^{1}, Nobuyuki Matubayasi

^{1,a),b)}and Masaru Nakahara

^{1,a),c)}

### Abstract

The solvation shell dynamics of supercritical water is analyzed by molecular dynamics simulation with emphasis on its relationship to the translational and rotational dynamics. The relaxation times of the solvation number , the velocity autocorrelation function , the angular momentum correlation function , and the second-order reorientational correlation function are studied at a supercritical temperature of over a wide density region of . The relaxation times are decomposed into those conditioned by the solvation number , and the effect of the short-ranged structure is examined in terms of its probability of occurrence. In the low to medium-density range of , the time scales of water dynamics are in the following sequence: . This means that the rotation in supercritical water is of the “in-shell” type while the translational diffusion is not. The comparison to supercritical benzene is also performed and the effect of hydrogen bonding is examined. The water diffusion is not of the in-shell type up to the ambient density of , which corresponds to the absence of the transition from the collision to the Brownian picture, whereas such transition is present in the case of benzene. The absence of the transition in water comes from the fast reorganization of the hydrogen bonds and the enhanced mobility of the solvation shell in supercritical conditions.

This work is supported by the Grant-in-Aid for Scientific Research (No. 18350004) from the Japan Society for the Promotion of Science and the Grant-in-Aid for Scientific Research on Priority Areas (No. 15076205) and the Nanoscience Program of the Next-Generation Supercomputing Project from the Ministry of Education, Culture, Sports, Science, and Technology. One of the authors (N.M.) is also grateful to the grant from the Association for the Progress of New Chemistry, the grant from JST-CREST (Japan Science Technology Agency-Core Research for the Evolutional Science and Technology), the grant from the Suntory Institute for Bioorganic Research, and the Supercomputer Laboratory of Institute for Chemical Research, Kyoto University. One of the authors (M.N.) further acknowledges the ENEOS Hydrogen Trust Fund.

I. INTRODUCTION

II. METHODS

A. Molecular dynamics simulation

B. Shell decomposition of the time correlation function

C. Physical concepts based on conditional correlation time

III. RESULTS AND DISCUSSION

A. Solvation shell dynamics

B. Translational dynamics

C. Rotational dynamics

IV. CONCLUSIONS

### Key Topics

- Hydrogen bonding
- 29.0
- Rotational dynamics
- 25.0
- Relaxation times
- 20.0
- Molecular dynamics
- 14.0
- Diffusion
- 13.0

## Figures

The probability of finding a molecule with other surrounding molecules for water (a) at and (b) at 0.01 and ; the probability of finding a molecule with for water (c) at and (d) at 0.01 and ; for benzene (e) at and (f) at 0.01 and . The solid and dashed lines in (a), (c), and (e) represent and at a supercritical temperature of and at an ambient state, respectively. The numbers in (a), (c), and (e) represent the bulk density in the unit of . (g) The average of the solvation number divided by the bulk density as a function of the bulk density . Open symbols represent the values at an ambient state.

The probability of finding a molecule with other surrounding molecules for water (a) at and (b) at 0.01 and ; the probability of finding a molecule with for water (c) at and (d) at 0.01 and ; for benzene (e) at and (f) at 0.01 and . The solid and dashed lines in (a), (c), and (e) represent and at a supercritical temperature of and at an ambient state, respectively. The numbers in (a), (c), and (e) represent the bulk density in the unit of . (g) The average of the solvation number divided by the bulk density as a function of the bulk density . Open symbols represent the values at an ambient state.

The relaxation time of the solvation shell as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . (c) of water conditioned by the number of hydrogen bonding as a function of . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively. For each and , the data at supercritical states correspond to the bulk densities of (a) , (b) , and (c) from top to bottom.

The relaxation time of the solvation shell as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . (c) of water conditioned by the number of hydrogen bonding as a function of . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively. For each and , the data at supercritical states correspond to the bulk densities of (a) , (b) , and (c) from top to bottom.

The self-diffusion coefficients of water and benzene plotted against the density in the form of the product . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The self-diffusion coefficients of water and benzene plotted against the density in the form of the product . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The velocity autocorrelation time as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively. For each , the data at supercritical states correspond to the bulk densities of (a) and (b) from top to bottom.

The velocity autocorrelation time as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively. For each , the data at supercritical states correspond to the bulk densities of (a) and (b) from top to bottom.

The ratio plotted against the density for water, benzene (OPLS-AA), and LJ. The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The ratio plotted against the density for water, benzene (OPLS-AA), and LJ. The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The normalized velocity autocorrelation function of water at for 1, (b) 5, (c) 10, and (d) 14. The data correspond to the bulk densities of from top to bottom. The data are absent at for , 10, and 14, at for , 10, and 14, at for and 14, at for and 14, at for , at for , at for , 5, and 10, and at 1.2 and due to the negligible probabilities for the corresponding .

The normalized velocity autocorrelation function of water at for 1, (b) 5, (c) 10, and (d) 14. The data correspond to the bulk densities of from top to bottom. The data are absent at for , 10, and 14, at for , 10, and 14, at for and 14, at for and 14, at for , at for , at for , 5, and 10, and at 1.2 and due to the negligible probabilities for the corresponding .

The normalized velocity autocorrelation function of benzene at for 1, (b) 5, (c) 10, and (d) 14. The data correspond to the bulk densities of from top to bottom. The data are absent at for , 10, and 14, at for , 10, and 14, at for and 14, at for and 14, at for , at for and 5, and at for , 5, and 10 due to the negligible probabilities for the corresponding .

The normalized velocity autocorrelation function of benzene at for 1, (b) 5, (c) 10, and (d) 14. The data correspond to the bulk densities of from top to bottom. The data are absent at for , 10, and 14, at for , 10, and 14, at for and 14, at for and 14, at for , at for and 5, and at for , 5, and 10 due to the negligible probabilities for the corresponding .

The angular momentum correlation time as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The angular momentum correlation time as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The reorientational correlation time as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The reorientational correlation time as a function of the solvation number ; (a) water at supercritical states of and and at an ambient state of and and (b) benzene (OPLS-AA) at supercritical states of and and at an ambient state of and . The filled and open symbols represent at a supercritical temperature of and at an ambient state, respectively.

The ratios (a) and (b) plotted against the density for water and benzene. The filled and open symbols represent and at a supercritical temperature of and at an ambient state, respectively.

The ratios (a) and (b) plotted against the density for water and benzene. The filled and open symbols represent and at a supercritical temperature of and at an ambient state, respectively.

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