Electrochimica Acta 209 (2016) Contents lists available at ScienceDirect. Electrochimica Acta

Transcription

1 Electrochimica Acta 209 (2016) Contents lists available at ScienceDirect Electrochimica Acta journal homepage: Geometry influence on corrosion in dynamic thin film electrolytes Hans Simillion a,, Nils Van den Steen a, Herman Terryn a, Johan Deconinck b a Research Group Electrochemical and Surface Engineering (SURF), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium b Department of Electrical Engineering and Power Electronics (ETEC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, 1050 Brussels, Belgium article info abstract Article history: Received 29 February 2016 Received in revised form 12 April 2016 Accepted 14 April 2016 Available online 25 April 2016 Keywords: Atmospheric corrosion Modeling Thin electrolyte films MITReM FEM Concentrated solutions Atmospheric corrosion is a complex problem, essentially an electrochemical process under confined thin electrolyte layers. Predictions require better mechanistic models to understand the underlying fundamental subprocesses on a microscopic level. We developed a mechanistic multi-ion transport and reaction model (MITReM) that considers time-dependent accumulation of concentrations in thin (NaCl) confined electrolyte layers. The model predicts local concentration and electrolyte potential distributions, from which corrosion rates are derived. Simulations in the confined dynamic film show that the chloride accumulation causes a deviation from the reverse proportionality of the corrosion current with the film thickness below films of 10 m. The oxygen distribution and local corrosion current densities demonstrate that the contribution of the edge effect decreases for thinner electrolyte layers. The influence of the electrode geometry on the current density also decreases with decreasing film thickness. These qualitative insights are essential for the development of atmospheric corrosion prediction tools and aid in the design and interpretation of electrochemical techniques for confined thin film electrolytes Elsevier Ltd. All rights reserved. 1. Introduction Atmospheric corrosion is characterised by the electrochemical degradation of a metal under thin electrolyte layers. Atmospheric conditions (temperature, humidity, salt deposition, etc...) influence the presence of thin aqueous electrolyte films and/or droplets on the metal surface. The complexity of the dynamic film is caused by evaporation/condensation, the presence of salts, corrosion products, etc. The effective corrosion rate is the result of the electrochemical interactions in the dynamic electrolyte. This makes atmospheric corrosion predictions very challenging. The industrial approach involves empirical methods to study the resulting corrosion effect (damage), as a function of environment. Long-term exposure tests [1 3] are very time consuming and result in rather inaccurate predictions. Accelerated tests [4 6] (i.a. salt-spray, humidity chambers tests) give quicker results, but the conditions are even further away from service conditions. As a result, these tests only provide a robust classification of specific materials in specific environments (often even for specific testing equipment). Furthermore, since only the corrosion damage (mass/thickness loss) is measured, these methods do not provide a quantitative view on the underlying mechanisms. Corresponding author. address: hsimilli@vub.ac.be (H. Simillion). On the other hand, the mechanistic understanding of the corrosion process is a central aim in an academic approach. The combination of surface-analytical and electrochemical techniques allows the quantification of metal oxidation and in extension corrosion processes. The problem here is that the assumptions for quantification require standard electrochemical setups, which are not representative for the thin electrolyte layers present in atmospheric corrosion conditions. Numerical simulations are proposed as a link between the electrochemical quantification and the outcome of (industrial) corrosion measurements. Concentrations and reaction rates are calculated based on basic material properties, kinetic coefficients and environmental parameters. Specific corrosion models are developed for pitting [7,8], crevice, galvanic corrosion [9 12], etc. Thébault et al. [13] published a 2D FEM model taking into account oxygen diffusion and electrolyte potential to describe the influence of film thickness and zinc/iron ratio in a galvanic couple. Later Thébault et al. [14] presented the Coupled Electrochemical Transport-Reaction (CETR) model in which they extended their work to take into account corrosion products in immersed conditions. A similar model is presented by Topa et al. [15]; with a multi-ion transport and reaction model (MITReM) they simulated the time-dependency of galvanic protection including corrosion products. Macdonald [16] presented the point defect model, which is a deterministic model for the prediction of the growth and breakdown of passive films. That model is in particular useful for the / 2016 Elsevier Ltd. All rights reserved.

2 150 H. Simillion et al. / Electrochimica Acta 209 (2016) prediction of localized corrosion attacks. Recently, Dolgikh et al. [17] applied the MITReM for a dynamic film. The dynamic simulation is limited to oxygen reduction in a one-dimensional geometry, taking into account the influence of chloride on the oxygen reduction reaction. Several electrochemical setups have been developed to measure the electrochemical properties of metals under thin electrolyte layers [18 20]. Publications as early as 1977 report the application of polarisation techniques to corrosion in thin condensed moisture layers [21]. Stratmann [22 24] presented in a series of papers techniques to determine the reaction kinetics of electrodes under thin layers. Others report the study of galvanic couples in thin layers [25,26,11]. Works from Yadav [9] and Zhang [26] focus on the corrosion of steel-zinc couples in drying conditions. A common observation in these systems is the increase of the corrosion current density for thinner electrolytes. This is explained by an increased rate of the oxygen reduction reaction (ORR), which limits the overall corrosion process. Stratmann et al.[23] observed a maximum corrosion current density for iron during wet-dry transitions. They assigned the decrease in corrosion rate to the precipitation of corrosion products in the highly alkaline environment, created by the ORR. The layer thickness at this maximum is reported at around 10 m. Hoerle [27] developed a model that supports this idea. Thin film electrolytes introduce another difficulty in the analytical quantification of electrochemical processes. The use of non-standard geometries complicates the analytical treatment of e.g. polarisation data. And common assumptions (bulk concentrations, uniform conductivity, parallel current lines,...) are no longer valid in thin film set-ups. This is even more pronounced during wet-dry cycles because concentrated electrolyte conditions are encountered during evaporation. These effects make the quantification of atmospheric corrosion so challenging, which explains the use of outdoor exposure tests. Our aim of the mechanistic model approach is to simulate corrosion processes in thin and ultra-thin films. The combination of electrolyte transport, precipitation and oxide formation models with models for condensation/evaporation describes the dynamic corrosion behaviour inside the electrolyte. This combination is essential to capture a more complete view of the atmospheric corrosion process. In this paper we introduce the dynamic behaviour during evaporation. With a moving mesh algorithm we simulate the evaporating electrolyte, which results in the accumulation of species. This influences intrinsic electrolyte properties like the solubility of oxygen and diffusion coefficients. These essential parameters affect the corrosion processes i.a. ion-mobility, electrolyte conductivity and oxygen uptake rate and transport. These aspects are demonstrated by applying the model on the (uniform) corrosion of zinc. Different geometrical configurations are elaborated to explore the influence of micro-electrodes on the local current density in combination with a varying electrolyte film. The insights obtained in this work induce further developments in atmospheric corrosion simulations and provide insights for the interpretation of electrochemistry in thin layers and/or when working with micro-electrode geometries. 2. Model description The simulation domain is the electrolyte, in which conservation of mass and Poisson s equation are expressed. The boundary conditions of these partial differential equations define the oxygen uptake rate (top boundary) and electrochemical electrode reactions (electrode boundary) Governing equations The conservation of mass can be written, for each individual species, i, as follows: c i t = N i + R i, (1) where N i (mol m 2 s 1 ) is the molar flux of species i with concentration c i (mol m 3 ) and R i (mol m 3 s 1 ) is the net production rate of species i due to chemical reactions. In this study corrosion products and chemical reactions inside the electrolyte are not considered, so R i = 0. This implies that the model results are not affected by the formation of corrosion products or any other change in the electrolyte composition. This means that the simulations in this work only look at initial and unchanging) electrolyte conditions. The molar flux, Ni, is the result of convection, diffusion and migration in the electrolyte. With the diluted model simplification this flux is given by: N i = c i v D }{{} i c i z ifd i c i, (2) }{{} RT }{{} convection diffusion migration where v (ms 1 ) is the solution velocity, D i (m 2 s 1 ) and z i are the diffusion coefficient and charge number of species i respectively; (V) is the electrostatic solution potential; T (K) is the (constant and uniform) temperature ( K); F Faraday s constant (96485 Cmol 1 ) and R the universal gas constant (8.31 J mol 1 K 1 ). In this work the convection term is neglected (c i v = 0), since the electrolyte is assumed stagnant and thin enough to neglect the effect of natural convection. Poisson s equation (eq. (3)) is added to the set of mass balance equations: ( ) = q = z i c i, (3) where is the dielectric constant of the solution ( F/m) and q is the free charge density, computed from the ion charge and local concentrations. In this work, 5 species concentrations are considered: [Na + ], [Cl ], [Zn 2+ ], [O 2 ], [OH ] so a set of 6 equations has to be solved. Note that [H + ] is not considered as an unknown, its concentration is directly calculated from the water dissociation equilibrium ([H + ] [OH ] = K w = 10 8 mol 2 m 6 ). The species parameters are given in Table 1 respectively Geometry and discretisation A (two-dimensional) cross section (see Fig. 1) of the electrolyte above the metal surface is considered in which the mass balance and Poisson s equations are solved. On the edges of the rectangular electrolyte, boundary conditions are applied. Note that, due to symmetry, only half of the geometry has to be meshed, which reduces the computational time. The mesh discretisation depends on the electrolyte thickness (ı) and the width of the electrode (2w). The mesh is refined around the electrode where the concentration Table 1 Charge, diffusion coefficients at infinite dilution of dissolved species considered in the model and fitting parameters for species diffusion correlation (eq. (8)). Species z i /( ) D 0 / (10 9 m 2 /s) i a i / (10 4 m 3 /mol) Na Cl OH O Zn H

3 H. Simillion et al. / Electrochimica Acta 209 (2016) Fig. 1. (Initial) geometry and computational domain with indication of boundaries. and potential gradients are the highest. The total number of triangle elements is between 1100 and 9100, with in total between 600 and 3200 nodes and in every node 6 unknowns to solve. Finer discretisations didn t improve the solution accuracy Mesh deformation The top boundary of the electrolyte moves downward to simulate evaporation. The moving mesh algorithm is based on a level set method [28] and an elastic body analogy [29]. The initial electrolyte height is 500 m in all simulations. Van den Steen et al. [30] provide a mechanistic model to predict evaporation/condensation rates as a function of environmental parameters and electrolyte properties. Combination with this work would link the physical corrosion model we describe here, with the actual simulated film thickness. In this work the evaporation (0.1 m/s) is considered constant in time and space (uniform film thickness). The mesh deformation velocity is set equal the imposed evaporation rate Boundary conditions Insulating boundaries. At the insulating boundaries (insulator, right) as well as the symmetry line (left), the ion flux of each species and therefore also the current density normal to the surface are equal to zero: N i 1 n = 0 (4) Top boundary - Air liquid interface flux. The oxygen flux entering at the top interface (F O2 ) is proportional to the difference between the local concentration (c O2 ) and the saturation concentration (c sat ). O 2 The dissolution rate (F = ms 1 ) is the proportionality factor [13]. The oxygen saturation concentration (solubility) O 2 depends on the chloride concentration (see further in section 2.5). For all other species an insulating boundary is considered (eq. (4)). N O2 1 n = F O2 = F O ([O 2 2 ] sat [O 2 ]) (5) Electrode reactions. At the electrode boundary, oxygen reduction and zinc oxidation are considered. The fluxes normal to the surface are given by the electrochemical reactions. These fluxes are calculated with an exponential expression in which the reaction rate depends on the local electrolyte potential () and local oxygen concentration (c O2 ). The electrode potential, V, (0.0 V) is homogenous and chosen as the reference potential for the system. All electrode reactions are defined on the whole electrode surface. The evolution of concentration and potential distribution defines the rate of each partial reaction. Anodic and cathodic areas are thus not explicitly defined, but evolve from the local and time dependent electrolyte properties. The total flux is the sum of all partial reactions: N i 1 n = e s ie, (6) where e is the rate of the electrode reaction e and s ie is the stoichiometric coefficient of species i in that reaction. The considered reactions and their kinetic parameters are given in Table 2. The total net current, integrated over the electrode width, is zero due to charge conservation in the domain. Hence, the resulting electrolyte potential reaches a value for which this condition is valid. The mixed potential theory is thus implicitly included in our model approach Oxygen saturation concentration The solubility of oxygen depends on the chloride concentration [31,32] and so indirectly also on the oxygen reduction current. Dolgikh et al. [17] applied this dependency for a one-dimensional Table 2 Electrochemical reactions. Reaction j/am 2 n k Oxygen reduction O 2 + H 2O +4e 4OH Zinc oxidation Zn Zn 2+ +2e k nf e nf RT (V ) c O k nf e nf RT (V ) The kinetic data is fitted from polarisation curves on pure zinc (99.5%) in a 0.01 M NaCl solution.

4 152 H. Simillion et al. / Electrochimica Acta 209 (2016) oxygen reduction model. The oxygen saturation concentration can be written as a function of chloride concentration: c sat O = 0.25 exp( [Cl ]). (7) 2 This involves that the oxygen uptake (eq. (5)) at the airliquid interface decreases with increasing chloride concentration. Imposed as a boundary condition, this flux limits the global corrosion process for high chloride concentrations. Its role is important, especially during dynamic evaporation simulations Diffusion coefficients In the same work Dolgikh et al. [17] showed a discrepancy in very thin films (<30 m) between the experimental and simulated current density. The simulated oxygen currents were higher than experimentally observed. A possible reason for this discrepancy is that their model did not take into account the effect of reduced ion mobility in concentrated solutions. Diffusivity in concentrated solutions deviates strongly from the diluted electrolyte model [33]. In this model a semi-empirical expression is used to correct diffusion constants: D i = D 0 i exp( a i [Cl ]), (8) where D 0 is the diffusion coefficient at infinite dilution and a i i a fitting parameter. The advantage of using this semi-empirical expression is that the set of equations remains valid for high concentrations. Therefore, concentrated solution models [34], which would increase the computational cost, are avoided Influence of diffusivity on electrolyte conductivity The diffusivities are intrinsically time and space dependent, since they depend on the local chloride concentration. The modified diffusivities have a direct effect on the electrolyte transport. The conductivity serves as a demonstration of this effect. The solution conductivity of a strong electrolyte follows Kohlrausch s Law: c = = 0 K c, (9) where is the molar conductivity, 0 is the limiting molar conductivity, K is a fitting constant and c is the molar concentration of the electrolyte. The equation is an application of the Debye-Hückel theory (DH), developed by Onsager [35]. Note that, in our model, the electrolyte conductivity ( = z 2 i F2 D i c i ) appears naturally as the migration term in the total RT ionic current (j = z i FN i ). With constant diffusion coefficients, the conductivity varies linearly with electrolyte concentration. However, this is not observed experimentally at higher concentrations. The semi-emperical model extension given in equation (8) corrects indirectly the effect on the conductivity. As ion mobilities and diffusivities are linked (D i = u i /RT), the electrolyte conductivity also changes in time and space. Therefore, Onsager s expression (eq. (9)) is compared (see Fig. 2) tothe corrected and uncorrected ion-conductivities. Both models show a consistent deviation from the linear model (with uncorrected diffusivities) and are in agreement with the experimental values [36]. To conclude the theoretical model setup; we extend current MITReM models with chloride dependency of (1) the oxygen solubility and of (2) the diffusion coefficients. With these two extensions we can describe the influence on the oxygen uptake rate, local and time-dependent conductivity and diffusion transport in concentrated solutions, during dynamic (evaporation) simulations. Fig. 2. The variation of the conductivity as a function of NaCl concentration. The expression for the ion-conductivity derived from eq. (8) agrees with the The Debye- Hückel theory and experimental values (source:[36]). 3. Influence of electrode width at constant electrolyte height The above described model has been applied on the geometry (see Fig. 1) with a varying width of the active metal surface (2w). The height of the electrolyte is kept constant at 500 m, which corresponds to a typical diffusion layer thickness in stagnant solutions [13] Access to local concentration and potential distributions Solving the set of equations provides concentration and potential profiles in the electrolyte. An example is given in Fig. 3. The local oxygen concentration drops (to almost zero) above the electrode due to its consumption in the reduction reaction. In the center of the electrode (at the symmetry line), the oxygen concentration has a linear profile normal to the surface. The local electrolyte potential only varies in the V range, since there is no applied (external) potential and the electrode potential is considered homogeneous (e.g. no galvanic effects). The potential variation is a result of ion distribution in the electrolyte caused by the electrochemical reactions. By integrating the local properties, global parameters can be obtained (average current, average Fig. 3. Simulated results for a electrode width of 1000 m (w = 500 m) and electrolyte height (ı) of 500m. (a) oxygen concentration and (b) potential distributions ina1wt% NaCl solution.

5 H. Simillion et al. / Electrochimica Acta 209 (2016) Fig. 4. Simulated oxygen distributions for variable electrode widths between 1000 m and 10 m. The electrolyte height is constant at ı = 500 m. concentration, corrosion potential,...), allowing a comparison between local electrochemical measurements [37,8,38] Influence of electrode width on the oxygen concentration distribution Fig. 4 shows the variation of oxygen distribution as a function of electrode width. The case without insulator (w = 1000 m) is equivalent to a one-dimensional system. This corresponds to a limiting diffusion current to an infinite planar electrode. Accordingly the oxygen profile has a linear distribution, along the whole electrolyte. In all other cases the oxygen profile depends on the electrode geometry. The average oxygen concentration is inversely proportional to the electrode width and the local concentration distribution deviates from the one-dimensional analogy. This results in a different current density distribution along the electrode. The diffusion current evolves from planar (for a large electrode) to a line source (for a thin electrode) Influence of electrode width on the average current density The effect of the electrode dimensions on the corrosion rate, is demonstrated by calculating the average corrosion current density (according to the electrochemical boundary conditions, see Table 2). Simulations for three different NaCl concentrations: 0.1 wt%, 1 wt%, and 10 wt% are presented in Fig. 5. It is clear that a smaller electrode results in a higher access to oxygen, which in turn increases the average current density. Fig. 5. Simulated corrosion currents controlled by limiting oxygen reduction on zinc with different electrode widths in NaCl electrolytes with a constant 500 m layer thickness Influence of electrode width on the local current density distribution The effect of the electrode width on the current density can be attributed to the edge effect. Due to non-uniform access to the electrode, the oxygen concentration at the edge of the electrode is higher than in the center. This effect is illustrated in Fig. 6. The current density is normalised with respect to the current density in the center of the electrode. The normalised current increases towards the edge (x w) of the electrode for all situations. This edge-effect is more pronounced for smaller electrodes. However for electrode widths below 300 m the current in the center of the electrode (x = 0) deviates from the linear limiting current and the Fig. 6. Simulated corrosion current density along the normalised electrode for different electrode widths in a 0.1 wt% NaCl solution with a constant 500 m layer thickness.

6 154 H. Simillion et al. / Electrochimica Acta 209 (2016) Fig. 7. Simulated corrosion current and average surface concentration of oxygen for discrete and constant film thicknesses increase for thinner electrolyte, due to a decrease in diffusion path. current density is no longer solely controlled by the electrolyte height but also by the electrode width itself. 4. Influence of (constant) electrolyte height In order to study the influence of the electrolyte height on the oxygen reduction, numerical simulations with different electrolyte thicknesses (but constant in time) were performed. The results in this section were obtained for a NaCl concentration of 1 wt% above an electrode of 1000 m in width (or w = 500 m) Oxygen profile and edge effect In Fig. 7 the increased current density is shown as a function of film thickness. The increased acces of oxygen in thinner films (due to a smaller diffusion layer) causes the increase in current density. Since these simulations are with a fixed electrolyte height, no change in NaCl concentration takes place. So no effect of evaporation is taken into account. The oxygen distribution profiles for some film thicknesses are shown in Fig. 8. Smaller electrolytes involve a higher oxygen concentration. Decreasing the film thickness also results in a higher area with a linear diffusion profile normal to the electrode. The decrease of the edge-effect is further explored in the next section. The evolution of the edge effect when the electrolyte layer decreases has been investigated by looking at the local current distribution along the electrode (see Fig. 9). Note that the overall increase in current density is related to a higher local oxygen concentration at the surface and that the surface concentration deviates from the zero-concentration condition for limiting current. The reduction current density is proportional to the local oxygen surface concentration according to the electrode reactions defined in Table 2. The local current density at the edge (x = 500 m) is higher than in the center of the electrode. The spread of this edge-effect reduces for decreasing film thickness, because initially the edge-effect is controlled by the width of the electrode, but for thinner electrolyte layers, the layer thickness becomes the controlling factor. The implication of these results towards atmospheric corrosion simulations is that we can ignore the edge effect if the electrolyte layer is much thinner than the electrode width. On the other hand, these simulations indicate that the quantification of electrochemical measurements of micro-electrodes should include a correction for the electrode geometry itself. Fig. 8. Oxygen concentration profiles in 1 wt% NaCl with parameters w = 500 m and ı = {100, 300, 500} m Access to partial current densities In the results previously shown in this paper, the corrosion process was limited by oxygen reduction. However, this is not expressed explicitly in the model, it is the result of the numerical simulation. The anodic and cathodic reactions are defined as electrochemical reactions and the electrolyte transport properties, together with the geometry, define the controlling conditions. Since Fig. 9. Local current density increases towards the edge of the electrode (edge effect). Thinner electrolyte layers (h«) result in a higher average current density and a decreased edge effect

7 H. Simillion et al. / Electrochimica Acta 209 (2016) them with global measurements (like the corrosion potential). A decrease in electrolyte layer, increases the oxygen reduction reaction which causes a shift of the corrosion potential, while not necessarily changing the behaviour of the anodic partial reaction. The polarisation curve is a result of all electrode reactions and the resulting equilibrium potential (corrosion potential) follows implicitly the mixed potential theory. 5. Time dependent electrolyte thickness Fig. 10. Partial current densities for the anodic and cathodic reactions. The total (measurable) current is the net sum of both and defines the corrosion potential and current. reduction and oxidation reactions are defined separately, we have access to the partial current densities with the simulations. The polarisation simulation for a 1 wt% NaCl solution with w = 1000 m ( 1D) serves as an example (see Fig. 10). Only the sum of the partial current densities (in red) can be measured experimentally. At the corrosion potential anodic and cathodic currents balance out, the corresponding current is the corrosion current. The oxygen diffusion limiting current is constant in the full potential window, which means that the corrosion current density is simply equal to this limiting current. Only the kinetics of the anodic electrochemical reactions (see Table 2) can be determined experimentally in this potential window. Fig. 11 shows identical results of simulated polarisations for different layer thicknesses ( m). The layer thickness only has an influence on the oxygen reduction reaction (ORR). From the global polarisation behaviour, however, an apparent change in both negative and positive sides of the polarisation curve could be observed. These polarisation curves clearly show how to interpret simulated local parameters and how to link For all previous static simulations the oxygen reduction was not limited by transport in the electrolyte but by the electrolyte height. This means that the thinner the film, the higher the oxygen access and the higher the corrosion current (Fig. 7). The oxygen uptake flux (eq. (5)) would limit the overal reaction, films below the micrometer range. Down to 1 m the uptake rate is still high enough and its effect not noticed. The reason behind is that the static simulations consider fixed electrolyte concentrations in which the NaCl concentration was moderate (max 10 wt%). During evaporation, however, a decrease in film thickness coincides with a concentration increase. With dynamic simulations we want to better describe the influence of evaporation. In Fig. 12 the evolution of the NaCl concentration during evaporation is simulated (with an initial electrolyte thickness of 500 m). A high NaCl concentration has an important impact on the saturation concentration of oxygen (eq. (7)) in the electrolyte and on the diffusion constants of all species (eq. (8)). The concentration limit is 6 M, which is considered as the maximum solubility of NaCl in water. A different initial concentration only offsets the increase in concentration, but the increase is independent of the initial concentration and evaporation rate Dynamic mesh deformation model The MITReM model is applied for zinc corrosion with the geometry as shown in Fig. 1, with w = 500 m, ı init. = 500 m and a dynamic top boundary. The simulation results presented in this paper are based on an evaporation rate of 0.1 m/s and an initial concentration of 0.1 wt%. The evaporation rate represents a continuous and constant decrease in total electrolyte thickness. Multiple combinations of evaporation rate and initial concentration were simulated. Only one evaporation rate is presented here, Fig. 11. The polarisation simulation for a 1 wt% NaCl solution with w = 1000 m shows an increase in corrosion current density and increase in corrosion potential for a decreasing layer thickness.

8 156 H. Simillion et al. / Electrochimica Acta 209 (2016) Fig. 14. The corrosion current in the dynamic simulation deviates from the static simulations below around 30 m. The maximum current density is observed at 10 m. The initial film thickness is 500 m and initial NaCl concentration 0.1 wt% Fig. 12. Rapid increase of sodium chloride concentration during evaporation starting from 500 m, shown for different initial concentrations. The concentration is limited at its saturation concentration of 6 M or 6000 mol/m 3. since the effect of concentration and rate of evaporation are superimposable (see Fig. 12) Concentrations under thin evaporating film During the drying process, two effects influence the corrosion process dynamically. One effect is the reduction of the diffusion layer length, which results in a higher oxygen concentration at the electrode. The other effect is the increase of electrolyte concentration during drying. Higher concentrations of NaCl decrease the solubility of oxygen and the diffusivity of all species. Fig. 13(c,d) shows the transient concentrations of Cl and O 2 at the electrode surface. During the initial chloride concentration increase, the oxygen diffusivity and solubility decrease but the effect of the reduced layer thickness dominates. Hence, the diffusion path is shorter and the surface concentration of oxy- gen increases. The oxygen concentrations reaches a maximum and decreases again. The uptake of oxygen from air to the electrolyte becomes the limiting factor, since the decreasing oxygen solubility determines the rate of the uptake. The corrosion current (Fig. 13 (b)) follows the surface concentration of oxygen, which is linked to the dependency of the oxygen reduction reaction on the local surface concentration of oxygen. The maximum current is observed around 10 m, which corresponds to what is found experimentally [23,39,27]. The corrosion potential (Fig. 13 (a)) variation can be explained by a variation in the in oxygen reduction, which displaces the equilibrium in anodic and cathodic currents, hence moving the corrosion potential. This is explained in detail in paragraph Comparing static and dynamic simulation The current density obtained in the dynamic (evaporation) simulation shows no significant deviation from the static simulation for a film thickness down to around 30 m (see Fig. 14). An important observation is that below this thickness, the corrosion rate starts to decrease. The deviation from the static simulations is important since below this point the corrosion process depends on the evolution of the film. The maximum is observed at 10 m, a value that Fig. 13. The evolution of (a) [Cl ] and (b) average oxygen concentration at the electrode surface during evaporation. The resulting corrosion potential (c) and current (d) follow.

9 H. Simillion et al. / Electrochimica Acta 209 (2016) Fig. 15. Corrosion current density for different electrode widths during evaporation (ı = 500 m, [NaCl] init = 0.1 wt%, h init = 500 m). depends on the initial NaCl concentration and initial film thickness. Both initial parameters define the electrolyte layer thickness of the critical chloride concentration [17] Effect of electrode width during evaporation The effect of the electrode width has also been studied during evaporation. In Fig. 15 the current density transient is shown for a variation from 500 to 2 m. The initial NaCl concentration is 0.1 wt%. The initial current density (at 500 m) is identical to the distribution shown in Fig. 5. During evaporation the current density increases for all electrode widths to reach a maximum around 10 m. For the thin electrode width (w = 10 m), the influence of evaporation is minimal, since the current density is controlled by the electrode width and not by the film thickness. The decreasing oxygen saturation concentration becomes only relevant at low thicknesses. The differences decrease during the evaporation process, which is in line with the decreasing edge effect (demonstrated in Fig. 9) for thinner electrolytes. This shows that the electrolyte layer becomes the controlling geometrical dimension for film layers below 10 m. 6. Conclusions A model of zinc corrosion under oxygen reduction control in a thin evaporating NaCl electrolyte has been proposed. The dynamic simulations provide a direct coupling between the mesh deformation and the increasing NaCl concentrations. This results in the intrinsically calculated effect on the oxygen solubility and diffusivity of all species as well as the conductivity. The insights obtained from our sensitivity study concern the influence of the electrode width and the edge effect, the comparison between static simulations and dynamic simulations and the decreasing importance of the electrode geometry when going to smaller electrolyte layers. These insights are essential in developing other models and combining them to get closer to real atmospheric corrosion conditions. The comparison between the dynamic simulations and the static simulations for different electrolyte heights (ı) demonstrate the deviation from Fick s law and the limiting current density equation. The maximum oxygen reduction current density is observed around 10 m. The decrease in current density for ı <10m is a direct result of decreased oxygen solubility and diffusivity, both function of Cl concentration. Different electrode geometries show that the local current density is a function of electrode height, electrolyte width and width of adjacent insulation. The observed edge-effect decreases for thin electrolytes, in which the electrolyte thickness becomes the main limiting factor. An important conclusion is that for practical simulations of atmospheric corrosion only the oxygen transport perpendicular to the surface needs to be considered. The geometry dependency also shows that electrochemical techniques require a correction when working with non-conventional setups such as micro-electrodes, micro-capilaries, etc... The proposed model is a new contribution towards dynamic atmospheric corrosion simulations. The simulation results provide a qualitative description of the influence of dynamic evaporation. The mechanistic approach facilitates expanding the model with elements such as corrosion products, passivation layers, electrode microstructures, galvanic couples, etc. In the future, this will be addressed in more detail to improve current model and make it applicable for longer time scales. The corrosion models are then to be combined with film thickness prediction models to compare with corrosion in outdoor atmospheres and indoor climate chamber tests. Aknowledgements This research was funded by The Long Term Structural Methusalem NANOMET. The author would also like to thank OCAS (Arcelor Mittal research center) for their financial support. References [1] C. Leygraf, T. Graedel, Atmospheric corrosion, Wiley, [2] D. de la Fuente, J.G. Castaño, M. Morcillo, Long-term atmospheric corrosion of zinc, Corrosion Science 49 (3) (2007) [3] D. de la Fuente, I. Díaz, J. Simancas, B. Chico, M. Morcillo, Long-term atmospheric corrosion of mild steel, Corrosion Science 53 (2) (2011) [4] F. Corvo, J. Minotas, J. Delgado, C. Arroyave, Changes in atmospheric corrosion rate caused by chloride ions depending on rain regime, Corrosion Science 47 (4) (2005) [5] N. LeBozec, N. Blandin, D. Thierry, Accelerated corrosion tests in the automotive industry: A comparison of the performance towards cosmetic corrosion, Materials and Corrosion 59 (11) (2008) [6] D. Thierry, N. LeBozec, Corrosion Products Formed on Confined Hot-Dip Galvanized Steel in Accelerated Cyclic Corrosion Tests, dx.doi.org 65 (11) (2012) [7] L.C. Abodi, J.A. DeRose, S. Van Damme, A. Demeter, T. Suter, J. Deconinck, Modeling localized aluminum alloy corrosion in chloride solutions under non-equilibrium conditions: Steps toward understanding pitting initiation, Electrochimica Acta 63 (2012) [8] S.G.R. Brown, N.C. Barnard, 3D computer simulation of the influence of microstructure on the cut edge corrosion behaviour of a zinc aluminium alloy galvanized steel, Corrosion Science 48 (8) (2006) [9] A.P. Yadav, A. Nishikata, T. Tsuru, Degradation mechanism of galvanized steel in wet dry cyclic environment containing chloride ions, Corrosion Science 46 (2) (2004) [10] R.M. Souto, Y. González-García, A.C. Bastos, A.M. Simões, Investigating corrosion processes in the micrometric range: A SVET study of the galvanic corrosion of zinc coupled with iron, Corrosion Science 49 (12) (2007) [11] A. Tahara, T. Kodama, Potential distribution measurement in galvanic corrosion of Zn/Fe couple by means of Kelvin probe, Corrosion Science 42 (4) (2000) [12] M. Mouanga, F. Andreatta, M.E. Druart, E. Marin, L. Fedrizzi, M.G. Olivier, A localized approach to study the effect of cerium salts as cathodic inhibitor on iron/aluminum galvanic coupling, Corrosion Science 90 (2015) [13] F. Thébault, B. Vuillemin, R. Oltra, C. Allely, K. Ogle, Modeling bimetallic corrosion under thin electrolyte films, Corrosion Science 53 (1) (2011) [14] F. Thébault, B. Vuillemin, R. Oltra, C. Allely, K. Ogle, Protective mechanisms occurring on zinc coated steel cut-edges in immersion conditions, Electrochimica Acta 56 (24) (2011) [15] V. Topa, A.S. Demeter, L. Hotoiu, D. Deconinck, J. Deconinck, A transient multiion transport model for galvanized steel corrosion protection, Electrochimica Acta 77 (2012) [16] D.D. Macdonald, The Point Defect Model for the Passive State, Journal of The Electrochemical Society 139 (12) (1992) [17] O. Dolgikh, A.C. Bastos, A. Oliveira, C. Dan, J. Deconinck, Influence of the electrolyte film thickness and NaCl concentration on the oxygen reduction current on platinum, Corrosion Science 102 (2016)

10 158 H. Simillion et al. / Electrochimica Acta 209 (2016) [18] E. Remita, E. Sutter, B. Tribollet, F. Ropital, X. Longaygue, C. Taravel-Condat, N. Desamais, A thin layer cell adapted for corrosion studies in confined aqueous environments, Electrochimica Acta 52 (27) (2007) [19] S. Palani, T. Hack, J. Deconinck, H. Lohner, Validation of predictive model for galvanic corrosion under thin electrolyte layers: An application to aluminium 2024-CFRP material combination, Corrosion Science 78 (2014) [20] A. Cox, S.B. Lyon, An electrochemical study of the atmospheric corrosion of mild steel-i. Experimental method, Corrosion Science 36 (7) (1994) [21] S.G. Fishman, C.R. Crowe, The application of potentiostatic polarization techniques to corrosion under thin condensed moisture layers, Corrosion Science 17 (1) (1977) [22] M. Stratmann, H. Streckel, On the atmospheric corrosion of metals which are covered with thin electrolyte layers I. Verification of the experimental technique, Corrosion Science 30 (6-7) (1990) [23] M. Stratmann, H. Streckel, On the atmospheric corrosion of metals which are covered with thin electrolyte layers II. Experimental results, Corrosion Science 30 (6-7) (1990) [24] M. Stratmann, H. Streckel, K.T. Kim, S. Crockett, On the atmospheric corrosion of metals which are covered with thin electrolyte layers-iii. The measurement of polarisation curves on metal surfaces which are covered by thin electrolyte layers, Corrosion Science 30 (6/7) (1990) [25] X. Liao, F. Cao, L. Zheng, W. Liu, A. Chen, J. Zhang, C. Cao, Corrosion behaviour of copper under chloride-containing thin electrolyte layer, Corrosion Science 53 (10) (2011) [26] X.G. Zhang, E.M. Valeriote, Galvanic corrosion of zinc/steel couple under thin layer electrolytes, XG Zhang, [27] S. Hœrlé, F. Mazaudier, P. Dillmann, G. Santarini, Advances in understanding atmospheric corrosion of iron. II. Mechanistic modelling of wet dry cycles, Corrosion Science 46 (6) (2004) [28] J.A. Sethian, Level set methods and fast marching methods: evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, Cambride University Press, [29] T. Wuilbaut, H. Deconinck, Algorithmic developments for a multiphysics framework, Ph.D. thesis, VKI - ULB (2008). [30] N. Van den Steen, H. Simillion, O. Dolgikh, H. Terryn, J. Deconinck, An integrated modeling approach for atmospheric corrosion in presence of a varying electrolyte film, Electrochimica Acta 187 (2016) [31] J.E. Sherwood, F. Stagnitti, M.J. Kokkinn, W.D. Williams, A standard table for predicting equilibrium dissolved oxygen concentrations in Salt Lakes dominated by sodium chloride, International Journal of Salt Lake Research 1 (1) (1992) 1 6. [32] F.J. Millero, F. Huang, A.L. Laferiere, Solubility of oxygen in the major sea salts as a function of concentration and temperature, Marine Chemistry 78 (4) (2002) [33] G.W. Hung, R.H. Dinius, Diffusivity of oxygen in electrolyte solutions, Journal of Chemical and Engineering Data 17 (4) (1972) [34] S. Van Damme, N. Smets, D. De Wilde, G. Weyns, J. Deconinck, Ion Transport Models for Electroanalytical Simulation. 1. Theoretical Comparison, The Journal of Physical Chemistry B 113 (10) (2009) [35] C.H. Langford, R.A. Beebe, The Development of Chemical Principles, Courier Corporation, [36] W.M. Haynes, CRC Handbook of Chemistry and Physics, 96th Edition, CRC Press, [37] A.S. Demeter, O. Dolgikh, A.C. Bastos, D. Deconinck, S. Lamaka, V. Topa, J. Deconinck, Multi-ion transport and reaction model used to improve the understanding of local current density measurements in presence of concentration gradients around a point current source, Electrochimica Acta 127 (2014) [38] F. Thébault, B. Vuillemin, R. Oltra, K. Ogle, C. Allely, Investigation of self-healing mechanism on galvanized steels cut edges by coupling SVET and numerical modeling, Electrochimica Acta 53 (16) (2008) [39] F. Mansfeld, S. Tsai, Laboratory studies of atmospheric corrosion I. Weight loss and electrochemical measurements, Corrosion Science 20 (7) (1980)

11 本文献由 学霸图书馆 - 文献云下载 收集自网络, 仅供学习交流使用 学霸图书馆 ( 是一个 整合众多图书馆数据库资源, 提供一站式文献检索和下载服务 的 24 小时在线不限 IP 图书馆 图书馆致力于便利 促进学习与科研, 提供最强文献下载服务 图书馆导航 : 图书馆首页文献云下载图书馆入口外文数据库大全疑难文献辅助工具