  We consider a simple cubic lattice self-avoiding walk model of 3-star
polymers adsorbed at a surface and then desorbed by pulling with an externally
applied force. We determine rigorously the free energy of the model in terms of
properties of a self-avoiding walk, and show that the phase diagram includes 4
phases, namely a ballistic phase where the extension normal to the surface is
linear in the length, an adsorbed phase and a mixed phase, in addition to the
free phase where the model is neither adsorbed nor ballistic. In the adsorbed
phase all three branches or arms of the star are adsorbed at the surface. In
the ballistic phase two arms of the star are pulled into a ballistic phase,
while the remaining arm is in a free phase. In the mixed phase two arms in the
star are adsorbed while the third arm is ballistic. The phase boundaries
separating the ballistic and mixed phases, and the adsorbed and mixed phases,
are both first order phase transitions. The presence of the mixed phase is
interesting because it doesn't occur for pulled, adsorbed self-avoiding walks.
In an atomic force microscopy experiment it would appear as an additional phase
transition as a function of force.
