118
E. O. Fetisov et al.
continuum approach (capillarity approximation, spherical cluster assumption, etc.),
provides several qualitative features describing activated first-order phase transformations. For example, (1) CNT allows for the existence of pre-nucleation clusters
in sub-saturated solutions, and (2) CNT shows that, as the concentration of ions is
increased, the cluster size distribution also shifts to larger clusters making their detection more probable. We agree with Gebauer et al. concluding statement “we would
like to point out that CNT does remain useful for describing and predicting nucleation
processes, including calcium carbonate, given adequate parametrization. In fact, it is
the only quantitative framework currently at hand, but it should be emphasized that
the molecular picture of CNT is merely a conceptual notion.” In this work, we have
used atomistic simulation and statistical mechanics to provide just such a molecular view of amorphous calcium carbonate clustering and how these results can be
successfully viewed through the lens of CNT. Since CNT allows for pre-nucleation
clusters to exist, there is no reason to discard CNT. Pre-nucleation clusters undoubtedly exist for hydrogen fluoride [7, 8] and ion-induced vapor-to-liquid nucleation
[5, 6] and also for solutions of alcohols in non-polar solvents [9–11] and electrolytes
at high concentrations [14, 27, 45]. In fact, pre-nucleation clusters are entirely consistent with a proper interpretation of CNT (e.g., see Smeets et al. [4]), and hence,
there is no need, as of yet, to require “non-classical” views on nucleation.
Acknowledgements During the review process, we became aware of the recent work of Gebauer
et al. [19]. We have thus added a paragraph in our finalized article addressing their critique of the
original work by Henzler et al. [18]. The authors would like to thank Jim De Yoreo and Ben Legg for
helpful discussions. PMF and MM simulations were performed at the Pacific Northwest National
Laboratory (PNNL) with support from the U.S. Department of Energy (DOE), Office of Science,
Office of Basic Energy Sciences (BES), Division of Material Sciences and Engineering. The solution
model and theoretical developments were supported by the DOE, Office of Science, BES, Division
of Chemical Sciences, Geosciences, and Biosciences. DFT simulations were performed within the
Materials Synthesis and Simulation Across Scales (MS 3 ) Initiative through the Laboratory Research
and Development Program at PNNL. The PMF calculations used resources of the National Energy
Research Scientific Computing Center, a DOE Office of Science User Facility supported by the DOE,
Office of Science under contract no. DE-AC02-05CH11231. AVBMC simulations used resources
of the Minnesota Supercomputing Institute and were supported through an award from the NSF
(CHE-1265849). PNNL is a multiprogram national laboratory operated for the DOE by Battelle
under contract no. DE-AC05-76RL01830.
5 Appendix
The following development is a generalization of the thermodynamics of clusters
to the case of two components. The one component case was established by Reiss
and Bowles [44]. This serves to define our thermodynamic references and make
a formal connection between molecular statistical mechanics and thermodynamics. We write expressions without internal molecular degrees of freedom for simplicity. Further generalization is straightforward. The (i 1 , i 2 ) component partition
function is defined as q (i 1 ,i 2 ) =
1
i 1 !i 2 !
γ
i 1
1 γ
i 2
2
dr
(i1)
1 dr
(i2)
2 e
−βU
, with the ideal gas par-
E. O. Fetisov et al.
continuum approach (capillarity approximation, spherical cluster assumption, etc.),
provides several qualitative features describing activated first-order phase transformations. For example, (1) CNT allows for the existence of pre-nucleation clusters
in sub-saturated solutions, and (2) CNT shows that, as the concentration of ions is
increased, the cluster size distribution also shifts to larger clusters making their detection more probable. We agree with Gebauer et al. concluding statement “we would
like to point out that CNT does remain useful for describing and predicting nucleation
processes, including calcium carbonate, given adequate parametrization. In fact, it is
the only quantitative framework currently at hand, but it should be emphasized that
the molecular picture of CNT is merely a conceptual notion.” In this work, we have
used atomistic simulation and statistical mechanics to provide just such a molecular view of amorphous calcium carbonate clustering and how these results can be
successfully viewed through the lens of CNT. Since CNT allows for pre-nucleation
clusters to exist, there is no reason to discard CNT. Pre-nucleation clusters undoubtedly exist for hydrogen fluoride [7, 8] and ion-induced vapor-to-liquid nucleation
[5, 6] and also for solutions of alcohols in non-polar solvents [9–11] and electrolytes
at high concentrations [14, 27, 45]. In fact, pre-nucleation clusters are entirely consistent with a proper interpretation of CNT (e.g., see Smeets et al. [4]), and hence,
there is no need, as of yet, to require “non-classical” views on nucleation.
Acknowledgements During the review process, we became aware of the recent work of Gebauer
et al. [19]. We have thus added a paragraph in our finalized article addressing their critique of the
original work by Henzler et al. [18]. The authors would like to thank Jim De Yoreo and Ben Legg for
helpful discussions. PMF and MM simulations were performed at the Pacific Northwest National
Laboratory (PNNL) with support from the U.S. Department of Energy (DOE), Office of Science,
Office of Basic Energy Sciences (BES), Division of Material Sciences and Engineering. The solution
model and theoretical developments were supported by the DOE, Office of Science, BES, Division
of Chemical Sciences, Geosciences, and Biosciences. DFT simulations were performed within the
Materials Synthesis and Simulation Across Scales (MS 3 ) Initiative through the Laboratory Research
and Development Program at PNNL. The PMF calculations used resources of the National Energy
Research Scientific Computing Center, a DOE Office of Science User Facility supported by the DOE,
Office of Science under contract no. DE-AC02-05CH11231. AVBMC simulations used resources
of the Minnesota Supercomputing Institute and were supported through an award from the NSF
(CHE-1265849). PNNL is a multiprogram national laboratory operated for the DOE by Battelle
under contract no. DE-AC05-76RL01830.
5 Appendix
The following development is a generalization of the thermodynamics of clusters
to the case of two components. The one component case was established by Reiss
and Bowles [44]. This serves to define our thermodynamic references and make
a formal connection between molecular statistical mechanics and thermodynamics. We write expressions without internal molecular degrees of freedom for simplicity. Further generalization is straightforward. The (i 1 , i 2 ) component partition
function is defined as q (i 1 ,i 2 ) =
1
i 1 !i 2 !
γ
i 1
1 γ
i 2
2
dr
(i1)
1 dr
(i2)
2 e
−βU
, with the ideal gas par-