CV/Pseudocapacitance Analysis: b-Value Kinetic Analysis

This Workflow uses the output data from Cyclic Voltammetry (CV) Data Extraction and Preprocessing or Cyclic Voltammetry (CV) Data Extraction and Preprocessing to determine the $b$ values for both forward (anodic) and reverse (cathodic) scans by power-law fitting of currents at the mid-point potential across different scan rates, used to identify the kinetic control mechanism of electrode reactions.

Prerequisites

First execute Cyclic Voltammetry (CV) Data Extraction and Preprocessing or Cyclic Voltammetry (CV) Data Extraction and Preprocessing to complete CV data extraction. The input folder should contain CV extraction results (Excel files) at multiple different scan rates to ensure statistical significance of the fitting.

Steps

Select input folder: Use the file picker to select the folder containing the output from Cyclic Voltammetry (CV) Data Extraction and Preprocessing or Cyclic Voltammetry (CV) Data Extraction and Preprocessing with CV data at different scan rates.
The system automatically extracts mid-point currents, performs fitting calculations, and generates kinetic analysis plots in log-log coordinates.

Scientific Principles

Power Law Relationship

In cyclic voltammetry, the peak current (or current at a specific potential) $i$ and scan rate $\nu$ satisfy a power-law relationship:

i = a \cdot \nu^b

where $a$ is a constant and $b$ is the kinetic index. Taking the logarithm of both sides yields the linear form:

\log i = b \cdot \log \nu + \log a

Physical Meaning of b-Value

The $b$ value is used to identify the rate-controlling step of the electrode process:

$b$ Value	Control Mechanism	Physical Meaning
$b \approx 0.5$	Diffusion-controlled	Current limited by reactant diffusion rate in solution
$b \approx 1.0$	Surface-controlled (capacitive behavior)	Current dominated by surface adsorption/desorption processes
$0.5 < b < 1.0$	Mixed control	Both diffusion and surface processes contribute

Mid-Point Potential Selection

This Workflow uses the current value at the mid-point potential $E_{\text{mid}}$ of the potential window as the analysis target:

E_{\text{mid}} = \frac{E_{\text{high}} + E_{\text{low}}}{2}

For the last complete cycle in each scan rate file, the absolute current values at $E_{\text{mid}}$ for forward and reverse scans are extracted, denoted as $i_a$ (anodic current) and $i_c$ (cathodic current) respectively.

Fitting Method

Least-squares linear fitting is performed in $\log \nu$ – $\log i$ space to obtain the $b$ values and goodness of fit $R^2$ for both anodic and cathodic processes separately.

Output

Log-log scatter plot with fitting curves: x-axis is scan rate $\nu$ (V/s), y-axis is current $i$ (A), both on logarithmic scales. The plot includes anodic (red) and cathodic (blue) datasets with their fitting lines, with legends annotating $b$ values and $R^2$ .
Data files: Raw data and fitting curve data are exported as separate CSV files.

Further Analysis

CV/Cdl: Double-Layer Capacitance and Electrochemically Active Surface Area Analysis: Linear fitting of $C_{\text{dl}}$ based on mid-point current differences across scan rates, for calculating electrochemically active surface area (ECSA)
CV: Coulombic Efficiency and Capacitance Calculation: Evaluating electrode reaction reversibility

CV: Plot Last Cycle CV/Cdl: Double-Layer Capacitance and Electrochemically Active Surface Area Analysis