Polymer Mushrooms Compressed Under Curved Surfaces

D.R.M. Williams; F.C. MacKintosh

doi:doi:10.1051/jp2:1995190

Numéro		J. Phys. II France Volume 5, Numéro 9, September 1995


Page(s)		1407 - 1417
DOI		https://doi.org/10.1051/jp2:1995190

DOI: 10.1051/jp2:1995190
J. Phys. II France 5 (1995) 1407-1417

Polymer Mushrooms Compressed Under Curved Surfaces

D.R.M. Williams^{1, 2} and F.C. MacKintosh^{3, 2}

¹ Institute of Advanced Studies, Research School of Physical Sciences and Engineering, The Australian National University, Canberra, Australia
² Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030, USA
³ Department of Physics, University of Michigan, Ann arbor MI 48109-1120, USA

(Received 6 January 1995, received in final form 6 May 1995, accepted 17 May 1995)

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 $h\sim r^\alpha$ , where h is the distance of the obstacle from the grafting surface and r is the radial coordinate. For $\alpha <1/2$ the chain is effectively confined to two dimensions. 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.