  We theoretically study the self-propulsion of a thin (slender) colloid driven
by asymmetric chemical reactions on its surface at vanishing Reynolds number.
Using the method of matched asymptotic expansions, we obtain the colloid
self-propulsion velocity as a function of its shape and surface
physico-chemical properties. The mechanics of self-phoresis for rod-like
swimmers has a richer spectrum of behaviours than spherical swimmers due to the
presence of two small length scales, the slenderness of the rod and the width
of the slip layer. This leads to subtleties in taking the limit of vanishing
slenderness. As a result, even for very thin rods, the distribution of
curvature along the surface of the swimmer, namely its shape, plays a
surprising role in determining the efficiency of propulsion. We find that thin
cylindrical self-phoretic swimmers with blunt ends move faster than thin
prolate spheroid shaped swimmers with the same aspect ratio.
