120
E. O. Fetisov et al.
microscopic statistical mechanics (cluster populations) and macroscopic thermodynamics (Gibbs free energies):
N
EQ
(i 1 ,i 2 ) = e
−βG (i 1 ,i 2 ) (γ TOT V )
N (1,0)
γ 1 V
i 1
N (0,1)
γ 2 V
i 2
.
(16)
References
1. Anwar J, Zahn D (2011) Uncovering molecular processes in crystal nucleation and growth by
using molecular simulation. Angew Chem Int Ed 50:1996–2013
2. Kathmann SM, Schenter GK, Garrett BC, Chen B, Siepmann JI (2009) Thermodynamics and
kinetics of nanoclusters controlling gas-to-particle nucleation. J Phys Chem C 113:10354–
10370
3. Gebauer D, Kellermeier M, Gale JD, Bergström L, Cölfen H (2014) Pre-nucleation clusters as
solute precursors in crystallisation. Chem Soc Rev 43:2348–2371
4. Smeets PJM, Finney AR, Habraken WJEM, Nudelman F, Friedrich H, Laven J, De Yoreo JJ,
Rodger PM, Sommerdijk NAJM (2017) A classical view on nonclassical nucleation. Proc Natl
Acad Sci 114:E7882–E7890
5. Keasler SJ, Kim H, Chen B (2012) Sign preference in ion-induced nucleation: Contributions
to the free energy barrier. J Chem Phys 137:174308
6. Oh K, Gao G, Zeng X (2001) Nucleation of water and methanol droplets on cations and anions:
the sign preference. Phys Rev Lett 86:5080–5083
7. Chen B, Siepmann JI (2000) A novel Monte Carlo algorithm for simulating strongly associating
fluids: applications to water, hydrogen fluoride, and acetic acid. J Phys Chem B 104:8725–8734
8. McGrath MJ, Ghogomu JN, Mundy CJ, Kuo IFW, Siepmann JI (2010) First principles Monte
Carlo simulations of aggregation in the vapor phase of hydrogen fluoride. Phys Chem Chem
Phys 12:7678–7687
9. Harwood DB, Peters CJ, Siepmann JI (2016) A Monte Carlo simulation study of the liquidliquid equilibria for binary dodecane/ethanol and ternary dodecane/ethanol/water mixtures.
Fluid Phase Equil 407:269–279
10. Stubbs JM, Siepmann JI (2002) Aggregation in dilute solutions of 1-hexanol in n-hexane: a
Monte Carlo simulation study. J Phys Chem B 106:3968–3978
11. Stubbs JM, Siepmann JI (2004) Binary phase behavior and aggregation of dilute methanol in
supercritical carbon dioxide: a Monte Carlo simulation study. J Chem Phys 121:1525–1534
12. Demichelis R, Raiteri P, Gale JD, Quigley D, Gebauer D (2011) Stable prenucleation mineral
clusters are liquid-like ionic polymers. Nat Commun 2:590
13. Gebauer D, Völkel A, Cölfen H (2008) Stable prenucleation calcium carbonate clusters. Science
322:1819–1822
14. Jiang H, Debenedetti PG, Panagiotopoulos AZ (2019) Nucleation in aqueous NaCl solutions
shifts from 1-step to 2-step mechanism on crossing the spinodal. J Chem Phys 150:124502
15. Bots P, Benning LG, Rodriguez-Blanco JD, Roncal-Herrero T, Shaw S (2012) Mechanistic
insights into the crystallization of amorphous calcium carbonate (ACC). Cryst Growth Des
12:3806–3814
16. Nielsen MH, Aloni S, De Yoreo JJ (2014) In situ TEM imaging of CaCO 3 nucleation reveals
coexistence of direct and indirect pathways. Science 345:1158–1162
17. Rodriguez-Blanco JD, Shaw S, Benning LG (2011) The kinetics and mechanisms of amorphous
calcium carbonate (ACC) crystallization to calcite, via vaterite. Nanoscale 3:265–271
18. Henzler K, Fetisov EO, Galib M, Baer MD, Legg BA, Borca C, Xto JM, Pin S, Fulton JL, Schenter GK, Govind N, Siepmann JI, Mundy CJ, Huthwelker T, De Yoreo JJ (2018) Supersaturated
calcium carbonate solutions are classical. Sci Adv 4:eaao6283
E. O. Fetisov et al.
microscopic statistical mechanics (cluster populations) and macroscopic thermodynamics (Gibbs free energies):
N
EQ
(i 1 ,i 2 ) = e
−βG (i 1 ,i 2 ) (γ TOT V )
N (1,0)
γ 1 V
i 1
N (0,1)
γ 2 V
i 2
.
(16)
References
1. Anwar J, Zahn D (2011) Uncovering molecular processes in crystal nucleation and growth by
using molecular simulation. Angew Chem Int Ed 50:1996–2013
2. Kathmann SM, Schenter GK, Garrett BC, Chen B, Siepmann JI (2009) Thermodynamics and
kinetics of nanoclusters controlling gas-to-particle nucleation. J Phys Chem C 113:10354–
10370
3. Gebauer D, Kellermeier M, Gale JD, Bergström L, Cölfen H (2014) Pre-nucleation clusters as
solute precursors in crystallisation. Chem Soc Rev 43:2348–2371
4. Smeets PJM, Finney AR, Habraken WJEM, Nudelman F, Friedrich H, Laven J, De Yoreo JJ,
Rodger PM, Sommerdijk NAJM (2017) A classical view on nonclassical nucleation. Proc Natl
Acad Sci 114:E7882–E7890
5. Keasler SJ, Kim H, Chen B (2012) Sign preference in ion-induced nucleation: Contributions
to the free energy barrier. J Chem Phys 137:174308
6. Oh K, Gao G, Zeng X (2001) Nucleation of water and methanol droplets on cations and anions:
the sign preference. Phys Rev Lett 86:5080–5083
7. Chen B, Siepmann JI (2000) A novel Monte Carlo algorithm for simulating strongly associating
fluids: applications to water, hydrogen fluoride, and acetic acid. J Phys Chem B 104:8725–8734
8. McGrath MJ, Ghogomu JN, Mundy CJ, Kuo IFW, Siepmann JI (2010) First principles Monte
Carlo simulations of aggregation in the vapor phase of hydrogen fluoride. Phys Chem Chem
Phys 12:7678–7687
9. Harwood DB, Peters CJ, Siepmann JI (2016) A Monte Carlo simulation study of the liquidliquid equilibria for binary dodecane/ethanol and ternary dodecane/ethanol/water mixtures.
Fluid Phase Equil 407:269–279
10. Stubbs JM, Siepmann JI (2002) Aggregation in dilute solutions of 1-hexanol in n-hexane: a
Monte Carlo simulation study. J Phys Chem B 106:3968–3978
11. Stubbs JM, Siepmann JI (2004) Binary phase behavior and aggregation of dilute methanol in
supercritical carbon dioxide: a Monte Carlo simulation study. J Chem Phys 121:1525–1534
12. Demichelis R, Raiteri P, Gale JD, Quigley D, Gebauer D (2011) Stable prenucleation mineral
clusters are liquid-like ionic polymers. Nat Commun 2:590
13. Gebauer D, Völkel A, Cölfen H (2008) Stable prenucleation calcium carbonate clusters. Science
322:1819–1822
14. Jiang H, Debenedetti PG, Panagiotopoulos AZ (2019) Nucleation in aqueous NaCl solutions
shifts from 1-step to 2-step mechanism on crossing the spinodal. J Chem Phys 150:124502
15. Bots P, Benning LG, Rodriguez-Blanco JD, Roncal-Herrero T, Shaw S (2012) Mechanistic
insights into the crystallization of amorphous calcium carbonate (ACC). Cryst Growth Des
12:3806–3814
16. Nielsen MH, Aloni S, De Yoreo JJ (2014) In situ TEM imaging of CaCO 3 nucleation reveals
coexistence of direct and indirect pathways. Science 345:1158–1162
17. Rodriguez-Blanco JD, Shaw S, Benning LG (2011) The kinetics and mechanisms of amorphous
calcium carbonate (ACC) crystallization to calcite, via vaterite. Nanoscale 3:265–271
18. Henzler K, Fetisov EO, Galib M, Baer MD, Legg BA, Borca C, Xto JM, Pin S, Fulton JL, Schenter GK, Govind N, Siepmann JI, Mundy CJ, Huthwelker T, De Yoreo JJ (2018) Supersaturated
calcium carbonate solutions are classical. Sci Adv 4:eaao6283