EIS/DRT Analysis: Mapping Frequency-Domain Impedance to Relaxation Time Distribution

If you’ve already looked at Nyquist/Bode plots but still want to understand “which kinetic process is actually dominating the response,” this Workflow is designed for that question.

It performs DRT (Distribution of Relaxation Times) analysis on the extracted EIS data, mapping frequency-domain impedance information to a time constant distribution, helping you more intuitively distinguish different processes (such as interfacial charge transfer, diffusion-related processes, etc.).

Prerequisites

First run EIS Extraction: CHI Instrument Data Preprocessing or In-Situ EIS Extraction: Donghua Instrument to ensure the input is a standardized EIS CSV (containing freq_hz, z_real_ohm, z_imag_ohm).

Steps

You can choose one of two options:

1. Select a directory (batch process all .csv files in the directory)
2. Or select a single .csv file (process only one sample)

The program automatically creates a drt_output directory and outputs results separately for each sample.

Analysis and Fitting Results

Each sample produces the following data files:

• fit_data.csv: Experimental impedance, DRT-reconstructed impedance, and residuals
• drt_data.csv: $\tau$ and $\gamma(\tau)$ distribution
• summary.json: Regularization parameters and solution summary (e.g., lambda_value, epsilon)

And the following plots:

• nyquist_fit.png: Experimental vs. DRT-fitted Nyquist comparison
• drt_tau.png: $\gamma$–$\tau$ distribution plot (logarithmic x-axis)
• residuals.png: Real/imaginary part residual plot
• *_drt_plots.opju: Origin project (also containing Nyquist, DRT, and residual plots)

Principle (Brief)

DRT represents impedance as a superposition of processes with different time constants. The core idea can be written as:

where:

• The peak positions of $\gamma(\tau)$ reflect the characteristic time scales of the corresponding processes
• Peak area/height is related to the contribution strength of that process

This makes it easier to resolve “multiple mechanisms superimposed” compared to just looking at Nyquist semicircles.

FAQ

• Why are some samples missing results? Common reasons include missing input columns or data containing invalid values; the program will skip and report the specific error.

Practical Tips

If this is your first time doing DRT, it’s recommended to first use EIS Plotting: Nyquist and Bode Visualization to quickly check whether curves are smooth and whether there are obvious outliers, then proceed to this step. This usually yields more stable and more interpretable results.