How does water freeze inside carbon nanotubes?

Abstract

Phase behavior of quasi-one-dimensional water conÿned 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 uids 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.

Phase diagram of water between hydrophobic surfaces

“…The first evidence for such transitions was again obtained from MD simulations combined with free-energy calculations: the simulations demonstrated that water inside a carbon nanotube freezes into four different forms of the ice nanotube, a class of quasi-one-dimensional crystalline ices. 17,18 The predicted formation of the ice nanotube was confirmed by experiments of Maniwa et al 19 The structure, dynamics, and thermodynamic properties of confined water depend on many factors such as confining geometry and physical and chemical properties of surfaces, and the effect of each factor is as yet little understood. Thus it is sensible to choose and study, among many possibilities, model systems with simpler geometries ͑e.g., slit and cylindrical pores͒ and simpler surfaces ͑e.g., structureless surfaces͒.…”

Multiwalled ice helixes and ice nanotubes

“…All MD simulations were performed by using a constant temperature/constant axial pressure ensemble (5,6). Periodic boundary conditions were applied only in the axial (z) direction.…”

Formation of ice nanotube with hydrophobic guests inside carbon nanotube

“…20 Divide the hollow space into n w subsystems, each of which is multiply occupied by guests, and take into account indistinguishability o f the same kind of guest molecules. Then, the relevant grandcanonical partition function is given as = e x p ( ; n w A 0 w ) nm X ng=0 expf (n g g ; f ng )g] nw (2) where f ng is the free energy of occupancy by n g guest molecules of the mass m in a subsystem. The average guest numberis calculated as < N g >= @ ln @( g ) = n w P ng=1 n g expf (n g g ; f ng )g] P ng=0 expf (n g g ; f ng )g] :…”

“…However, recent theoretical studies on water con ned in the carbon nanotube and the experimental studies followed have demonstrated that the con ned water freezes into crystalline structures that have n e v er been found in the bulk counterpart and exhibits continuous and discontinuous freezing transitions. 1,2 Computer simulation studies revealed that the structure of solid water in the zigzag (`, 0) single-walled carbon nanotube (SWCN) (with`=13, 14, ..., or 17) is quite di erent from the bulk ice structure it is a one-dimensional array o f n-gonal \rings", called an ice nanotube. 1,2 As in the ordinary ice, every water molecule in the carbon nanotube is hydrogen-bonded to its four neighbors in the solid state.…”

“…1,2 Computer simulation studies revealed that the structure of solid water in the zigzag (`, 0) single-walled carbon nanotube (SWCN) (with`=13, 14, ..., or 17) is quite di erent from the bulk ice structure it is a one-dimensional array o f n-gonal \rings", called an ice nanotube. 1,2 As in the ordinary ice, every water molecule in the carbon nanotube is hydrogen-bonded to its four neighbors in the solid state. Thus far, the simulations 1,2 with the TIP4P potential 3 have s h o wn that liquid water con ned in carbon nanotubes freezes into square, pentagonal, hexagonal, and heptagonal forms of the ice nanotube, each corresponding to n =4, 5, 6, and 7, respectively.…”