  We study the effect of a gradient of solvent quality on the coil-globule
transition for a polymer in a narrow pore. A simple self-attracting
self-avoiding walk model of a polymer in solution shows that the variation in
the strength of interaction across the pore leads the system to go from one
regime (good solvent) to the other (poor solvent) across the channel. This may
be thought analogous to thermophoresis, where the polymer goes from the hot
region to the cold region under the temperature gradient. The behavior of short
chains is studied using exact enumeration whilst the behavior of long chains is
studied using transfer matrix techniques. The distribution of the monomer
density across the layer suggests that a gate-like effect can be created, with
potential applications as a sensor.
