Polymer Mushrooms Compressed Under Curved Surfaces

We study the problem of a single surface-tethered polymer chain or “mushroom” compressed by a curved circularly symmetric obstacle, such as an atomic force microscope tip, in the presence of a good solvent. In response to the compression the chain breaks into a series of blobs. For an obstacle modeled as a finite disk we find an escape transition and hysteresis, as predicted in previous studies. We also examine compressions under concave and convex power-law shaped surfaces defined by $h\sim r^\alpha$, where $h$ is the distance of the obstacle from the grafting surface and $r$ is the radial coordinate. For $\alpha 1$ (i.e., all convex surfaces) the chain is effectively unconfined. Between these two limits the chain radius obeys a scaling relation $R_{\rm chain}\sim N^{3/(2\alpha+3)}$. Finally, we examine compression under a surface with sinusoidal roughness. In this case there can be a large number of “escape” transitions