Modeling growth of organized nanoporous structures by anodic oxidation.

Nanostructured porous oxides are produced by anodic dissolution of several metals. A scaling approach is introduced to explain pattern nucleation in an oxide layer, and a related microscopic model shows oxide growth with long nanopores. The scaling approach matches the time of ion transport across the thin oxide layer, which is related to metal corrosion, and the time of diffusion along the oxide/solution (OS) interface, which represents the extension of oxide dissolution. The selected pattern size is of order (dD(S)/v(O))(1/2), where d is the oxide thickness, v(O) is the migration velocity of oxygen ions across the oxide, and D(s) is the diffusion coefficient of H(+) ions along the oxide/solution interface. This result is consistent with available experimental data for those quantities, predicts the increase of pore size with the external voltage, and suggests the independence of pore size with the solution pH. Subsequently, we propose a microscopic model that expresses the main physicochemical processes as a set of characteristic lengths for diffusion and surface relaxation. It shows a randomly perturbed OS interface at short times, its evolution to pore nucleation and to stable growth of very long pores, in agreement with the mechanistic scenario suggested by two experimental groups. The decrease of the size of the walls between the pores with the interface tension is consistent with arguments for formation of titania nanotube arrays instead of nanopores. These models show that pattern nucleation and growth depend on matching a small number of physicochemical parameters, which is probably the reason for the production of nanostructured porous oxides from various materials under suitable electrochemical conditions.

New results from the contact theorem for the charge profile for symmetric electrolytes.

In this paper the contact value of the charge profile at a charged interface is presented as the sum of the normal component of the Maxwell electrostatic tensor and a new electrostatic property defined by the integral from the product of the gradient of the electrical potential and the singlet distribution function of coions (ions with sign of the charge equal to that of the interface). On physical arguments, it is conjectured that this new property is a monotonic function of the electrical charge at the wall and is limited by the bulk electrolyte pressure for large electrical charges at the wall. Using the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are derived and some related general properties are discussed.

Interplay of host volume variations and internal distortions in the course of intercalation into disordered matrices.

Based on a combination of the distortive lattice gas model and the maximum information entropy approach, the thermodynamics of insertion into disordered hosts is analyzed. It is found that the isotherm specificities can be explained as a cooperative interplay of the host volume expansion and the internal distortions, which tend to optimize the host structure inducing a local lowering of the insertion energetic cost. Behavior of amorphous LixWO3 films of different thicknesses is discussed in this context.

Constrained equilibrium as a tool for characterization of deformable porous media.

A new method for characterizing the deformable porous materials with noncritical adsorption probes is proposed. The mechanism is based on driving the adsorbate through a sequence of constrained equilibrium states with the insertion isotherms forming a pseudocritical point or a van der Waals-type loop. In the framework of a perturbation theory and Monte Carlo simulations we have found a link between the loop parameters and the host morphology. This allows one to characterize porous matrices through analyzing a shift of the pseudocritical point and a shape of the pseudospinodals.

Maximum entropy approach to power-law distributions in coupled dynamic-stochastic systems.

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of "global" constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a nonequilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.

Scaling theory in a model of corrosion and passivation.

We study a model for corrosion and passivation of a metallic surface after small damage of its protective layer using scaling arguments and simulation. We focus on the transition between an initial regime of slow corrosion rate (pit nucleation) to a regime of rapid corrosion (propagation of the pit), which takes place at the so-called incubation time. The model is defined in a lattice in which the states of the sites represent the possible states of the metal (bulk, reactive, and passive) and the solution (neutral, acidic, or basic). Simple probabilistic rules describe passivation of the metal surface, dissolution of the passive layer, which is enhanced in acidic media, and spatially separated electrochemical reactions, which may create pH inhomogeneities in the solution. On the basis of a suitable matching of characteristic times of creation and annihilation of pH inhomogeneities in the solution, our scaling theory estimates the average radius of the dissolved region at the incubation time as a function of the model parameters. Among the main consequences, that radius decreases with the rate of spatially separated reactions and the rate of dissolution in acidic media, and it increases with the diffusion coefficient of H(+) and OH(-) ions in solution. The average incubation time can be written as the sum of a series of characteristic times for the slow dissolution in neutral media, until significant pH inhomogeneities are observed in the dissolved cavity. Despite having a more complex dependence on the model parameters, it is shown that the average incubation time linearly increases with the rate of dissolution in neutral media, under the reasonable assumption that this is the slowest rate of the process. Our theoretical predictions are expected to apply in realistic ranges of values of the model parameters. They are confirmed by numerical simulation in two-dimensional lattices, and the expected extension of the theory to three dimensions is discussed.

On a mechanism of low-pressure insertion of chain molecules into crystalline matrices.

A microscopic mechanism of low-pressure insertion and separation of chain-like molecules in host matrices is proposed. It is shown that the intramolecular correlations combined to appropriate host activities are responsible for a low-pressure condensation of chain molecules. This allows to recover a fine structure of the isotherms and to explain recent experiments on the insertion of C(2)H(2) and CO(2) guest species into metal-organic microporous materials. We argue that the mechanism should be dominant in low-dimensional host geometries, where the effects related to the chain conformations or reorientations are strongly suppressed and the major factors are the chain connectivity and the segment packing.

Negative linear compressibility in confined dilatating systems.

The role of a matrix response to a fluid insertion is analyzed in terms of a perturbation theory and Monte Carlo simulations applied to a hard sphere fluid in a slit of fluctuating density-dependent width. It is demonstrated that a coupling of the fluid-slit repulsion, spatial confinement, and the matrix dilatation acts as an effective fluid-fluid attraction, inducing a pseudocritical state with divergent linear compressibility and noncritical density fluctuations. An appropriate combination of the dilatation rate, fluid density, and the slit size leads to the fluid states with negative linear compressibility. It is shown that the switching from positive to negative compressibility is accompanied by an abrupt change in the packing mechanism.

Contact conditions for the charge in the theory of the electrical double layer.

In this paper, from the Born-Green-Yvon equations of the liquid-state theory, we derive a general expression for the charge-density contact value at charged interfaces. This relation is discussed, in particular, for symmetrical electrolytes. We emphasize an essential coupling between the electric properties and the density profile. Limiting behavior at small and large charges at the interface is discussed.

Structural rearrangement of solid surfaces due to competing adsorbate-substrate interactions.

Employing a generalized lattice gas theory and the Brownian dynamics simulation, we show that the competing displacive interaction in an adsorbate may cause a continuous distortive transition in the underlying substrate. The threshold for the transition is determined by the competition of the substrate rigidity and the quasielastic energy induced by the adsorbate. In the presence of a strong pinning and repulsive lateral interaction, the resulting structure appears as a compromise between the square lattice of the substrate and the hexagonal arrangement of the adsorbate. For hexagonal substrate lattices the simulation demonstrates that various adsorbate structures (from honeycomb lattices to quasicrystalline pentagonal configurations) may be observed, depending on the effective radii of interaction. Due to the long-ranged coupling the substrate may acquire a substructure induced by the adsorbate. This paper represents a generalization of the work published in Phys. Rev. Lett. 81, 3904 (1998).

Fractal behavior in quantum statistical physics.

The properties of an ideal gas of spinless particles are investigated by using the path integral formalism. It is shown that the quantum paths exhibit a fractal character which remains unchanged in the relativistic domain provided the creation of new particles is avoided, and the Brownian motion remains the stochastic process associated with the quantum paths. These results are obtained by using a special representation of the Klein-Gordon wave equation. On the quantum paths the relation between velocity and momentum is not the usual one. The mean square value of the velocity depends on the time needed to define the velocity and its value shows the interplay between pure quantum effects and thermodynamics. The fractal character is also investigated starting from wave equations by analyzing the evolution of a Gaussian wave packet via the Hausdorff dimension. Both approaches give the same fractal character in the same limit. It is shown that the time that appears in the path integral behaves like an ordinary time, and the key quantity is the time interval needed for the thermostat to give to the particles a thermal action equal to the quantum of action. Thus, the partition function calculated via the path integral formalism also describes the dynamics of the system for short time intervals. For low temperatures, it is shown that a time-energy uncertainty relation is verified at the end of the calculations. The energy involved in this relation has not a thermodynamic meaning but results from the fact that the particles do not follow the equations of motion along the paths. The results suggest that the density matrix obtained by quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual route.

Electrostatics of a modulated membrane with specific adsorption.

We present a simple model for the electrostatic properties of a modulated membrane separating two different electrolyte solutions. The model is based on an extension to linear Gouy-Chapman theory. Starting from a Hamiltonian which contains a singular part for the surface contributions, we obtain within the mean-field approach a set of equations which allows us to study the equilibrium between the diffuse and singular parts of the charge carriers. It is shown that the interface modulation leads to a higher potential of zero charge compared to the flat system. The value of this effect depends on the interplay between the height and the characteristic length of the interface modulation and the Debye lengths on both sides, even if the adsorption occurs only on one side of the interface. In the latter case, the side where no adsorption occurs locally exhibits a diffuse charge distribution, which averages to zero, but which makes a contribution to the overall potential drop across the interface. We also calculate the electrostatic contribution to the elastic bending modulus of the membrane and show that specific adsorption of ions can destabilize the flat interface.