Shrinking a fixed mass of platinum into smaller spheres trades bulk for surface. For spherical nanoparticles of diameter d and density ρ, the mass-specific surface area is:
SA = 6000 / (ρ · d) [m² per g Pt, ρ in g/cm³, d in nm]
ρ(Pt) = 21.45 g/cm³ → a 3 nm particle gives SA ≈ 93 m²/g,
a 10 nm particle only ≈ 28 m²/g — same mass, 3× less active area.
Spreading that mass as a loading L (mg Pt per cm² of geometric electrode) turns SA into an electrochemically active surface area, expressed as a dimensionless roughness factor:
RF = ECSA / A_geo = 10 · SA · L [L in mg/cm²]
Oxygen-reduction (ORR) kinetics at the cathode follow Tafel behaviour: each roughness-factor multiple scales the geometric current density linearly, while overpotential η scales it exponentially through the Tafel slope b. The bottom panel plots this curve directly — log(current density) vs η — with a marker showing exactly where the current sliders sit on it:
j = j0,m · RF · 10^(η / b)
j0,m ≈ specific mass activity at 900 mV (here 0.02 mA/cm²_Pt, T-scaled)
b ≈ 70 mV/decade at 25 °C, rising with temperature
Together these three lines explain why fuel-cell catalyst research is a nanoparticle-sizing problem as much as a chemistry one: below ~2 nm, surface energy destabilises the particles (they sinter and lose area over time), so real electrodes target the 2–5 nm sweet spot balancing activity against durability.
- Diameter — resizes every rendered nanoparticle in the top-down bed and recomputes SA.
- Loading — how much Pt mass sits on the fixed 1 cm² patch of support; also controls how many particles are drawn.
- Overpotential η — how hard the cathode is driven away from equilibrium; drives current up exponentially via the Tafel term and moves the marker along the curve below.
- Temperature — raises the Tafel slope and the reference exchange-current density, roughly modelling faster ORR kinetics at typical PEMFC operating temperature; reshapes the Tafel curve's slope.
- Particle bed view — drag to pan, scroll/pinch to zoom around the cursor.