Chronoamperometric Data Research Articles

Electrodeposition of actinides: Optimization of deposition parameters by chronoamperometric studies

To quantify alpha-emitting radionuclides by alpha spectrometry, it is necessary to prepare a thin and uniform alpha source on a suitable substrate. Electrodeposition is the most used electrochemical technique for this purpose. In order to better understand the electrochemical process carried out in the electrodeposition of actinides, in particular the selection of the current densities applied, a chronoamperometric study of the electrodeposition of actinides (Th, U, Pu, Am and Cm), in three different electrolytes (Na2SO4/H2SO4, NH4NO3, NaF) using stainless steel and platinum as cathode and anode, respectively, is presented. The corresponding polarization curves (potential vs. current density), characteristic for each electrolyte and actinide used, were constructed from the chronoamperometric data, The limiting diffusion current as well as the minimum current necessary for the electrodeposition process to take place were determined. To achieve a quantitative electrodeposition of actinides, a balance between OH- production and the thickness of the OH- layer formed near the cathode must be reached. These parameters are controlled by the electrolyte used and the current density applied to the electrochemical system. Actinides were electrodeposited mainly in the form of oxides, according to Raman spectroscopy results.

Quantifying Resistive and Diffusive Kinetic Limitations of Thiophosphate Composite Cathodes in All-Solid-State Batteries

Increasing the specific capacity and rate performance of thiophosphate composite cathodes is a major challenge in solid-state battery development. Understanding the charge transport kinetics and rate-limiting mechanisms within the cathode is key towards efficient optimization. Herein, we use quantitative analysis of chronoamperometric rate performance data to differentiate between resistive and diffusive rate limitations of NCM811—Li6PS5Cl cathodes with different morphology and composition. We substantiate our findings with separate measurements of the effective ionic conductivity and Li+ diffusion coefficients using impedance spectroscopy and GITT techniques, respectively. Increasing the active material to solid electrolyte ratio is found to increase diffusive limitations, which originate from the small contact area between the active material and solid electrolyte. The diffusive limitation is especially pronounced for single crystal NCM811 cathodes at over 84% AM. Employing fine particle catholyte significantly increases the contact area, alleviates the diffusive limitation, and increases rate performance. These results provide guidelines towards bringing the solid-state battery performance levels closer to practical targets.

Diffusion Models of Mass Transport for the Characterisation of Amperometric Gas Sensors

AbstractA diffusion model for the analysis of chronoamperometric data in response to a concentration step is developed for amperometric gas sensors. This analysis avoids the difficulties with standard potentiodynamic measurements at the large specific area, high capacitance electrodes employed in these sensors. Despite the fact that typical devices comprise multiple layers with varying thicknesses and diffusivities, we show that typical chronoamperometric traces can be fitted to a simple diffusion model with a single parameter where L is an overall effective thickness of the diffusion barrier and D is an effective diffusion coefficient. Through a comparison of the transient and steady‐state current, independent estimates of L and D in the devices can be made. The model is also extended to cover cases with interfacial kinetic barriers; such kinetic limitations lead to a change in the effective values L and D, but the simple diffusion model remains a good fit to the data. This analysis shows that transient sensor responses can be characterised by a single parameter τ and conversely that deviations from this regression model cannot be assigned to (i) complex layer architectures or (ii) interlayer kinetic barriers. Instead, we show that non‐uniform accessibility effects arising from a distribution of diffusion rates across the device lead to deviations from the simple regression model, but that they may be captured approximately by a more complex model in which τ has a probability distribution.

Modelling diffusion controlled electro-deoxidation of metal oxide to metal in molten salt

Diffusion is a fundamental irreversible process intervening in the evolution of many out-of-equilibrium systems and is successfully described by Fick’s law obtained from non-equilibrium thermodynamics. Despite this, numerical simulations of solid state electro-deoxidation in the diffusion-controlled regime in molten salt remain elusive. Here, a new model for diffusion controlled three-phase interline (3PI) penetration in a porous cathode during electro-deoxidation is validated against experimental observation. This penetrating 3PI model is applied at high overpotential and benchmarked using the oxygen ionisation TiO2(s) + 4e− → Ti(s) + 2O2− at the 3PI. The model couples slow diffusive transport and fast oxygen ionisation while assuming a negligible ohmic potential drop in bulk molten CaCl2 electrolyte. The 14 nm s−1 penetration rate of the 3PI and the order of magnitude of 3PI currents (derived from an exchange current density and cathodic transfer coefficient of 0.32 A cm−2 and 0.01, respectively) in the chronoamperometric data for porous cathodes are in good agreement with experimental observation.

Cation Co-intercalation in Potassium Copper(II) Hexacyanoferrates.

The cation-insertion solid state electrochemistry of a potassium copper(II) hexacyanoferrate in contact with LiClO4 /DMSO, NaPF6 /DMSO, and KPF6 /DMSO electrolytes has been theoretically and experimentally studied using the voltammetry of immobilized particles methodology. Voltammetric data, combined with SEM/EDS analysis permit to determine a K0.876 CuII 1.328 FeIII 0.049 [FeIII 0.318 FeII 0.682 (CN)6 ] stoichiometry for the synthesized solid. Separation of electronic and ionic contributions to Gibbs energy changes can be made based on cyclic voltammetric and open circuit potential measurements. These parameters can be combined to measure values of the Gibbs energy of cation-independent electron transfer of 7.2±0.4 (K+ ), 7.1±0.5 (Na+ ) kJ mol-1 , in close agreement with the expected independence of this parameter on the electrolyte cation. The reduction Fe(III) centers bound to cyano groups exhibit a cation-dependent, essentially Nernstian character which can be described in terms of Na+ and K+ insertion/deinsertion while in the case of Li+ electrolytes there is significant co-cation diffusion. Chronoamperometric data provide estimates of the diffusion coefficients of Na+ , and K+ ions through the solid around 10-9 cm2 s-1 .

Excellent Structural Stability-Driven Cyclability in P2-Type Ti-Based Cathode for Na-Ion Batteries

In the current study, we have synthesized Ti-based P2-type Na0.7Ni0.2Cu0.1Ti0.65O2 (NNCT) through the sol–gel route and characterized it for its structural, electrical, and electrochemical properties. The analysis of X-ray diffraction (XRD) data confirmed the existence of a single P2 phase for the sample calcined at 950 °C with suppressed Na-ion vacancy ordering. Impedance studies and chronoamperometric data revealed that NNCT exhibited a poor conductivity of ∼1.37 × 10–7 S cm–1 at room temperature, with the electronic conductivity contribution to the total electrical conduction being only 0.4%. The sample exhibited specific capacities of 83, 54, and 42 mA h g–1 at discharge rates of 0.1C, 0.5C, and 1C, respectively, with remarkable cyclic stability of 96% capacity retention after 700 cycles at 0.5C which makes NNCT an attractive cathode for Na-ion batteries in stationary storage applications. The ex situ XRD analysis confirmed that NNCT maintains a single P2 phase during cycling between 2.0 and 4.2 V. NNCT also exhibited moisture stability, thus enabling the use of a cost-effective water-based slurry for cathode layer fabrication.

Determination of Ascorbic Acid in Pharmaceuticals and Food Supplements with the New Potassium Ferrocyanide-Doped Polypyrrole-Modified Platinum Electrode Sensor

This paper reports the results obtained from the determination of ascorbic acid with platinum-based voltammetric sensors modified with potassium hexacyanoferrate-doped polypyrrole. The preparation of the modified electrodes was carried out by electrochemical polymerization of pyrrole from aqueous solutions, using chronoamperometry. Polypyrrole films were deposited on the surface of the platinum electrode, by applying a constant potential of 0.8 V for 30 s. The thickness of the polymer film was calculated from the chronoamperometric data, and the value was 0.163 μm. Cyclic voltammetry was the method used for the Pt/PPy-FeCN electrode electrochemical characterization in several types of solution, including KCl, potassium ferrocyanide, and ascorbic acid. The thin doped polymer layer showed excellent sensitivity for ascorbic acid detection. From the voltammetric studies carried out in solutions of different concentrations of ascorbic acid, ranging from 1 to 100 × 10−6 M, a detection limit of 2.5 × 10−7 M was obtained. Validation of the analyses was performed using pharmaceutical products with different concentrations of ascorbic acid, from different manufacturers and presented in various pharmaceutical forms, i.e., intravascular administration ampoules, chewable tablets, and powder for oral suspension.

Electroreduction of Si(NCO)4 for Electrodeposition of Si

The electrochemical reduction and concomitant suitability of tetraisocyanatosilane, Si(NCO)4, as a precursor for Si electrodeposition has been examined. At T = 25 °C, voltammetric data indicated that the electroreductive pathway of Si(NCO)4 paralleled the electroreduction of SiCl4, albeit with attenuated current densities. At T = 150 °C, the measured current density increased significantly due to coupled reaction likely involving an electropolymerization of the tetraisocyanato ligand. At either temperature, the electrochemical response of Si(NCO)4 did not strongly depend upon the identity of the anion in the supporting electrolyte. A combination of chronoamperometric, electron microscopy, and X-ray photoelectron spectroscopy data were used to study the morphology and composition of the electrodeposited Si films at room temperature. The composition and morphology of the as-electrodeposited films were consistent with the formation of amorphous Si when using solid n +-Si electrodes, similar to what is observed during the electroreduction of SiCl4. Attempts to use Si(NCO)4 for Si crystal growth by the electrochemical liquid-liquid-solid (ec-LLS) process with a liquid e-GaIn electrode resulted in no appreciable crystalline Si product. Although Si(NCO)4 can be used for electrodeposition of amorphous Si onto solid electrodes at room temperature, more work is needed to identify conditions that would facilitate its use for ec-LLS.

Real-time 96-well optoelectronic micro plate for kinetic and stability investigation of cytochrome P450 BM3

Simultaneous optical and electrochemical measurements are advantageous for biosensor technology. Although this is easy for single samples, parallelization is challenging, when ensuring spatial and temporal compatibility of measurement techniques, especially if the device is to be integrated into existing laboratory routines. Here, we developed an electrochemical-optical 96-well micro plate (eco-MP) to track the bioelectrocatalysis of cytochrome P450 BM3 fluorometrically and chronoamperometrically in a simultaneous and real-time manner. Fluorometric readout enables unbiased quantitative determination of the enzymatic product resorufin in parallel to the chronoamperometric data acquisition. We implemented 96 miniaturized three-electrode setups in the eco-MP with a 3D-printed divided cell architecture leading to 192 half-cells. Using a conventional fluorescence reader we demonstrate the potential of the developed eco-MP to control and monitor the active state of cytochrome P450 BM3 over hours. The benefit of reactive oxygen species scavenging enzymes on bioelectrocatalytic activity of P450 BM3 could be time-resolved assessed. We applied the eco-MP also to investigate the tolerance of P450 BM3 to organic solvent dimethyl sulfoxide, as an example of an area in bioelectrocatalysis where high-throughput measurement devices will kick in. Overall, this work stresses the demand for convenient multiparametric sensor technology in the growing field of electrified interfaces.

Electrochemical and Theoretical Studies on the Artesunate Reduction

Malaria is the most devastating tropical disease in the world and this scenario is worsened by the absence of effective treatment. However, the plasmodium resistance to artemisinin does not show clinical relevance. The drug mechanism of action is associated to the endoperoxide moiety breakage. Artesunate is a semi-synthetic derivative of artemisinin and its absorption is facilitated due to its higher solubility in water. As a sesquiterpene lactone, artesunate can be electrochemically reduced in aqueous media on the glassy carbon electrode, having been studied by cyclic voltammetry, square wave voltammetry and chronoamperometry. The artesunate voltammetric reduction is diffusion-controlled and significantly irreversible. Its reduction is pH-independent, but from pH = 6.0 the cathodic current values increase in alkaline media, indicating that the proton-equilibrium occurs after the electron transfer step. The an values calculated vary from 0.30 to 0.37, leading to the 0.0975 s -1 value for k s . From the chronoamperometric data, two electrons (1.9 ± 0.4) are involved in the reduction process, being confirmed by the exact number of electrons obtained for artemisinin (1.9 ± 0.2). According to these results and computational findings, both drugs have the same reduction mechanism with the breakage of the endoperoxide bridge and consequent diol-derivative formation followed by the deoxy analog stabilization through the existence of a set of reactions involving protonation and charge transfer steps on the electrode surface. DOI: http://dx.doi.org/10.17807/orbital.v12i3.1439

Studying the Impact of Wall Shear Stress on the Development and Performance of Electrochemically Active Biofilms.

A laminar flow reactor was designed that provides constant and reproducible growth conditions for the bioelectrochemical observation of electroactive bacteria (EAB). Experiments were performed using four reactors in parallel to enable the comparison of EAB growth behavior and bioelectrochemical performance under different hydrodynamic conditions while simultaneously keeping biological conditions identical. With regard to the moderate flow conditions found in wastewater treatment applications, the wall shear stress was adjusted to a range between 0.4 mPa to 2.9 mPa. Chronoamperometric data indicate that early stage current densities are improved by a moderate increase of the wall shear stress. In the same way, current onset times were increasing slightly towards higher values of the applied wall shear stress. Long-term observations of EAB performance showed a decrease in current density and a leveling of the trend observed for the early stages of biofilm growth.

Electrochemical Nucleation of Silicon in Ionic Liquid-Based Electrolytes

Silicon is widely applied in a high number of industrial technologies, including different types of electronics, solar energy conversion and electrochemical energy storage. This extensively studied material has an exceptionally high theoretical capacity, more than ten times higher compared to the currently used graphite anodes in Li-ion batteries [1]. However, its main disadvantage is the huge volume expansion upon alloying with lithium, inducing disintegration of the electrode material, loss of electrical contact, poor reversibility and a rapid capacity fade [1]. It has been established that Si applied in a nanostructured or nanoparticulate form displays an enhanced electrochemical stability. Therefore, advanced production technologies have to be implemented in order to obtain cost-effectively the required electrochemically stable Si morphologies.Electrochemical methods offer a simple and low-cost deposition process. Furthermore, the electrodeposition is a versatile technique, allowing control of the morphology by adjusting the experimental conditions and obtaining deposits on different substrate geometries. However, due to the very low reduction potential and high reactivity of silicon precursors, it is impossible to deposit this element in aqueous electrolytes. Therefore, a broad variety of alternative media, including high temperature molten salts (HTMS) [2], conventional organic solvents [3] and ionic liquids (ILs) [4] has been researched.It is established that the initial stages of electrodeposition play an important role for the physical properties, stability and functional behavior of the final deposit. For example, homogeneous distribution of a high number density of small Si crystals would be beneficial for the electrochemical stability of the deposit during lithiation. Therefore, the nucleation and growth process of silicon deserves a special attention. Initial studies on the formation of Si nuclei in HTMS have been recently reported [2]. It was found that the diffusion limited nucleation process in HTMS (i.e. KF-LiF-K2SiF6) is instantaneous, followed by 3D growth [2]. However, due to the high temperatures (T > 800oC) and difficulties to perform the Si deposition economically in these electrolytes the research interest has turned to low temperature molten salts (LTMS).In our study we analyze the initial stages of Si electrodeposition in IL electrolytes by interpreting the chronoamperometric data (fig.1a) with a model accounting nucleation and growth under diffusion limitation, established by Scharifker et al. [5-7], eq.1. Vitreous carbon was selected as an inert substrate for the experiments and 1-butyl-1-methylpyrrolidinium bis (trifluoromethylsulfonyl) imide [BMP][TFSI] containing SiCl4 was chosen as an electrolyte.The current transients were quantitatively interpreted by a non-linear fitting procedure, applying a model equation for three-dimensional nucleation, eq.1. Eq.1 was modified with a term describing the surface charging phenomena, observed at the beginning of the silicon reduction, approximated to an exponential decay after Langmuir adsorption kinetics, eq.2. To prove the validity of this procedure, we extracted the charging currents (fig.1b) and fitted the resulting curves with the non-modified equation for 3D nucleation, where the respective output parameters remained nearly identical. According to eq.(3), the data for P1 should be constant for all fitted curves (i.e. potentials) since this parameter does not depend on other variables. This allows the value of the diffusion coefficient D =1.3×10−8 cm2 s−1 to be calculated. D was additionally confirmed by the analysis of the current maxima [5,6]. The data for the nucleation frequency, A and the number density of active sites, N0 obtained from the best fit are presented in Fig. 1c and show the typically observed linear increase as a function of the overpotential,η [7].Furthermore, we characterized the nucleation process by analyzing the current maxima in dimensionless coordinates (fig. 1d). According to the analysis the initial stages of the Si phase formation display an instantaneous behavior, showing a progressive character with decreasing the applied overpotential. The theoretically evaluated values for N0 correlate well with the crystal number density N, acquired by scanning electron microscopy. The talk will cover the main aspects of the electrochemical nucleation of Si in non-aqueous electrolytes and will provide a discussion on the major challenges towards understanding this process.

Bubble Evolution on Different Carbon Anode Designs in Cryolite Melt

The anode potential has been shown to be highly dependent on anode geometry and orientation in the Hall–Héroult process. This work is an experimental laboratory scale study of the effect of anode geometry and orientation on bubble formation and detachment for four different anode designs: horizontal (surface facing downwards), inverted horizontal (surface facing upwards), vertical, rod (with both vertical and horizontal surface). From polarization curves, it was found that the vertical anode and the inverted horizontal anode operated at lowest potentials. Above 1 A cm−2, the vertical anode showed the lowest potential. As the current increases, the transition towards smaller noise is pronounced for the horizontal anode and to some degree for the vertical anode and inverted horizontal anode. Fast Fourier Transform analysis of chronoamperometric data gave a dominant frequency only for the horizontal anode and the rod anode. The bubble release time corresponded well with the dominant frequency for the rod anode for all current densities and for the horizontal anode at lower current densities. Only random bubble noise was found for the vertical and the inverted horizontal anode and is probably due to a bubble-induced convection effectively removing the bubbles.

The Impact of Water Concentration on the Electro-Oxidation of Methanol on Platinum

The electro-oxidation of small organic molecules on platinum occurs via a mechanism that includes parallel reaction pathways and steps of adsorption/desorption and oxidation. The oxidation of adsorbed carbonaceous residues usually involves the participation of adsorbed oxygenated species. In this work, the impact of water concentration on the electro-oxidation of methanol on polycrystalline platinum was investigated, using phosphoric acid as supporting electrolyte. The bulk water concentration was varied from 14 to 50 mol L−1, and the system studied under both conventional and oscillatory regimes. Changing the [H2O]/[H3PO4] ratio implies changes in both water concentration and nature and population of electrosorbing anions. The developed strategy allowed at discriminating both effects and study in-depth the contribution of water concentration itself. Bulk water concentration was shown to play a major role on the electro-oxidation of methanol, and the lower the water concentration, the higher the potential at which the reaction sets in. Chronoamperometric data evidenced that water has a stronger impact on the reaction kinetics. The reaction order with respect to the water was estimated at different applied potentials and found to decrease as the potential increases. Concerning the potential oscillations, water concentration was found to affect the oscillatory frequency, waveform and amplitude. In summary, an increase in water concentration led to an increase in the oscillatory frequency; and the amplitude reaches a maximum when [H2O] = 30 mol L−1.

Editors' Choice—Review—Nanostructured Electrodes as Random Arrays of Active Sites: Modeling and Theoretical Characterization

This review presents the main principles underlying the theoretical description of the behavior of regular and random arrays of nanometric active sites. It is further shown how they can be applied for establishing a useful semi-analytical approximation of the arrays responses under diffusion limited conditions when they involve the common situation of active sites with identical sizes. This approximation is general and, as exemplified for different type of arrays, can be employed for describing the behavior of any array involving arbitrary distributions of their active sites onto the substrate surface. Furthermore, this efficient approach allows statistical characterization of active sites distributions of any array based on chronoamperometric data.

Open Source Software for the Real-Time Control, Processing, and Visualization of High-Volume Electrochemical Data.

Electrochemical sensors are major players in the race for improved molecular diagnostics due to their convenience, temporal resolution, manufacturing scalability, and their ability to support real-time measurements. This is evident in the ever-increasing number of health-related electrochemical sensing platforms, ranging from single-measurement point-of-care devices to wearable devices supporting immediate and continuous monitoring. In support of the need for such systems to rapidly process large data volumes, we describe here an open-source, easily customizable, multiplatform compatible program for the real-time control, processing, and visualization of electrochemical data. The software’s architecture is modular and fully documented, allowing the easy customization of the code to support the processing of voltammetric (e.g., square-wave and cyclic) and chronoamperometric data. The program, which we have called Software for the Analysis and Continuous Monitoring of Electrochemical Systems (SACMES), also includes a graphical interface allowing the user to easily change analysis parameters (e.g., signal/noise processing, baseline correction) in real-time. To demonstrate the versatility of SACMES we use it here to analyze the real-time data output by (1) the electrochemical, aptamer-based measurement of a specific small-molecule target, (2) a monoclonal antibody-detecting DNA-scaffold sensor, and (3) the determination of the folding thermodynamics of an electrode-attached, redox-reporter-modified protein.

Micromotor-Assisted Human Serum Glucose Biosensing.

Artificial self-propelled micromachines have shown great promise in biomedical sciences. In this work, we use Mg/Pt Janus micromotors with self-rejuvenating surfaces to enhance the electrochemical sensing performance and sensitivity toward glucose in human serum. The detection of glucose is based on the glucose oxidase enzyme and ferrocenemethanol shuttle system, where mass transfer was dramatically enhanced by the rapid motion of Mg/Pt Janus micromotors. The obtained chronoamperometric data show that Mg/Pt Janus micromotors play a synergistic role in enhancing the current response at millimolar concentrations of glucose in human serum. The current signals increased with the corresponding increase in amount of micromotors introduced. Furthermore, a linear relationship between current signal and glucose concentration was established, while the limit of detection improved when mobile Mg/Pt Janus micromachines were used. Glucose detection enhanced by micromachines may pave the way for their future applications in biomedicine and medical diagnostic devices.

Investigation of the electrocatalytic activity for ethanol oxidation of Pt nanoparticles modified with small amount (≤5 wt%) of CeO2

Pt is still the state of the art electrocatalyst for the oxidation of ethanol but it is poisoned by the CO-intermediates resulting in a slow ethanol oxidation reaction kinetic. Here, we show that the electrocatalytic activity of unsupported Pt nanoparticles for the ethanol electro-oxidation in acid medium can be significantly enhanced by the addition of small amounts of CeO2 nanoparticles (≤5wt%). Comparative studies on bare Pt, Pt-CeO21wt% and Pt-CeO2—5wt% catalysts composed of Pt nanoparticles with different sizes (from 10 to >40nm for bare Pt, and from 6 and 20nm for the Pt-CeO2 composites) revealed an increase of the microstrain with the decrease of the Pt's average particle size. Besides, there is a strong electronic interaction between the Pt and CeO2 nanoparticles, demonstrated by a systematic shift of the Pt 4f7/2 peak to lower binding energy with the addition of CeO2. Chronoamperometric data showed that the steady state current density normalized to Pt's electrochemical surface area for ethanol electro-oxidation is mainly governed by the microstrain, and it decreases with increasing strain. This trend is explained in terms of a more facile activation of the ethanol molecule at the surface of less strained Pt nanoparticles. Thus, the best performance was obtained with Pt-CeO2 1wt% formed by Pt nanoparticles with an average size of 18nm, reaching 1.0A·m−2 after 900s at 0.6V vs SCE.

Micelle Structure in a Deep Eutectic Solvent for the Electrochemical Preparation of Nanomaterials.

The self-aggregation of a surfactant in a deep eutectic solvent (DES) for electrodeposition is reported. The physical properties and electrochemical behavior of an anionic surfactant, sodium dodecyl sulfate (SDS), in a widely used DES, a choline chloride-urea mixture (ChCl-urea), were investigated. On the basis of surface tension and the conductivity measurements, the SDS micelles that were formed in the ChCl-urea system remained stable at higher temperatures, that is, 90 °C. Cyclic voltammetric and chronoamperometric data indicate that the addition of SDS to the DES may alter the nucleation and the growth processes that occur in the electrodeposition process. Scanning electron microscopy images show that the SDS adsorption prevents dendrite formation during the electrodeposition process. A simple mechanism for the formation of the SDS micelles in the DES system for electrodeposition is proposed.

Zinc Electrodeposition on Polycrystalline Copper: Electrochemical Study of Early-Stage Growth Mechanism

The early stage growth mechanism of zinc clusters electrodeposited on polycrystalline copper is studied by electrochemical methods. By analyzing the chronoamperometric and chronocoulometric data, nucleation and growth of the Zn layer as a function of time are investigated, and a growth model is proposed and discussed. Experimental and theoretical details about chronocoulometric data reveal a three-step growth mechanism. The results provide insights into the mechanism of electrodeposition of metallic particles. The same analysis process can also be described as the stripping mechanism. The formation and stripping mechanisms of a zinc adlayer can be predicted considering the contribution of four-different processes: a Langmuir-type adsorption/desorption process, the two-dimensional nucleation and growth in instantaneous and progressive cases, and a three-dimensional nucleation and growth process under diffusion-limited condition.