Takahiro Koishi

Coexistence and transition between Cassie and Wenzel state on pillared hydrophobic surface

Water droplets on rugged hydrophobic surfaces typically exhibit one of the following two states: (i) the Wenzel state [Wenzel RN (1936) Ind Eng Chem 28:988–994] in which water droplets are in full contact with the rugged surface (referred as the wetted contact) or (ii) the Cassie state [Cassie, ABD, Baxter S (1944) Trans Faraday Soc 40:546–551] in which water droplets are in contact with peaks of the rugged surface as well as the “air pockets” trapped between surface grooves (the composite contact). Here, we show large-scale molecular dynamics simulation of transition between Wenzel state and Cassie state of water droplets on a periodic nanopillared hydrophobic surface. Physical conditions that can strongly affect the transition include the height of nanopillars, the spacing between pillars, the intrinsic contact angle, and the impinging velocity of water nanodroplet (“raining” simulation). There exists a critical pillar height beyond which water droplets on the pillared surface can be either in the Wenzel state or in the Cassie state, depending on their initial location. The free-energy barrier separating the Wenzel and Cassie state was computed on the basis of a statistical-mechanics method and kinetic raining simulation. The barrier ranges from a few tenths of kBT0 (where kB is the Boltzmann constant, and T0 is the ambient temperature) for a rugged surface at the critical pillar height to ≈8 kBT0 for the surface with pillar height greater than the length scale of water droplets. For a highly rugged surface, the barrier from the Wenzel-to-Cassie state is much higher than from Cassie-to-Wenzel state. Hence, once a droplet is trapped deeply inside the grooves, it would be much harder to relocate on top of high pillars.

Measurement of contact-angle hysteresis for droplets on nanopillared surface and in the Cassie and Wenzel states: A molecular dynamics simulation study

We perform large-scale molecular dynamics simulations to measure the contact-angle hysteresis for a nanodroplet of water placed on a nanopillared surface. The water droplet can be in either the Cassie state (droplet being on top of the nanopillared surface) or the Wenzel state (droplet being in contact with the bottom of nanopillar grooves). To measure the contact-angle hysteresis in a quantitative fashion, the molecular dynamics simulation is designed such that the number of water molecules in the droplets can be systematically varied, but the number of base nanopillars that are in direct contact with the droplets is fixed. We find that the contact-angle hysteresis for the droplet in the Cassie state is weaker than that in the Wenzel state. This conclusion is consistent with the experimental observation. We also test a different definition of the contact-angle hysteresis, which can be extended to estimate hysteresis between the Cassie and Wenzel state. The idea is motivated from the appearance of the hysteresis loop typically seen in computer simulation of the first-order phase transition, which stems from the metastability of a system in different thermodynamic states. Since the initial shape of the droplet can be controlled arbitrarily in the computer simulation, the number of base nanopillars that are in contact with the droplet can be controlled as well. We show that the measured contact-angle hysteresis according to the second definition is indeed very sensitive to the initial shape of the droplet. Nevertheless, the contact-angle hystereses measured based on the conventional and new definition seem converging in the large droplet limit.

Large-scale molecular-dynamics simulation of nanoscale hydrophobic interaction and nanobubble formation

We performed large-scale molecular-dynamics simulation of nanoscale hydrophobic interaction manifested by the formation of nanobubble between nanometer-sized hydrophobic clusters at constrained equilibrium. Particular attention is placed on the tendency of formation and stability of nanobubbles in between model nanoassemblies which are composed of hydrophobic clusters (or patches) embedded in a hydrophilic substrate. On the basis of physical behavior of nanobubble formation, we observed a change from short-range molecular hydrophobic interaction to midrange nanoscopic interaction when the length scale of hydrophobe approaches to about 1 nm. We investigated the behavior of nanobubble formation with several different patterns of nonpolar-site distribution on the nanoassemblies but always keeping a constant ratio of nonpolar to polar monomer sites. Dynamical properties of confined water molecules in between nanoassemblies are also calculated.

Extended study of molecular dynamics simulation of homogeneous vapor-liquid nucleation of water

Using the simple point charge/extended water model, we performed molecular dynamics simulations of homogeneous vapor-liquid nucleation at various values of temperature T and supersaturation S, from which the nucleation rate J, critical nucleus size n(*), and the cluster formation free energy DeltaG were derived. As well as providing lots of simulation data, the results were compared with theories on homogeneous nucleation, including the classical, semi-phenomenological, and scaled models, but none of these gave a satisfactory explanation for our results. It was found that two main factors made the theories fail: (1) The average cluster structure including the nonspherical shape and the core structure that is not like the bulk liquid and (2) the forward rate which is larger than assumed by the theories by about one order of magnitude. The quantitative evaluation of these factors is left for future investigations.

An 8.61 Tflop/s Molecular Dynamics Simulation for NaCl with a Special-Purpose Computer: MDM

We performed molecular dynamics (MD) simulation of 33 million pairs of NaCl ions with the Ewald summation and obtained a calculation speed of 8.61 Tflop/s. In this calculation we used a special-purpose computer, MDM, which we have developed for the calculations of the Coulomb and van der Waals forces. The MDM enabled us to perform large scale MD simulations without truncating the Coulomb force. It is composed of MDGRAPE-2, WINE-2 and a host computer. MDGRAPE-2 accelerates the calculation for real-space part of the Coulomb and van der Waals forces. WINE-2 accelerates the calculation for wavenumber-space part of the Coulomb force. The host computer performs other calculations. With the completed MDM system we performed an MD simulation similar to what was the basis of our SC2000 submission for a Gordon Bell prize. With this large scale MD simulation, we can dramatically decrease the fluctuation of the temperature less than 0.1 Kelvin.

Large scale molecular dynamics simulation of nucleation in supercooled NaCl

Nucleation of NaCl was reproduced by using molecular dynamics simulation. We carried out MD simulations in the 13 824 ion system under the free boundary condition. Critical nucleus size, nucleation time lag, and nucleation rate were directly estimated from simulation results without using nucleation theory. We also carried out MD simulations in the 13 824 and 125 000 ion systems under the periodic boundary condition to compare the results with those of the free boundary condition. A single crystal and a polycrystal were formed in our simulation. We investigated the difference of the nucleation process of a single crystal and a polycrystal. All simulations were calculated by using the special purpose computer, MDGRAPE-2, for molecular dynamics simulation.

Transport Coefficients in Molten NaCl by Computer Simulation

By using well-known pairwise potentials, the transport coefficients such as diffusion constant, viscosities and electrical conductivities in molten NaCl have been simulated as a function of temperature. In deriving the conductivity, a nonequilibrium molecular dynamics technique has newly applied and obtained results at several temperatures agree quantitatively with the experimental results. Using the simulated diffusion constants, D + and D - , and the partial electrical conductivities σ + and σ - , deviations from the Nernst-Einstein relation, for positive and negative ions Δ + and Δ - , at several temperatures are also estimated. The average values for Δ + and Δ - are the order of 0.1 and comparable to the experimental result.

Partial Conductivities of a Molten Salt Based on Langevin Equation

Based on the Langevin equations for cations and anions in a molten salt, the ionic partial conductivities are discussed in connection with their masses. These partial conductivities are shown in terms of current-current correlation functions as an extension of Kubo theory. And these partial conductivities are also described in terms of conductivity tensors which are introduced from the macroscopic irreversible thermodynamic viewpoint. These theoretical results are justified by the molecular dynamics simulations carried out for molten NaCl and NaI.

Computer Simulation of Molten Li2CO3-K2CO3 Mixtures.

We have carried out the molecular dynamics simulation for molten Li 2 CO 3 -K 2 CO 3 mixtures. The structural feature was revealed from the obtained radial distribution function and angular distribution function. The dynamic properties such as diffusion constant and the electrical conductivity were also derived. The nonequilibrium molecular dynamics was performed to calculate the electrical conductivity. The relation of the concentration dependence of dynamical properties and structural change was discussed.We have carried out the molecular dynamics simulation for molten Li 2 CO 3 -K 2 CO 3 mixtures. The structural feature was revealed from the obtained radial distribution function and angular distribution function. The dynamic properties such as diffusion constant and the electrical conductivity were also derived. The nonequilibrium molecular dynamics was performed to calculate the electrical conductivity. The relation of the concentration dependence of dynamical properties and structural change was discussed.We have carried out the molecular dynamics simulation for molten Li 2 CO 3 -K 2 CO 3 mixtures. The structural feature was revealed from the obtained radial distribution function and angular distribution function. The dynamic properties such as diffusion constant and the electrical conductivity were also derived. The nonequilibrium molecular dynamics was performed to calculate the electrical conductivity. The relation of the concentration dependence of dynamical properties and structural change was discussed.

A 281 Tflops calculation for X-ray protein structure analysis with special-purpose computers MDGRAPE-3

We have achieved a sustained calculation speed of 281 Tflops for the optimization of the 3-D structures of proteins from the X-ray experimental data by the Genetic Algorithm - Direct Space (GA-DS) method. In this calculation we used MDGRAPE-3, special-purpose computer for molecular simulations, with the peak performance of 752 Tflops. In the GA-DS method, a set of selected parameters which define the crystal structures of proteins is optimized by the Genetic Algorithm. As a criterion to estimate the model parameters, we used the reliability factor R1 which indicates the statistical difference between the calculated and the measured diffraction data. To evaluate this factor it is necessary to reconstruct the diffraction patterns of the model structures every time the model is updated. Therefore, in this method the nonequispaced Discrete Fourier Transformation (DFT) used to calculate the diffraction patterns dominates most of the computation time. To accelerate DFT calculations, we used the special-purpose computer, MDGRAPE-3. A molecule, Carbamoyl-Phosphate Synthetase was investigated. The final reliability factors were much smaller than the typical values obtained in other methods such as the Molecular Replacement (MR) method. Our results successfully demonstrate that high-performance computing with GA-DS method on special-purpose computers is effective for the structure determination of biological molecules and the method has a potential to be widely used in near future.