Abstract
A model is proposed to estimate the surface free energy of a small polymer crystal with numerous emergent cilia. For such a model the partition function of a polymer constrained to remain in a cone is computed. The partition function of the polymer in a cone is found to behave similarly to the polymer in a wedge discussed by Lauritzen and DiMarzio [1]. The estimated end surface free energy per unit area for the small extended chain crystal is found to increase with increasing area, implying the presence of cumulative surface stress in such crystals. The forces between the cilia are reduced if folds are inserted in the surface.