Let's say I have a polymer, of contour length $L_p$ and persistence length $P$, positioned between two parallel plates separated by a distance $z$. I slowly squeeze the plates together until only two-dimensional diffusion is observed. Under the worm-like chain (WLC) model, how will the force curve, $F(z)$, scale as a function of the distance between the plates?
As a sort of addendum... I'm curious how compression of the polymer between two parallel plates contrasts with the force curve associated with packing the polymer in a spherical cage? In the latter case of the spherical cage, I'm not exactly sure that the WLC model is relevant when the cross-sectional dimensions of the cage approach the polymer's persistence length.
Update - To make a prediction, the problem of squeezing a WLC or FJC polymer between two plates is probably more straightforward than that of 'crushing' a polymer into a spherical ball (which could perhaps be experimentally accomplished by placing a hydrophilic polymer into increasingly 'bad'/non-polar solvent) since it avoids having to estimate any bending energies. So, focusing on the 3D --> 2D scenario, my guess is that the energy to accomplish the task of squeezing the polymer until only two dimensional diffusion is observed would be similar to that of reducing one degree of diffusional freedom of a monoatomic gas - i.e. (Number of persistence length units in polymer) * $\frac{1}{2}(kB)(T)$. I would also predict that the force curve is non-linear, since the probability density for the location of a particular persistence length segment of a polymer is probably not uniform across the gap between the plates. However, that's simply a guess.