= Solution
For an <ideal chain>, independent <Kuhn length> steps give the <random walk> relation
$$
\langle R_{\mathrm{sub}}^2\rangle=g b^2,\qquad \boxed{\sigma\sim b\sqrt g,\quad g\sim(\sigma/b)^2,}
$$
where $R_{\mathrm{sub}}$ denotes the end-to-end displacement of a subchain. Equivalently the mass-size <fractal> exponent is $2$. Numerical factors depend on the chosen definition of blob diameter.
A subchain smaller than the adsorption height explores three dimensions much as a free <ideal chain> does. At scales exceeding $\xi$, <adsorption> restricts its perpendicular extent to order $\xi$, so the coil is anisotropic. Its in-plane projection may still have a <random walk> law for an <ideal chain>, but the isotropic three-dimensional blob construction cannot be extrapolated to $\sigma>\xi$. This is the reason to use <adsorption blobs> of size $\xi$.
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