that dissolution is still in progress at this stage, and so these are overestimates of the equilibrium cluster sizes. It is important to note that all of these concentrations are higher than experimental ones, which are typically performed at 10 mM. While extrapolation to this concentration is not possible, due to the fact that simulations did not fully equilibrate, it is highly likely that ion pairs and small ion associates would also be found in solution at this value. It is sensible to conclude that even in the limit of high pH, dense liquids are unlikely to exist at experimental concentrations.

Closer inspection of theS(t) curves shows a strong stochastic element to the dissolution process, and this was seen most clearly at 20 mM. To investigate this further, Figure 6.6 (a) providesS as a function of time, and is extended (compared with Figure 6.5 (a)) to include early dissolution. This shows a sudden and rapid decrease of S between 5–15 ns, superimposed on a slower but consistent decrease through the rest of the simulation. This change in rate can be explained by consid- ering coordination probabilities; Figure 6.6 (b) shows the carbon to calcium binding probabilities as a function of time during the simulation. Around 10 ns, the prob- ability of calcium coordinating to three anions decreased, and this was associated with an increase of calcium binding to a single anion. Conceptually, this is a change from a relatively compact cluster (where calcium binds to three and four carbons), to a system where there is predominantly ion pairs, and small ion associates in so- lution.Visual observation of the cluster at this stage showed the cluster “opening” to maximise ion solvation.

The cluster size distributions over the final 6 ns of simulation are provided in Figure 6.6 (c). At the end of the trajectory clusters continued to decrease in size and, ideally, further simulation would provide information on the extent to

(a) (b)

(c) _(d)

Figure 6.6: 42 ns simulation of 20 CaCO₃ in water at a concentration of 20 mM. (a): Average cluster size as a function of time; (b): average coordination probabilities of calcium toN carbons over time; (c): cluster size probability distributions calculated in 2 ns windows from the final 6 ns of simulation; and (d), a snapshot (with oxygen and hydrogen omitted) from the final 2 ns of simulation. Calcium is shown in yellow while carbonate and bicarbonate ion centres are shown in purple and blue. Green lines show coordinating ions where the distance between calcium and carbon is<3.825 ˚A.

which equilibrium had been achieved. Ion pairs dominated in solution showed by the peak atN = 5; however, contrary to simulations at moderately basic pH, peaks are observed atN _≈15. This suggests clusters reached a maximum size of around three formula units, in fact the average size of the largest cluster during the final 2 ns of simulation was measured as 5.5_±0.8 ions. From the calculated composition probabilities of associated species, ion pairs were most common (P = 0.63), followed by binding of two calcium and carbonate ions (P = 0.21). The probability of finding three calcium and three carbonate ions in a cluster was 0.05. The concentration of these species is likely to be much lower at equilibrium and a concentration of 10 mM. A snapshot in Figure 6.6 (d) shows the types of clusters which were found after 40 ns of simulation.

At the highest concentration, 51 mM, a large cluster was found at the end of the simulation (see Figure E.4 (b)). This was formed of 16 ions, with an average coordination of two between ion centres, and can be considered DLNP. The extent to which this cluster will further dissolve is unknown, as the system was still relatively far from equilibrium by 52 ns of simulation. The cluster size distribution provided in Figure E.4 (a) from the end of simulation shows a large concentration of ion pairs and a smaller concentration of larger associates. Analysis of the cluster compositions showed that 81% of associates were ion pairs, 9% were ion trimers and the remaining 10% were larger clusters.