Simulation of Diffusion-Controlled Growth of Interdependent Nuclei under Potentiostatic Conditions

The problem of diffusion-controlled growth following an instantaneous nucleation event was studied within the framework of a new numerical model, considering the spatial distribution of hemispherical nuclei on the electrode surface and the mutual influence of growing nuclei via the collision of 3D diffusion fields. The simulation of the diffusion-controlled growth of hexagonal and random ensembles was performed at the overpotential-dependent number density of nuclei. The diffusion flow to each nucleus within a random ensemble was simulated by the finite difference method using the derived analytical expressions for the surface areas and the volumes formed at the intersection of 3D diffusion fields with the side faces of a virtual right prism with a Voronoi polygon base. The implementation of this approach provides an accurate calculation of concentration profiles, time dependences of the size of nuclei, and current transients. The results, including total current density transients, growth exponents, and nucleus size distribution, were compared with models developed within the concept of planar diffusion zones, the mean-field approximation and the Brownian dynamics simulation method, as well as with experimental data from the literature. The prospects of the model for studying the initial stages of electrocrystallization were discussed.

Unveiling the Impact of the Cations and Anions in Ionic Liquid/Glyme Hybrid Electrolytes for Na-O2 Batteries

A series of hybrid electrolytes composed of diglyme and ionic liquids (ILs) have been investigated for Na-O₂ batteries, as a strategy to control the growth and purity of the discharge products during battery operation. The dependence of chemical composition of the ILs on the size, purity, and distribution of the discharge products has been evaluated using a wide range of experimental and spectroscopic techniques. The morphology and composition of the discharge products found in the Na-O₂ cells have a complex dependence on the physicochemical properties of the electrolyte as well as the speciation of the Na⁺ and superoxide radical anion. All of these factors control the nucleation and growth phenomena as well as electrolyte stability. Smaller discharge particle sizes and largely homogeneous (2.7 ± 0.5 μm) sodium superoxide (NaO₂) crystals with only 9% of side products were found in the hybrid electrolyte containing the pyrrolidinium IL with a linear alkyl chain. The long-term cyclability of Na-O₂ batteries with high Coulombic efficiency (>90%) was obtained for this electrolyte with fewer side products (20 cycles at 0.5 mA h cm^-2). In contrast, rapid failure was observed with the use of the phosphonium-based electrolyte, which strongly stabilizes the superoxide anion. A high discharge capacity (4.46 mA h cm^-2) was obtained for the hybrid electrolyte containing the pyrrolidinium-based IL bearing a linear alkyl chain with a slightly lower value (3.11 mA h cm^-2) being obtained when the hybrid electrolyte contained similar pyrrolidinium-based IL bearing an alkoxy chain.

Extraordinary regularities of zinc dendrites’ growth under appropriate electrolysis conditions

A case study is given of dendritic growth during zinc electrolysis in conditions that promote it. Subject of the main interest was how the electrolysis parameters affect the duration of dendrites life. The selected set of parameters did provide a surprisingly regular dendrite?s life, i.e. period from start of the electrolysis until dendrites detachment from the cathode. Dendrite?s growth did proceed with lowering of the zinc current efficiency, and the end of life was manifested by intensive hydrogen evolution due to corrosion of detached zinc deposit in the acid electrolyte. Current efficiency was successfully followed by the bubble counting technique, invented especially for kinetic studies of gas including reactions. The acquired results on dendrites? life duration were so exact that it was easy to unify all five mono-variable dependencies into one five-variable expression. The calculated values of life duration did differ from the measured ones by only ?3%! This is a proof that the developed expression accurately presents the real nature of dendritic growth under the applied conditions, i.e. 0.5 to 2 M zinc (II) ions, 0.41 to 3.06 M H2SO4, 10 to 2500 mg dm-3 copper (II) ions, 0.14 to 14 g dm-3 hexamethylenetetramine, and 4.25 to 103 mA dm-2 current density. The eventual broader region of Zn dendrites? strict regular growth is not excluded.

Simulation of 3D Electrochemical Phase Formation: Mixed Growth Control

Processes of nucleation and growth largely determine the structure and properties of thin films obtained by electrodeposition on foreign substrates. Theoretical aspects of the initial stages of electrochemical phase formation under constant and variable overpotentials are considered in this work. Simulation of multiple nucleation with mixed (charge transfer, and diffusion) controlled growth was performed for three cases (cyclic voltammetry, potentiostatic electrodeposition, and galvanostatic electrodeposition). The influence of the bulk concentration of depositing ions and the exchange current density at the electrolyte/nucleus interface on cyclic voltammograms (CVs), transients of current and overpotential, as well as the number and size of non-interacting new-phase nuclei was analyzed. It is found that, under galvanostatic conditions, the number of nuclei decreases as the concentration of depositing ions increases due to a more rapid decrease in overpotential. The proposed model was applied to determine the diffusion coefficient, exchange current density, and transfer coefficient considering the experimental CV.

Single Atom Nucleation of Cobalt over Graphene Oxide: Theory and Experimental Study

Nucleation and growth mechanism of Co electrodeposition over graphene oxide (GO) was studied using cyclic voltammetry (CV) and chronoamperometry techniques. The studies were performed over an aqueous electrolyte containing 10 mM CoSO₄·7H₂O maintained at an initial pH of 2.5. CV studies established that the deposition mechanism was diffusion-controlled and irreversible. Chronoamperometry studies revealed the presence of three concurrent processes: an initial adsorption current, which indicated adatom layer formation, 3D nucleation and growth of Co islands over GO, and hydrogen evolution over the deposited Co nanoclusters. It was observed that the nucleation rate increased with increasing the overpotential (η) for deposition (from 2.71 × 10⁴ cm^-2 s^-1 at η = 0.35 V to 3.62 × 10⁶ cm^-2 s^-1 at η = 0.90 V). Application of the classical theory of nucleation over the chronoamperometry results suggested that the free energy of formation of the critical nucleus was lower than room temperature thermal energy. This indicated that the nucleation and growth process was not activation-controlled but rather a kinetically controlled process. Application of Milchev's atomistic theory revealed that every single atom of Co deposited over the GO sheet was a supercritical nucleus that could grow into a cluster irreversibly.

Theoretical modeling of electrochemical nucleation and growth of a single metal nanocluster on a nanoelectrode

Theory of the initial stages of electrochemical formation and growth of a single metal nanocluster on an indifferent nanoelectrode has been developed and analyzed. General theoretical time dependences of the current and nanocluster size have been presented for the case of diffusion controlled growth at potentio- and galvanostatic deposition, and cyclic voltammetry.

The models of formation and growth of a single nanocluster on a nanoelectrode are presented for three basic electrochemical methods (cyclic voltammetry, potentiostatic and galvanostatic electrodeposition).

Electrodeposition of Indium on Glassy Carbon from Tetrabutylammonium Chloride Containing Solutions

The effectiveness of tetrabutylammonium chloride (TBACh) as inhibition additive of dendritic growth of indium has been investigated by means of cyclic voltammetry and chronoamperometry methods. The rotating disk electrode (RDE) method allowed the calculation of the diffusion coefficient of In3+ ions using the Levich equation, at 25 °C is 4.41 × 10–6 cm2/s. Diffusion coefficient of indium ions determined by chronoamperometry using the Cottrell law (6.63 × 10–6 cm2/s) is in consistent with the value calculated by the Levich equation. The addition of tetrabutylammonium ions to the electrolyte reduces the diffusion coefficient and inhibits the cathodic process by increasing the activation energy from 10.5 kJ/mol to 20.7 kJ/mol. The indium nucleation and growth on glassy carbon in chloride solutions was studied by single potentiostatic pulse techniques. The nucleation mechanism was evaluated by analyzing the influence of different TBACh ion concentration and applied potentials. The electrocrystallization mechanisms were determined by fitting the experimental non-dimensional current transients on the basis nucleation and growth model developed by Scharifker-Hills. The type of nucleation corresponding to the progressive three-dimensional nucleation with diffusion control is determined. Based on theoretical models of 3D multiple nucleation from the potentiostatic current transients were calculated nucleation characteristics, such as the stationary nucleation rate, saturation nucleus density and the average grains radius of indium deposits. The leveling action of TBACh on the electrodeposition of indium at concentration of 10-4 M was found.

Numerical insights into the early stages of nanoscale electrodeposition: nanocluster surface diffusion and aggregative growth

Fundamental understanding of the early stages of electrodeposition at the nanoscale is key to address the challenges in a wide range of applications. Despite having been studied for decades, a comprehensive understanding of the whole process is still out of reach. In this work, we introduce a novel modelling approach that couples a finite element method (FEM) with a random walk algorithm, to study the early stages of nanocluster formation, aggregation and growth, during electrochemical deposition. This approach takes into account not only electrochemical kinetics and transport of active species, but also the surface diffusion and aggregation of adatoms and small nanoclusters. The simulation results reveal that the relative surface mobility of the nanoclusters compared to that of the adatoms plays a crucial role in the early growth stages. The number of clusters, their size and their size dispersion are influenced more significantly by nanocluster mobility than by the applied overpotential itself. Increasing the overpotential results in shorter induction times and leads to aggregation prevalence at shorter times. A higher mobility results in longer induction times, a delayed transition from nucleation to aggregation prevalence, and as a consequence, a larger surface coverage of smaller clusters with a smaller size dispersion. As a consequence, it is shown that a classical first-order nucleation kinetics equation cannot describe the evolution of the number of clusters with time, N(t), in potentiostatic electrodeposition. Instead, a more accurate representation of N(t) is provided. We show that an evaluation of N(t), which neglects the effect of nanocluster mobility and aggregation, can induce errors of several orders of magnitude in the determination of nucleation rate constants. These findings are extremely important towards evaluating the elementary electrodeposition processes, considering not only adatoms, but also nanoclusters as building blocks.

Electrochemical phase formation: classical and atomistic theoretical models

The process of electrochemical phase formation at constant thermodynamic supersaturation is considered in terms of classical and atomistic nucleation theories. General theoretical expressions are derived for important thermodynamic and kinetic quantities commenting also upon the correlation between the existing theoretical models and experimental results. Progressive and instantaneous nucleation and growth of multiple clusters of the new phase are briefly considered, too.

Morphology of nanoclusters and nanopillars formed in nonequilibrium surface growth for catalysis applications

We consider growth of nanoclusters and nanopillars in a model of surface deposition and restructuring yielding morphologies of interest in designing catalysis applications. Kinetic Monte Carlo numerical modeling yields examples of the emergence of face centered cubic (fcc) symmetry surface features in Pt-type metal nanostructures, allowing evaluation of the fraction of the resulting active sites with desirable properties, such as (111)-like coordination, as well as suggesting the optimal growth regimes.

Intrinsic heterogeneity in liposome suspensions caused by the dynamic spontaneous formation of hydrophobic active sites in lipid membranes

The spontaneous, dynamic formation of hydrophobic active sites in lipid bilayer membranes is studied and characterized. It is shown that the rates of formation and consumption of these active sites control at least two important properties of liposomes: their affinity for hydrophobic surfaces and the rate by which they spontaneously release encapsulated molecules. The adhesion and spreading of liposomes onto hydrophobic polystyrene nanoparticles and the spontaneous leakage of an encapsulated fluorescent dye were monitored for different liposome compositions employing Cryo-TEM, DLS, and fluorescence measurements. It was observed that an apparently homogeneous, monodisperse liposome suspension behaves as if composed by two different populations: a fast leaking population that presents affinity for the hydrophobic substrate employed, and a slow leaking population that does not attach immediately to it. The results reported here suggest that the proportion of liposomes in each population changes over time until a dynamic equilibrium is reached. It is shown that this phenomenon can lead to irreproducibility in, for example, spontaneous leakage experiments, as extruded liposomes leak much faster just after preparation than 24 h afterward. Our findings account for discrepancies in several experimental results reported in the literature. To our knowledge, this is the first systematic study addressing the issue of an existing intrinsic heterogeneity of liposome suspensions.

Real-time in situ atomic force microscopy imaging of bismuth crystal growth

We have performed real-time atomic force microscopy (AFM) imaging of bismuth crystals that were grown under electrochemical control at low overpotentials to ensure a slow growth rate and allow in situ observation of the growth. A two step chronoamperometric potential was applied to a boron-doped diamond (BDD) working electrode with a short high overpotential, -0.4 V (2 s), to nucleate the bismuth, and then a long low overpotential for slow growth, -0.32 V (4.4 h). Growth rates of individual crystals and detailed growth mechanisms could be followed in real time because of the slow crystal growth. The close proximity of the AFM tip and tip holder to the working electrode appears to hinder the diffusion of bismuth to the BDD surface, as evidenced by the significantly lower density of crystals under the cantilever as compared to the rest of the electrode, therefore slowing down the growth process.