Progress Snapshot — Ch1 Complete → Ch2 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:
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
- Understand the physical meaning of Fick's first and second laws
- Master the discretization of the spherical-coordinate diffusion equation
- Understand tridiagonal matrix solution techniques
- Analyze concentration distribution inside particles
4. Next Session Entry Point
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