  Although the stretching of polymers and biomolecules is important in numerous
settings, their response when confined to two-dimensions is relatively
poorly-studied. In this paper, we derive closed-form analytical expressions for
the two-dimensional force-extension response of a freely-jointed chain under
force control. Our principal results relate end-to-end distance to total force
under two modes of stretching: i) when force is applied only to the free of the
chain, and ii) when the applied force is distributed uniformly throughout the
chain. We have verified both analytical models by Brownian dynamics simulation
of molecules adsorbed strongly to a substrate. The total force required is
always larger if distributed throughout the chain than when it is only applied
to one end of the chain, and the nature of its divergence to infinity as
extension approaches contour length is different.
