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During silver electrodeposition on Au nanoparticle (NP)-covered highly oriented pyrolitic graphite, a transition from an initial growth of microsized particles to the growth of dendrites with pine tree shape (nanotrees) is observed, which is an advancement for material growth with hierarchical surface roughness. Using kinetic Monte Carlo simulations of an electrodeposition model, those results are explained by the interplay of diffusive cation flux in the electrolyte and relaxation of adsorbed atoms by diffusion on quenched crystal surfaces. First, simulations on NP-patterned substrates show the initial growth of faceted silver particles, followed by the growth of nanotrees with shapes similar to the experiments. Next, simulations on electrodes with large prebuilt particles explain the preferential nanotree growth at corners and edges as a tip effect. Simulations on wide flat electrodes relate the nanotree width with two model parameters describing surface diffusion of silver atoms: maximal number of random hops (

International audience; We present a stochastic three dimensional cellular automata model of aqueous corrosion. We consider the cathodic reaction with dissolved oxygen and different concentrations of the oxidizer. We study the role and the stability of the passive layer and its effect on the kinetics, surface morphology and roughness of the metallic surface. The model considers balanced spatially separated anodic and cathodic reactions and is capable of illustrating the cathodic control of the corrosion rate. Besides the electrochemical reactions, we take into account ionic diffusion, acido/basic neutralization. Results are compared to aqueous corrosion of Fe in near neutral solution.

The bulk structure of stainless steels (SS) consists of mostly convex grains whose thin (one nm) planar interfaces are called grain boundaries (GB). There are industrial contexts where SS exposed to aggressive oxidative media undergo a fast degradation due to inter-granular corrosion (IGC), a preferential attack that occurs at the grain boundaries, propagating along them and leading to grains detachment. To address the IGC issue, we developed a 3D synchronous cellular automata (CA) model. Our first goal was to obtain a GB corrosion rate that could be as isotropic as possible. We performed full angular studies, with respect to the spatial orientation of a single grain boundary, in three different cases of grid (array of cells) geometry (cubic, hexagonal close-packed (HCP), face-centered cubic (FCC)). The HCP grid appears to be the best choice, as far as isotropy of the GB corrosion rate is concerned.

A cellular automaton model is used for 3D simulations of metal corrosion in electrolyte solutions in potentiostatic conditions. The focus of this research is the formation of the passive layer on the metal surface. A general, mesoscopic-scale model is used. It contains only the elements necessary to reproduce the most important features of passivation. It is a 3D version of the 2D model presented in our previous papers. The simulations are run on graphics processing units which allow an effective operation on large 3D lattices. We consider the influence of three factors: the rate of corrosion (related to the electric potential), solubility of the corrosion products and their adhesion or absence of adhesion to the metal surface. For each set of the parameters we wait in the simulation run for the system to attain the steady state. Then we collect data characterizing steady-state properties such as electric current density, passive layer thickness, its roughness and overall morphology. The qualitative properties of passivation are reproduced in our 3D simulations confirming the conclusions based on earlier, 2D simulations.

The lattice fluid model of the system with short range and long range Coulomb interactions is suggested. In the framework of the collective variables method, the screening of the Coulomb interactions in the bulk is considered. It is shown that the Debye length includes additional concentration dependence inversely proportional to the square root of the mean concentration of vacant sites like what is known at the plane boundary. The Coulomb interaction contribution to the free energy of the system is calculated in the approach close to the mean spherical approximation and is given in an analytical form. The influence of the variation of the crystal field near the system boundary on the structure and characteristics of the electric double layer is investigated. As compared to the system with equal crystal potentials at the lattice sites throughout the system the pronounced difference for the electric capacitance appears at low absolute values of the surface potential and it is more pronounced for negative electric potentials. The capacitance diverges as the potential values at which the electric field tends to zero and attains negative values in regions of the surface potentials depending on their polarity and values of the surface crystal potential. Negative values of the capacitance may indicate the thermodynamic instability of the system that can result from neglecting the short range interaction contribution., Comment: 20 pages, 5 figures

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International audience; In this paper, a 3D cellular automata approach of intergranular corrosion in presented. A model is proposed, along with experimental results both qualitatively (groove morphology, groove angle distribution) and quantitatively (mass loss, corrosion rate, corrosion front evolution). Simulations have been performed using a new asynchronous algorithm: the choice of the most adequate grid is also discussed. The model investigates the statistical variation of the corrosion front and provides useful information to make predictions on material ageing.

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A simple lattice model of a solid electrolyte presented as a xy-slab geometry system of mobile cations on a background of energetic landscape of the host system and a compensating field of uniformly distributed anions is studied. The system is confined in the z-direction between two oppositely charged walls, which are in parallel to xy-plane. Besides the long-range Coulomb interactions appearing in the system, the short-range attractive potential between cations is considered in our study. We propose the mean field description of this model and extend it by taking into account correlation effects at short distances. Using the free energy minimization at each of z-coordinates, the corresponding set of non-linear equations for the chemical potential is derived. The set of equations was solved numerically with respect to the charge density distribution in order to calculate the cations distribution profile and the electrostatic potential in the system along z-direction under different conditions. An asymmetry of charge distribution profile with respect to the midplane of the system is observed. The effects of the short-range interactions and pair correlations on the charge and electric field distributions are demonstrated.

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A solid state electrolyte is considered as a system consisting of cations moving through the volume of a solid body and anions whose mobility can be neglected due to their large size compared to the size of the cations. Accordingly, in the homogeneous case local charge compensation takes place. Under the action of an external electric field, cations create in the near electrode area inhomogeneous redistribution of mobile charges and electric field. The model is used for the statistical­mechanical description of high­temperature ionic conductors and current sources. To obtain the free energy functional of the mobile charge subsystem depending on the distribution of their density, the cluster expansion scheme for the renormalized Mayer functions is used. The Hamiltonian of a system consisting of electric charges moving in the field of single­particle cell potentials of average forces is used as the basis one. The binary function of the host system is expressed in terms of the screened potentials and the potentials of the average forces based on the results of the method of collective variables. The internal energy of the system is calculated taking into account the short­ and long­range effects. The Gibbs – Duhem relation was used for calculating the free energy functional of the system. The distribution of the number density of moving particles and the electric potential in the near electrode region were found from the condition of extremality of the free energy. The potentials of average forces are obtained as a result of solving a system of integral equations in the lattice approximation, with accounting of the short­ and long­range effects. The transition from the correlative function to the correlation function allowed us to identify the correlated and uncorrelated parts of the electric potential. The linear contributions of the deviation of the charge concentrations from a uniform distribution to the chemical potential are considered. The calculations take into account the contribution of the correlation between the particles in the first three coordination spheres that leads to attraction of the first, repulsion of the second and third neighbors. The description is carried out using a linear differential equation of the fourth­order with complex values of the roots of the characteristic equation. The paper analyzes the results of the analytical solution.

Intergranular corrosion can affect stainless steels even if they are in a non-sensitized state. This is the case when the corrosive medium is particularly oxidizing such as in hot and concentrated nitric acid [1]. Intergranular corrosion is characterized by the formation of triangular grooves at the level of the grain boundaries. Their progression leads to the detachment of grains with a certain periodicity. This corrosion type is quite well described and modeled by different techniques when the medium remains the same [2-3]. Nevertheless, the medium may vary in some industrial chemical processes. Therefore, this work has investigated the impact of non-stationary conditions on the evolution of the intergranular corrosion. The intergranular corrosion kinetics of a 310L stainless steel was first studied in nitric acid with different levels of VO2 + concentrations in stationary conditions. Then non-stationary experiments were performed by varying the concentration of VO2 + as a function of time by periods. The corrosion kinetics was characterized by the evolution of the mass loss of the samples and of the geometry of the grooves (angle and depth) optically measured on cross sections. Numerical simulations were also performed by cellular automata [3]. A hexagonal close-packed (HCP) grid was chosen for the simulations. A realistic 3D granular structure of the stainless steel was modeled with a Voronoi algorithm. Two corrosion probabilities (for the grains and the grain boundaries) were adequately chosen for driving the time evolution in each conditions. These probabilities were kept constant in stationary conditions and varied with time by periods in non-stationary conditions. The simulated mass loss and the surface morphology reflects the same pattern of the experiments. In stationary conditions, the corrosion reaches a steady state after a transient period corresponding to the detachment of the first layer of grains: the corrosion rate and the specific surface in contact with the solution (increased by the formation of grooves) becomes constant. The characteristics of the steady state are directly dependent on the concentration of VO2 +. In non-stationary conditions, it appears that the characteristics of the intergranular corrosion (mass loss and geometry of the grooves) at a given period are influenced by the characteristics reached after the previous period (in other chemical conditions). This influence is only transient during a time corresponding approximately to the duration necessary to the consumption of a layer of grains. [1] Fauvet, P., Corrosion issues in nuclear fuel reprocessing plants. Nuclear corrosion science and engineering. D. Feron, Woodhead Publishing. 22 (2012) 679-728. [2] B.Gwinner et al., Towards a reliable determination of the intergranular corrosion rate of austenitic stainless steel in oxidizing media. Corrosion Science 107 (2016) 60-75. [3] D.Di Caprio et al., 3D cellular automata simulations of intra and intergranular corrosion. Corrosion Science 112 (2016) 438-450.

International audience; Intergranular corrosion (IGC) is one of the attacks that a material may suffer. It is characterized by a preferential attack to grain boundaries, which induces an acceleration of the material degradation. As an example, it can concern stainless steels (SS), when exposed to oxidizing media (e.g. HNO_3), as in the chemical industry or in the nuclear fuel reprocessing industry. Fully understand the degradation mechanism is an important challenge.IGC is characterized by the formation of triangular grooves at grain boundary level. Their progression leads, with a certain periodicity, to grain dropping, which causes an acceleration of the corrosion phenomenon. From a quantitative point of view, the description of IGC kinetics is still incomplete: in particular, the IGC evolution at bulk level, is quite uneasy to access by experiments. Numerical simulations can, in this case, provide more information and improve the knowledge.Cellular Automata (CA) can model any complex reality through simple rules and space-time discretization, and are particularly suitable to model IGC. The goal of this work is to simulate with CA the kinetics of degradation by IGC, to match as accurately as possible the experimental results. A hexagonal close-packed (HCP) grid is chosen for the simulations. The granular material structure is modeled through the Voronoi algorithm, while two corrosion probabilities (for grain and grain boundary species) drive the time evolution. With appropriate time and space equivalences, CA simulations are then able to reproduce accurately the experiments in terms of corrosion propagation velocity. The surface morphology reflects the same pattern as in the experiments : after the first transitory phase, grains start detaching from the material and accelerate the IGC process. The material-solution interface is then studied through the time evolution of the solution-grain boundary distribution. Results show an important dependence on the choice of the two corrosion probabilities.

We study the formation of deposits with dendritic morphology using numerical simulations of a model of electrodeposition and diffusion of the adsorbed material. The model considers a diffusive flux...

International audience; The porosity of the anodic films grown on aluminium substrates depends on various operating conditions related to the anodization electrolyte and to the applied electrical parameters, as well as to the substrate itself. In the present study, three different aluminium substrates were studied and anodized: AA 1050 (rolled; thickness = 1 mm), AA 2024 T3 (rolled; 1 mm), and AA 2024 T3 (machined; 3 mm). For each type of anodic film, the porosity, as well as its changes during anodization, was accurately characterized using both field‐emission gun scanning electron microscopy (FEG‐SEM) and a reanodization technique. Moreover, for the first time, the corresponding tortuosity was quantified for all studied substrates. Results for rolled AA 2024 T3 and for machined AA 2024 T3 especially showed significant differences in tortuosity values, contributing towards clarifying, in part, their different wettability characteristics or anticorrosion behaviour, so far not clearly explained.

International audience; We use stochastic Cellular Automata (CA) based modelling for corrosion studies at a mesoscopic scale. Physico-chemical phenomena that cannot be satisfactorily described by standard deterministic and macroscopic methods are represented. Materials are described by a 3D lattice where each cell has a state. Phenomena are represented as simple transition rules defining the evolution of the cells with given probabilities. Diffusion in the electrolyte is modelled as a random walk. Charge transfer corresponds to simultaneous anodic and cathodic reactions with special emphasis on their electric connection ensuring electric balance. We study evolution of pitting corrosion in terms of pit size morphology and acidity of the electrolyte. Starting from metal covered by a passive layer with a single defect, a cavity starts growing inside the metal and notably the exterior basic environment delays the dissolution of the protective passive layer. Results are in accordance with published experimental results on pitting corrosion.

Numerical modelling is an effective tool for predicting corrosion. We make use of a stochastic Cellular Automata (CA)-based modelling for corrosion studies at a mesoscopic scale. Physico-chemical phenomena that cannot be satisfactorily described by standard deterministic and macroscopic methods are here taken into account. In this CA modelling, materials and their environments are described by a 3D lattice, where each cell has a state. The physico-chemical phenomena are represented as simple rules that define the temporal evolution of the states of the cells. These rules can be combined to model complex systems. Our model is stochastic in the sense that the transition rules are given probabilities and diffusion in the electrolyte is modelled as a random walk. Simultaneous anodic and cathodic reactions describe the corrosion mechanisms. Special emphasis is given to the electric connection between the anodic and cathodic cells. The anodic and cathodic reactions occur simultaneously, maintaining the ...

We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G>>1), a detachment probability epsilon, Two-column format with 12 pages, 7 figures included

International audience; In this paper we use cellular automata approach to model scanning electrochemical microscopy (SECM) experiments. We simulate SECM current vs distance curve for a negative feedback mode. It shows the effect of the deformation of the diffusion layer around the UME tip close to the substrate surface. We also simulate an experiment where the UME serves to locally dissolve an electrochemically inhomogeneous substrate as a consequence the substrate's geometry changes during the experiment. Our approach gives both quantitative and qualitative information on the simulated experiments. We show that simulations of real three dimensional experiments are already feasible on relatively cheap multigraphical processor unit (GPU) cards in a standard desktop workstation.

The concept of mean potentials is used for calculating the free energy and chemical potential distribution in a crystalline nonhomogeneous medium, taking into account Coulomb interactions. The lattice version of the equations determining the mean potentials is considered. The closed system of algebraic equations for the mean potentials is formulated and solved. The interparticle interaction potential is split into a short range part, screened Coulomb interaction and the rest of long range Coulomb interaction. The former two interactions are considered in detail, while the long range part is suggested to take into account in the mean spherical approximation. The chemical potential on a given site depends on the concentration distribution over the whole system.

International audience; We present a stochastic three dimensional (3D) model for corrosion at a mesoscopic scale. The competition between uniform and localized corrosion is studied, with special emphasis given to the connection between the anodic and cathodic reactions. Even if the reactions happen at different places, they are linked and occur simultaneously, maintaining an electric balance. We focused on the particular case of an occluded corrosion on a metal covered by a non reactive layer, where two growth regimes are evidenced and controlled by the diffusion of species in the electrolyte.

We present a cellular automata approach to the morphology evolution of a corroding metal surface. In the model, we consider a morphology dependent corrosion probability of a site on the corrosion front. Selecting the model parameters we are able to reproduce a variety of different pit shapes and morphological regimes ranging from narrow pore-like channels to broader cavities. In the model, we control the ratio between localised and uniform corrosion. A diffusion process is also taken into account. The model is capable of predicting different scenarios for the evolution of the corrosion front in time.

In this paper, we discuss the phenomenon of a spontaneous polarisation of a neutral hard planar interface for valence asymmetric coulombic systems. Within a field theoretical description, we account for the existence of non trivial charge density and electric potential profiles. The analysis of the phenomenon shows that the effect is related to combinatorics in relation with the existence of the two independent species cations and anions. This simple and basic feature is related to the quantum mechanical properties of the system. The theoretical results are compared with numerical simulations data and are shown to be in very good agreement, which a fortiori justifies our physical interpretation., Comment: 12 pages, 11 figures

A simple model for the effect of intergranular corrosion on overall corrosion processes is investigated using a cellular automata approach. The corroding polycrystalline material consists of domains and their boundaries. The domains represent the monocrystalline cores while their boundaries represent the inter granular defects. Either, a periodic pattern or randomly generated domains of Voronoi tessellation are used to represent the polycrystalline structure. The parameters of the model, taking into account the polycrystalline aspect of corrosion, are the domain density and the corrosion probabilities of metal grain core and grain boundary sites. The corrosion probability for grain boundary is set to a value higher than it is for the grain core. A complex surface structure appears with a high geometrical roughness when defects are not too dense. A strong correlation is established between the roughness evolution, the metal crystalline properties and the corrosion mechanism of metal dissolution. This work concerns simulations in 3D and extends the previous work limited to 2D simulations. (C) 2016 Elsevier Ltd. All rights reserved.

In this paper, we discuss an extension of a field theoretical approach for the description of the double layer containing ions of finite size. In particular, the density profile and the differential capacitance are presented in the low-temperature regime, and excluded volume effects are discussed. Simple approximations are presented which allow for analytic expressions. Our results are compared to Monte Carlo simulation data.

Cyclic voltammetry is modeled using a probabilistic cellular automata (CA). The system is built up by simple evolution rules representing diffusion and electrochemical reactions. A connection between the CA model and electrochemistry is established using the electric charge of each cell and the chemical species that it represents. We studied two different kinetic regimes of electronic transfer at the electrode, which could be described by the Nernst and Butler–Volmer theories. In the evolution rules, we define probabilities that are directly related to the properties of the system and are described in terms of the electric potential. CA features are thus associated to macroscopic quantities and simulations are compared with experimental data from literature and validated with simulations using the standard finite element models (FEM). This work consolidates CA modeling as a quantitative approach for this domain of application and shows the capabilities of relatively cheap graphical processor units (GPU) on standard desktop workstation to model 3D complex systems.

We apply a field-theoretical approach to study the structure and thermodynamics of a two-Yukawa fluid confined by a hard wall. We derive mean field equations allowing for numerical evaluation of the density profile which is compared to analytical estimations. Beyond the mean field approximation, analytical expressions for the free energy, the pressure, and the correlation function are derived. Subsequently, contributions to the density profile and the adsorption coefficient due to Gaussian fluctuations are found. Both the mean field and the fluctuation terms of the density profile are shown to satisfy the contact theorem. We further use the contact theorem to improve the Gaussian approximation for the density profile based on a better approximation for the bulk pressure. The results obtained are compared to computer simulation data., 32 pages, 6 figures

A field theoretical approach is used to describe the properties of ionic solutions near a charged wall. The properties of ions are accounted for by the hard sphere effect and interaction coefficients a++, a−− and a+− determining short range correlation in the system other than the hard sphere repulsion. The effect of these coefficients on the differential capacity curves depends on the polarization. For symmetric interaction coefficients, a++=a−−=a+−, we observe the Gouy–Chapman minimum in dilute solutions at the potential of zero charge (pzc) which becomes a maximum in concentrated solutions. This minimum is surrounded by two maxima. For a given hard sphere diameter the capacity at these maxima depends on a++ or a−− for the negative and positive charge density, respectively, and decreases with more positive coefficient values meaning more repulsive interactions between counterions. At extreme charge densities the capacity becomes independent of bulk ionic concentration, but we do not observe a limiting constant value as we do without the hard sphere effect. If the interaction coefficient a+− is different from a++ and a−−, the capacity close to the pzc differs from the Gouy–Chapman value. The theoretical double layer capacity curves are compared with those obtained experimentally in various electrolytes on various metals as well as calculated using a different theoretical approach.

We present a field theory to describe liquids where the field represents the density. In terms of this field, the Hamiltonian contains the ideal entropy and the interaction between the density fields. The approach is illustrated with the Yukawa interaction and presented in the grand canonical ensemble formalism. In this framework, first, we derive a relation specific to the field theory. This relation is equivalent to the ‘equation of motion’ in field theory for interacting quantum particles. Then, focusing on the effect of the fluctuations, we calculate thermodynamic quantities beyond the mean field. The pressure, the density and the compressibility at a given chemical potential in the quadratic approximation and beyond are given. The aim of this paper is to illustrate the importance and the role of the ideal entropy in this type of approach. The density and the compressibility at a given chemical potential are calculated perturbatively in various ways. Whether from their field theoretical definition, or...

We use a field theoretical approach to study ionic systems. In this paper we illustrate this formalism in a grand canonical ensemble for the long range Coulomb potential. For the inhomogeneous system near a hard neutral plane wall we go beyond the well known Debye–Huckel electrolyte results and predict the existence of a desorption profile. The results are compared with well established sum rules for ionic systems and thermodynamic relations are verified. We also calculate the differential capacitance in a slab using the linear response theory. The capacitance is calculated from the charge–charge correlations for the neutral system using the fluctuation–dissipation theorem.

We study a thin film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio R of adatoms with a single bond and of the detachment probability epsilon per additional nearest neighbor (NN), respectively with activation energies are Es and Eb. If R and epsilon independently vary, regimes of low and high porosity are separated at 0.075 < epsilon_c < 0.09, with vanishingly small porosity below that point and finite porosity for larger epsilon. Alternatively, for fixed values of Es and Eb and varying temperature, the porosity has a minimum at Tc, and a nontrivial regime in which it increases with temperature is observe above that point. This is related to the large mobility of adatoms, resembling features of equilibrium surface roughening. In this high-temperature region, the deposit has the structure of a critical percolation cluster due to the non-desorption condition. The pores are regions enclosed by blobs of the corresponding percolating backbone, thus the distribution of pore size s is expected to scale as s^{-tau} with tau ~ 1.45, in reasonable agreement with numerical estimates. Roughening of the outer interface of the deposits suggests Villain-Lai-Das Sarma scaling below the transition. Above the transition, the roughness exponent alpha ~ 0.35 is consistent with the percolation backbone structure via the relation alpha = 2-d_B, where d_B is the backbone fractal dimension., 15 pages, 10 figures

Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured., 11 pages, 10 figures included

We analyse the fluctuations of electric variables in a simple case of semi-infinite electrolyte solution bound by a neutral hard wall. We use the statistical field theory with the effective Hamiltonian that yields the Debye–Huckel theory in the bulk. Although there is no profile for the average electrical quantities the fluctuations are influenced by the presence of the hard wall. We have calculated the profile for the electrical potential fluctuation at a given point across the interface. Analytic expression for the charge–charge and potential–potential correlation function is given. Some perspectives for a further study on the electric variables fluctuations in inhomogeneous electrolyte systems are presented.

A review of corrosion process modeling using cellular automata methods is presented. This relatively new and growing approach takes into account the stochastic nature of the phenomena and uses physico-chemical rules to make predictions at a mesoscopic scale. Milestone models are analyzed and perspectives are established.

We develop a cellular automata modelisation of SECM experiments to study corrosion in molten salt media for generation IV nuclear reactors. The electrodes used in these experiments are cylindrical glass tips with a coaxial metal wire inside. As the result of simulations we obtain the current approach curves of the electrodes with geometries characterized by several values of the ratios of glass to metal area at the tip. We compare these results with predictions of the known analytic expressions, solutions of partial differential equations for flat uniform geometry of the substrate. We present the results for other, more complicated substrate surface geometries e. g. regular saw modulated surface, surface obtained by Eden model process, ...

We investigate the behavior of the many-body correlation functions in the vicinity of the gas-liquid critical point. We use the framework of the liquid state theory and, accordingly, no reference to an effective Landau-Ginzburg Hamiltonian is made. The critical condition is introduced by means of the equation of state. From the Baxter equation relating the many-body correlation functionsh(n) andh(n+1), we find that the integrals of all theh(n) diverge at the critical point. Then we present strong arguments and this leads to GKS-like inequalities, under some limiting conditions: the interparticle distances must be large and the thermodynamic state of the system must be close to the critical point. In order to get these inequalities, an upper bound forh(n) is obtained. Particular attention must be paid to the fact that the usual asymptotic approximations of the liquid state theory are no longer valid.

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.

Our research on employing the cellular automata methodology to corrosion and passivation phenomena is reviewed. Examples of a peculiar pit development are found and presented. The diffusion rate in the corroding medium is argued and shown in the simulation results to affect mainly the characteristic length scale for the corrosion process. New data for the pitting corrosion development on a planar interface are presented and discussed.

A simple model describes uniform and localised corrosion. We use a mesoscopic cellular automata (CA) type approach, which has proved a powerful tool in the study of rough metal–electrolyte interfaces. The model accounts for two corrosion kinetics and their relative spatial localisation. The competition between the two forms of kinetics of corrosion is shown to reproduce several types of morphology of corrosion ranging from narrow pits or larger cavities to rough surfaces. Simulation and experimental results are compared providing insight on the relation between kinetics and morphologies of the corrosion front. We emphasize the importance of stochastic simulations in relation to CA.

We present simulation results for a simple lattice gas cellular automata model of passivation. The lattice sites representing the corrosion product are produced at the corroding surface and diffuse executing a random walk. Asymmetric simple exclusion rules of the random walk account for an attractive potential between the corrosion product particles. The particles can aggregate and when sufficiently numerous form a compact phase on the corroding surface. The model predicts a transition from the active to passive state when increasing the reactivity of the surface. The transition is characterized by a sudden increase in the surface coverage of the corrosion product interpreted as a passive layer formation. The layer blocks contact of the metal surface with the environment and reduces the corrosion rate. The model reproduces the known paradox of passivity—the surface must be reactive enough for the layer to form. A further increase in the bare reactivity reduces largely the observed reaction rate. The simulations yield information on the morphological changes of the surface layer before and after the transition. In terms of the corrosion current, the active state is described by the current increase with the polarizing potential according to the Tafel law while in the passive state the current is independent of the anodic potential. Our simple model reproduces principal features of passivation.

Using a statistical field approach we investigate the structure of an electrolyte solution in contact with a neutral impenetrable wall. The Hamiltonian contains the Coulomb interaction and the ideal entropy. At the level of the quadratic approximation, the Hamiltonian yields the Debye-Huckel theory in the bulk. Analytic expressions of the charge-charge and potential-potential inhomogeneous correlation functions are obtained. Exact asymptotic results for point ion charge correlation functions are obtained and the profile for the fluctuation of the electric potential is calculated. We also consider the term beyond the quadratic expansion of the ideal entropy in the Hamiltonian. With this term a higher order coupling between charge density and number density produces a non-trivial profile for the total ion density. This density profile is consistent with the contact theorem and the related surface tension calculated from the Gibbs adsorption isotherm.

In this paper, we briefly discuss a field theory approach of classical statistical mechanics. We show how an essentially entropic functional accounts for fundamental symmetries related to quantum mechanical properties which hold out in the classical limit of the quantum description. Within this framework, energetic and entropic properties are treated at equal level. Based on a series of examples on electrolytes, we illustrate how this framework gives simple interpretations where entropic fluctuations of anions and cations compete with the energetic properties related to the interaction potential.