Effects of Adsorbate Diffusion and Edges in a Transition from Particle to Dendritic Morphology during Silver Electrodeposition.

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 (G) and probability of hop per neighbor (P). Finally, simulations with small electrode seeds confirm the transition from initially compact particles to the nucleation of nanotrees and provide estimates of the transition sizes as a function of those parameters. The simulated compact and dendritic deposits show dominant (111) surface orientation, as observed in experiments. Extrapolations of simulation results to match microparticle and nanotree sizes lead to G = 4 × 1011 and P = 0.03, suggesting to interpret those sizes as diffusion lengths on the growing surfaces and giving diffusion coefficients 2 to 3 × 10-13 m2/s for deposited silver atoms. These results may motivate studies to relate diffusion coefficients with atomic-scale interactions.

Crossover from compact to branched films in electrodeposition with surface diffusion.

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 ε<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_{c} of that layer increases with G but is weakly affected by ε. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_{c}∼G^{γ}, with γ=1/[2(1-ν)]≈0.43, where ν≈0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_{c} can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter ε are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity.

Transition from compact to porous films in deposition with temperature-activated diffusion.

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 ε per additional nearest neighbor, respectively, with activation energies are E(s) and E(b). If R and ε independently vary, regimes of low and high porosity are separated at 0.075≤ε(c)≤0.09, with vanishingly small porosity below that point and finite porosity for larger ε. Alternatively, for fixed values of E(s) and E(b) and varying temperature, the porosity has a minimum at T(c), and a nontrivial regime in which it increases with temperature is observed 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 nondesorption. 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(-τ̃) with τ̃≈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 α≈0.35 is consistent with the percolation backbone structure via the relation α=2-d(B), where d(B) is the backbone fractal dimension.

Crossover from anomalous to normal diffusion in porous media.

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.

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.

Ion transfer processes at ionic liquid based redox active drop deposited on an electrode surface.

Ion transfer across the boundary formed at an ionic liquid drop deposited on an electrode immersed in aqueous solution, generated by electrochemical redox reaction at the electrode-ionic liquid interface, is studied to obtain information about the ability of anions to be transferred into a room temperature ionic liquid.