RAPID COMMUNICATIONS PHYSICAL REVIEW E 92, 030301(R) (2015) Dynamics of supercooled water in nanotubes: Cage correlation function and diffusion coefﬁcient Mahdi Khademi, Rajiv K. Kalia, and Muhammad Sahimi * Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1211, USA (Received 14 January 2015; revised manuscript received 13 July 2015; published 29 September 2015) Dynamics of low-temperature water in nanostructured materials is important to a variety of phenomena, ranging from transport in cement and asphaltene, to conformational dynamics of proteins in “crowded” cellular environments, survival of microorganisms at very low temperatures, and diffusion in nanogeoscience. Using silicon-carbide nanotubes as a prototype of nanostructured materials, extensive molecular dynamics simulations were carried out to study the cage correlation function C(t ) and self-diffusivity D of supercooled water in the nanotubes. C(t ), which measures changes in the atomic surroundings inside the nanotube, follows the Kohlrausch-Williams-Watts law, C(t ) ∼ exp[−(t/τ ) β ], where τ is a relaxation time and β is a topological exponent. For the temperature range 220 K <T  273 K, we ﬁnd β ≃ 0.438, in excellent agreement with and conﬁrming the prediction by Phillips [Rep. Prog. Phys. 59, 1133 (1996)], β = 3/7. The self-diffusivity manifests a transition around 230 K, very close to 228 K, the temperature at which a fragile-to-strong dynamic crossover is supposed to happen. Thus the results indicate that water does not freeze in the nanotube over the studied temperature range, and that the Stokes-Einstein relation breaks down. DOI: 10.1103/PhysRevE.92.030301 PACS number(s): 61.20.Ja, 64.70.D−, 81.07.De I. INTRODUCTION Water, in addition to being a fundamental ingredient of life, has many unusual properties [1], such as the lowest density at 4 ◦ C, as well as its coexistence within two distinct forms—polymorphism [2]—and the abnormal behavior of its isothermal compressibility, isobaric heat capacity, and thermal expansion coefﬁcient at temperatures between homogeneous nucleation (231 K) and its melting point of 273 K, all of which have been studied intensively. In addition, water can be in a supercooled state between 273 K and about 230 K [1]. The supercooled liquid state is important from a biological standpoint because it can preserve microorganism during freezing. In contrast to other liquids, at 273 K and lower temperatures, water volumetric expansion is associated with reduction in the entropy due to the tetrahedral symmetry of the local order around each water molecule [1], related to hydrogen bonding. Under bulk conditions three forms of glassy water exist, namely, low-density amorphous (LDA) ice, and high-density and very high-density amorphous (HDA and VHDA, respectively) ice. The region between homogeneous nucleation temperature (231 K) and crystallization tempera- ture is above the glass transition temperature of 165 K. The gradual crystallization process by decreasing the temperature has been explained by the hypothesis that there exists a liquid- liquid critical point, based on structural changes governed by hydrogen bonds during water clustering process, and the development of a tetrahedral-coordinated network. The nature of water at 228 K, which has been hypothesized to be a second, low-temperature critical point of water, is still under investigation. Even more interesting and important phenomena occur when water is in conﬁned media. Understanding various properties of water in such media is highly important to many physical, chemical, and biological phenomena, as they appear * moe@usc.edu to be fundamentally different from their bulk counterparts. For example, diffusion of water in nanopores and nanotubes is governed by a process that is different from the bulk phase [3–5], because while diffusion under bulk conditions follows the Einstein relation and only local temperature and pressure inﬂuence the transport process, the same is not true about water diffusion in a conﬁned medium. In such a medium the interactions of water molecules with the solid walls, which are mainly of the van der Waals and Coulombic type, affect their mobility and usually reduce the rate of molecular diffusion [6,7]. Moreover, a water molecule in the bulk is, on average, hydrogen-bonded to four neighboring molecules. If one hydrogen bond breaks, the O-H-O conﬁguration moves away from linearity by more than 25 ◦ , and as three or four H- bonds are broken, the molecules undergo rotational diffusion. This is not, however, the case in a conﬁned medium. Thus, de- spite considerable experimental and theoretical-computational works to understand the possible deviations of the behavior of water molecules in conﬁned media from that in the bulk, no reasonably complete understanding of the properties of water in conﬁned media has emerged. For example, it is not yet clear whether the Stokes-Einstein relation is followed by water molecules in nanotubes. One way of achieving subcooling is [8] to use pores larger than a critical size of 3–4 nm, in which water freezes to a mixture of cubic crystals and amorphous ice. In smaller pores, however, water does not crystallize. Another possibility is to study the behavior of water in nanotubes. Kolesnikov et al. [9] investigated the behavior of encapsulated water inside carbon nanotubes (CNTs), and reported an anomalous “soft” dy- namics characterized by pliable hydrogen bonds, anharmonic intermolecular potentials, and large-amplitude motions. They proposed that the structure of water in nanotubes consists of a square-ice sheet wrapped into a cylinder inside the CNT with the interior molecules being in a chainlike conﬁguration, and that the motion of the water molecules is enhanced along the chains. Such an enhanced motion well below the freezing point has been veriﬁed experimentally. 1539-3755/2015/92(3)/030301(6) 030301-1 ©2015 American Physical Society