  We consider a simple lattice model of a topological phase transition in open
polymers. To be precise, we study a model of self-avoiding walks on the simple
cubic lattice tethered to a surface and weighted by an appropriately defined
writhe. We also consider the effect of pulling the untethered end of the
polymer from the surface.
  Regardless of the force we find a first-order phase transition which we argue
is a consequence of increased knotting in the lattice polymer, rather than due
to other effects such as the formation of plectonemes.
