Polymer coil in slit confinement ($R_{\parallel }\sim b{N}^{3/4}(b/D{)}^{1/4}$)

In a slit, a confinement blob is three-dimensional but the chain of blobs forms a two-dimensional self-avoiding walk. With $g\sim (D/b{)}^{5/3}$ and in-plane exponent $3/4$, $R_{\parallel }\sim D(N/g{)}^{3/4}$. There is no single preferred axial extension as in a tube. A strictly planar chain confined further to a narrow strip is a different geometry and gives $X\sim L(b/D{)}^{1/3}$ under the two-dimensional blob estimate.