Jayendran C. Rasaiah

Water conduction through the hydrophobic channel of a carbon nanotube

Confinement of matter on the nanometre scale can induce phase transitions not seen in bulk systems. In the case of water, so-called drying transitions occur on this scale 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 surface. 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 axis. 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 structures, 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.

Integral Equation Methods in the Computation of Equilibrium Properties of Ionic Solutions

Computations have been made for a system of charged hard spheres with parameters chosen to correspond to an aqueous solution of a 1 − 1 electrolyte in the range from 0.001 to 1M. Correlation functions were computed by the analogues of the HNC and PY integral equations due to Allnatt in which the integral equations are constructed after the Mayer resummation has been performed on the expansion of g(r). Activity and osmotic coefficients are computed both by the compressibility and pressure equations and tested for consistency. Based on this test and others, including a comparison with computations published by Carley, it is concluded that the HNC equation gives very accurate results for this primitive model at least up to 1M. The accurate results show that the effect of the excluded volume of the hard‐sphere cores has been considerably underestimated in earlier treatments of the primitive model.

From hydrophobic to hydrophilic behaviour: A simulation study of solvation entropy and free energy of simple solutes

We describe atomistic simulations of the free energy and entropy of hydration of ions in aqueous solution at 25 °C using a simple point charge model (SPC/E) for water and charged spherical Lennard-Jones solutes. We use a novel method with an extended Lagrangian or Hamiltonian in which the charge and the size of the ions are considered as dynamical variables. This enables us to determine thermodynamic properties as continuous functions of solute size and charge and to move smoothly from hydrophilic to hydrophobic solvation conditions. On passing between these extremes, the entropy of solvation goes through maxima. For example it shows a double maximum as a function of charge at constant size and a single maximum as a function of size at constant (non-zero) charge. These maxima correspond to extremes of structure-breaking and are associated with the disappearance of the second solvation shell in the radial distribution function; no anomalies are seen in the first shell. We also present direct evidence of th...

Mobility and solvation of ions in channels

In this paper we present some results from a simulation study of the mobility and solvation of ions and uncharged molecules in aqueous solution in smooth cylindrical channels at room temperature. This ideal system provides a reference system with which to compare the behavior of water and ions in real porous materials such as zeolites, bucky tubes, and biological channels. We find that in channels of radii between 2.5 and 5.5 A the water molecules form a cylindrical solvation shell inside the channel walls with some evidence of a second shell in the center of the largest channel. Not all protons are involved in hydrogen bonding and a number point toward the walls. We attribute this to the concavity of the surface. When a sodium ion is added it tends to lie in the center of the channel where it can form the most complete solvation shell. Its diffusion rate decreases in smaller channels until it moves too slowly in a channel of 2 A radius to be detected in our simulations. This decrease is only partly due to an increase in the mean square force on the ion. A range of ions of different sizes were studied in a channel with radius 3 A. While the smaller of these ions (F−, Na+, and Ca++) lie preferentially in the center of the channel, larger ions (Cl−, I−, and Cs+) penetrate some way into the layer of water inside the wall and methane and ions with the charges turned off move next to the wall. Landau free energy analysis shows that this change is due to the balance between entropy and energy. The behavior in smooth channels is quite the opposite of what has been observed in experimental studies and simulations of Gramicidin (pore radius of 2 A), where Cs+ lies closer to the center of the channel and Na+ lies off the axis. This difference can be attributed to the specific molecular structure of the gramicidin pores (e.g., the presence of carbonyl groups). As in bulk solutions, the mobilities of the ions in smooth channels increase to a maximum with ion size and decrease with increasing magnitude of the charge on the ion, while uncharged species diffuse much more rapidly and show a monotonic decrease with size. This behavior is related to the characteristics of the fluctuations of the forces on the solute molecules.

Filling and emptying kinetics of carbon nanotubes in water

The kinetics of water filling and emptying the interior channel of carbon nanotubes is studied by molecular dynamics simulations. Filling and emptying occur predominantly by sequential addition of water to or removal from a single-file chain inside the nanotube. Advancing and receding water chains are orientationally ordered. This precludes simultaneous filling from both tube ends, and forces chain rupturing to occur at the tube end where a water molecule donates a hydrogen bond to the bulk fluid. We use transition path concepts and a Bayesian approach to identify a transition state ensemble that we characterize by its commitment probability distribution. At the transition state, the tube is filled with all but one water molecule. Filling thermodynamics and kinetics depend sensitively on the strength of the attractive nanotube–water interactions. This sensitivity increases with the length of the tubes.

Electric field and temperature effects on water in the narrow nonpolar pores of carbon nanotubes

Water molecules in the narrow cylindrical pore of a (6,6) carbon nanotube form single-file chains with their dipoles collectively oriented either up or down along the tube axis. We study the interaction of such water chains with homogeneous electric fields for finite closed and infinite periodically replicated tubes. By evaluating the grand-canonical partition function term-by-term, we show that homogeneous electric fields favor the filling of previously empty nanotubes with water from the bulk phase. A two-state description of the collective water dipole orientation in the nanotube provides an excellent approximation for the dependence of the water-chain polarization and the filling equilibrium on the electric field. The energy and entropy contributions to the free energy of filling the nanotube were determined from the temperature dependence of the occupancy probabilities. We find that the energy of transfer depends sensitively on the water-tube interaction potential, and that the entropy of one-dimensionally ordered water chains is comparable to that of bulk water. We also discuss implications for proton transfer reactions in biology.

Molecular dynamics simulation of ionic mobility. I. Alkali metal cations in water at 25 "C

We describe a series of molecular dynamics simulations performed on model cation‐water systems at 25 °C representing the behavior of Li+, Na+, K+, Rb+, and Cs+ in an electric field of 1.0 V/nm and in its absence. The TIP4P model was used for water and TIPS potentials were adapted for the ion‐water interactions. The structure of the surrounding water molecules around the cations was found to be independent of the applied electric field. Some of the dynamic properties, such as the velocity and force autocorrelation functions of the cations, are also field independent. However, the mean‐square displacements of the cations, their average drift velocities, and the distances traveled by them are field dependent. The mobilities of the cations calculated directly from the drift velocity or the distance traveled by the ion are in good agreement with each other and they are in satisfactory agreement with the mobilities determined from the mean‐square displacement and the velocity autocorrelation function in the absence of the field. They also show the same trends with ionic radii that are observed experimentally; the magnitudes are, however, smaller than the experimental values in real water by almost a factor of 2. It is found that the water molecules in the first solvation shell around the small Li+ ion are stuck to the ion and move with it as an entity for about 190 ps, while the water molecules around the Na+ ion remain for 35 ps, and those around the large cations stay for 8–11 ps before significant exchange with the surroundings occurs. The picture emerging from this analysis is that of a solvated cation whose mobility is determined by its size as well as the static and dynamic properties of its solvation sheath and the surrounding water. The classical solventberg model describes the mobility of Li+ ions in water adequately but not those of the other ions.

Integral Equation Computations for Aqueous 1–1 Electrolytes. Accuracy of the Method

The computations described earlier [J. Chem. Phys. 48, 2742 (1968)] have been carried out for a variety of primitive‐model parameters representative of aqueous 1–1 electrolyte solutions at 25°C. A number of tests, some new, have been applied to assess the accuracy of the results. One test involves a square‐mound model, for which some results are also given. The hypernetted‐chain equation is found to be quite satisfactory for these models up to 1M electrolyte concentration.

Computer simulation studies of aqueous sodium chloride solutions at 298 K and 683 K

molecular models for the water solvent. The solvent densities were 0.997 g cm 23 at 298 K and 0.35 gc m 23 and 0.175 g cm 23 at 683 K. The ion‐ion and ion‐solvent distribution functions were calculated and compared with corresponding functions for a continuum model of the solvent also determined by computer simulation. Our studies confirm the presence of significant amounts of ion pairing and clustering at supercritical conditions as seen in visualizations of the equilibrium configurations of the solution. However, the degree of pairing and clustering of ions in supercritical solutions is significantly different for discrete and continuum representations of the solvent. Simulations of a 1 molal solution of NaCl at 683 K, using a discrete molecular model for the solvent at a density of 0.35 g cm 23 , show the presence of a single megacluster of 10 sodium and chloride ions in a system of 555 water molecules. Three smaller clusters containing positive and negative charges are observed at 683 K when the electrolyte concentration is reduced to 0.5 molal at a solvent density of 0.35 g cm 23 and also at a lower solvent density of 0.175 g cm 23 . Molecular dynamics simulations of the velocity auto correlation functions of Na 1 and Cl 2 ions have distinct forms related to the cluster to which the ion belongs. The diffusion coefficients of Na 1 and Cl 2 ions, at infinite dilution, are larger at 683 K than at 298 K, and decrease with increasing electrolyte concentration. They are nearly equal to each other in the one molal solution at 683 K, which may correspond to a supersaturated solution in which the large cluster of sodium and chloride ions moves as an entity over an observed lifetime greater than 200 ps.

Computations for Higher Valence Electrolytes in the Restricted Primitive Model

A detailed account of the hypernetted chain (HNC) equation for 1–1, 2–1, 3–1, and 2–2 electrolytes in the restricted primitive model (charged hard spheres of equal size) is given, and comparisons are made with some other approximations for the excess thermodynamic functions. On the basis of self‐consistency tests, it is concluded that at a given concentration, the osmotic coefficients from the HNC approximation decrease in accuracy as the charges on the ions are increased. By comparison with the Monte Carlo results of Card and Valleau, it is concluded that the excess energy functions for all of these electrolytes are accurate to within a few percent. It is found that the HNC and DHLL + B2 approximations show certain anomalies in the thermodynamic functions of 2–2 electrolytes which also occur in real electrolytes but are not predicted to occur in some of the other theories developed recently. The charge densities around ions, derived from the HNC theory, are compared with the well‐known predictions of Deb...