EDL Capacitance

EDL Capacitance in Water 

 Calculating the actual capacitance of a water fuel cell requires understanding how the Electric Double Layer contributes to the total capacitance. This page explains how to account for EDL effects in your VIC circuit calculations. 

 Total WFC Capacitance Model 

 The total capacitance of a water fuel cell is not simply the geometric parallel-plate capacitance. It includes contributions from multiple components: 

 Series Combination of Capacitances: 

 1/C total = 1/C geo + 1/C edl,anode + 1/C edl,cathode 

 Where: 

 

 C geo = geometric (parallel-plate) capacitance 

 C edl,anode = double layer capacitance at anode 

 C edl,cathode = double layer capacitance at cathode 

 

 Geometric Capacitance 

 The geometric capacitance depends on electrode geometry and water's dielectric constant: 

 For Parallel Plate Electrodes: 

 C geo = ε₀ × ε r × A / d 

 Where ε r ≈ 80 for water at room temperature 

 For Concentric Tube Electrodes: 

 C geo = (2π × ε₀ × ε r × L) / ln(r outer /r inner ) 

 Where L is the tube length, r is the radius 

 EDL Capacitance Density 

 The EDL capacitance is typically specified per unit area: 

 Electrode Material 

 C dl (µF/cm²) 

 Notes 

 Stainless Steel 316 

 20-40 

 Common WFC electrode 

 Stainless Steel 304 

 15-35 

 Also commonly used 

 Platinum 

 25-50 

 High catalytic activity 

 Graphite/Carbon 

 10-20 

 Lower EDL capacitance 

 Titanium 

 30-60 

 Oxide layer affects value 

 Calculating Total EDL Capacitance 

 EDL Capacitance for an Electrode: 

 C edl = c dl × A 

 Where: 

 

 c dl = specific EDL capacitance (µF/cm²) 

 A = electrode surface area (cm²) 

 

 Example Calculation 

 Given: 

 

 

 Electrode area: 100 cm² 

 Electrode gap: 1 mm 

 c dl : 25 µF/cm² (for stainless steel) 

 

 

 Calculate: 

 Geometric capacitance: 

 C geo = (8.854×10⁻¹² × 80 × 0.01) / 0.001 = 7.08 nF 

 EDL capacitance per electrode: 

 C edl = 25 µF/cm² × 100 cm² = 2500 µF = 2.5 mF 

 Total capacitance: 

 1/C total = 1/7.08nF + 1/2.5mF + 1/2.5mF 

 C total ≈ 7.08 nF (EDL contribution is negligible when C edl >> C geo ) 

 When EDL Matters Most 

 The EDL capacitance becomes significant when: 

 Condition 

 EDL Impact 

 Reason 

 Very small electrode gap 

 Minimal 

 C geo becomes very large 

 Large electrode gap (>5mm) 

 Minimal 

 C geo is small, dominates total 

 Small electrode area 

 Significant 

 C edl becomes comparable to C geo 

 High frequency operation 

 Significant 

 EDL may not fully form 

 Frequency Dependence 

 The EDL capacitance is not constant with frequency: 

 Low frequency (<100 Hz): Full EDL capacitance available 

 Medium frequency (100 Hz - 10 kHz): EDL partially developed 

 High frequency (>10 kHz): EDL contribution decreases; diffuse layer can't follow 

 This frequency dependence is modeled using the Cole-Cole relaxation model (covered in Chapter 3). 

 Effect of Water Purity 

 The ionic content of water affects both conductivity and EDL behavior: 

 Water Type 

 Conductivity 

 EDL Thickness 

 C dl Effect 

 Deionized 

 <1 µS/cm 

 ~100 nm 

 Lower C dl 

 Distilled 

 1-10 µS/cm 

 ~30 nm 

 Moderate C dl 

 Tap water 

 200-800 µS/cm 

 ~1 nm 

 Higher C dl 

 With electrolyte (NaOH, KOH) 

 >1000 µS/cm 

 <1 nm 

 Highest C dl 

 In the VIC Matrix Calculator 

 The VIC Matrix Calculator's Water Profile settings account for EDL effects: 

 Electrode material: Determines specific C dl 

 Water conductivity: Affects EDL thickness and capacitance 

 Temperature: Influences dielectric constant and ion mobility 

 EDL thickness parameter: Allows fine-tuning based on measurements 

 Practical Tip: For most VIC calculations using typical electrode gaps (1-3mm), the geometric capacitance dominates. However, for very close electrode spacing or when precise tuning is needed, including EDL effects can improve accuracy. 

 Next: The Helmholtz Model →