^{1}, Miguel A. Gonzalez

^{1}, Juan L. Aragones

^{1}and C. Valeriani

^{1}

### Abstract

We investigate vapor bubble nucleation in metastable TIP4P/2005 water at negative pressure via the Mean First Passage Time (MFPT) technique using the volume of the largest bubble as a local order parameter. We identify the bubbles in the system by means of a Voronoi-based analysis of the molecular dynamics trajectories. By comparing the features of the tessellation of liquid water at ambient conditions to those of the same system with an empty cavity we are able to discriminate vapor (or interfacial) molecules from the bulk ones. This information is used to follow the time evolution of the largest bubble until the system cavitates at 280 K above and below the spinodal line. At the pressure above the spinodal line, the MFPT curve shows the expected shape for a moderately metastable liquid from which we estimate the bubble nucleation rate and the size of the critical cluster. The nucleation rate estimated using Classical Nucleation Theory turns out to be about 8 order of magnitude lower than the one we compute by means of MFPT. The behavior at the pressure below the spinodal line, where the liquid is thermodynamically unstable, is remarkably different, the MFPT curve being a monotonous function without any inflection point.

This work has been funded by Grant Nos. FIS2010/16159 of the MEC, P2009/ESP-1691 of CAM, and the Marie Curie Integration Grant PCIG-GA-2011-303941 (ANISOKINEQ). C.V. also acknowledges financial support from a Juan de La Cierva Fellowship. We acknowledge Carlos Vega for helpful discussions and a critical reading of the manuscript.

I. INTRODUCTION

II. METHODS

A. Algorithm used for the Voronoi tessellation

B. Molecular dynamics simulations

III. VORONOI TESSELLATION AS A TOOL FOR DETECTING BUBBLES

A. Test case: Liquid water with an empty cavity

B. Metastable and unstable water

IV. MEAN FIRST-PASSAGE TIMES AND NUCLEATION RATES

V. DISCUSSION AND CONCLUSIONS

### Key Topics

- Nucleation
- 56.0
- Cavitation
- 17.0
- Carbon nanotubes
- 14.0
- Molecular liquids
- 11.0
- Polyhedra
- 11.0

## Figures

Particles A and B have not been identified by the grid as Voronoi neighbours. As a consequence the filled region would be ascribed to both particles (and it would be counted twice). Since A and B have C and D as common neighbors, the expansion of the initial list for A and B to include particles with a given number of common neighbors (see step 2 in the text) would allow to divide the filled volume among A and B.

Particles A and B have not been identified by the grid as Voronoi neighbours. As a consequence the filled region would be ascribed to both particles (and it would be counted twice). Since A and B have C and D as common neighbors, the expansion of the initial list for A and B to include particles with a given number of common neighbors (see step 2 in the text) would allow to divide the filled volume among A and B.

Distribution of VP volumes for TIP4P/2005 water at 298 K, 1 bar. The difference between the systems is that in one of them an empty spherical cavity of 30 molecules has been created.

Distribution of VP volumes for TIP4P/2005 water at 298 K, 1 bar. The difference between the systems is that in one of them an empty spherical cavity of 30 molecules has been created.

Distribution of VP nonsphericity parameter for the systems of Fig. 2 .

Distribution of VP number of faces for the systems of Fig. 2 .

Anisotropic factor α as a function of volume for the systems of Fig. 2 . The black line α = 1.5 − 19*(*V* − 0.04) separates bulk molecules from interfacial molecules.

Anisotropic factor α as a function of volume for the systems of Fig. 2 . The black line α = 1.5 − 19*(*V* − 0.04) separates bulk molecules from interfacial molecules.

Time evolution of the average volume per molecule for two runs of a point in the metastable region (T = 280 K, p = −2250 bar). The sharp increase of the volume at the end of the simulations corresponds to cavitation events.

Time evolution of the average volume per molecule for two runs of a point in the metastable region (T = 280 K, p = −2250 bar). The sharp increase of the volume at the end of the simulations corresponds to cavitation events.

Distribution of the reduced VP volumes for metastable water (T = 280 K, p = −2250 bar) compared to that of liquid water at ambient conditions with a cavity. VO is the average volume of the liquid molecules.

Distribution of the reduced VP volumes for metastable water (T = 280 K, p = −2250 bar) compared to that of liquid water at ambient conditions with a cavity. VO is the average volume of the liquid molecules.

Anisotropic factor as a function of volume for metastable water (red crosses) compared to that of liquid water (empty blue circles). The black line α = 1.5 − 18*(*V* − 0.048) separates liquid-like molecules from vapor (interfacial) molecules.

Anisotropic factor as a function of volume for metastable water (red crosses) compared to that of liquid water (empty blue circles). The black line α = 1.5 − 18*(*V* − 0.048) separates liquid-like molecules from vapor (interfacial) molecules.

Anisotropic factor as a function of volume for unstable water (red crosses) (T = 280 K, p = −2630 bar) compared to that of liquid water (empty blue circles) (scaled).

Anisotropic factor as a function of volume for unstable water (red crosses) (T = 280 K, p = −2630 bar) compared to that of liquid water (empty blue circles) (scaled).

Time evolution of the volume of the largest bubble for the runs of Fig. 6 .

Comparison of the MFPT obtained for metastable (blue) and unstable (red) TIP4P/2005 water at 280 K. Since the trajectories change very little from one configuration to the next one, we only analyze them every 0.5 ps. Notice that a different scale is used for each of the curves (metastable liquid on the left axis and unstable on the right axis). Standard deviations of τ have been computed for each curve and three points at low, medium, and large volumes.

Comparison of the MFPT obtained for metastable (blue) and unstable (red) TIP4P/2005 water at 280 K. Since the trajectories change very little from one configuration to the next one, we only analyze them every 0.5 ps. Notice that a different scale is used for each of the curves (metastable liquid on the left axis and unstable on the right axis). Standard deviations of τ have been computed for each curve and three points at low, medium, and large volumes.

A snapshot of the growth of a bubble. The image on the top corresponds to a precritical bubble and the image on the bottom corresponds to a postcritical one along the same trajectory (the configurations are separated by 0.02 ps).

A snapshot of the growth of a bubble. The image on the top corresponds to a precritical bubble and the image on the bottom corresponds to a postcritical one along the same trajectory (the configurations are separated by 0.02 ps).

MFPT for metastable water using two different VP parameters to distinguish liquid from “vapor” molecules.

MFPT for metastable water using two different VP parameters to distinguish liquid from “vapor” molecules.

MFPT for metastable water for three different sampling times (configurations are analyzed every Δt ps).

MFPT for metastable water for three different sampling times (configurations are analyzed every Δt ps).

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