1. Arrhenius Kinetics Engine: k(T) = A ·
exp(-Ea / RT) · f(pH) · Rbot. Models phytochemical reduction of
Cu2+ → Cu0 (Ea = 42.5 kJ/mol, pKa = 7.8).
2. LaMer Nucleation & Avrami Growth: Burst nucleation rate J(T)
∝ exp(-ΔG* / kBT) followed by sigmoidal phase conversion α(t) = 1 -
exp(-(keff t)n).
3. Dynamic Stepwise Oxidation Kinetics: Differential rate model
for progressive oxidation (Cu0 → Cu2O → CuO) under oxygen partial
pressure PO2.
4. Temperature-Dependent Nucleation & Thermal Ripening: Nuclei
radius r0(T) decreases with higher temperature supersaturation; thermal ripening rate
d(t)3 = d03 + Krip(T) · t.
5. Beer–Lambert Spectroscopy Law: Absorbance A(λ) =
ε(λ) · c · l, with Surface Plasmon Resonance (SPR) absorption peak
λmax ≈ 540 - 615 nm.
6. Scherrer XRD Crystallite Calculation: D = (K ·
λ) / (β · cos θ). Derives primary fcc Cu0 (111) crystallite
domain size from Bragg peak broadening βFWHM.
7. Stokes–Einstein DLS Dynamics: Hydrodynamic diameter
DH = (kBT) / (6π η(T) Ddiff) incorporating
temperature-dependent water viscosity η(T) via Vogel-Fulcher-Tammann (VFT) equation.
8. DLVO Theory & Zeta Potential (ζ): Electrostatic double
layer repulsion vs vdW attraction Vtotal(r) = Vvdw + Vedl. Stable
colloids require |ζ| ≥ 30 mV (Vmax >> kBT).