  We study the entropic force due to a fluctuating semiflexible polymer that is
grafted from one end and confined by a rigid and rough wall from the other end.
We show how roughness of the wall modifies the entropic force. In addition to
the perpendicular force that is present in the case of a flat wall, roughness
of the wall adds a lateral component to the force. Both perpendicular and
lateral components of the force are examined for different values of amplitude
and wavelength of the roughness and at different temperatures. The lateral
force is controlled by the local slope of the wall while the perpendicular
force is only sensitive to the curvature of the wall. We show that for small
compression, the entropic force is increased by increasing the curvature of the
confining wall. In addition to the biophysical relevance, the results may also
be useful in developing an AFM based experimental technique for probing the
roughness of surfaces.
