Polymer Scaling & Flory Exponent

Self-avoiding walks (SAW) model polymer chains in good solvent — each monomer repels all others, preventing self-intersection. This excluded volume effect causes the chain to swell beyond the ideal Gaussian case (ν=0.5). Flory (1949) used a mean-field energy balance between elastic entropy and excluded volume energy to derive ν = 3/(d+2), giving ν=3/5=0.6 in 3D. The exact 3D value from renormalization group theory is ν ≈ 0.5876, making Flory's estimate remarkably accurate. The end-to-end distance scales as R ~ bN^ν, where b is the Kuhn length. The scaling plot shows log(R) vs log(N) across multiple runs; the slope measures ν.