Diffusion Anomaly at Low Temperatures in Confined Systems from the Rare Events Method

Existence of a size-dependent diffusivity maximum for uncharged solutes in water and its implications

Recent studies suggest that there exists a size-dependent diffusivity maximum in binary mixtures interacting via Lennard-Jones potential when the size of one of the two components is varied (Ghorai, P. K.; Yashonath, S. J. Phys. Chem., 2005, 109, 5824). We discuss in the present paper the importance of the existence of a size-dependent maximum for an uncharged solute in liquid or amorphous solid water and its relation to the ionic conductivity maximum in water. We report molecular dynamics investigations into the size dependence of the self-diffusivity, D, of the uncharged solutes in water at low temperatures (30 K) with immobile as well as mobile water. We find that a maximum in self-diffusivity exists as a function of the size of solute diffusing within water at low temperatures but not at high temperatures. This is due to the relatively weak interactions between the solute and the water compared to the kinetic energy at room temperature. Previously, we have shown that a similar maximum exists for guests sorbed in zeolites and is known as the levitation effect (LE). Thus, it appears that the existence of a size-dependent maximum is universal and extends from zeolites to simple liquids to solvents of polyatomic species. We examine the implications of this for the size-dependent maximum in ionic conductivity in polar solvents known for over a hundred years. These results support the view that the size-dependent maximum seen for ions in water has its origin in the LE (see Ghorai, P. Kr.; Yashonath, S.; Lynden-Bell, R. M. J. Phys. Chem. 2005, 109, 8120).

Evidence in Support of Levitation Effect as the Reason for Size Dependence of Ionic Conductivity in Water: A Molecular Dynamics Simulation

We report extensive molecular dynamics simulations of (i) model ions in water at high concentrations as a function of the size and charge of the ion as well as (ii) realistic simulation of Cl- and Br- ions at low concentrations in water at room temperature. We also analyze existing experimental data in light of the results obtained here. The halide ion simulations have been carried out using the interaction potentials of Koneshan et al. (J. Phys. Chem. B 1998, 102, 4193). We compute structural and dynamical properties of ions in water and explore their variation with size and charge of the ion. We find that ions of certain intermediate sizes exhibit a maximum in self-diffusivity in agreement with previous experimental measurements and computer simulations. We analyze molecular dynamics trajectories in light of the previous understanding of the levitation effect (LE) and the recent suggestion that ionic conductivity has its origin in LE (J. Phys. Chem. B 2005, 109, 8120). We report the distribution of void and neck radii that exist amidst water. Our analysis suggests that the ion with maximum self-diffusivity is characterized by a lower activation energy and a single-exponential decay of F(s)(k,t). The behavior of these and other related quantities of the ion with maximum self-diffusivity are characteristic of the anomalous regime of the LE. The simulation results of Br- and Cl- ions in water also yield results in agreement with the predictions of LE. A plot of experimental conductivity data in the literature for alkali ions in water by Kay and Evans (J. Phys. Chem. 1966, 70, 2325) also yields a lower activation energy for the ion with maximum conductivity in excellent agreement with the LE. To the best of our knowledge, none of the existing theories predict a lower activation energy for the ion with maximum conductivity.

Isomers of cyclo-Heptasulfur and Their Coordination to Li+: an Ab Initio Molecular Orbital Study

The potential energy hypersurfaces (PESs) of heptasulfur (S7) and of [LiS7]+ have been investigated by ab initio molecular orbital calculations at the G3X(MP2) level of theory. Besides the chair-like seven-membered ring (1a) as the global minimum structure, eight local minimum structures and one transition state have been located on the PES of S7. The barrier for pseudorotation of 1a is only 5.6 kJ mol(-1). The boat-like S7 ring (1b) is 12.1 kJ mol(-1) less stable than 1a, followed by three isomers of connectivity S6=S and four open-chain isomers. On the basis of multireference calculations at the MRCI(4,4)+Q/6-311G(d) level, the most stable open-chain form of S7 is a triplet of relative energy 133.1 kJ mol(-1). Thus, the reaction energy (deltaE0) for the ring opening of 1a is 133.1 kJ mol(-1), halfway between those of the highly symmetrical rings S6 and S8. Because of their strong multireference characters, the stabilities of the biradicalic singlet chains are significantly overestimated by the single-reference-based G3X(MP2) method. The calculated vibrational spectrum of 1a is in good agreement with experimental data. The various isomers of S7 form stable complexes with Li+ with coordination numbers of 1-4 for the metal atom and binding energies in the range of -93.8 to -165.7 kJ mol(-1). A total of 15 isomeric complexes have been located, with 13 of them containing cyclic ligands. The global minimum structure (2a) is composed of 1a, with the Li+ cation linked to the four negatively charged sulfur atoms (symmetry C(s)). The corresponding complex 2c containing the ligand 1b is by 23.4 kJ mol(-1) less stable than 2a, and a bicyclic crown-shaped LiS7 cation (2e) is by 34.9 kJ mol(-1) less stable than 2a. Even less stable are four complexes with the branched S6=S ligand. SS bond activation by polarization of the valence electrons takes place on coordination of Li+ to cyclo-S7 (1a).

Levitation Effect: Distinguishing Anomalous from Linear Regime of Guests Sorbed in Zeolites through the Decay of Intermediate Scattering Function and Wavevector Dependence of Self-Diffusivity

Previous work investigating the dependence of self-diffusivity, D, on the size of the guest diffusing within the porous solid such as zeolite has reported the existence of an anomalous maximum in the diffusion coefficient (J. Phys. Chem. 1994, 98, 6368). Two distinct regimes of dependence of D on sigma(gg), diameter of the guest were reported. D proportional to 1/sigma(gg)2, often referred to as linear regime (LR), is found when sigma(gg) is smaller than sigma(v), the diameter of the void. A maximum in D has been observed when sigma(gg) is comparable to sigma(v) and this regime is referred to as anomalous regime (AR). Here we report the intermediate scattering function for a particle from LR and AR in zeolite faujasite. A particle from LR exhibits a biexponential decay while a particle from AR exhibits a single-exponential decay at small k. Variation with k of the full width at half-maximum of the self-part of the dynamic structure factor is nonmonotonic for a particle in the linear regime. In contrast, this variation is monotonic for a particle in the anomalous regime. These results can be understood in terms of the existence of energetic barrier at the bottleneck, the 12-ring window, in the path of diffusion. They provide additional signatures for the linear regime and anomalous regimes and therefore for levitation effect (LE).