Meaning
Differential equation describing how non-steady-state chemical diffusion causes penetrant concentration within a medium to change over spatial dimensions and time. Applying Fick second law allows plastic component designers to model the rate of moisture ingress into hygroscopic polymers or the depletion rate of antioxidants over the service life of a molded part. The law governs isotropic, concentration-independent transport, whereas strain-induced diffusion or glass transition structural relaxation require modified viscoelastic transport models.
Concentration Gradients
Time-dependent mass transfer depends directly on the second spatial derivative of penetrant concentration multiplied by the diffusion coefficient. In non-steady conditions, initial penetrant uptake occurs rapidly near the outer surface before penetrating deep into the polymer core. When evaluating plastic containers holding active ingredients, calculations based on Fick second law reveal how long barrier properties will hold before chemical breakthrough occurs.
Temperature increases accelerate this non-steady uptake by increasing polymer chain free volume and penetrant diffusivity.
Moisture Ingress
Polyamide structural components absorb ambient moisture until equilibrium saturation is reached. Hydrolytic plasticization lowers mechanical modulus and alters dimensional tolerances as water molecules diffuse inward. Engineering specifications define allowable storage humidity levels based on predicted diffusion depth calculated across expected exposure times.
Boundary Conditions
Solving the diffusion equation requires defining constant surface concentration or zero-flux internal boundaries. Complex geometry requires numerical discretization across spatial meshes. Mold surface skin morphology alters initial surface diffusion rates relative to core predictions.
