Confinement of matter on the nanometre scale can induce phase transitions not seen in bulk systems1. In the case of water, so-called drying transitions occur on this scale2,3,4,5 as a result of strong hydrogen-bonding between water molecules, which can cause the liquid to recede from nonpolar surfaces to form a vapour layer separating the bulk phase from the surface6. Here we report molecular dynamics simulations showing spontaneous and continuous filling of a nonpolar carbon nanotube with a one-dimensionally ordered chain of water molecules. Although the molecules forming the chain are in chemical and thermal equilibrium with the surrounding bath, we observe pulse-like transmission of water through the nanotube. These transmission bursts result from the tight hydrogen-bonding network inside the tube, which ensures that density fluctuations in the surrounding bath lead to concerted and rapid motion along the tube axis7,8,9. We also find that a minute reduction in the attraction between the tube wall and water dramatically affects pore hydration, leading to sharp, two-state transitions between empty and filled states on a nanosecond timescale. These observations suggest that carbon nanotubes, with their rigid nonpolar structures10,11, might be exploited as unique molecular channels for water and protons, with the channel occupancy and conductivity tunable by changes in the local channel polarity and solvent conditions.

Water conduction through the hydrophobic channel of a carbon nanotube

Gold is known as a shiny, yellow noble metal that does not tarnish, has a face centred cubic structure, is non-magnetic and melts at 1336 K. However, a small sample of the same gold is quite different, providing it is tiny enough: 10 nm particles absorb green light and thus appear red. The meltingtemperature decreases dramatically as the size goes down. Moreover, gold ceases to be noble, and 2–3 nm nanoparticles are excellent catalysts which also exhibit considerable magnetism. At this size they are still metallic, but smaller ones turn into insulators. Their equilibrium structure changes to icosahedral symmetry, or they are even hollow or planar, depending on size. The present tutorial review intends to explain the origin of this special behaviour of nanomaterials.

Size matters: why nanomaterials are different

In recent years, tremendous research effort has been aimed at increasing the energy density of supercapacitors without sacrificing high power capability so that they reach the levels achieved in batteries and at lowering fabrication costs For this purpose, two important problems have to be solved: first, it is critical to develop ways to design high performance electrode materials for supercapacitors; second, it is necessary to achieve controllably assembled supercapacitor types (such as symmetric capacitors including double-layer and pseudo-capacitors, asymmetric capacitors, and Li-ion capacitors) The explosive growth of research in this field makes this review timely Recent progress in the research and development of high performance electrode materials and high-energy supercapacitors is summarized Several key issues for improving the energy densities of supercapacitors and some mutual relationships among various effecting parameters are reviewed, and challenges and perspectives in this exciting field are also discussed This provides fundamental insight into supercapacitors and offers an important guideline for future design of advanced next-generation supercapacitors for industrial and consumer applications

Recent Advances in Design and Fabrication of Electrochemical Supercapacitors with High Energy Densities

Numerical Initial Value Problems in Ordinary Differential Equations

We review the current state of knowledge of phase separation and phase equilibria in porous materials. Our emphasis is on fundamental studies of simple fluids (composed of small, neutral molecules) and well-characterized materials. While theoretical and molecular simulation studies are stressed, we also survey experimental investigations that are fundamental in nature. Following a brief survey of the most useful theoretical and simulation methods, we describe the nature of gas‐liquid (capillary condensation), layering, liquid‐liquid and freezing/melting transitions. In each case studies for simple pore geometries, and also more complex ones where available, are discussed. While a reasonably good understanding is available for phase equilibria of pure adsorbates in simple pore geometries, there is a need to extend the models to more complex pore geometries that include effects of chemical and geometrical heterogeneity and connectivity. In addition, with the exception of liquid‐liquid equilibria, little work has been done so far on phase separation for mixtures in porous media.

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Phase separation in confined systems

We present a review of experimental, theoretical, and molecular simulation studies of confinement effects on freezing and melting We consider both simple and more complex adsorbates that are confined in various environments (slit or cylindrical pores and also disordered porous materials) The most commonly used molecular simulation, theoretical and experimental methods are first presented We also provide a brief description of the most widely used porous materials The current state of knowledge on the effects of confinement on structure and freezing temperature, and the appearance of new surface-driven and confinement-driven phases are then discussed We also address how confinement affects the glass transition

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Effects of confinement on freezing and melting.

We report molecular simulation studies of the freezing behavior of fluids in nano-porous media. The effect of confinement is to induce spatial constraints as well as energetic heterogeneity on the confined fluid, thereby altering the bulk phase behavior drastically. We consider the effect of the fluid-wall interaction energy on the shift of the freezing temperature and on the fluid structure, using a novel approach to calculate the free energy surface based on Landau theory and order parameter formulation. Corresponding states theory is then used to map out the global freezing behavior of a Lennard-Jones (LJ) fluid in model slit-shaped pores of varying fluid-wall interaction strengths. Using LJ parameters fitted to thermophysical property behavior, we predict the qualitative freezing behavior for a variety of fluids and nano-porous materials, based on a global freezing diagram. We have attempted to verify these predictions by comparing with experimental data for several systems, and show that in these cases, the experimental observations and the predictions are in agreement.

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Effect of the fluid-wall interaction on freezing of confined fluids: Toward the development of a global phase diagram

Using molecular simulations and free energy calculations based on Landau theory, we show that freezing/melting behavior of fluids of small molecules in pores of simple geometry can be understood in terms of two main parameters: the pore width H* ~expressed as a multiple of the diameter of the fluid molecule ! and a parameter a that measures the ratio of the fluid-wall to the fluid‐fluid attractive interaction. The value of the a parameter determines the qualitative nature of the freezing behavior, for example, the direction of change in the freezing temperature and the presence or absence of new phases. For slit-shaped pores, larger a values lead to an increase in the freezing temperature of the confined fluid, and to the presence of a hexatic phase. For pores that accommodate three or more layers of adsorbate molecules several kinds of contact layer phase ~inhomogeneous phases in which the contact layer has a different structure than the inner layers! are observed. Smaller a values lead to a decrease in the freezing temperature. The parameter H* determines the magnitude of shift in the freezing temperature, and can also affect the presence of some of the new phases. Results are presented as plots of transition temperature vs a for a particular pore width. Experimental results are also presented for a variety of adsorbates in activated carbon fibers~ACF! covering a wide range of a values; the ACF have slit-shaped pores with average pore width 1.2 nm. The experimental and simulation results show qualitative agreement. © 2002 American Institute of Physics. @DOI: 10.1063/1.1426412#

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Global phase diagrams for freezing in porous media

We report both experimental measurements and molecular simulations of the melting and freezing behavior of simple fluids in porous media. The experimental studies are for carbon tetrachloride and nitrobenzene in controlled pore glass (CPG) and Vycor. Differential scanning calorimetry (DSC) was used to determine the melting point in the porous materials for each of the glass samples. In the case of nitrobenzene (which has a nonzero dipole moment), dielectric spectroscopy was also used to determine melting points. Measurements by the two methods were in excellent agreement. The melting point was found to be depressed relative to the bulk value for both fluids. With the exception of smallest pores, the melting point depression was proportional to the reciprocal of the pore diameter, in agreement with the Gibbs-Thomson equation. Structural information about the different confined phases was obtained by measuring the dielectric relaxation times using dielectric spectroscopy. Monte Carlo simulations were used to determine the shift in the melting point, T m , for a simple fluid in pores having both repulsive and strongly attractive walls. The strength of attraction to the wall was shown to have a large effect on the shift in T m , with T m being reduced for weakly attracting walls. For strongly attracting walls, such as graphitic carbon, the melting point increases for slit-shaped pores. For such materials, the adsorbed contact layer is shown to melt at a higher temperature than the inner adsorbed layers. A method for calculating the free energies of solids in pores is presented, and it is shown that the solid-liquid transition is first order in these systems.

Malgorzata Sliwinska-Bartkowiak

Papers

Phase separation in confined systems

Effects of confinement on freezing and melting.

Effect of the fluid-wall interaction on freezing of confined fluids: Toward the development of a global phase diagram

Global phase diagrams for freezing in porous media

Phase Transitions in Pores: Experimental and Simulation Studies of Melting and Freezing†