What Controls the Limit of Supercooling and Superheating of Pinned

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

What Controls the Limit of Supercooling and Superheating of Pinned Ice Surfaces? Pavithra Madhavi Naullage, Yuqing Qiu, and Valeria Molinero J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b00300 • Publication Date (Web): 15 Mar 2018 Downloaded from http://pubs.acs.org on March 15, 2018

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Organisms that thrive in sub-cooling conditions produce antifreeze proteins and glycoproteins that halt the growth and recrystallization of ice,1-5 enabling them to prevent cold-induced damage.3-4 The adsorption-inhibition model is widely used to explain the action of antifreeze proteins.2, 6 This model poses that the proteins bind irreversibly to ice,2 arresting the growth of the crystal at supercooled conditions by forcing the creation of a metastable curved ice surface.7 Despite extensive studies on ice growth and recrystallization by antifreeze molecules,6, 8-12 it remains elusive13 whether and how does the curvature of the ice surface at a given degree of supercooling depend on properties of the ice-binding molecules. Ice-binding proteins possess the unique ability to both lower the freezing point (freezing hysteresis)14 and raise the melting point (melting hysteresis)15-17 of ice, giving rise to a temperature gap between freezing and melting known as thermal hysteresis (TH).18 The melting and freezing hystereses correspond to the maximum superheating and supercooling that can be attained before, respectively, ice melts completely or grows irreversibly over the ice-pinning molecules. The same phenomenon is observed in the presence of molecules that inhibit Ostwald ripening recrystallization of ice by preventing the growth of larger crystals at the expense of the melting of smaller ones.19 Experiments indicate that both thermal hysteresis and ice recrystallization inhibition (IRI) are molecule-specific properties. For example, antifreeze glycoproteins display high IRI activity, but only possess moderate or weak TH activity.1, 20-21 Polyvinyl alcohol (PVA), a synthetic macromolecule, is an excellent agent for ice recrystallization inhibition, but produces little thermal hysteresis.22 Recent studies have shown that antifreeze proteins assembled on dendritic architectures exhibit enhanced thermal hysteresis and ice recrystallization inhibition activities.23. Moreover, for a given ice binding molecule and concentration, the melting hysteresis is generally found to be smaller than the freezing hysteresis.8, 15 These results raise the question of what properties of the ice binding molecules control the ice recrystallization inhibition and freezing and melting hystereses. Figure 1 shows a scheme of the Ostwald ripening process of ice recrystallization and the role of ice-binding molecules on stopping it. The ratio of area to volume for particles of different sizes modulates their thermodynamic stability. An ice particle of radius Rp is in thermodynamic equilibrium with the liquid when the free energies of both phases are equal, which is described by the GibbsThomson relation: Tm(Rp) = Tmbulk – !E K/Rp,

!

(1)


2

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model27 and model ice binding molecules28-30 to elucidate, first, how does the curvature of the ice front depend on the degree of supercooling and distance between pinned molecules, and, second, what determines the thermal hysteresis on melting and freezing, i.e. the maximum curvature that can be attained before, respectively, ice melts completely or grows irreversibly over the pinned molecules. We start by solving a thermodynamic model to predict the angle # of the metastable curved ice surface as a function of the distance d between the pinning molecules and the degree of supercooling !T = Tm(Rp) – T, where Tm(Rp) is well-approximated by Tmbulk if the ice particle is large. The model is identical for supercooling and superheating; the only difference is that for the latter !T = T - Tm(Rp) and the ripples are concave. The free energy of formation of a single ripple at the ice surface has three contributions: a favorable one arising from its volume Vr, an unfavorable one due to the creation of a curved surface of area Ar, and a contribution due to the three-phase line lIBM-ice-water between the icebinding molecule, ice and water: !G = !µ Vr/v + "sl (Ar – Aflat) + $lIBM-ice-water

(2)

where v is the molar volume of ice, "sl is the surface tension of the ice-liquid interface (which in principle could depend – albeit weakly – on the ice plane,31 but here is taken as an average, see Supp. Info. D), Aflat is the area of the flat surface replaced by the ripple, and $ and lIBM-ice-water are the line tension and length of the three-phase IBM-ice-water interface. !µ = µs"µl is difference in chemical potential between ice and liquid, which for low supercooling is well approximated by !µ = " !Hm !T /Tm, where !Hm is the enthalpy of melting. The line tension term is the only contribution to the free energy of the curved surface that accounts for properties specific to the ice-binding molecule. The line tension $ may depend on the specific orientation and chemistry of the ice-binding molecule; however, it is generally very small, on the order of a pN.32-35 Moroever, as the length lIBM-ice-water of the ice-liquid-IBM contact line is independent of the curvature of the surface, the line tension contribution in eq. 2 should be identical for all metastable states. Therefore, although the line tension could change the relative stability of the metastable curved surface with respect to the all-ice (or all-liquid) stable state, it cannot change the position (i.e. surface curvature) of the free energy minima predicted by minimization of eq. 2. The macroscopic thermodynamics approach on which eq. 2 has been shown to be valid for water particles as small as 1 nm;36 hence it should also be valid for the treatment of curved ice surfaces with molecules at distances larger than 1 nm. We note that the larger the distance d between the ice binding molecules, the more accurate should be the use of macroscopic thermodynamics and the !


4

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approximation of neglecting the contribution of the line tension to the free energy. In what follows we assume the validity of macroscopic thermodynamics and neglect the line tension contribution and then use molecular simulations to assess the validity of these approximations. We first solve the free energy of the model of eq. 2, neglecting the line tension, for a cylindrical cap geometry, has been observed in simulations of ice pinned by an antifreeze protein37 and in experiments38 of ice pinned by PVA. Replacing the area of a cylindrical cap, Ar = volume, Vr =

! ! !!!!!!!"#!!! !!"# !! !

!!!! !! ! !"# !

, and its

, we express the free energy of formation of the cylindrical ripple per

unit of length L, as a function of the angle #, supercooling or superheating !T and distance d between pinning molecules: !! !!!!!! !

!!

! ! !!!!!!!"#!!! !!! !!! !!"# !! !

!!!!

!!

!!!! ! !"#$ !

! !!!!" .

(3)

Figure 2a shows the free energy of a single isolated ripple as a function of local surface curvature for ripples pinned by molecules at a fixed distance d and two values of supercooling !T. The free energy curves have two minima separated by a barrier. The most stable state, at # = -90o corresponds to all ice in supercooled systems or all liquid in superheated ones. The metastable states correspond to stationary curved ice surfaces. The contact angle # of the metastable curved surface shifts to lower values, i.e. larger curvatures as shown in Figure 1, on increasing supercooling or superheating. The evolution of the curvature of a metastable ice ripple with the degree of supercooling or superheating is obtained from the condition!!!!!!!"!!!!! != 0. This results in a Gibbs-Thomson type of relation between the degree of supercooling or superheating and the curvature of the metastable crystal surface in the presence of pinning molecules: !! ! ! !!

!!" !!! !! !!!

!"#$!! ! !! !!!!"#$!!,

(4)

where !P = 2 for cylindrical cap ripples and !P = 4 for spherical cap ripples. Cylindrical and spherical caps are two limiting cases of the more generic case of ellipsoidal caps, for which we expect !P to range between 2 and 4, depending on the ratio of the axes of the ellipsoid. Note that the values of !P in eq. 4 are different from those for !E in eq. 1. This is because not only the geometries of ice are subtly different (spheres or cylinders of radii R in eq. 1 and spherical caps or cylindrical caps with constant base d and variable radii R in eq. 4) but, most significantly, because eq. 1 is the solution for phase

!


5



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Figure 3. PVA prevents the growth of ice through the Gibbs Thomson effect. (a) Snapshot of the simulation box showing the separation between the bound PVA molecules, each with DP 20. Ice lattice is represented with silver sticks, bound OH groups with red balls, unbound OH groups with blue balls and the carbon backbone in green sticks (b) Snapshot of the side view of the curved ice front showing the contact angle # = 38!!!! o of the surface curvature for !T = 10 K. Hydroxyl groups that are bound to ice is shown in red balls. We refer the reader to ref. 28 for a detailed discussion of the mechanism of binding of PVA to ice. Superheating of ice has been reported in the presence of ice-binding molecules.16-17 Consistently, we find that ice pinned by PVA as shown in Figure 3a can be superheated to 279 K. At that temperature, the crystal partially melts to produce a concave surface pinned by the IBMs (Supporting Figure S2), with an average depth of 2.5!!!0.3 Å at the middle distance between the PVA molecules. This corresponds to # = 79!!!3o, in excellent agreement with the # = 77!!!2o predicted by eq. 4 for !T = 6 K and d = 5 nm (Figure 2b). To our knowledge, this is the first validation with molecular simulations of a thermodynamic model of metastable growth or melting of a pinned crystal surface. The concentration of ice-binding molecules in solution and their binding free energy to ice determine the distribution of distances between them on the ice surface. We find that, for a given set of distances between IBMs, the curvature of the ice surface at a given degree of supercooling or superheating is a thermodynamic property independent of the nature of the ice-binding molecules. In what follows we focus on understanding what determines the maximum superheating and supercooling that can be achieved before ice irreversibly melts or grows, respectively. That is, what determines the melting and freezing hystereses. Figure 4 shows that ice grows irreversibly, within a few nanoseconds, in the simulations at 11 K supercooling when the crystal surface is pinned by PVA molecules in the same configurations shown in Figure 3. The irreversible growth of ice starts with the nucleation of crystal bridges that connect neighboring ice ripples. Through the process of ice growth, PVA is engulfed by the ice but never detaches from the surface. Likewise, irreversible melting of the pinned ice crystal occurs after 3 ns in the simulations when the temperature is raised to 6 K above the equilibrium melting point. In that case, liquid bridges nucleate between PVA and ice, detaching the molecule from the crystal. As the molecule unbinds, the ice melts, propagating the phase transition. The detachment of PVA always starts with a terminal OH group and proceeds by a backward zipper mechanism (Supporting Figure S3). The simulations predict that the melting hysteresis is smaller than the freezing hysteresis, consistent with experimental results.17

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when # = 30 !!2o. For the binding geometry of Figure 4, bridging of the gap between ripples is akin to the nucleation event of capillary condensation,70-71 albeit in a wedge made by the stable phase. The thermal hysteresis is controlled by the kinetics of nucleation, which we find to be sensitive to the arrangement of the IBMs on the ice surface. In the simulations discussed above, the separation between PVA molecules in the direction parallel to their axis is very small, ~1 nm, making it impossible for ice to grow between that gap. To investigate how does the existence of comparable distances between ice-binding molecules in the two directions impact the thermal hysteresis, we prepare a simulation cell with shorter PVA molecules (degree of polymerization 9) aligned as in Figure 3a, but leaving 5 nm gaps in the directions parallel and perpendicular to their main axes. This pinning geometry leads to a curved ice surface, shown in Supporting Figure S4, that allows for growth of ice between the IBMs in the two directions. On cooling, the ice grows increasingly tall surrounding PVA. Irreversible crystallization occurs when the ice surface closes over the ice-binding molecule, as shown in Supporting Figure S5. The freezing hysteresis of this surface, 4 K, is much smaller than the 10 K for the arrangement of PVA in Figure 3, despite having ripples that are intermediate between cylindrical and spherical (or “stones on a pillow”2 geometry), which would according to eq. 4 result in lower curvature for a given degree of supercooling. We interpret that ice grows faster at even lower curvature for the surface with significant gaps between IBMs in the two directions because shorter ice bridges are needed to advance the engulfment of a molecule surrounded by ice in all directions. The kinetics of nucleation depends on the observation time scales, which are ~9 orders of magnitude different in experiments and our molecular simulations. To assess the effect of observation time scales on the kinetics of freezing, we compute the freezing hysteresis of the antifreeze protein of Tenebrio molitor, TmAFP in simulations and compare it with the experimental results of Drori et al.13 The experiments indicate that when the average distance between centers of mass of TmAFP is d = 7 nm, the freezing hysteresis is !T $ 0.73 K.13 Here we use the recently developed united atom protein model of ref. 29, which is compatible with the mW water model, to perform simulations of TmAFP bound to ice in a square lattice configuration with d = 5 nm in the two directions from the boundary of the protein (Figure 5a). That configuration has average distance d = 7.4 nm from the centers of the proteins, closely matching the average distance in the experiment.13 We find that the ice surface is stable up to 100 ns at 9 K supercooling but overgrows the protein quickly when the temperature is decreased 1 K further, as shown in Figure 5. The freezing hysteresis in the simulations is an order of magnitude larger than in the experiment. One possible origin of the discrepancy is the existence of a distribution

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We find that the size and interactions of the ice-binding molecule have a significant impact on the thermal hysteresis. This is already evident in the distinct values of freezing hysteresis we determine for ice pinned with TmAFP or PVA separated by exactly the same distances, 10 K and 4 K, and in agreement with the poorer antifreeze activity of PVA compared to antifreeze proteins.13,

22, 45

The

irreversible growth of ice on supercooling occurs through formation of an ice bridge long enough to connect adjacent ripples just above the height of the IBM. For IBMs separating cylindrical ripples, the length Dbridge,min of the shortest ice bridge over the IBM is always larger than Dbridge, min = 2 (hIBM+%water) tan# + wIBM,

(5)

where # is the contact angle of the ice surface, and hIBM and wIBM the length and width of the IBM (Supporting Figure S6), %water = 0.35 nm is the size of a water molecule (that together with hIBM determines the height at which the shorter ice bridge can form). According to eq. 5, the size of the IBM is a key parameter in determining its freezing hysteresis. The wider and taller the IBM, the longer the bridge needed to nucleate the ice overgrowth at a given supercooling (i.e. a given #). PVA is a very narrow molecule, with hIBM $ wIBM $ 0.7 nm, which would result in Dbridge,min = 2.0 nm for # = 33o (we measure 1.9 nm in the simulations of Figure 4). The small width and height of PVA explains why it has a very poor freezing hysteresis for the large distances d between PVA in experiments,38 while bulkier ice-binding molecules, such as TmAFP, require longer bridging distances for a given curvature of the surface and produce larger freezing hysteresis.23 To systematically investigate the relationship between bulkiness of the ice-binding molecule and their freezing and melting hystereses, we prepare IBMs that are cutouts of monolayers of linear alcohols (MLA) with n = 4, 8 and 12 carbons in the alcohol chains. Each of these model IBMs contain seven alcohol molecules, arranged in a triangular lattice (filled hexagon) 0.8 nm in diameter. The length of the hydrocarbon chain modulates the height of the IBM: 0.5 nm for n = 4, 1 nm for n = 8, and 1.5 nm for n = 12. For comparison, the MLA IBM with n = 12 has the same height as TmAFP. We set the distances between the OH heads of the alcohols to match exactly those in the basal plane of ice, and the water-OH interaction strength to be 10% higher than for water-water interactions (Supp. Info. B). This results in surfaces that bind strongly to ice.29 The MLA IBMs are bound to ice in a rectangular pattern, separated by distances 4.2 and 4.9 nm (4.6 and 5.3 nm if measured from the center of the IBMs) in the two Cartesian directions, as shown in Supporting Figure S1. Supporting Movie S1 shows the process of engulfment of the IBMs by ice after reaching the limit of supercooling: ice grows around

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the IBMs until a fluctuation allows ice to reach the top of an IBM and bridge over its height, followed by the cooperative propagation of ice over all other IBMs. Table 1 shows that the freezing hysteresis increases with the height of the ice-binding molecule, consistent with what is expected from eq. 5. The bulkier the IBMs, the lower the probability of ice bridging over them, and the larger the freezing hysteresis. Likewise, the wider the IBM, the larger is the barrier for their engulfment, as can be seen in the lower freezing hysteresis of ice pinned with equally tall MLA IBM with n = 12 and TmAFP at comparable distances, 6 and 10 K in the simulations. These results indicate that the height and width of the IBM are important parameters in the control of the maximum curvature that can be sustained by the ice surface. Our analysis suggests that size of the IBM is an important factor in determining the exceptionally high antifreeze activity achieved with dendritic assemblies of antifreeze proteins,23 and the poor freezing hysteresis of PVA, a skinny molecule with a narrow footprint at the ice surface.22, 45 We note that ice recrystallization inhibitors must prevent the growth and melting of particles that initially are of comparable sizes, i.e. that have small difference in equilibrium melting temperatures. This illuminates why, even though both the melting and freezing hysteresis of PVA are small, they are sufficient to prevent the recrystallization of micron sized ice particles, making PVA a potent ice recrystallization inhibitor.

Table 1. The Freezing Hysteresis and Melting Hysteresis for Model IBMs with Different Chain Lengths. (%wo/%wo = 1.1) Chain length, n

hIBM (nm)

THfreezing (K)

THmelting (K)H

4

0.5

4

5

8

1.0

5

5

12

1.5

6

5

The irreversible melting of superheated ice depends on the formation of liquid bridges underneath the IBMs. As the IBMs sit on the ice surface, their protrusion inside the ice phase does not depend on the height of the molecule. This suggests that, different from the freezing hysteresis, the melting hysteresis should not depend on the overall height of the IBM. Indeed, Table 1 shows that to

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be the case for the MLA IBMs with same binding strength and footprint at the ice surface, but different height. In general, we expect the freezing hysteresis to be sensitive to the height and width of the IBM (as shown above) and the melting hysteresis to be mostly sensitive to the width, as it controls the barrier for unbinding the molecule from ice. Note that the melting hysteresis is larger than the freezing hysteresis for the shortest MLA IBM (n = 4). This indicates that, for this particular IBM, the barriers involved on detaching the strongly bound molecule from ice are higher than the cost of bridging ice over it. This anomaly may arise from the perfect matching to ice and strong water-OH interaction of the model MLA IBMs. To assess the effect of the strength of binding to ice on the thermal hysteresis, we compute the thermal hysteresis of the MLA IBM with n = 8 with strength of water-OH 90% and 80% of the initial value. This scaling of the interactions decreases the free energies of binding between the extended monolayer and ice to 74% and 46% of initial value, respectively (Supp. Table S1). We find that the IBMs with the weaker interactions cannot sustain the growth of ice; the molecules detach from the surface despite their favorable binding free energy. For the IBM with strength of water-OH interaction reduced to 90%, we find that both TH and MH decrease by 1 K of the initial value in Table 1. These results suggest that a strong binding to ice, not merely a favorable one, is key for the antifreeze activity of ice-binding molecules. In summary, we derive the Gibbs-Thomson relation between the curvature # of a metastable pinned surface, the degree of supercooling or superheating !T and the distance d between the pinning molecules. We find that the line tension of the liquid-crystal-pinning molecule interface does not impact the equilibrium curvature because its contribution is independent of #. The thermodynamic model quantitatively predicts the curvature of ice in molecular simulations of ice pinned by PVA at both supercooled and superheated temperatures. Different from the equilibrium curvature, the maximum curvature that the metastable surface can attain before irreversibly growing or melting is a nonequilibrium property that strongly depends on the size of the ice-binding molecules. Our results indicate that the asymmetry between freezing and melting hystereses found in experiments arises from the unequal ability of antifreeze proteins to protrude inside the ice and liquid phases, which results in smaller barriers to nucleate the liquid phase for a given degree of curvature of the ice surface. The conclusions presented here for superheating and supercooling of ice should be valid for any combination of pinned metastable surface. Classical nucleation theory could be used to predict the rate of formation of the bridges of the stable phase that engulf the pinning molecule and lead to the

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irreversible growth or melting of the stable phase. We expect the analysis of this work to be valuable for understanding the structural features that bestow on antifreeze proteins their exceptional melting and freezing hysteresis and for the design of synthetic ice binding molecules72 with potent thermal hysteresis and ice recrystallization activities.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website. This includes a movie that shows the irreversible growth of ice over ice-binding molecules and a pdf document that details the simulation settings, models, systems, and analysis. Supporting Table S1 shows the evolution of ice-binding strength as a function of interactions of ice-binding molecule with water, Supporting Figure S1 the initial configuration of ice-binding molecules on ice, Supporting Figure S2 the concave ice surface pinned by PVA at superheating conditions, Supporting Figure S3 the detachment of PVA from ice just above the limit of superheating, Supporting Figures S4 and S5 the evolution of the ice surface pinned by PVA molecules two degrees of supercooling, and Supporting Figure S6 a scheme of the geometry considered in deriving equation 5.

Acknowledgements. We gratefully acknowledge Yamila A. Perez Sirkin for help with the contact angle calculations and Ido Braslavsky for stimulating discussions. This work was supported by the National Science Foundation through award CHE-1305427 “Center for Aerosol Impacts on Climate and the Environment”. We thank the Center for High Performance Computing at the University of Utah for technical support and a grant of computer time.

References 1. DeVries, A. L.; Wohlschlag, D. E., Freezing Resistance in Some Antarctic Fishes. Science 1969, 163, 1073-1075. 2. Raymond, J. A.; DeVries, A. L., Adsorption Inhibition as a Mechanism of Freezing Resistance in Polar Fishes. Proc. Natl. Acad. Sci. 1977, 74, 2589-2593. 3. Knight, C.; Driggers, E.; DeVries, A., Adsorption to Ice of Fish Antifreeze Glycopeptides 7 and 8. Biophys. J. 1993, 64, 252-259. !


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4. Knight, C. A.; Cheng, C. C.; DeVries, A. L., Adsorption of Alpha-Helical Antifreeze Peptides on Specific Ice Crystal Surface Planes. Biophys. J. 1991, 59, 409-418. 5. Shtukenberg, A. G.; Ward, M. D.; Kahr, B., Crystal Growth with Macromolecular Additives. Chem Rev 2017, 117, 14042-14090. 6. Yeh, Y.; Feeney, R. E., Antifreeze Proteins:! Structures and Mechanisms of Function. Chem. Rev. 1996, 96, 601-618. 7.

Wilson, P., Explaining Thermal Hysteresis by the Kelvin Effect. Cryo Letters 1993, 14, 31–36.

8. Voets, I. K., From Ice-Binding Proteins to Bio-Inspired Antifreeze Materials. Soft Matter 2017, 13, 4808-4823. 9. Gilbert, J. A.; Davies, P. L.; Laybourn-Parry, J., A Hyperactive, Ca2+!Dependent Antifreeze Protein in an Antarctic Bacterium. FEMS Microbiol. Lett. 2005, 245, 67-72. 10. Duman, J. G.; Olsen, T. M., Thermal Hysteresis Protein Activity in Bacteria, Fungi, and Phylogenetically Diverse Plants. Cryobiology 1993, 30, 322-328. 11. Wu, D. W.; Duman, J. G.; Xu, L., Enhancement of Insect Antifreeze Protein Activity by Antibodies. Biochim. Biophys. Acta, Protein Struct. Mol. Enzymol. 1991, 1076, 416-420. 12. Sidebottom, C.; Buckley, S.; Pudney, P.; Twigg, S.; Jarman, C.; Holt, C.; Telford, J.; McArthur, A.; Worrall, D.; Hubbard, R., Phytochemistry: Heat-Stable Antifreeze Protein from Grass. Nature 2000, 406, 256. 13. Drori, R.; Davies, P. L.; Braslavsky, I., Experimental Correlation between Thermal Hysteresis Activity and the Distance between Antifreeze Proteins on an Ice Surface. RSC Adv. 2015, 5, 7848-7853. 14. Tyshenko, M. G.; Doucet, D.; Davies, P. L.; Walker, V. K., The Antifreeze Potential of the Spruce Budworm Thermal Hysteresis Protein. Nat. Biotechnol. 1997, 15, 887-890. 15. Celik, Y.; Graham, L. A.; Mok, Y.-F.; Bar, M.; Davies, P. L.; Braslavsky, I., Superheating of Ice Crystals in Antifreeze Protein Solutions. Proc. Natl. Acad. Sci. 2010, 107, 5423-5428. 16. Knight, C.; DeVries, A., Melting Inhibition and Superheating of Ice by an Antifreeze Glycopeptide. Science 1989, 245, 505-507. 17. Celik, Y.; Graham, L. A.; Mok, Y.-F.; Bar, M.; Davies, P. L.; Braslavsky, I., Superheating of Ice Crystals in Antifreeze Protein Solutions. Proc. Natl. Acad. Sci. 2010, 107, 5423-5428. 18. Davies, P. L., Ice-Binding Proteins: A Remarkable Diversity of Structures for Stopping and Starting Ice Growth. Trends Biochem. Sci. 2014, 39, 548-555. 19. Knight, C. A.; Wen, D.; Laursen, R. A., Nonequilibrium Antifreeze Peptides and the Recrystallization of Ice. Cryobiology 1995, 32, 23-34.

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20. Olijve, L. L.; Meister, K.; DeVries, A. L.; Duman, J. G.; Guo, S.; Bakker, H. J.; Voets, I. K., Blocking Rapid Ice Crystal Growth through Nonbasal Plane Adsorption of Antifreeze Proteins. Proc. Natl. Acad. Sci. 2016, 113, 3740-3745. 21. Budke, C.; Dreyer, A.; Jaeger, J.; Gimpel, K.; Berkemeier, T.; Bonin, A. S.; Nagel, L.; Plattner, C.; DeVries, A. L.; Sewald, N., Quantitative Efficacy Classification of Ice Recrystallization Inhibition Agents. Cryst. Growth Des. 2014, 14, 4285-4294. 22. Inada, T.; Lu, S.-S., Thermal Hysteresis Caused by Non-Equilibrium Antifreeze Activity of Poly(Vinyl Alcohol). Chem. Phys. Lett. 2004, 394, 361-365. 23. Phippen, S. W.; Stevens, C. A.; Vance, T. D.; King, N. P.; Baker, D.; Davies, P. L., Multivalent Display of Antifreeze Proteins by Fusion to Self-Assembling Protein Cages Enhances Ice-Binding Activities. Biochemistry 2016, 55, 6811-6820. 24. Petrov, O. V.; Furó, I., A Joint Use of Melting and Freezing Data in Nmr Cryoporometry. Microporous Mesoporous Mater. 2010, 136, 83-91. 25. Petrov, O.; Furó, I., Curvature-Dependent Metastability of the Solid Phase and the FreezingMelting Hysteresis in Pores. Phys. Rev. E 2006, 73, 011608. 26. Congdon, T.; Notman, R.; Gibson, M. I., Antifreeze (Glyco)Protein Mimetic Behavior of Poly(Vinyl Alcohol): Detailed Structure Ice Recrystallization Inhibition Activity Study. Biomacromolecules 2013, 14, 1578-1586. 27. Molinero, V.; Moore, E. B., Water Modeled as an Intermediate Element between Carbon and Silicon. J. Phys. Chem. B 2009, 113, 4008-4016. 28. Naullage, P. M.; Lupi, L.; Molinero, V., Molecular Recognition of Ice by Fully Flexible Molecules. J. Phys. Chem. C 2017, 121, 26949-26957. 29. Qiu, Y.; Odendahl, N.; Hudait, A.; Mason, R.; Bertram, A. K.; Paesani, F.; DeMott, P. J.; Molinero, V., Ice Nucleation Efficiency of Hydroxylated Organic Surfaces Is Controlled by Their Structural Fluctuations and Mismatch to Ice. J. Am. Chem. Soc. 2017, 139, 3052-3064. 30. Hudait, A.; Odendahl, N.; Qiu, Y.; Paesani, F.; Molinero, V., Ice Nucleating and Antifreeze Proteins Recognize Ice through a Diversity of Anchored Clathrate and Ice-Like Motifs. J. Am. Chem. Soc. 2018, under review. 31. Espinosa, J. R.; Vega, C.; Sanz, E., Ice–Water Interfacial Free Energy for the Tip4p, Tip4p/2005, Tip4p/Ice, and Mw Models as Obtained from the Mold Integration Technique. J. Phys. Chem. C 2016, 120, 8068-8075. 32. Qiu, Y.; Molinero, V., Morphology of Liquid–Liquid Phase Separated Aerosols. J. Am. Chem. Soc. 2015, 137, 10642-10651. 33. Lupi, L.; Kastelowitz, N.; Molinero, V., Vapor Deposition of Water on Graphitic Surfaces: Formation of Amorphous Ice, Bilayer Ice, Ice I, and Liquid Water. J Chem Phys 2014, 141, 18C508.

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Page 18 of 20

34. Factorovich, M. H.; Molinero, V.; Scherlis, D. A., Hydrogen-Bond Heterogeneity Boosts Hydrophobicity of Solid Interfaces. J Am Chem Soc 2015, 137, 10618-10623. 35. Qiu, Y.; Lupi, L.; Molinero, V., Is Water at the Graphite Interface Vapor-Like or Ice-Like? J. Phys. Chem. B 2018. 36. Factorovich, M. H.; Molinero, V.; Scherlis, D. A., Vapor Pressure of Water Nanodroplets. J. Am. Chem. Soc. 2014, 136, 4508-4514. 37. Kuiper, M. J.; Morton, C. J.; Abraham, S. E.; Gray-Weale, A., The Biological Function of an Insect Antifreeze Protein Simulated by Molecular Dynamics. Elife 2015, 4, e05142. 38. Lu, S.-S.; Inada, T.; Yabe, A.; Zhang, X.; Grandum, S., Microscale Study of Poly (Vinyl Alcohol) as an Effective Additive for Inhibiting Recrystallization in Ice Slurries. Int. J. Refrig. 2002, 25, 562-568. 39. Findenegg, G. H.; Jähnert, S.; Akcakayiran, D.; Schreiber, A., Freezing and Melting of Water Confined in Silica Nanopores. ChemPhysChem 2008, 9, 2651-2659. 40. Schreiber, A.; Ketelsen, I.; Findenegg, G. H., Melting and Freezing of Water in Ordered Mesoporous Silica Materials. Phys. Chem. Chem. Phys. 2001, 3, 1185-1195. 41. Moore, E. B.; Allen, J. T.; Molinero, V., Liquid-Ice Coexistence Below the Melting Temperature for Water Confined in Hydrophilic and Hydrophobic Nanopores. J. Phys. Chem. C 2012, 116, 75077514. 42. Moore, E. B.; De La Llave, E.; Welke, K.; Scherlis, D. A.; Molinero, V., Freezing, Melting and Structure of Ice in a Hydrophilic Nanopore. Phys. Chem. Chem. Phys. 2010, 12, 4124-4134. 43. Johnston, J. C.; Molinero, V., Crystallization, Melting, and Structure of Water Nanoparticles at Atmospherically Relevant Temperatures. J. Am. Chem. Soc. 2012, 134, 6650-6659. 44. Gibson, M. I., Slowing the Growth of Ice with Synthetic Macromolecules: Beyond Antifreeze(Glyco) Proteins. Polym. Chem. 2010, 1, 1141-1152. 45. Budke, C.; Koop, T., Ice Recrystallization Inhibition and Molecular Recognition of Ice Faces by Poly(Vinyl Alcohol). ChemPhysChem 2006, 7, 2601-2606. 46. Weng, L.; Stott, S. L.; Toner, M., Molecular Dynamics at the Interface between Ice and Poly (Vinyl Alcohol) and Ice Recrystallization Inhibition. Langmuir 2017. 47. Moore, E. B.; Molinero, V., Growing Correlation Length in Supercooled Water. J. Chem. Phys. 2009, 130, 244505. 48. Moore, E. B.; Molinero, V., Is It Cubic? Ice Crystallization from Deeply Supercooled Water. Phys. Chem. Chem. Phys. 2011, 13, 20008-20016. 49. Nguyen, A. H.; Jacobson, L. C.; Molinero, V., Structure of the Clathrate/Solution Interface and Mechanism of Cross-Nucleation of Clathrate Hydrates. J. Phys. Chem. C 2012, 116, 19828-19838.

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Page 19 of 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50. Lu, J.; Qiu, Y.; Baron, R.; Molinero, V., Coarse-Graining of Tip4p/2005, Tip4p-Ew, Spc/E, and Tip3p to Monatomic Anisotropic Water Models Using Relative Entropy Minimization. J. Chem. Theory Comput. 2014, 10, 4104-4120. 51. Moore, E. B.; Molinero, V., Structural Transformation in Supercooled Water Controls the Crystallization Rate of Ice. Nature 2011, 479, 506-8. 52. Jacobson, L. C.; Kirby, R. M.; Molinero, V., How Short Is Too Short for the Interactions of a Water Potential? Exploring the Parameter Space of a Coarse-Grained Water Model Using Uncertainty Quantification. J Phys Chem B 2014, 118, 8190-8202. 53. Lu, J.; Chakravarty, C.; Molinero, V., Relationship between the Line of Density Anomaly and the Lines of Melting, Crystallization, Cavitation, and Liquid Spinodal in Coarse-Grained Water Models. J Chem Phys 2016, 144, 234507. 54. Factorovich, M. H.; Molinero, V.; Scherlis, D. A., Vapor Pressure of Water Nanodroplets. J Am Chem Soc 2014, 136, 4508-4514. 55. Perez Sirkin, Y. A.; Factorovich, M. H.; Molinero, V.; Scherlis, D. A., Vapor Pressure of Aqueous Solutions of Electrolytes Reproduced with Coarse-Grained Models without Electrostatics. J Chem Theory Comput 2016, 12, 2942-2949. 56. Hudait, A.; Qiu, S.; Lupi, L.; Molinero, V., Free Energy Contributions and Structural Characterization of Stacking Disordered Ices. Phys. Chem. Chem. Phys. 2016, 18, 9544-9553. 57. Jacobson, L. C.; Molinero, V., A Methane"Water Model for Coarse-Grained Simulations of Solutions and Clathrate Hydrates. J. Phys. Chem. B 2010, 114, 7302-7311. 58. Nguyen, A. H.; Koc, M. A.; Shepherd, T. D.; Molinero, V., Structure of the Ice–Clathrate Interface. J. Phys. Chem. C 2015, 119, 4104-4117. 59. Shepherd, T. D.; Koc, M. A.; Molinero, V., The Quasi-Liquid Layer of Ice under Conditions of Methane Clathrate Formation. J. Phys. Chem. C 2012, 116, 12172-12180. 60. Lupi, L.; Hanscam, R.; Qiu, Y.; Molinero, V., Reaction Coordinate for Ice Crystallization on a Soft Surface. J. Phys. Chem. Lett. 2017, 8, 4201-4205. 61. Lupi, L.; Kastelowitz, N.; Molinero, V., Vapor Deposition of Water on Graphitic Surfaces: Formation of Amorphous Ice, Bilayer Ice, Ice I, and Liquid Water. J. Chem. Phys. 2014, 141, 18C508. 62. Lupi, L.; Molinero, V., Does Hydrophilicity of Carbon Particles Improve Their Ice Nucleation Ability? J. Phys. Chem. A 2014, 118, 7330-7337. 63. Lupi, L.; Hudait, A.; Peters, B.; Grünwald, M.; Mullen, R. G.; Nguyen, A. H.; Molinero, V., Role of Stacking Disorder in Ice Nucleation. Nature 2017, in press, DOI 10.1038/nature24279. 64. Lupi, L.; Hudait, A.; Molinero, V., Heterogeneous Nucleation of Ice on Carbon Surfaces. J. Am. Chem. Soc. 2014, 136, 3156-3164.

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Page 20 of 20

65. Jacobson, L. C.; Hujo, W.; Molinero, V., Thermodynamic Stability and Growth of Guest-Free Clathrate Hydrates: A Low-Density Crystal Phase of Water. J Phys Chem B 2009, 113, 10298-10307. 66. Jacobson, L. C.; Hujo, W.; Molinero, V., Amorphous Precursors in the Nucleation of Clathrate Hydrates. J Am Chem Soc 2010, 132, 11806-11811. 67. Moore, E. B.; Molinero, V., Structural Transformation in Supercooled Water Controls the Crystallization Rate of Ice. Nature 2011, 479, 506-508. 68. Jacobson, L. C.; Kirby, R. M.; Molinero, V., How Short Is Too Short for the Interactions of a Water Potential? Exploring the Parameter Space of a Coarse-Grained Water Model Using Uncertainty Quantification. J. Phys. Chem. B 2014, 118, 8190-8202. 69. Mochizuki, K.; Qiu, Y.; Molinero, V., Promotion of Homogeneous Ice Nucleation by Soluble Molecules. J. Am. Chem. Soc. 2017, 139, 17003-17006. 70. Factorovich, M. H.; González Solveyra, E.; Molinero, V.; Scherlis, D. A., Sorption Isotherms of Water in Nanopores: Relationship between Hydropohobicity, Adsorption Pressure, and Hysteresis. J Phys Chem C 2014, 118, 16290-16300. 71. de la Llave, E.; Molinero, V.; Scherlis, D. A., Water Filling of Hydrophilic Nanopores. J Chem Phys 2010, 133, 034513. 72. Biggs, C. I.; Bailey, T. L.; Stubbs, C.; Fayter, A.; Gibson, M. I., Polymer Mimics of Biomacromolecular Antifreezes. Nat. Commun. 2017, 8, 1546.

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