PEGylation Stealth Shield — Brush Cross-Section (2D)

This 2D cross-section simulator draws a PEG-coated drug-delivery nanoparticle as a disk: a solid core ringed by a radial brush of PEG chains whose height is computed live from Alexander–de Gennes scaling theory as you tune grafting density and chain length. A population of opsonin proteins diffuses toward the surface from every direction in the plane, each one testing the same steric-shielding adsorption probability derived from that brush height; proteins that stick build a visible corona, and once coverage crosses a recognition threshold a macrophage sweeps in and clears the particle, with the whole cycle's rate read out as an estimated circulation half-life. The 3D source's brush-height formula has a real ~37% discontinuity right at the mushroom-to-brush crossover from an uncorrected scaling prefactor; this version fixes it with a matching constant derived from continuity at the crossover, so brush height now grows smoothly as density or chain length increase — showing directly why denser, longer PEG coatings mean nanoparticles survive longer in the bloodstream.