  We show that when a self-avoiding polymer chain is pulled off a sticky
surface by force applied to the end segment, it undergoes a first-order
thermodynamic phase transition albeit without phase coexistence. This unusual
feature is demonstrated analytically by means of a Grand Canonical Ensemble
(GCE) description of adsorbed macromolecules as well as by Monte Carlo
simulations of an off-lattice bead-spring model of a polymer chain. Theoretical
treatment and computer experiment can be carried out both in the constant-force
f statistical ensemble and in the constant-height h ensemble. We find that the
force-assisted desorption undergoes a first-order dichotomic phase transition
whereby phase coexistence between adsorbed and desorbed states does not exist.
In the f-ensemble the order parameter (the fraction of chain contacts with the
surface) is characterized by huge fluctuations when the pulling force attains a
critical value f_D. In the h-ensemble, in contrast, fluctuations are always
finite at the critical height h_D. The derived analytical expressions for the
probability distributions of the basic structural units of an adsorbed polymer,
such as loops, trains and tails, in terms of the adhesive potential and f or h,
provide a full description of the polymer structure and behavior upon
force-assisted detachment. In addition, one finds that the hitherto
controversial value of the universal critical adsorption exponent \phi depends
essentially on the extent of interaction between the loops adsorbed chain so
that \phi may vary within the limits 0.39 < \phi < 0.59.
