POLYMERS TETHERED TO CURVED INTERFACES - A SELF-CONSISTENT-FIELD ANALYSIS

We consider the equilibrium properties of chains tethered by one end to a curved, impenetrable interface, using a self-consistent-field model. The segment density profiles, layer thickness, and distribution of chain ends are numerically calculated. The interface curvature at which chain properties significantly deviate from the planar limit is, as anticipated, of the same order of magnitude as the chain dimensions. The chain dimensions follow scaling power laws only in the limit of high interface curvature or chain molecular weight. An exclusion zone in the distribution of chain ends appears near the interface, the size of which depends linearly on layer thickness. The ratio of exclusion zone height to brush thickness does not decrease smoothly with interface curvature but obtains maximum values at finite interface radii. The corrections to the value of the ratio of exclusion zone height to brush thickness, in the limit of infinite molecular weight, scale reasonably well with an anticipated molecular weight power law of -1/3.