= Alexander-de Gennes brush model
{c}
{title2=$H\sim Na(sa^2)^{(1-\nu)/(2\nu)}$}
A scaling model of overlapping end-grafted <polymers> assigns each chain a column of lateral width $D\sim s^{-1/2}$ at <grafting density> $s$. Each <concentration blob> contains $g\sim(D/a)^{1/\nu}$ statistical segments, and stacking $N/g$ blobs gives <polymer brush> height $H\sim ND/g$. For assumed segment <volume> $a^3$, the mean <volume fraction> is $\phi\sim Na^3s/H$. It assumes a long many-segment-blob brush and supplies scaling powers rather than a precise chain-end distribution.
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