= Polymer-blend interface width
{title2=$w=2a/\sqrt{6\chi}$}
For a strongly segregated, symmetric long-chain <polymer> blend, take the square-gradient functional $F/(k_BT\rho_0)=\int[\chi\phi(1-\phi)+a^2(\phi')^2/(24\phi(1-\phi))]dz$. Its first integral equates the two terms, giving $\phi'=\sqrt{24\chi}\,\phi(1-\phi)/a$. Thus $\phi=[1+\tanh(z/\ell)]/2$ with $\ell=a/\sqrt{6\chi}$. The inverse-central-slope width $w=1/\phi'(0)=2\ell$ differs by a factor two from the tanh-argument scale. The <continuum approximation> is marginal when these <lengths> approach the statistical segment size. An observed width can additionally include roughness and instrument broadening.
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