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Molecular Dynamics Simulation of Ice Crystal Growth Inhibition by CTAB Naoya Shimazu, Daisuke Takaiwa, Donguk Suh, Touru Kawaguchi, Takuya Fuse, Takashi Kaneko, and Kenji Yasuoka Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01903 • Publication Date (Web): 10 Jul 2018 Downloaded from http://pubs.acs.org on July 11, 2018

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Molecular Dynamics Simulation of Ice Crystal Growth Inhibition by CTAB Naoya Shimazu1, Daisuke Takaiwa1, Donguk Suh1, Touru Kawaguchi2, Takuya Fuse2, Takashi Kaneko2, Kenji Yasuoka1 1

2

Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

DENSO CORPORATION, 500-1 Minamiyama, Komenoki-cho, Nisshin-shi, Aichi 470-0111, Japan

Abstract Recent experiments have found that hexadecyl-trimethyl-ammonium bromide (CTAB) to have superior ice nucleation inhibition properties [J. Phys. Chem. B 121, 6580]. The mechanism on how the inhibition takes place remains unclear. Therefore, molecular dynamics was used to simulate ice crystallization of a water/CTAB/ice system. The ice crystallization rate for a pure water system was compared for the basal [0001], first prism [10-10], and secondary prism plane [11-20], where the basal plane grew the slowest followed by the first prism plane. When CTAB was added to the ice-liquid water system, crystallization was clearly impeded. Even when ice starts growing away from the CTAB molecule, the hydrophilic head would at some point protrude and get caught in the water/ice interface. Once the head of the CTAB was encapsulated in the advancing interface, the hydrophobic body would wriggle around and disrupt the formation of hydrogen bond networks that are essential for ice growth. When the interface clears the length of the body of the CTAB molecule, ice crystallization resumes at its normal pace. In summary, the inhibition of ice growth is a combination of the hydrophilic head acting as an anchor and the dynamic motion of the hydrophobic tail hindering stable hydrogen bonding for ice growth.

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Introduction Ice crystals are readily observed in nature and throughout our daily lives. The formation of ice starts from water in a liquid or vapor state moving into a secondary solid state, and crystal growth occurs once ice nuclei are formed from the initial state. Depending on the application one would need to induce ice growth or inhibit the phase transition1-3. Though ice crystallization is ubiquitous, a full understanding of the physics of the phenomenon is still lacking. Ice nucleation in many cases starts in nanoscale, where only a few dozen water molecules form essential hydrogen bond networks for the crystal embryo to grow. Molecular dynamics has been recognized as an effective tool to visualize and gather in-depth information on the dynamic nonequilibrium phase transition process. One of the first successful ice nucleation simulations by molecular dynamics was performed by Matsumoto et al.4. Prior to the nucleation study, Nada and Furukawa5 focused on ice crystal growth on different hexagonal ice planes and studied the hydrogen bonding network of the water molecules near the interface, which propagates crystallization. Carignano6 found that cubic ice can be found sporadically during the growth of hexagonal ice. A great deal of attention has also been centered on materials that inhibit ice crystallization such as antifreeze proteins (AFP). Since the discovery of the protein in the plasma of an arctic fish by Scholander et al.7, similar proteins were also found in other species like insects and mushrooms8-11 and direct confirmation of AFPs impeding crystal growth was possible12-13. In terms of simulation, the adsorption characteristics of the AFPs on ice were analyzed14-16. The hydrophilic group of the protein first attaches onto the ice crystal and the hydrophobic part repels further water molecules approaching the surface of the ice. Though advancements in molecular simulations have been made, since AFPs are large and


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have complex helix structures, there are still many limitations in acquiring further knowledge from the results. Therefore, amphiphilic molecules such as surfactants, which are smaller and simpler molecules relative to AFPs have been studied to understand the ice crystallization inhibition effect. An amphiphilic molecule by definition means that it simultaneously has a hydrophilic and hydrophobic part on the same molecule17. Kuwabara et al.18 studied various types of surfactant molecules in subcooled ultrapure water BMQW (buffered Milli-Q water). In their study, surfactants were dissolved into an ice-seeded BMQW+AgI system and the freezing temperature was measured. Among the surfactants, hexadecyl-trimethyl-ammonium bromide (CTAB) was found to generate a great degree of subcooling, but there was no report on the detailed ice nucleation inhibition mechanism. More recently, Inada et al.19 studied a variety of surfactants and confirmed CTAB to have the most anti-ice nucleating characteristics. The study also examined the concentration effect of CTAB and proposed a mechanism in how the surfactant will retard ice growth. Consequently, in this study we will focus on how a CTAB molecule affects ice crystal growth to observe the kinetic process. The next section provides the simulation setup followed by the analysis methods and results.

Simulation Setup Molecular dynamics was used to simulate the phase transition phenomenon. The standard TIP4P/Ice water model was chosen because the melting point of the force field is similar to that of experiments20. A CTAB molecule was constructed using the OPLS-AA force field21, where the atomic parameters of a n-decyl trimethyl ammonium bromide (DeTAB) molecule modeled by Jorge22 were substituted to replicate each atom in the CTAB molecule. The overall structure of a CTAB, which has 16 alkyl groups composed of either methyl (CH3) or


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ethyl (CH2), is illustrated in Fig 1(a). Specifics on the alkyl group corresponding to the nodes of the CTAB are in Fig 1 (b). Furthermore, a detailed list of parameters for the water and surfactant molecule are in Table 1, where GROMACS 4.5.5 was used to run the simulations. Preliminary calculations on ice crystal growth were conducted under the conditions in table 2 to find the melting point for the solution in Fig 2. When performing the calculations, information regarding the interfacial tension is essential in controlling the pressure normal to the direction of the flat interface. Unfortunately, the interfacial tension is unknown, so a system of 1600 water molecules forming a hexagonal ice crystal structure with fixed Lx and Ly values, which are lengths in the x- and y-direction, was constructed. An NPT ensemble was used to equilibrate the ice crystal, but since the ice lattice length changes for different temperature and pressure conditions, the averages were taken to fix the system size in the xyplane. The equilibrated temperature was used as the initial temperature for the melting point investigation temperature. Using the fixed system size (Lx and Ly) determined from the previous ice crystal equilibration procedure, a water/CTAB solution system was equilibrated. Finally, the ice crystal and solution systems were merged to form Fig 2. An NLxLyPzH ensemble was used to investigate the melting point of the solution.

Results from Preliminary Setup The results for the melting point of the CTAB solution are in Fig 3, where the calculation results for a water/ice system are also plotted for comparison. The melting point of the solution increases initially but eventually fluctuates around 269.07K after the fourth iteration. This new melting point for the water/ice/CTAB solution is about 3K lower than the water/ice melting point of 271.93 K, where the original study20 for TIP4P/Ice found the melting point to be at 272.2. Therefore, quenching was conducted below this newly determined melting


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point for the solution.

Simulation Conditions for Crystal Growth Based on the acquired melting point from the previous section, freezing temperatures were set at 260K. A summary of the simulation conditions is in Table 3, where the sole difference from the aforementioned preliminary calculations is in the fact that an NLxLyPzT ensemble was used for crystal growth observations contrary to the NLxLyPzH ensemble.

Results Interface Identification Method In order to calculate the ice crystal growth rate, the location of the water/ice planar interface within the system over time is required. The density distribution of the system and the local tetrahedral order parameter was evaluated and compared to assess the evolution of the planar interface. The following are the details of each method.

Density Profile A three-step method was used to trace the movement of the water/ice interface as crystallization occurs. 1. Reposition the center of the crystallized ice block to the origin of the system. 2. Calculate the density distribution of the water molecules in the system in the perpendicular direction of the interface and average for a number of steps as in Fig 4. 3. Identify the interface when the averaged density value exceeds 1.6 g/cm3. The value in step 3 was chosen because values greater than 1.5 g/cm3 showed stable lattice patterning compared to the liquid region.


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Local tetrahedral order parameter 23-24 The local tetrahedral order parameter focuses on the angle of two of the four water molecules that are closest to the target water molecule, where the structure factor Sө becomes

2

Sθ =

3 3 4  1 ∑ ∑  cos θ jk +  . 32 j =1 k = j +1  3

(1)

The advantage of this interface evaluation method is that no time average is necessary, so a real-time evolution is attainable. Again a three-step method is used to obtain the interface using this method. 1. Reposition the center of the crystallizing ice block to the origin of the system. 2. Calculate the order parameter for each molecule and plot the values in the perpendicular direction of the interface as in Fig 5. 3. Fit the values to a tanh and define the interface as the point where the fit exceeds a separately calculated threshold value.

To obtain the threshold value, two separate systems that consist solely of bulk ice and water were each evaluated. The order parameter of the water molecules for systems that only had ice or liquid were calculated to obtain the threshold value. The local tetrahedral order parameter was calculated for each molecule in the single phase bulk systems and the distribution was plotted in Fig 6. Since the evaluated systems are single phase, the order parameter should gather to a specific value but a distribution exists. The order parameter values for the ice system tend to gather at low values, whereas the opposite happens with the water system. Based on Fig. 6, the intersection between the values at 0.022 was taken as the threshold value and was used throughout the work.


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A summary of the interface location over time attained by two different threshold values and the density profile method is in Fig 7. A threshold value of 0.040 was tested based on the tanh profile in Fig 5. The comparison showed that the threshold value for 0.040 and the density profile method are in good agreement, so we conclude both methods to be adequate.

Ice Crystal Growth Inhibition Effect To verify if CTAB inhibits ice crystal growth, a water/ice two-phase system and water/CTAB/ice system were compared. The inhibition effect was evaluated by comparing the ice crystal growth rate, which was obtained from the advancement of the water/ice interface. The aforementioned two-phase system was first simulated. The simulation results for the different faces are in table 3. For convenience, the right and left-hand side of the system in Fig 2 (with or without CTAB) will be referred to as interface A and B, respectively. The water/ice interface essentially advanced at a steady rate, where the secondary prism [11-20] face grew the fastest followed by the prismatic [10-10] and basal plane [0001]. This is qualitatively consistent with the results from Nada and Furukawa25. Snapshots of the evolution of ice crystal growth in the water/CTAB/ice system for the [10-10] plane are in Fig 8. Systems, where the CTAB molecule equilibrated away from the ice block, were chilled to 260 K and the simulations were terminated at 120 ns. As seen in Fig 8, crystallization occurs very quickly between 0~8 ns, but the phase transition is clearly retarded during 8~90 ns as the CTAB interacts with the interface. Once the interface clears all influence from the surfactant molecule, crystallization resumes at its normal rate until the simulation was terminated at 120 ns. The corresponding time evolution of the interface positions for the water/ ice and water/CTAB/ice systems are plotted in Fig 9 and the ice ACS Paragon Plus Environment

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crystal growth rates are summarized in table 4. The evolution plots for other faces can be found in supplementary materials. In panel (a) of Fig 9, the water/ice system and that with CTAB initially have a similar growth rate, but the slope drastically declines at a certain point. To understand the growth rate decline, the positions of the head and tail of the CTAB molecule were superimposed with the interface position in panel (b). One can observe that the growth rate change directly coincides when the interface meets the head of the CTAB. Crystallization is hindered until the interface completely clears contact with the CTAB molecule, which happens when it passes the tail position. Based on this observation it is evident that the CTAB inhibits crystal growth. Further observations revealed that the head is more likely to engage with the interface than the tail, and from the comparison with the system without CTAB, one can deduce the CTAB influence is short range. Once the CTAB head comes in contact with the interface, the molecule overall changes its orientation to be perpendicular to the interface, and the inhibition effect comes from the ethyl groups from the body. On a separate note, the bromide ion did not show any significant influence on the growth rate for all cases. A summary of the crystal growth rates for the different ice faces in table 4 clearly shows a decrease compared with the ice-water system in table 3. The decrease becomes more pronounced when the interface and CTAB directly interact with each other, and the inhibition effect is the greatest for the fastest growing [11-20] face.

Hydrogen Bonding around CTAB Since the inhibition effect is clear, the ice crystallized around CTAB was observed in Fig 10. Four frames of the CTAB molecule perpendicular to the xy-plane were focused and magnified. The right-most frame shows the head-group of the CTAB, which is hydrophilic,


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whereas all other frames show the hydrophobic organic groups. Coinciding with the previous observation that the head will initially contact the advancing interface, the ice crystal structure is relatively preserved in contrast with the body and tail of the CTAB. Considering the head is larger than the other organic groups in the body or tail, the hydrogen bonds are more intact. The voids caused by the CTAB body and tail are larger and considering how the molecule wriggles around the interface, it is easy to perceive how the formation of stable hydrogen bonds will be disrupted by its motion.

Conclusion Molecular dynamics was used to simulate ice crystallization of a water/CTAB/ice system. Once the melting point was evaluated the quenching temperature was determined. The local tetrahedral bond order parameter was used to quantify the advancing water/ice interface. A clear ice crystallization inhibition effect could be observed for systems that had the CTAB molecule. The inhibition mechanism originates from the amphiphilic nature of the molecule, where the hydrophilic head will first engage with the advancing water/ice interface and once the head encroaches the crystallizing region, the dynamic motion of the hydrophilic body and tail will further impede the hydrogen bonds that try to consolidate. This inhibition mechanism is similar to that of antifreeze proteins. The inhibition effect was strongest for ice growing from the secondary prism plane, which is the fastest crystallizing ice plane. Further studies on the CTAB concentration and other characteristics will be investigated to be able to design a more effective ice crystallization inhibitor.

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spruce budworm antifreeze protein interacting with ice crystals: Basal plane affinity confers hyperactivity. Biophys. J. 2008, 95 (1), 333-341. 13.

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antifreeze glycoprotein kinetics at the ice interface reveals a two-step reversible adsorption mechanism. Crystal Growth & Design 2008, 8 (10), 3666-3672. 14.

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supercooling activities of surfactants. Cryobiology 2014, 69 (1), 10-16. 19.

Inada, T.; Koyama, T.; Tomita, H.; Fuse, T.; Kuwabara, C.; Arakawa, K.; Fujikawa, S., Anti-Ice

Nucleating Activity of Surfactants against Silver Iodide in Water-in-Oil Emulsions. The Journal of

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and amorphous water: TIP4P/Ice. Journal of Chemical Physics 2005, 122 (23), 234511. 21.

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Minimizations for Crystals of Cyclic-Peptides and Crambin. Journal of the American Chemical

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Bromide Micelles. Langmuir 2008, 24 (11), 5714-5725. 23.

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(a)

(b) Figure 1. Schematics for C16TAB, where all hydrogen atoms are omitted. (a) Each node represents a carbon atom within the chain. (b) Compressed model of panel (a), which shows the specifications for the carbon atoms in each node that corresponds to Table 1. The end with the N-atom will be referred as the head of the CTAB, whereas the methyl group on the other end is the tail.


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Figure 2. Snapshot of preliminary ice crystal growth simulation. The water molecules of the ice block that was initially placed inside the system were colored blue.

Figure 3 Melting point evaluation for TIP4P/Ice and TIP4P/Ice-CTAB solution.


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Figure 4 Density profile of water molecules in the system.

Figure 5 The order parameter Sө and its fitting line.


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Figure 6 Probability distribution of order parameter value for water molecules in a bulk liquid and ice system. The order parameter value at the intersection for the two lines is the threshold value.

Figure 7 Distance between the interface and the center of the ice for different threshold values and the density profile method.


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(a)

(b)

(c)

(d) Figure 8 Snapshots of crystallization occurring on the [10-10] face for the water/CTAB/ice system. (a) 0ns (b) 8ns (c) 90ns (d) 120ns


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(a)

(b) Figure 9 (a) Interface position evolution comparison of water/ice and water/CTAB/ice system for [1010] face. Interface A and the dotted lines are the slopes used to calculate the crystal growth rates. (b) Evolution of the interface and CTAB head and tail positions of the data in panel (a).


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Figure 10 Snapshots of hydrogen bonding around the CTAB molecule immersed in ice for different positions at the same time.


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Table 1. List of parameters for CTAB corresponding to the schematic in Fig 1 (b). Atom type N C (in MH) C (in EH) C (in MT) C (in ET) H Br Bond lengths N-C C-C C-H

Dihedral angle N-C-C-C C-N-C-C N-C-C-H C-N-C-H C-C-C-C C-C-C-H H-C-C-H

ε (KJ mol-1) 0.7113 0.2761 0.2761 0.2761 0.2761 0.1255 0.3766

q (e) 0.00 0.07 0.13 -0.18 -0.12 0.06 -1.00

Length (nm) 0.1471 0.1529 0.1090

Bond angle C-N-C N-C-C N-C-H

Ө0 (deg) 113.0 111.2 109.5

C0 5.772 3.042 0.803 0.632 2.929 0.628 0.628

C-C-C C-C-H H-C-H C2 0.958 0.519 0.000 0.000 0.209 0.000 0.000

112.7 110.7 107.8 C3 -4.058 -2.209 -3.213 -2.527 -1.674 -2.510 -2.510

Mass 14.007 12.011 12.011 12.011 12.011 1.008 79.904

σ(nm) 0.325 0.350 0.350 0.350 0.350 0.250 0.462

C1 -2.671 -1.351 2.410 1.895 -1.464 1.883 1.883

Table 2. Calculations conditions for ice growth in solution System pressure System temperature Basic Ice Number of Conditions Water molecules Liquid Number of CTAB Water Force Field CTAB Boundary condition Calculation Pressure control Method Temperature control Electrostatic interaction

0.1 MPa 260 K 1600 4800 2 TIP4P/Ice OPLS-AA 3D PBC Parrinello-Rahman Nosé-hoover PME

Table 3. Ice crystal growth rate summary for different faces for the water/ice system. Interface [0001] [10-10] [11-20]

Crystal Growth Rate (Å/ns) A B Average 0.695 0.645 0.670 0.782 0.972 0.887 1.055 0.943 0.999


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Table 4 Ice crystal growth rate summary for the water/CTAB/ice system. The results from the water/ ice system from table 3 are inserted for comparison. The averaged results for the water/CTAB/ice system are divided by duration on whether the CTAB has come in contact with the interface. Type

[0001] [10-10] [11-20]

Crystal Growth Rate (Å/ns) Water/ice Water/CTAB/ice No CTAB CTAB influence influence 0.670 0.620 0.335 0.887 0.815 0.220 0.999 0.770 0.180


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