How does water freeze inside carbon nanotubes?

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Abstract

Phase behavior of quasi-one-dimensional water confined inside a carbon nanotube is studied in the thermodynamic space of temperature, pressure, and diameter of the cylindrical container. Four kinds of solid-like ordered structures—ice nanotubes—form spontaneously from liquid-like disordered phases at low temperatures. In the model system that comprises of TIP4P water molecules interacting with each other via short-range Lennard–Jones and long-range Coulomb site–site potentials under a periodic boundary condition in the axial direction, the phase change occurs either discontinuously or continuously depending on the path in the thermodynamic space. That the isotherms for a given diameter are found to be similar to those around the liquid–gas critical point of fluids suggests existence of a phase boundary terminated by a critical point. The apparently-complex phase behavior is accounted for by noting that the phase boundaries are layered surfaces in the three-dimensional thermodynamic space and some of the surfaces are terminated by critical lines.

Introduction

Phase behavior of water is very rich; there are 13 polymorphic phases of bulk ice identified experimentally thus far [1], the high- and low-density amorphous phases observed experimentally [2], [3], and the high- and low-density liquid phases suggested by simulations in the experimentally inaccessible region [4], [5]. Recent studies of phase behavior of water confined in narrow spaces have suggested the possibility of various condensed phases of water, and phase transitions between them in quasi-two-dimensional (Q2D) water [6], [7]. Here, we present some recent results on water confined in very narrow cylindrical spaces—quasi-one-dimensional (Q1D) water—under various thermodynamic conditions. Specifically, we examine water confined inside carbon nanotubes since they provide well-defined cylindrical spaces and can be wet by low-surface-tension liquids including water [8].

Encapsulation of a second phase inside carbon nanotubes offers a new avenue to investigate dimensionally confined phase transitions [9], [10]. When pure liquid water is encapsulated inside narrow carbon nanotubes, water molecules would be expected to line up into some quasi-one-dimensional structures, and on freezing, may exhibit quite different crystalline structures from bulk ice. Crystallization of water is known to be highly non-universal [11], i.e., the stable (or metastable) ice phase selected upon crystallization depends sensitively on the external environment. Thus, the first question we try to address is what type of crystalline lattice could be selected on cooling the confined water in narrow carbon nanotubes. Confinement may change not only resulting crystalline structures but also the way liquids freeze. For example, it has been conjectured [12] that in carbon nanotubes confined matter may exhibit an uncommon solid–liquid critical point [13] beyond which distinction between solid and liquid no longer exists. Thus the second question to be raised here is how water freezes and melts inside carbon nanotubes.

Section snippets

Model system

The model system consists of N molecules confined inside a cylindrical pore of diameter D. The intermolecular interaction is taken to be the TIP4P water whose potential energy is given by the sum of the long-range Coulomb potential and the short-range Lennard–Jones (LJ) potential between the interaction sites. The potential function is truncated at 8.75Å by a switching function. The force field of the model carbon nanotube is taken to be a LJ potential integrated over the cylindrical area of

Structures of Q1D water at low temperatures

Shown in Fig. 1 are structures of the TIP4P water in the cylindrical hollow space of the model carbon nanotubes at low- and high-temperatures. The low-T phases are those reached by cooling stepwise the high-T phases under Pzz=50MPa. It is clear that the high-T phases have disordered structures with incomplete hydrogen-bond networks whereas the low-T phases have ordered structures with perfect networks. Specifically, the low-T phases are Q1D n-gonal ‘ice nanotubes’ [16] composed of n-membered

Phase behavior of Q1D water

Now we consider how the liquid-like disordered phases turn into the solid-like phases. Fig. 2 shows molar volume changes against temperature for six systems (R=13,…,18) under 50MPa. For R=16 and 17, there are discontinuous changes in volume and hysteresis loops. It is meant by ‘discontinuous’ that there is a sudden change of the quantity when measured in units of 5K. These discontinuous changes correspond to structural changes between liquid-like and solid-like phases (hexagonal and heptagonal

Phase diagram

Before we discuss the phase diagrams of confined water, some remarks are given on what we mean by ‘phase boundary’ in the Q1D systems. We note that although computer simulation cannot prove or disprove the existence of a true phase transition, or singularity in the partition function, in the thermodynamic limit N→∞, extrapolation of its results at finite N to the thermodynamic limit is commonly accepted in 2D and 3D systems because we know there exist true phase transitions. A Q1D system,

Acknowledgements

KK wishes to thank Professor B. Widom for valuable discussions on the phase transition. KK and HT are supported by Japan Society for the Promotion of Science (JSPS), the Japan Ministry of Education, and IMS. XCZ is supported by US National Science Foundation and ONR. KK is visiting Cornell University under JSPS Fellowship for Research Abroad 2001.

References (18)

  • C. Lobban et al.

    J. Chem. Phys.

    (2000)
  • O. Mishima et al.

    Nature

    (1984)
  • O. Mishima et al.

    Nature

    (1984)
  • P.H. Poole et al.

    Nature

    (1992)
  • H. Tanaka

    Nature

    (1996)
  • K. Koga et al.

    Phys. Rev. Lett.

    (1997)
  • K. Koga et al.

    Nature

    (2000)
  • E. Dujardin et al.

    Science

    (1994)
  • J. Sloan et al.

    J. Mater. Chem.

    (1997)
There are more references available in the full text version of this article.

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