= Solution
A <depletion force> requires \b[mobile nonadsorbing <polymers> excluded from the gap], rather than grafted chains alone. If their depletion layers overlap when the plate separation is $h<2\delta$, the overlap restores accessible solution volume and increases <polymer> <entropy>. For ideal, dilute depletants of bulk osmotic pressure $\Pi$, an idealized interaction free energy per plate area is
$$
\boxed{W(h)\simeq-\Pi(2\delta-h)\quad(0<h<2\delta),\qquad W(h)\simeq0\quad(h\geq2\delta).}
$$
Its attractive pressure is $-\Pi$ in the overlap interval. The layer thickness is of order the ideal-coil <radius of gyration>, $\delta\sim R_g=b_0\sqrt{N/6}$, so \b[the range scales as $N^{1/2}$]. For the supplied chain parameters, $R_g\simeq81.6$ nm and an order-of-magnitude two-layer range is 163 nm. Grafted brushes instead oppose compression through stretching and osmotic penalties; they can coexist with depletion attraction if free depletants are present, but the mere existence of a grafted layer does not create a reservoir of depleting chains. The source does not specify that reservoir's concentration, so its attraction magnitude cannot be calculated.
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