= Polymer-brush volume fraction
{title2=$\phi=Nv_0s/H$}
Conservation of material in a uniform <polymer brush> gives its mean <volume fraction> as $Nv_0s/H$, with material <volume> $v_0$ per counted segment, chain <length> $N$, <grafting density> $s$ and height $H$. Identifying $v_0$ with $a^3$ is an extra coarse-graining assumption. The <Alexander-de Gennes brush model> then gives $\phi\sim(sa^2)^{(3\nu-1)/(2\nu)}$, including powers $2/3$ in a <good solvent> and $1/2$ in a <theta solvent>.
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