Zitao Ni

Ph.D. in Materials Science and Engineering

Progress Snapshot — Ch1 Complete → Ch2 Begins

Progress Snapshot: Chapter 1 Complete → Chapter 2 Begins

Snapshot Date: 2026-05-22
Completed: Chapter 1 (Fundamental Concepts & OCV)
Next: Chapter 2 (Diffusion Equation)
Overall Progress: 2/8 Weeks Complete

1. Overall Learning Roadmap

Chapter Topic Status
Chapter 1 Electrochemical Fundamentals & OCV ✅ Complete
Chapter 2 Diffusion Equation (Fick’s Second Law) ← Current
Chapter 3 Butler-Volmer Kinetics ⏳
Chapter 4 Full SPM Implementation ⏳
Chapter 5 SPMe Model ⏳
Chapter 6 P2D Model ⏳
Chapter 7 Advanced Applications ⏳

2. Chapter 1 Completion Summary

2.1 SPM Fundamentals Mastered

Knowledge Area Proficiency
Electrochemical simulation concepts (digital twin) Understood
Three core assumptions of SPM Understood
Parameter naming convention {quantity}_{phase}_{position} Mastered
Cell SOC → Electrode SOC conversion Mastered
N/P capacity ratio calculation Mastered
Nernst equation (thermodynamic basis) Understood
Graphite tanh-fitted OCV Understood
NMC polynomial OCV Understood
Comparison of Nernst vs. empirical fits Capable of Analysis

2.2 Completed Code Modules

File Implementation
spm/parameters.py Complete battery parameters, automatic SOC conversion, 1C current derivation
spm/model.py Four OCV functions, BV inversion, diffusion matrix construction, SPMModel class
visualize_ocv.py OCV curve visualization (Nernst vs. empirical)

2.3 Key Formulas Reviewed

Nernst Equation:
$$
OCV(\theta) = U_0 + \frac{RT}{F} \cdot \ln!\left(\frac{\theta}{1-\theta}\right)
$$

Lithium Conservation (SOC Exchange Rate):
$$
\frac{\Delta SOC_p}{\Delta SOC_n} = \frac{N_{\mathrm{total}}}{P_{\mathrm{total}}}
$$

N/P Capacity Ratio:
$$
\mathrm{N/P} = \frac{c_{s,\mathrm{max}}^n \cdot \varepsilon_s^n \cdot L_n}{c_{s,\mathrm{max}}^p \cdot \varepsilon_s^p \cdot L_p}
$$

3. Chapter 2 Learning Focus

Diffusion Equation — Equation #2 of the SPM Framework

The SPM four-equation landscape:

1
2
3
4
graph TD
    O["① OCV Curves<br/>Complete"] --> B["③ Butler-Volmer<br/>Next Chapter"]
    D["② Diffusion Equation<br/>← Current"] --> V["④ Voltage Coupling<br/>Chapter 4"]
    B --> V

The Central Role of the Diffusion Equation: It bridges OCV (thermodynamics) and Butler-Volmer (kinetics). Diffusion provides the surface lithium concentration of particles, which directly determines both the OCV value and the reaction overpotential.

Core Formulas

Fick’s Second Law (Spherical Coordinates):
$$
\frac{\partial c}{\partial t} = D \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 \frac{\partial c}{\partial r} \right)
$$

Numerical Method: Implicit Euler + tridiagonal matrix (scipy.linalg.solve_banded)

Learning Objectives

  1. Understand the physical meaning of Fick’s first and second laws
  2. Master the discretization of the spherical-coordinate diffusion equation
  3. Understand tridiagonal matrix solution techniques
  4. Analyze concentration distribution inside particles

4. Next Session Entry Point

1
Please read learning/learning_notes_02_diffusion/session_02_background.md to begin this session.

5. Plan File Index

File Path Description
Master Plan learning_plan.md Full 8-week roadmap (unchanged)
This Snapshot learning_plan_01-02.md Chapter 1 → Chapter 2 snapshot (this file)
Next Entry ../learning_notes_02_diffusion/session_02_background.md Chapter 2 background + plan

Progress Snapshot 01-02 · 2026-05-22

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