= Solution
\b[<Brownian motion>] is the fluctuating motion of a suspended particle produced by thermal molecular collisions. Using the standard <Brownian displacement conventions>, in a uniform fluid without external drift, mean displacement is zero but mean-square displacement grows with time. For overdamped <diffusion>, $\langle\Delta x^2\rangle=2Dt$ in one coordinate and $\langle|\Delta\mathbf r|^2\rangle=6Dt$ in three dimensions, with $D=k_BT/\zeta$ and Stokes friction $\zeta=6\pi\eta a$ for a no-slip sphere.
Brownian transport brings <nanoparticles> into encounters and allows them to explore configurations during <self-assembly>. Reversible interactions permit rearrangement toward low-free-energy structures; interactions that are too strong can instead trap disordered aggregates. <Thermal fluctuations> also oppose localization in shallow traps. The symbol $\zeta$ avoids confusing friction with an unrelated chemical potential.
Back to article page
