Heterogeneous Nucleation Mechanism of Potassium Iodide on Graphene Surface in Water

: In this work, molecular dynamic (MD) simulations are applied to investigate the heterogeneous nucleation mechanism of KI on a graphene surface in water. As graphene is immersed in water, it mainly affects the structure of interfacial water (the topmost water layer at the interface between the substance and water). To maximize the hydrogen bonding of water, the dissolved solutes tend to accumulate to form the aggregate at the graphene surface, which undoubtedly affects the nucleation pathways of solutes in water. In comparison with homogeneous nucleation, a lower barrier may be expected during the heterogeneous nucleation of KI on a graphene surface in water. Therefore, as the graphene is immersed in water, this facilitates solute nucleation. From this work, it may be derived that heterogeneous nucleation may be closely related to the geometric characteristics of foreign surfaces, especially their geometric shape


Introduction
The nucleation of crystals from a solution is a ubiquitous process that plays important roles in physics, chemistry, engineering, and material science.In general, nucleation processes can be classed as homogeneous and heterogeneous [1].In fact, nucleation in liquids occurs heterogeneously more often than not.In heterogeneous nucleation, the surfaces of some different substances act as the center upon which the first atoms, ions, or molecules of the crystal become properly oriented.Therefore, it is crucial to understand the fundamentals of heterogeneous nucleation in order to achieve control over these properties.
Nucleation is generally described using the classical nucleation theory (CNT).For heterogeneous nucleation, it is customarily formulated within the CNT framework in terms of geometric arguments, ∆G Heterogene ous = ∆G Homogeneou s • f (θ), where f (θ) is the shape factor changing from zero to one [2].This is based on Young's equation related to the interfacial tension between a crystal and a liquid, a crystal and a foreign solid surface, or a liquid and a foreign surface.Building upon the works of Volmer [3] and Fletcher [4], nucleation is easiest on a concave surface and most difficult on a convex surface, while nucleation on a planar surface is always in between [5].
Recently, many works [6][7][8][9][10][11][12] have been conducted to investigate the thermodynamics and kinetics of crystal nucleation in solutions.Different from the classical crystallization pathways in aqueous solutions, the intermediate phases appear in solutions before nucleation, such as amorphous calcium carbonate (ACC) [11,12].Additionally, to explain an intermediate phase in the nonclassical nucleation pathway, various views have been proposed, such as the two-step mechanism of nucleation of crystals in a solution [13][14][15].This means that amorphous nuclei are first formed, and an amorphous-to-crystalline transition takes place in the middle of the amorphous phase.
In Kiselev et al.'s study [16], surface defects, such as steps, cracks, and cavities, are thought to be responsible for the high ice nucleation efficacy of potassium (K) feldspar particles.This was also found in Friddle and Thürmer's work [17]; this means that ice rapidly spreads along the steps of a feldspar surface.According to Pach and Verdaguer's study [18] on the ice nucleation on feldspar particles, nucleation is dominated by natural microsized pores exposed at the surface of the mineral upon cleavage.In Bi et al.'s MD calculations [23] on ice nucleation on graphene, compared with planar surfaces, concave wedges may promote ice nucleation due to their special geometry.
In this work, MD simulations are utilized to investigate the heterogeneous nucleation of KI on graphene surfaces in aqueous solutions.The simulation details are described in the Methods section.In the Results and Discussion section, the focuses are the effects of graphene surfaces on the dissolved behaviors of KI in water and the heterogeneous nucleation mechanism of KI in aqueous solutions.The conclusions are given in the last section.

Methods
MD simulations are carried out using the GROMACS (version 5.14) [24,25] package.A simple point charge/extended (SPC/E) model was used for the water molecules.The nonpolarizable force field developed by Horinek et al. [26] was utilized to model the ions.In fact, the ion force fields were parameterized in conjunction with the SPC/E water model to reproduce the first peaks in the ion-water radial distribution functions (RDF), as well as ion solvation-free energies and entropies [26].Furthermore, the OPLSAA force field was used to simulate the interactions between carbon atoms in graphene.
To simulate the heterogeneous nucleation of KI crystal in water, two graphene sheets were embedded into saturated KI solutions.To understand the dependence of the dissolved behaviors of KI salts on the ion concentrations, various systems are simulated (Table 1).Additionally, MD simulations were also conducted on pure KI solutions (Table 1), which are utilized as references to evaluate the effects of graphene surfaces on the structure of KI solutions.The simulations were carried out using NVT.The simulated temperature was kept at 300 K, employing Nose-Hoover thermostat dynamics.The simulated box was kept at 41.75 Å × 38.28 Å × 50.53 Å.The sheets were fixed in the simulations.Additionally, periodic boundary conditions were applied in all three directions.The Lennard-Jones interactions were truncated at 1.0 nm.The particle mesh Ewald method was used to calculate the long-range electrostatics forces.Additionally, each simulation time was 100 ns, with a time step of 2 fs.
The simulated results were analyzed using PLUMED (version 2.4) [27,28].To distinguish the crystalline configurations from the solutions, LQ4 order parameters were Crystals 2024, 14, 208 3 of 14 calculated and utilized to measure the degree of order during the nucleation of KI in the systems.Additionally, the metadynamics method [29,30] of Laio and Parrinello was utilized to reconstruct the free energy landscape as a function of the order parameters (Supplementary Materials).

Ion Distribution around Surface
As KI salts are dissolved into water, they dissociate into the hydrated ions.Based on the calculated RDFs, it was found that the KI RDFs have a first contact maximum at 3.05 Å (CIPs, contact ion pairs), a second solvent-separated maximum at 5.15 Å (SSIPs, solvent-separated ion pairs), and a weak third maximum at about 7.15 Å, corresponding to the attraction of fully hydrated ions.With increasing KI concentrations, this leads to a rise in the first maximum and a fall in the second KI RDFs (Figure 1).This means that the dissolved K + and I − ions tend to form CIPs rather than SSIPs.Similar observations were also found in other studies [31][32][33][34] on the structure of NaCl and LiCl solutions in the absence of such a surface.The simulated results were analyzed using PLUMED (version 2.4) [27,28].To distinguish the crystalline configurations from the solutions, LQ4 order parameters were calculated and utilized to measure the degree of order during the nucleation of KI in the systems.Additionally, the metadynamics method [29,30] of Laio and Parrinello was utilized to reconstruct the free energy landscape as a function of the order parameters (Supplementary Materials).

Ion Distribution around Surface
As KI salts are dissolved into water, they dissociate into the hydrated ions.Based on the calculated RDFs, it was found that the KI RDFs have a first contact maximum at 3.05 Å (CIPs, contact ion pairs), a second solvent-separated maximum at 5.15 Å (SSIPs, solvent-separated ion pairs), and a weak third maximum at about 7.15 Å, corresponding to the attraction of fully hydrated ions.With increasing KI concentrations, this leads to a rise in the first maximum and a fall in the second KI RDFs (Figure 1).This means that the dissolved K + and I − ions tend to form CIPs rather than SSIPs.Similar observations were also found in other studies [31][32][33][34] on the structure of NaCl and LiCl solutions in the absence of such a surface.Additionally, more KI salts decrease the separations between the K + and I − ions (Figure 1).This can also be found in the gI-I(r) and gK-K(r) of the KI solutions, especially for the second peaks (Figure 2).Therefore, the dissolved ions are not uniformly distributed in the solutions and tend to accumulate in water.This has also been found in other studies on NaCl and LiCl solutions [35,36].Additionally, more KI salts decrease the separations between the K + and I − ions (Figure 1).This can also be found in the g I-I (r) and g K-K (r) of the KI solutions, especially for the second peaks (Figure 2).Therefore, the dissolved ions are not uniformly distributed in the solutions and tend to accumulate in water.This has also been found in other studies on NaCl and LiCl solutions [35,36].
Based on the MD simulations, the increase in KI concentrations may lead to I − and K + ions aggregating in water.In our recent work [36] on the structure of NaCl solutions, this is termed as an aggregate.According to the calculated g KI (r), the ion is engaged with the aggregate when the distance between K + and I − is less than 5.05 Å, with no water molecules between them (Figure 3).Similar concepts have also been proposed to reflect solute aggregation, such as ACC or prenucleation clusters (PNCs) [37,38].
In the MD simulations, the ion pair was found not only in the high-KI-concentration solution but also in the low-KI-concentration solution.However, with increasing KI concentrations, more ion pairs in water appear (Figure 3).This has been demonstrated through experimental measurements [39,40].Additionally, as the graphene sheets are immersed into the solutions, the number of ion pairs is higher than that in pure KI solutions (Figure 3).In addition, in the graphene-KI-H 2 O system (KI:H 2 O = 50:2100), the maximum KI aggregate size is five.However, the maximum aggregate size in the pure KI solutions (KI:H 2 O = 50:2099) is four.These findings may be related to the effects of graphene sheets on the dissolved behaviors of KI in water.Based on the MD simulations, the increase in KI concentrations may lead to I − and K + ions aggregating in water.In our recent work [36] on the structure of NaCl solutions, this is termed as an aggregate.According to the calculated gKI(r), the ion is engaged with the aggregate when the distance between K + and I − is less than 5.05 Å, with no water molecules between them (Figure 3).Similar concepts have also been proposed to reflect solute aggregation, such as ACC or prenucleation clusters (PNCs) [37,38].In the MD simulations, the ion pair was found not only in the high-KI-concentration solution but also in the low-KI-concentration solution.However, with increasing KI concentrations, more ion pairs in water appear (Figure 3).This has been demonstrated through experimental measurements [39,40].Additionally, as the graphene sheets are  Based on the MD simulations, the increase in KI concentrations may lead to I − and K + ions aggregating in water.In our recent work [36] on the structure of NaCl solutions, this is termed as an aggregate.According to the calculated gKI(r), the ion is engaged with the aggregate when the distance between K + and I − is less than 5.05 Å, with no water molecules between them (Figure 3).Similar concepts have also been proposed to reflect solute aggregation, such as ACC or prenucleation clusters (PNCs) [37,38].In the MD simulations, the ion pair was found not only in the high-KI-concentration solution but also in the low-KI-concentration solution.However, with increasing KI concentrations, more ion pairs in water appear (Figure 3).This has been demonstrated through experimental measurements [39,40].Additionally, as the graphene sheets are Generally, the Gibbs dividing surface (GDS) is utilized to distinguish the liquid-vapor interface (Supplementary Materials).From the MD simulations, the ion densities relative to the GDS can be determined (Figure 4).Both the cations and anions form a dense layer on the graphene surface, i.e., an apparent ionic double layer near the surface.This is in agreement with Dočkal et al. [41] and Chen et al.'s [42] simulations on graphene-aqueous solution interfaces.Additionally, compared with potassium ions, a higher iodide ion density can be found at the graphene-water interface.This means that the iodides show more surface affinity than the potassium ions.Regarding the origin of ion interfacial distribution, this is closely related to the effects of the hydrophobic surface of the graphene.solutions (KI:H2O = 50:2099) is four.These findings may be related to the effects of graphene sheets on the dissolved behaviors of KI in water.
Generally, the Gibbs dividing surface (GDS) is utilized to distinguish the liquidvapor interface (Supplementary Materials).From the MD simulations, the ion densities relative to the GDS can be determined (Figure 4).Both the cations and anions form a dense layer on the graphene surface, i.e., an apparent ionic double layer near the surface.This is in agreement with Dočkal et al. [41] and Chen et al.'s [42] simulations on graphene-aqueous solution interfaces.Additionally, compared with potassium ions, a higher iodide ion density can be found at the graphene-water interface.This means that the iodides show more surface affinity than the potassium ions.Regarding the origin of ion interfacial distribution, this is closely related to the effects of the hydrophobic surface of the graphene.
Additionally, it was found that the ion pairs are not uniformly distributed in the solutions.In comparison with the interior of the solution, the ion pairs tend to accumulate at the graphene-water interface (Figure 5).This is in accordance with Smith and Rick's simulations [43] of aqueous solutions.Due to the appearance of foreign surfaces in aqueous solutions, this promotes the formation of solute aggregates in water, which tend to accumulate on the foreign surfaces.Additionally, it was found that the ion pairs are not uniformly distributed in the solutions.In comparison with the interior of the solution, the ion pairs tend to accumulate at the graphene-water interface (Figure 5).This is in accordance with Smith and Rick's simulations [43] of aqueous solutions.Due to the appearance of foreign surfaces in aqueous solutions, this promotes the formation of solute aggregates in water, which tend to accumulate on the foreign surfaces.In fact, ion distribution around an interface has attracted the attention of many scholars [44][45][46][47][48][49].This means that different ions feature different degrees of density enhancement at the interface.In general, the larger and more polarizable anions can be attracted to the electrolyte-air interface, with a propensity for the well-known Hofmeister series [50].To understand the physical mechanism of ion interfacial selectivity, various explanations have been presented, such as ion polarization [51][52][53], ion solvation [54], ion size [55,56], interfacial charge and cavitation [57,58], ionic dispersion forces [59], and the delicate balances between the electrostatic and Lennard-Jones (LJ) forces [49,60].Of course, this is related to the effects of foreign surfaces on the dissolved behaviors of solutes in water.
As the salts are dissolved into water, interfaces appear between the ions and water.As foreign substances are immersed in water, interfaces also appear between the substances and solutions.Regarding ion absorption on the substance surface, this may be closely related to the thermodynamic stability of the solutions.In other words, to make In fact, ion distribution around an interface has attracted the attention of many scholars [44][45][46][47][48][49].This means that different ions feature different degrees of density enhancement at the interface.In general, the larger and more polarizable anions can be attracted to the electrolyte-air interface, with a propensity for the well-known Hofmeister series [50].To understand the physical mechanism of ion interfacial selectivity, various explanations have been presented, such as ion polarization [51][52][53], ion solvation [54], ion size [55,56], interfacial charge and cavitation [57,58], ionic dispersion forces [59], and the delicate balances between the electrostatic and Lennard-Jones (LJ) forces [49,60].Of course, this is related to the effects of foreign surfaces on the dissolved behaviors of solutes in water.
As the salts are dissolved into water, interfaces appear between the ions and water.As foreign substances are immersed in water, interfaces also appear between the substances and solutions.Regarding ion absorption on the substance surface, this may be closely related to the thermodynamic stability of the solutions.In other words, to make the systems more thermodynamically stable, the ions tend to accumulate to form the aggregate around the hydrophobic surface.
In principle, as foreign substances are immersed into aqueous solutions, the thermodynamic functions may contain various interaction energies: where ∆G Solute-water and ∆G Surface-water represent the interactions between the solutes and water, and the foreign surfaces and water, respectively; ∆G Solute-solute and ∆G Surface-solute represent the interactions between the solutes, and the surfaces and solutes, respectively.Before the ions are affected by foreign substances, they must approach the foreign surfaces.
It was found that ion interfacial adsorption may be closely related to the structural rearrangement of water molecules.It is necessary to investigate the structure of water and the effects of dissolved solutes on the water structure.OH vibrations are sensitive to hydrogen bonding and are widely used to investigate the structure of water.In our recent works [61,62], it has been observed that in the presence of three-dimensional hydrogen-bonded networks, OH vibrations primarily depend on hydrogen bonding within the first shell of a water molecule (local hydrogen bonding), and the effects of hydrogen bonding beyond the first shell on OH vibrations are weak.For ambient water, the Raman OH stretching band may be reasonably deconvoluted into five sub-bands, each associated with different OH vibrations engaged in various local hydrogen bonds.
Numerous experimental and theoretical works have been carried out to investigate the structure of liquid water.To date, various structural models have been proposed, broadly categorized into (a) mixture and (b) continuum models [63,64].Based on our Raman spectroscopic studies [61,62] on ambient water, a water molecule interacts with the neighboring water molecules (in the first shell) through various local hydrogen-bonded networks, such as DDAA (double donor-double acceptor, tetrahedral hydrogen bonding), DDA (double donor-single acceptor), DAA (single donor-double acceptor), and DA (single donor-single acceptor) hydrogen bonding.In addition, the hydrogen bonds of water are influenced by the changes in temperature, pressure, dissolved salt, and confined environment, which may be rearranged to oppose these changes.
As the salts are immersed in water, they dissociate into hydrated ions.The interactions between the dissolved ions and water molecules around them undoubtedly affect the structure of water.The OH vibrations are dependent on local hydrogen bonds, and the dissolved ions mainly affect the structure of water molecules within the first coordination shells.This may be demonstrated by the experimental measurements of the structure and dynamics of water around the ions, such as neutron and X-ray diffraction [65], X-ray absorption spectroscopy [66], femtosecond time-resolved infrared (fs-IR) vibrational spectroscopy [67,68], and optical Kerr effect spectroscopy [69], respectively.These indicate that the effect of the ions on water is largely limited to the first solvation shell.
When the salts (or foreign substances) are immersed in aqueous solutions, they mainly affect the structure of the topmost water layer at the interface (interfacial water).Therefore, the water may be divided into interfacial and bulk water.To understand the driving force of ion interfacial adsorption, it is necessary to investigate the changes in the hydrogen bonding of water.
In this study, the geometric definition of hydrogen bonding is applied to identify hydrogen bonds in water [70].According to this definition, a hydrogen bond is considered to be present between two neighboring water molecules if the oxygen-oxygen distance (r OO ) and the angle between the two water molecules (∠OOH) are both less than 3.5 Å and 30 • , respectively.
When the KI salts are dissolved in water, this leads to a decrease in the number of hydrogen bonds in water (Figure 6).It is related to the interfacial water of solutes and external surfaces.However, with increasing KI concentrations, the effects of KI on the hydrogen bonding (∂HB/∂KI (Mole fraction)) of water become weak.This is due to the decrease in the ion surface area available for interfacial water molecules.Additionally, this is also in accordance with our recent study [36] on the structure of NaCl solutions.This means that, with increasing KI concentrations, the dissolved ions are accumulated and repelled to the graphene-water interfaces.Regarding the origin of ion accumulation around the surface, it is ascribed to maximize the hydrogen bonds of water (or bulk water).In our recent works, based on the structural studies on water [61,62] and the air/water interface [71], hydration free energy is derived and applied to investigate the physical origin of hydrophobic effects.With increasing solute concentrations, this is divided into the initial and hydrophobic solvation processes, corresponding to the different dissolving behaviors of solutes in water, such as dispersed and accumulated distributions in water.Therefore, hydrophobic effects are reasonably ascribed to the structural competition between hydrogen bonding in bulk and interfacial water [72].In the process of hydrophobic effects, to maximize the hydrogen bonds of water, the dissolved ions are aggregated in water.In fact, this concept may be applied to understand ion aggregation in aqueous solutions.
As the foreign substances are immersed in water, interfaces appear between the particles and water, which mainly affect the structure of interfacial water.To maximize the hydrogen bonds of bulk water, the dissolved solutes tend to aggregate at the foreign surfaces.In combination with our recent study [72], this is due to hydrophobic interactions.In thermodynamics, no barrier is necessary to overcome in the formation of a solute aggregate.In addition, the formation of ion aggregates and interfacial adsorption makes the system more thermodynamically stable.

Heterogeneous Nucleation Mechanism
To investigate the mechanism of heterogeneous nucleation, MD simulations of the KI-saturated solutions in the presence of two graphene sheets were conducted.To evaluate the effects of external surfaces on nucleation, the homogeneous nucleation of KI in water was also carried out.Based on the calculated RDFs, the order parameters were calculated during the nucleation of KI in water, which were used to determine the FES using the metadynamics method.With reference to homogeneous nucleation of KI in solutions, this is utilized to investigate the effects of foreign surfaces on the KI nucleation in aqueous solutions.In our recent works, based on the structural studies on water [61,62] and the air/water interface [71], hydration free energy is derived and applied to investigate the physical origin of hydrophobic effects.With increasing solute concentrations, this is divided into the initial and hydrophobic solvation processes, corresponding to the different dissolving behaviors of solutes in water, such as dispersed and accumulated distributions in water.Therefore, hydrophobic effects are reasonably ascribed to the structural competition between hydrogen bonding in bulk and interfacial water [72].In the process of hydrophobic effects, to maximize the hydrogen bonds of water, the dissolved ions are aggregated in water.In fact, this concept may be applied to understand ion aggregation in aqueous solutions.
As the foreign substances are immersed in water, interfaces appear between the particles and water, which mainly affect the structure of interfacial water.To maximize the hydrogen bonds of bulk water, the dissolved solutes tend to aggregate at the foreign surfaces.In combination with our recent study [72], this is due to hydrophobic interactions.In thermodynamics, no barrier is necessary to overcome in the formation of a solute aggregate.In addition, the formation of ion aggregates and interfacial adsorption makes the system more thermodynamically stable.

Heterogeneous Nucleation Mechanism
To investigate the mechanism of heterogeneous nucleation, MD simulations of the KI-saturated solutions in the presence of two graphene sheets were conducted.To eval-uate the effects of external surfaces on nucleation, the homogeneous nucleation of KI in water was also carried out.Based on the calculated RDFs, the order parameters were calculated during the nucleation of KI in water, which were used to determine the FES using the metadynamics method.With reference to homogeneous nucleation of KI in solutions, this is utilized to investigate the effects of foreign surfaces on the KI nucleation in aqueous solutions.
According to the MD simulations, the K + and I − ions accumulate to form an aggregate, and KI nucleation first takes place in the aggregate.This is in agreement with the other experimental and theoretical studies [36][37][38] on nucleation.Different from the solute aggregate, a periodic crystal lattice can appear as nucleation takes place in the aggregate.In comparison with the KI RDFs prior to nucleation, the second peak is well split into two peaks as the KI crystal appears in the solute aggregate (Figure 7).As the KI crystal grows, these two peaks become stronger, and another peak at 9.4 Å can also be detected in the calculated RDFs.gregate.In comparison with the KI RDFs prior to nucleation, the second peak is well split into two peaks as the KI crystal appears in the solute aggregate (Figure 7).As the KI crystal grows, these two peaks become stronger, and another peak at 9.4 Å can also be detected in the calculated RDFs.It was found that the nucleation of the KI crystal first takes place within the ion aggregate.This means that the ion aggregate may correspond to the nucleation site with a lower nucleation barrier.In our recent study [36] on homogeneous NaCl nucleation in a solution, a critical aggregate (Aggc) was proposed, which is the largest aggregate, as the nucleation occurs in water.From this study, the Aggc is determined to be 187 during homogeneous KI nucleation (Figure 8).However, as the graphene surfaces appear in the solution, the size of Aggc is determined to be 78 in the graphene-KI-H2O system (Figure 8).In comparison with homogeneous nucleation, heterogeneous nucleation is expected to take place more easily.In the work, the aggregate and non-aggregate are, respectively, labeled as the nucleus and non-nucleus zones.It was found that the nucleation of the KI crystal first takes place within the ion aggregate.This means that the ion aggregate may correspond to the nucleation site with a lower nucleation barrier.In our recent study [36] on homogeneous NaCl nucleation in a solution, a critical aggregate (Aggc) was proposed, which is the largest aggregate, as the nucleation occurs in water.From this study, the Aggc is determined to be 187 during homogeneous KI nucleation (Figure 8).However, as the graphene surfaces appear in the solution, the size of Aggc is determined to be 78 in the graphene-KI-H 2 O system (Figure 8).In comparison with homogeneous nucleation, heterogeneous nucleation is expected to take place more easily.In the work, the aggregate and non-aggregate are, respectively, labeled as the nucleus and non-nucleus zones.
During the simulations, the LQ4 order parameters of nucleus and non-nucleus zones are determined during both heterogeneous and homogeneous nucleation processes.From Figure 8, it is observed that as KI crystals nucleate and grow in the solutions, there is an increase in these order parameters.Moreover, the LQ4 parameters of nucleus zones precede those of non-nucleus zones, indicating that nucleation is triggered and driven by the formation of KI crystal nuclei in water.Therefore, these calculated LQ4 order parameters can be used to measure the nucleation process of KI crystals in the solutions.During the simulations, the LQ4 order parameters of nucleus and non-nucleus zones are determined during both heterogeneous and homogeneous nucleation processes.From Figure 8, it is observed that as KI crystals nucleate and grow in the solutions, there is an increase in these order parameters.Moreover, the LQ4 parameters of nucleus zones precede those of non-nucleus zones, indicating that nucleation is triggered and driven by the formation of KI crystal nuclei in water.Therefore, these calculated LQ4 order parameters can be used to measure the nucleation process of KI crystals in the solutions.
Based on the calculated LQ4 order parameters, the free energy surface (FES) can be determined through METAD calculations, as shown in Figure 9.In this study, it is observed that only one barrier is encountered during KI nucleation in water, specifically corresponding to the nucleation of KI in the largest aggregate (Aggc).There is no barrier that must be overcome during the formation of the ion aggregate.This finding contrasts with the two-step nucleation process described in previous works [13][14][15], where amorphous nuclei initially form, followed by an amorphous-to-crystalline transition in the middle of the amorphous phase, and two barriers are expected in the nucleation process according to that model.Due to the hydrophobic interactions, the dissolved K + and I − ions tend to accumulate to form the aggregate in order to maximize the number of hydrogen bonds in water.Of course, this makes the system more thermodynamically stable, which also lowers the nucleation barrier.In comparison with the CNT, a revised CNT (Rev-CNT) is proposed: where ΔGH represents the hydrophobic interactions related to the formation of a solute aggregate in water.Based on the calculated LQ4 order parameters, the free energy surface (FES) can be determined through METAD calculations, as shown in Figure 9.In this study, it is observed that only one barrier is encountered during KI nucleation in water, specifically corresponding to the nucleation of KI in the largest aggregate (Aggc).There is no barrier that must be overcome during the formation of the ion aggregate.This finding contrasts with the two-step nucleation process described in previous works [13][14][15], where amorphous nuclei initially form, followed by an amorphous-to-crystalline transition in the middle of the amorphous phase, and two barriers are expected in the nucleation process according to that model.From our recent study [72] on hydrophobic interactions, the ∆GH is affected by the hydrophobic interactions related to the ion aggregate, which is due to the difference in Gibbs energy as the solutes transform from dispersed to accumulated distributions in water.In other words, ∆GH may relate to the molecular number during the transformation from interfacial to bulk water when the solutes aggregate in the solutions.Due to the hydrophobic interactions, the dissolved K + and I − ions tend to accumulate to form the aggregate in order to maximize the number of hydrogen bonds in water.Of course, this makes the system more thermodynamically stable, which also lowers the nucleation barrier.In comparison with the CNT, a revised CNT (Rev-CNT) is proposed: where ∆G H represents the hydrophobic interactions related to the formation of a solute aggregate in water.
From our recent study [72] on hydrophobic interactions, the ∆G H is affected by the hydrophobic interactions related to the ion aggregate, which is due to the difference in Gibbs energy as the solutes transform from dispersed to accumulated distributions in water.In other words, ∆G H may relate to the molecular number during the transformation from interfacial to bulk water when the solutes aggregate in the solutions.Therefore, this is expressed as: where the first (second) item represents Gibbs energy of interfacial water after (before) the solutes aggregate in water, m represents the solute number of the aggregate, n Interfacial → bulk water represents the number of water molecules that changed from interfacial to bulk water during the solute association in water, and ∆G DDAA represents the Gibbs energy of DDAA (tetrahedral) hydrogen bonding.This may be used to explain why nucleation first occurs within Aggc in the nucleation process.Additionally, this is also extended to understand the effects of foreign surfaces on the nucleation process in water.
From the calculated FES depicted in Figure 9, it is evident that nucleation in the nucleus zone precedes that in the non-nucleus zone, which aligns with the observed changes in LQ4 order parameters.Additionally, in comparison with KI homogeneous nucleation within the nucleus zone, a lower nucleation barrier is observed when KI nucleation occurs in the nucleus zone during the heterogeneous nucleation process (Figure 9).This difference can be attributed to the presence of graphene sheets in the system.The introduction of foreign surfaces facilitates solute nucleation in aqueous solutions, a phenomenon that is consistent with theoretical studies on the mechanism of heterogeneous nucleation.
Additionally, based on the MD simulations, only one water molecular layer (or no water molecules) can be found between the aggregate and the graphene sheets when KI nucleation occurs in Aggc (Figure 9).The dissolved solutes mainly affect the structure of interfacial water.It is believed that KI nucleation tends to take place on foreign surfaces.In fact, this is related to the distribution of ion aggregate around the foreign surface.
In addition, the foreign surfaces affect KI nucleation in solutions, which is also reflected in the difference in the induction period (t ind ) between KI homogeneous and heterogeneous nucleation.The t ind is defined as the time that elapses between the creation of supersaturation and the formation of a cluster of a detectable size.In comparison with KI homogeneous nucleation, the t ind of heterogeneous nucleation is shortened (Figure 8).In other words, the rate of KI heterogeneous nucleation is higher than that of homogeneous nucleation.
From the above discussion, the foreign surfaces mainly affect the structure of interfacial water.To maximize the number of hydrogen bonds in water, the dissolved solutes tend to aggregate at the external surfaces to minimize the ratio of surface area (solute-water interface) to volume of aggregate.It is derived that the formation of an aggregate may be related to the geometric characteristics of foreign substances, especially the geometric shape (Figure 10).To maximize the number of hydrogen bonds in water, the dissolved solutes tend to accumulate at the corner of a concave surface (Figure 10).In comparison with flat and convex surfaces, nucleation may first occur at convex foreign surfaces (Figure 10).This may be used to control the sequence of nucleation in water.Of course, further studies are necessary.
water interface) to volume of aggregate.It is derived that the formation of an aggregate may be related to the geometric characteristics of foreign substances, especially the geometric shape (Figure 10).To maximize the number of hydrogen bonds in water, the dissolved solutes tend to accumulate at the corner of a concave surface (Figure 10).In comparison with flat and convex surfaces, nucleation may first occur at convex foreign surfaces (Figure 10).This may be used to control the sequence of nucleation in water.Of course, further studies are necessary.The interfacial water layers are indicated by dashed lines.To maximize the number of hydrogen bonds in water, the ion aggregate tends to accumulate with the foreign surfaces to minimize the ratio of surface area to volume.It was found that nucleation is the easiest on a concave surface, and most difficult on a convex surface, while nucleation on a planar surface is always in between.
By increasing the concentrations, the solutes tend to aggregate in water.The formation of ion aggregates lowers the nucleation barrier [36].The foreign substances mainly affect the hydrogen bonding of interfacial water.When they are immersed into solutions, to maximize the number of hydrogen bonds in water, the solutes tend to accumulate to form an aggregate at the foreign surfaces.In comparison with homogeneous nucleation, a lower barrier may be expected for heterogeneous nucleation in solutions.When the foreign surfaces are immersed in water, this promotes solute nucleation in water.The interfacial water layers are indicated by dashed lines.To maximize the number of hydrogen bonds in water, the ion aggregate tends to accumulate with the foreign surfaces to minimize the ratio of surface area to volume.It was found that nucleation is the easiest on a concave surface, and most difficult on a convex surface, while nucleation on a planar surface is always in between.
By increasing the concentrations, the solutes tend to aggregate in water.The formation of ion aggregates lowers the nucleation barrier [36].The foreign substances mainly affect the hydrogen bonding of interfacial water.When they are immersed into solutions, to maximize the number of hydrogen bonds in water, the solutes tend to accumulate to form an aggregate at the foreign surfaces.In comparison with homogeneous nucleation, a lower barrier may be expected for heterogeneous nucleation in solutions.When the foreign surfaces are immersed in water, this promotes solute nucleation in water.

Conclusions
In this work, MD simulations are used to investigate the heterogeneous nucleation mechanism of KI on graphene surfaces in water.From this study, the following conclusions are derived: (1) The foreign substances mainly affect the hydrogen bonding of interfacial water.
To maximize the number of hydrogen bonds in water, the dissolved ions tend to accumulate to form an aggregate at the foreign surfaces, which may be related to hydrophobic interactions.(2) Nucleation tends to occur within the solute aggregate.In comparison with homogeneous nucleation, a lower barrier may be expected in the heterogeneous nucleation process.As foreign surfaces are immersed in solutions, nucleation is promoted in solutions.(3) Based on this work, it is believed that heterogeneous nucleation may be closely related to the geometric characteristics of foreign substances, especially their shape.

Supplementary Materials:
The following supporting information can be downloaded at: https: //www.mdpi.com/article/10.3390/cryst14030208/s1,In this work, Steinhardt parameters [73] were used to measure the degree of order during the nucleation of KI in the systems.Additionally, the metadynamics method [29,30] was utilized to reconstruct the free energy landscape as a function of the order parameters.In addition, the Gibbs dividing surface (GDS) was used to distinguish the liquid-vapor interface.They are described in the Supplementary Materials.

Figure 1 .
Figure 1.The calculated radial distribution functions between K + and I − ions (g K-I (r)) of various graphene-KI-H 2 O systems.

Crystals 2024 , 15 Figure 2 .
Figure 2. The radial distribution functions between I − ions (gI-I(r)) (a) and between K + ions (gK-K(r)) (b) of various KI solutions in the presence of graphene sheets.

Figure 3 .
Figure 3.The ion pair number of KI in graphene-KI-H2O systems.The blank square is the ion pair number of pure KI solutions (KI:H2O, 50:2099).The inset shows the SSIP and CIP (ion pair) in KI solutions.

Figure 2 .
Figure 2. The radial distribution functions between I − ions (g I-I (r)) (a) and between K + ions (g K-K (r)) (b) of various KI solutions in the presence of graphene sheets.

Figure 2 .
Figure 2. The radial distribution functions between I − ions (gI-I(r)) (a) and between K + ions (gK-K(r)) (b) of various KI solutions in the presence of graphene sheets.

Figure 3 .
Figure 3.The ion pair number of KI in graphene-KI-H2O systems.The blank square is the ion pair number of pure KI solutions (KI:H2O, 50:2099).The inset shows the SSIP and CIP (ion pair) in KI solutions.

Figure 3 .
Figure 3.The ion pair number of KI in graphene-KI-H 2 O systems.The blank square is the ion pair number of pure KI solutions (KI:H 2 O, 50:2099).The inset shows the SSIP and CIP (ion pair) in KI solutions.

Figure 4 .
Figure 4.The ion and O atom density of KI solutions at the graphene/water interface.The Gibbs dividing surface is indicated by a dashed line.

Figure 4 .
Figure 4.The ion and O atom density of KI solutions at the graphene/water interface.The Gibbs dividing surface is indicated by a dashed line.

Figure 5 .
Figure 5.The distribution of ion pair number of KI in graphene-KI-H2O systems.The Gibbs dividing surface is indicated by a dashed line.

Figure 5 .
Figure 5.The distribution of ion pair number of KI in graphene-KI-H 2 O systems.The Gibbs dividing surface is indicated by a dashed line.

Crystals 2024 , 15 Figure 6 .
Figure 6.The changes in hydrogen bonding number of graphene-KI-H2O systems.Increasing the KI concentrations decreases the number of hydrogen bonds in water.However, the effects of KI on hydrogen bonding (∂HB/∂KI (mole fraction)) become weak (inlet).The blank square represents the hydrogen bond number of pure KI solutions (KI:H2O, 50:2099).

Figure 6 .
Figure 6.The changes in hydrogen bonding number of graphene-KI-H 2 O systems.Increasing the KI concentrations decreases the number of hydrogen bonds in water.However, the effects of KI on hydrogen bonding (∂HB/∂KI (mole fraction)) become weak (inlet).The blank square represents the hydrogen bond number of pure KI solutions (KI:H 2 O, 50:2099).

Figure 7 .
Figure 7.The gK-I(r) during KI nucleation from graphene-KI-H2O systems.The corresponding configurations are shown.Water molecules and graphene are shown in CPK representation.The I − and K + ions are drawn in cyan and pink spheres.

Figure 7 .
Figure 7.The g K-I (r) during KI nucleation from graphene-KI-H 2 O systems.The corresponding configurations are shown.Water molecules and graphene are shown in CPK representation.The I − and K + ions are drawn in cyan and pink spheres.

Figure 8 .
Figure 8.The LQ4 of nucleus (aggregate) and non-nucleus (non-aggregate) zones during both the heterogeneous (a,b) and homogeneous (c,d) nucleation processes in solutions.As nucleation occurs in the aggregate, the critical aggregate is determined (a,c); the corresponding order parameters are indicated by dashed lines.

Figure 8 .
Figure 8.The LQ4 of nucleus (aggregate) and non-nucleus (non-aggregate) zones during both the heterogeneous (a,b) and homogeneous (c,d) nucleation processes in solutions.As nucleation occurs in the aggregate, the critical aggregate is determined (a,c); the corresponding order parameters are indicated by dashed lines.

Crystals 2024 , 15 Figure 9 .
Figure 9.The FES as the function of LQ4 during the nucleation within nucleus (aggregate) and non-nucleus (non-aggregate) zones in graphene-KI-H2O system (KI:H2O, 276:1648) and pure KI solutions (KI:H2O, 276:1647).(a,b) The graphene surfaces in KI solutions decrease the barrier of nucleation within nucleus zone.(c-e) For the graphene-KI-H2O system, as nucleation occurs within Aggc, the various configurations of KI related to Aggc are shown.

Figure 9 .
Figure 9.The FES as the function of LQ4 during the nucleation within nucleus (aggregate) and non-nucleus (non-aggregate) zones in graphene-KI-H 2 O system (KI:H 2 O, 276:1648) and pure KI solutions (KI:H 2 O, 276:1647).(a,b) The graphene surfaces in KI solutions decrease the barrier of nucleation within nucleus zone.(c-e) For the graphene-KI-H 2 O system, as nucleation occurs within Aggc, the various configurations of KI related to Aggc are shown.

Figure 10 .
Figure 10.The dependence of heterogeneous nucleation on the geometric shape of foreign surface.The interfacial water layers are indicated by dashed lines.To maximize the number of hydrogen bonds in water, the ion aggregate tends to accumulate with the foreign surfaces to minimize the ratio of surface area to volume.It was found that nucleation is the easiest on a concave surface, and most difficult on a convex surface, while nucleation on a planar surface is always in between.

Figure 10 .
Figure 10.The dependence of heterogeneous nucleation on the geometric shape of foreign surface.The interfacial water layers are indicated by dashed lines.To maximize the number of hydrogen bonds in water, the ion aggregate tends to accumulate with the foreign surfaces to minimize the ratio of surface area to volume.It was found that nucleation is the easiest on a concave surface, and most difficult on a convex surface, while nucleation on a planar surface is always in between.

Table 1 .
The simulated systems in this work.