Polymer Mushrooms Compressed Under Curved Surfaces

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Abstract
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∼rα, where h is the distance of the obstacle from the grafting surface and r is the radial coordinate. For α1 (i.e., all convex surfaces) the chain is effectively unconfined. Between these two limits the chain radius obeys a scaling relation Rchain∼N3/(2α+3). Finally, we examine compression under a surface with sinusoidal roughness. In this case there can be a large number of “escape” transitions

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