104
E. O. Fetisov et al.
namic conventions when describing nucleation processes, and care is needed to avoid
misinterpretations. We hope that the current, more extensive, contribution will clarify
the interpretation and reduce the chance for any further confusion.
2 Methods
2.1 Construction of a Molecular-Based Potential Model
The need to construct a reduced potential model for the initial stages of nucleation of
CaCO 3 is at least partially predicated on the fact that it would require a million water
molecules to study 100 ion-pairs at the experimentally relevant supersaturations, e.g.,
concentration of 5 mM. One of the challenges in constructing a reduced model is to
retain an appropriate amount of molecular detail to be predictive while reducing the
computational complexity to perform converged simulations at experimentally relevant conditions. Another motivating factor in choosing a reduced interaction model
between the Ca
2+ and CO
2−
3 ions is the evidence from experiment and simulation
where the initial stages of nucleation involve hydrated ACC. Thus, one may reasonably treat the water molecules implicitly. To this end, we utilize the intrinsic potential
of mean force (PMF) of ion pairing in solution as our primary tool for creating a
reduced model for the initial stages of CaCO 3 nucleation. We emphasize that the
use of intrinsic is meant to convey that this PMF corresponds to infinite dilution;
i.e., it does not include many-body ion–ion interactions beyond the ion pair. To the
extent that this can be realized in an actual simulation relies on the efficiency of the
interaction potential. For the purposes of this study, we utilize both empirical and
quantum mechanical interaction potentials and choose to construct our PMFs of ion
pairing utilizing a single ion pair and about 100 water molecules. As alluded to above,
we use the intrinsic PMF to capture the important highly correlated, water-mediated
short-range interactions between ions.
The concept of using the intrinsic ion–ion PMF as the fundamental interaction
to effectively reproduce collective properties of a solution at finite concentrations
has been recently investigated [20]. An important ingredient for any model will be
the need to accurately capture some of the clustering free energetics as reflected in
the measured concentration-dependent osmotic coefficients. To this end, we have
demonstrated that indeed, the two-body PMF for ion pairing is able to capture collective effects as determined by the osmotic coefficients for NaCl salt up to 1 M [20].
This is an indication that the solvent-mediated ion-pairing effects are well reproduced and that the ion–water correlation, embedded at the mean field level in the
PMF, dominates at low to moderate electrolyte concentrations. This provides a proof
of concept that a coarse-graining approach using the ion–ion PMF as the fundamental interaction provides a good starting point to construct a theory of clustering and
provides insights into the initial stages of nucleation.
E. O. Fetisov et al.
namic conventions when describing nucleation processes, and care is needed to avoid
misinterpretations. We hope that the current, more extensive, contribution will clarify
the interpretation and reduce the chance for any further confusion.
2 Methods
2.1 Construction of a Molecular-Based Potential Model
The need to construct a reduced potential model for the initial stages of nucleation of
CaCO 3 is at least partially predicated on the fact that it would require a million water
molecules to study 100 ion-pairs at the experimentally relevant supersaturations, e.g.,
concentration of 5 mM. One of the challenges in constructing a reduced model is to
retain an appropriate amount of molecular detail to be predictive while reducing the
computational complexity to perform converged simulations at experimentally relevant conditions. Another motivating factor in choosing a reduced interaction model
between the Ca
2+ and CO
2−
3 ions is the evidence from experiment and simulation
where the initial stages of nucleation involve hydrated ACC. Thus, one may reasonably treat the water molecules implicitly. To this end, we utilize the intrinsic potential
of mean force (PMF) of ion pairing in solution as our primary tool for creating a
reduced model for the initial stages of CaCO 3 nucleation. We emphasize that the
use of intrinsic is meant to convey that this PMF corresponds to infinite dilution;
i.e., it does not include many-body ion–ion interactions beyond the ion pair. To the
extent that this can be realized in an actual simulation relies on the efficiency of the
interaction potential. For the purposes of this study, we utilize both empirical and
quantum mechanical interaction potentials and choose to construct our PMFs of ion
pairing utilizing a single ion pair and about 100 water molecules. As alluded to above,
we use the intrinsic PMF to capture the important highly correlated, water-mediated
short-range interactions between ions.
The concept of using the intrinsic ion–ion PMF as the fundamental interaction
to effectively reproduce collective properties of a solution at finite concentrations
has been recently investigated [20]. An important ingredient for any model will be
the need to accurately capture some of the clustering free energetics as reflected in
the measured concentration-dependent osmotic coefficients. To this end, we have
demonstrated that indeed, the two-body PMF for ion pairing is able to capture collective effects as determined by the osmotic coefficients for NaCl salt up to 1 M [20].
This is an indication that the solvent-mediated ion-pairing effects are well reproduced and that the ion–water correlation, embedded at the mean field level in the
PMF, dominates at low to moderate electrolyte concentrations. This provides a proof
of concept that a coarse-graining approach using the ion–ion PMF as the fundamental interaction provides a good starting point to construct a theory of clustering and
provides insights into the initial stages of nucleation.