- Email: [email protected]
Modeling nanoscale ice adhesion
Accepted Manuscript
Modeling nanoscale ice adhesion Senbo Xiao , Jianying He , Zhiliang Zhang PII: DOI: Reference:
S0894-9166(17)30121-0 10.1016/j.camss.2017.05.001 CAMSS 26
To appear in:
Acta Mechanica Solida Sinica
Received date: Revised date: Accepted date:
10 April 2017 1 May 2017 2 May 2017
Please cite this article as: Senbo Xiao , Jianying He , Zhiliang Zhang , Modeling nanoscale ice adhesion, Acta Mechanica Solida Sinica (2017), doi: 10.1016/j.camss.2017.05.001
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Modeling Nanoscale Ice Adhesion Senbo Xiao1,*, Jianying He1 and Zhiliang Zhang1 1
NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian
University of Science and Technology (NTNU), Trondheim 7491, Norway *
CR IP T
Email: [email protected]
ABSTRACT
Anti-icing is crucial for numerous instruments and devices in low temperature circumstance. One of the approaches in anti-icing is to reduce ice adhesion strength,
AN US
seeking spontaneous de-icing processes by natural forces of gravity or by winds. In order to enable tailored surface icephobicity design, research requires a good theoretical understanding of the atomistic interacting mechanisms between water/ice molecules and their adhering substrates. Herein, this work focuses on using atomistic modeling and molecular dynamics simulation to build a nanosized ice-cube adhering
M
onto silicon surface, with different contact modes of solid-solid and solid-liquid-solid
ED
patterns. This study provides atomistic models for probing nanoscale ice adhesion mechanics and theoretical platforms for explaining experimental results.
CE
PT
Keywords: anti-icing, atomistic modeling, molecular dynamics.
I. INTRODUCTION
AC
Anti-icing research is driven by practical urgent needs in low-temperature
applications, as well as preventing injuries and saving lives in winter seasons 1. It is a new research topic and progresses extremely fast2. One of the focuses in anti-icing is to scrutinize the fundamentals of ice adhesion, i.e. to understand the atomistic interactions between water molecules and their adhering substrates, and ultimately to reduce ice adhesion strength by utilizing rational nanomechanical knowledge1. The nanoscale mechanisms of ice-adhesion turn out to be highly complex. It is believed that both van der Waals forces and electrostatic interactions are important to 1
ACCEPTED MANUSCRIPT
ice adhesion3,4. It is proven that a thin amorphous water layer can significantly reduce ice adhesion strength5, demonstrating the effects of interface water on ice adhesion. It is also reported that ice-slippery surfaces are highly promising for icephobic applications6. In order to construct systematic base for the full solution of unwanted excessive icing, all these encouraging studies need further atomistic-level investigation on ice adhesion mechanics. Yet, large-scale all-atom modeling is rarely
CR IP T
documented. Nanoscale deicing studies employing molecular dynamics simulation and transferable force-field parameters are still limited. It is the purpose of this study to understand nanoscale ice adhesion by computational approach. This article covers the modeling of an ice-cube on a silicon substrate in a direct solid-solid adhesion, and
AN US
in a solid-liquid-solid adhering mode with a sandwiched interfacial amorphous water layer. This study provides all-atom models for theoretical studies on nanoscale iceadhesion mechanics like those reported by Xiao et al.7, as well as tools for explaining experimental results.
M
II. METHODS
The first step in modeling atomistic ice adhesion is to choose the right water or
ED
ice molecule model. There are couples of transferable all-atom water models available, such as SPC8, SPC/E9, TIP3P, TIP4P10, and so on. Currently, all the popular water
PT
models are designed to reproduce the buck properties of water. How these water models can be used to study interface adhesion mechanics is subjected to further
CE
systematic testing. Here, the TIP4p/ice water model is chosen for modeling both an ice-cube and an aqueous water layer, given that it is reported to have appropriately
AC
reproduced ice and water properties as well as phase transition11. The TIP4p/ice water model also has a bulk melting point close to 273 K. All other water models give much lower melting points12, for example, 232 K for TIP4p water model10. We note that the ice melting temperatures of the available water models are different from experiments. It is unfeasible to study ice nucleation by atomistic modeling and molecular dynamics simulation based on the popular water models nowadays. The biggest challenge is the very small simulation time scale of the all-atom molecular dynamics simulation 2
ACCEPTED MANUSCRIPT
methodology. It is not the purpose of this very short manuscript to tackle such a big task. Rather, the choice of temperature in this modeling study is under the consideration of realizing the solid-solid and the solid-liquid-solid ice contact modes. The silicon substrate uses parameters from the popular OPLS force field13, and interacts with the TIP4p/ice water model via van der Waals forces. Two atomistic models are built in this study, capturing solid-solid and solid-
CR IP T
liquid-solid ice adhesion modes, as shown in Fig. 1. An ice-cube with geometry of 7.67.12.1 nm3 was constructed, with molecular structure of ice Ih, featuring the most common ice found in the biosphere14. The ice-cube was brought onto a silicon substrate, with and without a sandwiched water layer of 1.0 nm in thickness. The
AN US
silicon substrate has a (100) surface area of 22.2722.54 nm2, and expands infinitely by being treated with periodic boundary condition. The two systems are thus assembled together with all the molecular structures as close as possible, but without atomic overlap. The sizes of the systems range roughly from 45500 to 83000 atoms,
M
depending on the system setup.
Further structural optimization and equilibration are needed for obtaining stable
ED
adhesion of the ice-cube on the silicon surface. The molecular dynamics simulation package, GROMACS 5.0.515, is employed to achieve such a goal. The simulation
PT
parameters are the same as those in a former report7. Energy minimization utilizing steepest descent algorithm is first used to remove any possible close atom contacts.
CE
Subsequently, system equilibration of the models is carried out. Because the ice-cube and the sandwiched water layer models in this study are not in their bulk states, their
AC
melting points are previously found to be around 220 K7. In order to maintain structural stability, the ice-cube is coupled to a temperature of 180 K. The water layer is maintained at a temperature of 255 K for its fluidity. The silicon substrate is position-fixed during the course of simulations. Both systems are equilibrated for 100 ns. The final equilibrated structures are shown in Fig. 1.
3
ACCEPTED MANUSCRIPT
III. RESULTS The ice-cube adheres onto the silicon substrate stably during the equilibration simulations, both with and without the sandwiched water layer. As shown in Fig. 1(a), the ice-cube can directly adhere onto the substrate in a solid-solid contact mode, and maintains its molecular structure of ice Ih. In contrast, the ice-cube exchanges water
CR IP T
molecules with the sandwiched interfacial water layer on the substrate in the solidliquid-solid contact mode during the simulation. At the end of the 100 ns equilibration, there is no clear border between ice-cube and the amorphous water. As depicted in Fig. 1(b), there is a stable ice Ih structure on top of the ice-water mixture, and an
adhesion mode is thus established.
AN US
amorphous yet fluidic water layer underneath. An effective solid-liquid-solid ice
The center-of-mass (COM) of the ice-cube finds a stable distance to the substrate surface during the equilibration. The ice-cube is placed onto the substrate in a way of avoiding atomic overlap, either with or without a sandwiched water layer, which
M
possibly results in gaps between atomistic sizes. The adhering process of the ice-cube seals these gaps. As shown in Fig. 2, the distance between the COM of the ice-cube
ED
and the substrate surface first decreases and then stabilized at a certain value. The icecube in the solid-solid contact mode reaches stable adhering distance much faster than
PT
in the solid-liquid-solid mode, namely ~1 ns vs. ~14 ns. Such time difference is expected, because the sandwiched water layer needs longer time to reach an
CE
equilibrated state.
AC
IV. SUMMARY This study focuses on modeling two adhesion modes of a nanoscale ice-cube on
silicon surface. The modeling approach adopts transferable all-atom force-field parameters, and can be used for large-scale molecular dynamics simulations for probing ice adhesion mechanics7. The results show a fast adhering process of the icecube onto the silicon substrate, with and without a sandwiched water layer, which indicates the effectiveness of atomistic modeling for nanoscale anti-icing study. These
4
ACCEPTED MANUSCRIPT
atomistic models provide a computational platform for enriching the theoretical base
AC
CE
PT
ED
M
AN US
CR IP T
of anti-icing research.
5
ACCEPTED MANUSCRIPT
ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from Statoil ASA (Norway) through the project of nanotechnology for anti-icing application, NTNU stjerneprogram, and the Research Council of Norway through the FRINATEK project Towards Design of Super-Low Ice Adhesion Surfaces (SLICE, 250990). The
AC
CE
PT
ED
M
AN US
Science (NOTUR NN9110k and NN9391k).
CR IP T
computational resources are provided by Norwegian Metacenter for Computational
6
ACCEPTED MANUSCRIPT
CR IP T
FIGURES AND FIGURE CAPTIONS
Figure 1. Atomistic structures of ice-cubes on silicon surfaces. (a) an ice-cube on a
AN US
smooth (100) silicon surface, showing snapshots of both initial structure (left) and after-100 ns equilibration (right); (b) the same ice-cube with a sandwiched interfacial amorphous water layer on the silicon surface, with initial (left) and equilibrated structures at 100 ns. Initial ice molecules are colored in white, and water molecules in
AC
CE
PT
ED
M
red. Silicon atoms are colored in gold.
7
AN US
CR IP T
ACCEPTED MANUSCRIPT
Figure 2. The height of the center-of-mass (COM) of the ice-cube from the silicon surface. The ice-cube finds a stable adhering state in two systems, signified by the
AC
CE
PT
ED
M
long stable plateaus of both curves.
8
ACCEPTED MANUSCRIPT
1
Kreder, M. J., Alvarenga, J., Kim, P. & Aizenberg, J. Design of anti-icing surfaces: smooth, textured or slippery? Nature Reviews
2
Lv, J., Song, Y., Jiang, L. & Wang, J. Bio-inspired strategies for anti-icing. ACS nano 8, 3152-3169 (2014).
3
CR IP T
Materials 1, 15003 (2016).
Wilen, L., Wettlaufer, J., Elbaum, M. & Schick, M. Dispersion-
AN US
force effects in interfacial premelting of ice. Physical Review B 52, 12426 (1995). 4
Ryzhkin, I. A. & Petrenko, V. F. Physical mechanisms responsible
5
ED
6270 (1997).
M
for ice adhesion. The Journal of Physical Chemistry B 101, 6267-
Chen, J., Luo, Z., Fan, Q., Lv, J. & Wang, J. Anti‐ Ice Coating
Wong, T.-S. et al. Bioinspired self-repairing slippery surfaces with
CE
6
PT
Inspired by Ice Skating. Small 10, 4693-4699 (2014).
pressure-stable omniphobicity. Nature 477, 443-447 (2011). Xiao, S., He, J. & Zhang, Z. Nanoscale deicing by molecular
AC
7
dynamics simulation. Nanoscale 8, 14625-14632 (2016).
8
Berendsen, H. J., Postma, J. P., van Gunsteren, W. F. & Hermans, J. in Intermolecular forces
9
331-342 (Springer, 1981).
Berendsen, H., Grigera, J. & Straatsma, T. The missing term in effective pair potentials. J. phys. Chem 91, 6269-6271 (1987). 9
ACCEPTED MANUSCRIPT
10
Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. & Klein, M. L. Comparison of simple potential functions for simulating liquid water. The Journal of chemical physics 79, 926935 (1983). Abascal, J., Sanz, E., Garcia Fernandez, R. & Vega, C. A potential
CR IP T
11
model for the study of ices and amorphous water: TIP4P/Ice. The Journal of chemical physics 122, 234511 (2005).
Vega, C., Sanz, E. & Abascal, J. The melting temperature of the
AN US
12
most common models of water. The Journal of chemical physics 122, 114507 (2005).
Jorgensen, W. L. & Tirado-Rives, J. The OPLS [optimized
M
13
potentials for liquid simulations] potential functions for proteins,
ED
energy minimizations for crystals of cyclic peptides and crambin.
14
PT
Journal of the American Chemical Society 110, 1657-1666 (1988). Lobban, C., Finney, J. & Kuhs, W. The structure of a new phase of
Abraham, M. J. et al. GROMACS: High performance molecular
AC
15
CE
ice. Nature 391, 268-270 (1998).
simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1, 19-25 (2015).
10
Modeling nanoscale ice adhesion Senbo Xiao , Jianying He , Zhiliang Zhang PII: DOI: Reference:
S0894-9166(17)30121-0 10.1016/j.camss.2017.05.001 CAMSS 26
To appear in:
Acta Mechanica Solida Sinica
Received date: Revised date: Accepted date:
10 April 2017 1 May 2017 2 May 2017
Please cite this article as: Senbo Xiao , Jianying He , Zhiliang Zhang , Modeling nanoscale ice adhesion, Acta Mechanica Solida Sinica (2017), doi: 10.1016/j.camss.2017.05.001
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Modeling Nanoscale Ice Adhesion Senbo Xiao1,*, Jianying He1 and Zhiliang Zhang1 1
NTNU Nanomechanical Lab, Department of Structural Engineering, Norwegian
University of Science and Technology (NTNU), Trondheim 7491, Norway *
CR IP T
Email: [email protected]
ABSTRACT
Anti-icing is crucial for numerous instruments and devices in low temperature circumstance. One of the approaches in anti-icing is to reduce ice adhesion strength,
AN US
seeking spontaneous de-icing processes by natural forces of gravity or by winds. In order to enable tailored surface icephobicity design, research requires a good theoretical understanding of the atomistic interacting mechanisms between water/ice molecules and their adhering substrates. Herein, this work focuses on using atomistic modeling and molecular dynamics simulation to build a nanosized ice-cube adhering
M
onto silicon surface, with different contact modes of solid-solid and solid-liquid-solid
ED
patterns. This study provides atomistic models for probing nanoscale ice adhesion mechanics and theoretical platforms for explaining experimental results.
CE
PT
Keywords: anti-icing, atomistic modeling, molecular dynamics.
I. INTRODUCTION
AC
Anti-icing research is driven by practical urgent needs in low-temperature
applications, as well as preventing injuries and saving lives in winter seasons 1. It is a new research topic and progresses extremely fast2. One of the focuses in anti-icing is to scrutinize the fundamentals of ice adhesion, i.e. to understand the atomistic interactions between water molecules and their adhering substrates, and ultimately to reduce ice adhesion strength by utilizing rational nanomechanical knowledge1. The nanoscale mechanisms of ice-adhesion turn out to be highly complex. It is believed that both van der Waals forces and electrostatic interactions are important to 1
ACCEPTED MANUSCRIPT
ice adhesion3,4. It is proven that a thin amorphous water layer can significantly reduce ice adhesion strength5, demonstrating the effects of interface water on ice adhesion. It is also reported that ice-slippery surfaces are highly promising for icephobic applications6. In order to construct systematic base for the full solution of unwanted excessive icing, all these encouraging studies need further atomistic-level investigation on ice adhesion mechanics. Yet, large-scale all-atom modeling is rarely
CR IP T
documented. Nanoscale deicing studies employing molecular dynamics simulation and transferable force-field parameters are still limited. It is the purpose of this study to understand nanoscale ice adhesion by computational approach. This article covers the modeling of an ice-cube on a silicon substrate in a direct solid-solid adhesion, and
AN US
in a solid-liquid-solid adhering mode with a sandwiched interfacial amorphous water layer. This study provides all-atom models for theoretical studies on nanoscale iceadhesion mechanics like those reported by Xiao et al.7, as well as tools for explaining experimental results.
M
II. METHODS
The first step in modeling atomistic ice adhesion is to choose the right water or
ED
ice molecule model. There are couples of transferable all-atom water models available, such as SPC8, SPC/E9, TIP3P, TIP4P10, and so on. Currently, all the popular water
PT
models are designed to reproduce the buck properties of water. How these water models can be used to study interface adhesion mechanics is subjected to further
CE
systematic testing. Here, the TIP4p/ice water model is chosen for modeling both an ice-cube and an aqueous water layer, given that it is reported to have appropriately
AC
reproduced ice and water properties as well as phase transition11. The TIP4p/ice water model also has a bulk melting point close to 273 K. All other water models give much lower melting points12, for example, 232 K for TIP4p water model10. We note that the ice melting temperatures of the available water models are different from experiments. It is unfeasible to study ice nucleation by atomistic modeling and molecular dynamics simulation based on the popular water models nowadays. The biggest challenge is the very small simulation time scale of the all-atom molecular dynamics simulation 2
ACCEPTED MANUSCRIPT
methodology. It is not the purpose of this very short manuscript to tackle such a big task. Rather, the choice of temperature in this modeling study is under the consideration of realizing the solid-solid and the solid-liquid-solid ice contact modes. The silicon substrate uses parameters from the popular OPLS force field13, and interacts with the TIP4p/ice water model via van der Waals forces. Two atomistic models are built in this study, capturing solid-solid and solid-
CR IP T
liquid-solid ice adhesion modes, as shown in Fig. 1. An ice-cube with geometry of 7.67.12.1 nm3 was constructed, with molecular structure of ice Ih, featuring the most common ice found in the biosphere14. The ice-cube was brought onto a silicon substrate, with and without a sandwiched water layer of 1.0 nm in thickness. The
AN US
silicon substrate has a (100) surface area of 22.2722.54 nm2, and expands infinitely by being treated with periodic boundary condition. The two systems are thus assembled together with all the molecular structures as close as possible, but without atomic overlap. The sizes of the systems range roughly from 45500 to 83000 atoms,
M
depending on the system setup.
Further structural optimization and equilibration are needed for obtaining stable
ED
adhesion of the ice-cube on the silicon surface. The molecular dynamics simulation package, GROMACS 5.0.515, is employed to achieve such a goal. The simulation
PT
parameters are the same as those in a former report7. Energy minimization utilizing steepest descent algorithm is first used to remove any possible close atom contacts.
CE
Subsequently, system equilibration of the models is carried out. Because the ice-cube and the sandwiched water layer models in this study are not in their bulk states, their
AC
melting points are previously found to be around 220 K7. In order to maintain structural stability, the ice-cube is coupled to a temperature of 180 K. The water layer is maintained at a temperature of 255 K for its fluidity. The silicon substrate is position-fixed during the course of simulations. Both systems are equilibrated for 100 ns. The final equilibrated structures are shown in Fig. 1.
3
ACCEPTED MANUSCRIPT
III. RESULTS The ice-cube adheres onto the silicon substrate stably during the equilibration simulations, both with and without the sandwiched water layer. As shown in Fig. 1(a), the ice-cube can directly adhere onto the substrate in a solid-solid contact mode, and maintains its molecular structure of ice Ih. In contrast, the ice-cube exchanges water
CR IP T
molecules with the sandwiched interfacial water layer on the substrate in the solidliquid-solid contact mode during the simulation. At the end of the 100 ns equilibration, there is no clear border between ice-cube and the amorphous water. As depicted in Fig. 1(b), there is a stable ice Ih structure on top of the ice-water mixture, and an
adhesion mode is thus established.
AN US
amorphous yet fluidic water layer underneath. An effective solid-liquid-solid ice
The center-of-mass (COM) of the ice-cube finds a stable distance to the substrate surface during the equilibration. The ice-cube is placed onto the substrate in a way of avoiding atomic overlap, either with or without a sandwiched water layer, which
M
possibly results in gaps between atomistic sizes. The adhering process of the ice-cube seals these gaps. As shown in Fig. 2, the distance between the COM of the ice-cube
ED
and the substrate surface first decreases and then stabilized at a certain value. The icecube in the solid-solid contact mode reaches stable adhering distance much faster than
PT
in the solid-liquid-solid mode, namely ~1 ns vs. ~14 ns. Such time difference is expected, because the sandwiched water layer needs longer time to reach an
CE
equilibrated state.
AC
IV. SUMMARY This study focuses on modeling two adhesion modes of a nanoscale ice-cube on
silicon surface. The modeling approach adopts transferable all-atom force-field parameters, and can be used for large-scale molecular dynamics simulations for probing ice adhesion mechanics7. The results show a fast adhering process of the icecube onto the silicon substrate, with and without a sandwiched water layer, which indicates the effectiveness of atomistic modeling for nanoscale anti-icing study. These
4
ACCEPTED MANUSCRIPT
atomistic models provide a computational platform for enriching the theoretical base
AC
CE
PT
ED
M
AN US
CR IP T
of anti-icing research.
5
ACCEPTED MANUSCRIPT
ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from Statoil ASA (Norway) through the project of nanotechnology for anti-icing application, NTNU stjerneprogram, and the Research Council of Norway through the FRINATEK project Towards Design of Super-Low Ice Adhesion Surfaces (SLICE, 250990). The
AC
CE
PT
ED
M
AN US
Science (NOTUR NN9110k and NN9391k).
CR IP T
computational resources are provided by Norwegian Metacenter for Computational
6
ACCEPTED MANUSCRIPT
CR IP T
FIGURES AND FIGURE CAPTIONS
Figure 1. Atomistic structures of ice-cubes on silicon surfaces. (a) an ice-cube on a
AN US
smooth (100) silicon surface, showing snapshots of both initial structure (left) and after-100 ns equilibration (right); (b) the same ice-cube with a sandwiched interfacial amorphous water layer on the silicon surface, with initial (left) and equilibrated structures at 100 ns. Initial ice molecules are colored in white, and water molecules in
AC
CE
PT
ED
M
red. Silicon atoms are colored in gold.
7
AN US
CR IP T
ACCEPTED MANUSCRIPT
Figure 2. The height of the center-of-mass (COM) of the ice-cube from the silicon surface. The ice-cube finds a stable adhering state in two systems, signified by the
AC
CE
PT
ED
M
long stable plateaus of both curves.
8
ACCEPTED MANUSCRIPT
1
Kreder, M. J., Alvarenga, J., Kim, P. & Aizenberg, J. Design of anti-icing surfaces: smooth, textured or slippery? Nature Reviews
2
Lv, J., Song, Y., Jiang, L. & Wang, J. Bio-inspired strategies for anti-icing. ACS nano 8, 3152-3169 (2014).
3
CR IP T
Materials 1, 15003 (2016).
Wilen, L., Wettlaufer, J., Elbaum, M. & Schick, M. Dispersion-
AN US
force effects in interfacial premelting of ice. Physical Review B 52, 12426 (1995). 4
Ryzhkin, I. A. & Petrenko, V. F. Physical mechanisms responsible
5
ED
6270 (1997).
M
for ice adhesion. The Journal of Physical Chemistry B 101, 6267-
Chen, J., Luo, Z., Fan, Q., Lv, J. & Wang, J. Anti‐ Ice Coating
Wong, T.-S. et al. Bioinspired self-repairing slippery surfaces with
CE
6
PT
Inspired by Ice Skating. Small 10, 4693-4699 (2014).
pressure-stable omniphobicity. Nature 477, 443-447 (2011). Xiao, S., He, J. & Zhang, Z. Nanoscale deicing by molecular
AC
7
dynamics simulation. Nanoscale 8, 14625-14632 (2016).
8
Berendsen, H. J., Postma, J. P., van Gunsteren, W. F. & Hermans, J. in Intermolecular forces
9
331-342 (Springer, 1981).
Berendsen, H., Grigera, J. & Straatsma, T. The missing term in effective pair potentials. J. phys. Chem 91, 6269-6271 (1987). 9
ACCEPTED MANUSCRIPT
10
Jorgensen, W. L., Chandrasekhar, J., Madura, J. D., Impey, R. W. & Klein, M. L. Comparison of simple potential functions for simulating liquid water. The Journal of chemical physics 79, 926935 (1983). Abascal, J., Sanz, E., Garcia Fernandez, R. & Vega, C. A potential
CR IP T
11
model for the study of ices and amorphous water: TIP4P/Ice. The Journal of chemical physics 122, 234511 (2005).
Vega, C., Sanz, E. & Abascal, J. The melting temperature of the
AN US
12
most common models of water. The Journal of chemical physics 122, 114507 (2005).
Jorgensen, W. L. & Tirado-Rives, J. The OPLS [optimized
M
13
potentials for liquid simulations] potential functions for proteins,
ED
energy minimizations for crystals of cyclic peptides and crambin.
14
PT
Journal of the American Chemical Society 110, 1657-1666 (1988). Lobban, C., Finney, J. & Kuhs, W. The structure of a new phase of
Abraham, M. J. et al. GROMACS: High performance molecular
AC
15
CE
ice. Nature 391, 268-270 (1998).
simulations through multi-level parallelism from laptops to supercomputers. SoftwareX 1, 19-25 (2015).
10