In Hydrodynamic Voltammetry (HDV) analysis, not every part of the hydrodynamic voltammogram is suitable for Levich and Koutecky-Levich analysis. These analyses work best when the current exhibits a distinct plateau region, indicating that mass transport limitations have been reached.
The Applied Potential Range (for HDV) feature allows users to perform Levich and Koutecky-Levich analyses
within a specific potential range. For example, setting the range to (-1, 1) means the analysis will
focus on the potential window between -1V and 1V.
By defining this potential range, users can exclude sections of the voltammogram that are not suitable for analysis, ensuring more accurate and reliable results.
(-1, 1) means that the analysis will focus on the potential from
-1V to 1V.
Chronoamperometry is an electrochemical technique where a constant potential is applied to an electrode, and the resulting current is measured as a function of time. This technique is used to study the kinetics of electrochemical reactions, diffusion processes, and the stability of electrode materials.
In chronoamperometry, a potential step is applied to the working electrode, and the resulting current decay is monitored. The initial current spike is due to the rapid charging of the electrical double layer and the immediate electrochemical reaction. Over time, the current decreases as the concentration of the electroactive species near the electrode surface is depleted and diffusion controls the rate of the reaction.
The current response in chronoamperometry for a diffusion-controlled process is described by the Cottrell equation:
Where:
Chronoamperometry is used in various applications, including:
This setting allows you to choose which cycle number to display in the output.
Electrochemical experiments often involve multiple cycles of data collection, especially in cyclic voltammetry. The cycle number refers to which of these data collection cycles is displayed. For instance, if you select cycle 9, the system will show the data from the 9th cycle.
The Cycle Range parameter specifies the range of cycles (or scan numbers) that the software will analyze in a cyclic voltammetry (CV) experiment. This parameter allows you to focus on a specific subset of the overall data, excluding the initial or final cycles that may not represent the steady-state behavior of the system.
You can set this parameter by defining the starting and ending cycle numbers that you want to include in the analysis. This is particularly useful when the initial cycles may contain artifacts or the final cycles may show signs of degradation or instability.
Example: If you want to analyze cycles 2 through 15, you would set the Cycle Range as range(2,
16). This means the software will analyze from the second cycle up to, but not including, the 16th cycle (so
cycles 2 to 15).
This flexibility allows you to tailor the analysis to the specific regions of the data that are most relevant to your research objectives, ensuring that the analysis is focused and accurate.
The "Discard scan rate from" and "Discard scan rate after" parameters allow you to exclude specific scans from the beginning and end of your dataset before conducting analysis. These parameters are particularly useful in ensuring that your analysis focuses only on the most relevant and accurate data, avoiding any potential artifacts or inconsistencies in the initial and final scans.
You can set these parameters based on your experimental needs, such as the behavior of the peaks and the conditions under which the scans were obtained.
Example:
If your analysis involves multiple peaks, you can set the "Discard scan rate from" and "Discard scan rate after" parameters individually for each peak (for example: Discard scan rate from [(1, 0, 1)], Discard scan rate after [(1, 1, 0)]). This indicates that you have three peaks to analyze. For peak 1: Analysis includes scans between the first and last, excluding those two. For peak 2: Analysis includes all scans except the last one. For peak 3: Analysis includes all scans except the first one.
This allows you to discard the scans that might interfere with the accurate identification of specific peaks. For instance, one peak might require excluding certain low scan rates to prevent overlap with another peak, while another peak might benefit from a different range of scan rates.
As the scan rate changes, the current peaks in your dataset may shift, causing them to merge with other peaks or become less visible. This can lead to inaccurate or misleading results. By carefully selecting which scans to include in your analysis—specifically by discarding the initial and final scans that might introduce errors—you can ensure that each peak remains distinct and that your analysis is more accurate.
When analyzing multiple peaks, adjusting the scan rates for each peak helps prevent overlap, ensuring that each peak is analyzed within the most appropriate range. This improves the precision of your results and leads to more reliable conclusions in your study.
The diffusion coefficient, denoted as \(D\), is a measure of the rate at which particles or molecules spread out or diffuse through a medium. It is typically expressed in units of square centimeters per second (cm²/s) or square meters per second (m²/s). The diffusion coefficient is an important parameter in describing the kinetics of diffusion-controlled processes.
Consider a solute with a diffusion coefficient of \(1 \times 10^{-5}\) cm²/s in a solution. This means that, on average, the solute molecules will diffuse through the solvent at a rate of \(1 \times 10^{-5}\) square centimeters per second. The higher the diffusion coefficient, the faster the molecules move through the medium.
The diffusion coefficient (\(D\)) is used in various contexts, including:
The initial concentration, denoted as \(C_0\), refers to the concentration of a substance in a solution at the beginning of an experiment or reaction. It is typically measured in moles per cubic centimeter (mol/cm³) or moles per liter (M).
Kinematic viscosity (\(\nu\)) is a measure of a fluid's resistance to flow under the influence of gravity. It is defined as the ratio of the dynamic viscosity (\(\mu\)) to the density (\(\rho\)) of the fluid. Kinematic viscosity is typically expressed in units of square meters per second (m²/s) or Stokes (St), where 1 St = \(10^{-4}\) m²/s.
The kinematic viscosity (\(\nu\)) can be calculated using the following equation:
Where:
The table below lists the kinematic and dynamic viscosities of some common liquids at standard conditions (typically 20°C or 25°C).
| Liquid | Dynamic Viscosity (μ) (Pa·s) | Density (ρ) (kg/m³) | Kinematic Viscosity (ν) (m²/s) |
|---|---|---|---|
| Water (20°C) | 1.002 × 10-3 | 998 | 1.004 × 10-6 |
| Ethanol (20°C) | 1.074 × 10-3 | 789 | 1.361 × 10-6 |
| Glycerol (20°C) | 1.49 | 1260 | 1.183 × 10-3 |
| Mercury (25°C) | 1.526 × 10-3 | 13534 | 1.127 × 10-7 |
| Olive Oil (25°C) | 8.1 × 10-2 | 918 | 8.82 × 10-5 |
| Honey (25°C) | 2 - 10 | 1400 | 1.43 × 10-3 to 7.14 × 10-3 |
Table: Dynamic and Kinematic Viscosity of Common Liquids
Levich Equation: The Levich equation describes the relationship between the limiting current and the rotation speed of a rotating disk electrode (RDE) in an electrochemical cell. It is used to determine the diffusion coefficient of the reacting species and the kinetics of the reaction.
Where:
If you have a series of limiting current values measured at different rotation speeds, you can plot \(I_L\) versus \(\omega^{1/2}\). The slope of the resulting line can be used to determine the diffusion coefficient of the reactant.
Koutecky-Levich Equation: The Koutecky-Levich equation combines the kinetics of the electron transfer process with the mass transport limitation to provide a comprehensive understanding of the reaction mechanism.
Where:
The kinetic current \(I_k\) is given by:
Where:
If you plot \(\frac{1}{I}\) versus \(\frac{1}{\omega^{1/2}}\), you will get a straight line. The intercept gives \(\frac{1}{I_k}\) (the inverse of the kinetic current), and the slope provides \(\frac{1}{I_L}\) (the inverse of the Levich current).
Suppose you measure the limiting current \(I_L\) at different rotation speeds:
Plotting \(I_L\) versus \(\omega^{1/2}\) gives a straight line. From the slope, you can calculate the diffusion coefficient \(D\).
Using the same data, plot \(\frac{1}{I}\) versus \(\frac{1}{\omega^{1/2}}\). The intercept gives \(\frac{1}{I_k}\), and the slope provides \(\frac{1}{I_L}\). From this plot, you can determine the kinetic parameters of the reaction.
By combining these analyses, you gain a deeper understanding of both the mass transport and kinetic aspects of your electrochemical reaction.
The number of electron transfer, denoted as \(n\), refers to the number of electrons involved in an electrochemical reaction. It is a key parameter in determining the stoichiometry of the reaction and is used in various electrochemical equations to describe the process.
In the reduction of copper ions:
\(n = 2\), indicating that two electrons are involved in the reduction of one copper ion.
The Number of Potentials to Show setting allows users to define how many potential values within the selected potential range will be used for Levich and Koutecky-Levich regression. This feature ensures that users can focus on a manageable subset of data points for analysis.
After selecting the applied potential range, users can specify the number of potentials they wish to include in the analysis. By adjusting this parameter, users can balance between obtaining detailed regression results and avoiding overloading the analysis with unnecessary data points.
By controlling the number of potentials to show, users can fine-tune the balance between simplicity and precision in their Levich and Koutecky-Levich analysis.
You set these parameters by defining the potential ranges where you expect peaks to occur. When searching for peaks, it's crucial that the "Peak Range (Top)" and "Peak Range (Bottom)" parameters have the same number of pairs. This ensures that the software can correctly align and analyze peaks across both the positive and negative directions.
[($value_{i}$, $value_{f}$)][($value_{1i}$, $value_{1f}$), \dots, ($value_{ni}$,
$value_{nf}$)](0, 0.2) and the "Peak Range (Bottom)" similarly, say, (0,
-0.2) if you expect a corresponding negative peak.
(-1, -0.70), (0, -0.2), (0.25,
-0.5)(-1, 0.70), (0, 0.2), (0.25,
0.5)By setting these ranges, the software will search for peaks within the specified voltage ranges in both the positive and negative directions, providing you with a comprehensive analysis of your cyclic voltammogram data.
In a typical hydrodynamic voltammogram, you may have thousands of potential points (e.g., over 10,000 potentials) and their corresponding response currents. Calculating the slope for each potential during Levich and Koutecky-Levich analysis could be time-consuming, even for a computer. To address this issue, the Potential Step feature allows users to skip certain potentials and calculate the slope only at every nth potential, as defined by the user.
This feature optimizes the analysis process by reducing the computational load while still providing meaningful results.
By using the Potential Step feature, users can streamline their analysis without sacrificing too much accuracy, especially when dealing with large datasets.
The Randles–Ševčík analysis is a method used in electrochemistry to analyze cyclic voltammetry data. It relates the peak current observed in a cyclic voltammogram to the scan rate, the concentration of the electroactive species, and the diffusion coefficient. This analysis is particularly useful for reversible electrochemical reactions.
The Randles–Ševčík equation for a reversible reaction at 25°C is given by:
Where:
Randles–Ševčík analysis is commonly used to:
Example:
Suppose you perform CV experiments for a redox couple with the following parameters:
By plotting the peak current (ip) versus the square root of the scan rate (ν1/2), you obtain a straight line. The slope of this line (s) is related to the diffusion coefficient (D) by the Randles–Ševčík equation:
From the slope, you can solve for the diffusion coefficient D.
The rate constant, denoted as \(k\), is a proportionality constant in the rate equation of a chemical reaction. It provides a measure of the speed at which a reaction occurs. The rate constant is specific to a given reaction at a particular temperature and is typically determined experimentally.
For a first-order reaction:
where [A] is the concentration of the reactant. The rate constant \(k\) has units of s\(^{-1}\).
For a second-order reaction:
where [A] and [B] are the concentrations of the reactants. The rate constant \(k\) has units of M\(^{-1}\)s\(^{-1}\).
The rate constant (\(k\)) is used in various contexts, including:
The Regression Time Range in the chronoamperometry module specifies the portion of the experimental data that will be used for linear regression analysis. In electrochemical experiments, the current response changes over time, and the Regression Time Range allows users to focus on a specific period where the current behavior is most suitable for extracting kinetic parameters like the diffusion coefficient.
By selecting an appropriate range of the term \(\frac{nFAC_0}{\sqrt{\pi} t^{1/2}}\), you ensure that only the relevant part of the data is considered, improving the accuracy of the regression analysis.
The Regression Time Range is typically input as a two-element array or tuple, such as \([start, end]\), where both start and end refer to the values of the term \(\frac{nFAC_0}{\sqrt{\pi} t^{1/2}}\).
Note: The start and end values are not time intervals, but refer to the term \(\frac{nFAC_0}{\sqrt{\pi} t^{1/2}}\), which includes time as a factor. You are selecting the range of this term for the regression analysis.
This option allows you to select the scan rate of interest for display in millivolts per second (mV/s). The scan rate determines how quickly the potential is swept during the experiment, which influences the current response in cyclic voltammetry or other electrochemical techniques.
Selecting a specific scan rate will display the current-potential curve corresponding to that scan rate. For example, if you choose 50 mV/s, the curve corresponding to a scan rate of 50 mV/s will be shown.
The term Smoothed/Smoothing Level (σ) refers to a parameter used in various data analysis and signal processing techniques to reduce noise and smooth out fluctuations in data. The smoothing level is often represented by the Greek letter σ, which indicates the standard deviation of the Gaussian kernel used in the smoothing process.
Smoothing is commonly applied in the following contexts:
Choosing σ:
The surface area, denoted as \(A\), refers to the area of the electrode that is in contact with the electrolyte in an electrochemical cell. It is typically measured in square centimeters (cm²).
The Tafel analysis is a method used in electrochemistry to determine the kinetics of an electrochemical reaction. It involves analyzing the Tafel plot, which is a plot of the logarithm of the current density (\(\log j\)) versus the overpotential (\(\eta\)). The Tafel equation describes the relationship between the overpotential and the current density, providing insights into the reaction mechanism and the rate-determining step.
The Tafel equation for an anodic reaction is given by:
Where:
For a cathodic reaction, the Tafel equation is:
Tafel analysis is commonly used to:
Example:
Suppose you perform electrochemical measurements for a reaction and obtain the following data:
Plotting \(\eta\) versus \(\log j\) yields a straight line. The Tafel slope (\(b\)) can be determined from the slope of this line, and the intercept (\(a\)) can be found from the y-intercept.
Tafel analysis is an electrochemical method used to determine the kinetics of electrochemical reactions by analyzing the relationship between overpotential and current density. It provides insights into how fast electron transfer occurs at the electrode surface, which is particularly useful for studying both anodic (oxidation) and cathodic (reduction) reactions.
The Tafel equation is expressed as:
where:
Tafel analysis enables the calculation of key parameters, such as the transfer coefficient (\(\alpha\)) and the exchange current density, which are essential for understanding the mechanisms of electrochemical reactions.
In this software, Tafel analysis is employed to calculate the anodic and cathodic transfer coefficients based on experimental data. This can be done using both non-mass-transport corrected and mass-transport corrected methods, depending on the specific conditions of the electrochemical system.
This method applies the classical Tafel analysis directly to the experimental data without accounting for the limitations caused by mass transport. The anodic (\(\alpha_a\)) and cathodic (\(\alpha_c\)) transfer coefficients are calculated using the following equations as defined by IUPAC:
where \( j_{a, \text{corr}} \) and \( j_{c, \text{corr}} \) are the anodic and cathodic current densities, respectively, corrected for experimental conditions.
This method accounts for the influence of mass transport on the electrochemical reaction, following the approach suggested by Danlei Li et al. (2018). The transfer coefficient is determined by:
This method has also been employed in research, such as Bacil et al.'s study on dopamine oxidation at gold electrodes, demonstrating its wide applicability.
The software allows users to select between these two methods based on the experimental setup, providing flexibility and accurate analysis depending on whether or not mass transport effects need to be considered. By analyzing the Tafel slopes, users can gain valuable insights into the electron transfer kinetics of their system.
Temperature is just temperature, nothing to explain.
If you need to convert between different temperature units, here are the relevant formulas:
The transfer coefficient, denoted by α (alpha), is a fundamental parameter in electrochemistry that describes the fraction of the electrical energy that contributes to the rate of an electrochemical reaction. It plays a key role in understanding the kinetics of electron transfer at the electrode surface.
α quantifies the symmetry of the energy barrier for the forward and reverse reactions in an electrochemical system. It typically ranges between 0 and 1, where:
The transfer coefficient is commonly used in the Butler-Volmer equation to describe the kinetics of electrochemical reactions. It helps determine the current-voltage relationship in the system, particularly under non-equilibrium conditions. A higher transfer coefficient can lead to faster reaction rates under an applied potential.
The transfer coefficient α can also be obtained from Tafel analysis, which involves plotting the overpotential against the logarithm of the current density. The slope of the Tafel plot is directly related to the transfer coefficient and provides insights into the kinetics of the electrochemical reaction.
Details about these options are coming soon. Please keep default setting and check back later for updated explanations and instructions.