The Statistical Mechanics of Solution-Phase Nucleation …
103
[12, 13]. Moreover, in order to sample any clusters, some simulations of solutionphase nucleation are performed at such high supersaturations that one may find no
barrier to nucleation [12]. This situation should be considered as something akin to
supersaturation-assisted spinodal decomposition—a case where the interfacial surface energy is misinterpreted to be zero by increasing the driving force so much that
there seems to be no barrier. Jiang et al. recently carried out large-scale simulations
for NaCl solutions and found that the nucleation mechanism is qualitatively altered
as the spinodal is crossed [14].
Recent transmission electron microscopy (TEM) as well as synchrotron X-ray
diffraction and small- and wide-angle scattering measurements (WAXS) revealed
that nucleation of CaCO 3 from supersaturated solutions occurred via the following
stages: (1) transformation into the hydrated amorphous calcium carbonate (ACC)
polymorph that (2) dehydrates concurrent with local ordering to transform into the
vaterite polymorph, and then (3) into the calcite polymorph [15–17]. The “structure”
of ACC remains an open question as no Bragg peaks were observed in its WAXS
signal and only a broad diffuse background was observed caused by scattering from
ACC and the aqueous solution. Gebauer et al. employed titration measurements
using a special electrode [13] to characterize the Ca
2+ activity. These measurements
revealed that the Ca
2+ activity of supersaturated CaCO 3 solutions was far less than
the added CaCl 2 leading to the conclusion that a large amount of Ca
2+ was tied up
in bound species. The size and composition of the bound species were thought to be
large nm-sized clusters as determined by sedimentation coefficients and supported by
contrast fluctuations of early cryo-TEM images of supersaturated CaCO 3 solutions.
A few years later, molecular dynamics (MD) simulations performed using empirical interaction potentials at unphysically large supersaturations of CaCO 3 produced
numerical evidence of prenucleation clusters (PNCs) [12]. Thus, as discussed in the
preceding paragraph, the titration and MD results support the so-called non-classical
picture of nucleation. However, re-analysis of the interpretation of the titration data
found that the presence of PNCs is not needed to explain the measured trends. Furthermore, recent experiments by Henzler et al. [18] using supersaturated solutions
of CaCO 3 found no detectable X-ray signals corresponding to any PNCs larger than
the ion pair.
Here, we will expand on the theoretical and simulation work presented by Henzler et al. [18], where the purported findings of PNCs were revisited using a solution
model of CaCO 3 derived from the quantum mechanical potential of mean force for
ion pairing between Ca
2+ and CO
2−
3 in aqueous solution. This work provided a comprehensive simulation, theory, and experimental study that was able to predict the
experimental titration curves of Gebauer et al. [13] in addition to providing new experimental evidence based on state-of-the-art use of X-rays. Theoretical and simulation
details are presented here for an audience of practitioners in solution thermodynamics, simulation, and statistical mechanics and will provide a fundamental theoretical
framework to study the initial stages of nucleation of a variety of electrolyte systems.
We would also like to note that, recently, Gebauer et al. published a perspective [19],
in which the conclusions reached by Henzler et al. [18] had been labeled as void.
Unfortunately, Gebauer et al. [19] and Henzler et al. [18] use different thermody-
103
[12, 13]. Moreover, in order to sample any clusters, some simulations of solutionphase nucleation are performed at such high supersaturations that one may find no
barrier to nucleation [12]. This situation should be considered as something akin to
supersaturation-assisted spinodal decomposition—a case where the interfacial surface energy is misinterpreted to be zero by increasing the driving force so much that
there seems to be no barrier. Jiang et al. recently carried out large-scale simulations
for NaCl solutions and found that the nucleation mechanism is qualitatively altered
as the spinodal is crossed [14].
Recent transmission electron microscopy (TEM) as well as synchrotron X-ray
diffraction and small- and wide-angle scattering measurements (WAXS) revealed
that nucleation of CaCO 3 from supersaturated solutions occurred via the following
stages: (1) transformation into the hydrated amorphous calcium carbonate (ACC)
polymorph that (2) dehydrates concurrent with local ordering to transform into the
vaterite polymorph, and then (3) into the calcite polymorph [15–17]. The “structure”
of ACC remains an open question as no Bragg peaks were observed in its WAXS
signal and only a broad diffuse background was observed caused by scattering from
ACC and the aqueous solution. Gebauer et al. employed titration measurements
using a special electrode [13] to characterize the Ca
2+ activity. These measurements
revealed that the Ca
2+ activity of supersaturated CaCO 3 solutions was far less than
the added CaCl 2 leading to the conclusion that a large amount of Ca
2+ was tied up
in bound species. The size and composition of the bound species were thought to be
large nm-sized clusters as determined by sedimentation coefficients and supported by
contrast fluctuations of early cryo-TEM images of supersaturated CaCO 3 solutions.
A few years later, molecular dynamics (MD) simulations performed using empirical interaction potentials at unphysically large supersaturations of CaCO 3 produced
numerical evidence of prenucleation clusters (PNCs) [12]. Thus, as discussed in the
preceding paragraph, the titration and MD results support the so-called non-classical
picture of nucleation. However, re-analysis of the interpretation of the titration data
found that the presence of PNCs is not needed to explain the measured trends. Furthermore, recent experiments by Henzler et al. [18] using supersaturated solutions
of CaCO 3 found no detectable X-ray signals corresponding to any PNCs larger than
the ion pair.
Here, we will expand on the theoretical and simulation work presented by Henzler et al. [18], where the purported findings of PNCs were revisited using a solution
model of CaCO 3 derived from the quantum mechanical potential of mean force for
ion pairing between Ca
2+ and CO
2−
3 in aqueous solution. This work provided a comprehensive simulation, theory, and experimental study that was able to predict the
experimental titration curves of Gebauer et al. [13] in addition to providing new experimental evidence based on state-of-the-art use of X-rays. Theoretical and simulation
details are presented here for an audience of practitioners in solution thermodynamics, simulation, and statistical mechanics and will provide a fundamental theoretical
framework to study the initial stages of nucleation of a variety of electrolyte systems.
We would also like to note that, recently, Gebauer et al. published a perspective [19],
in which the conclusions reached by Henzler et al. [18] had been labeled as void.
Unfortunately, Gebauer et al. [19] and Henzler et al. [18] use different thermody-