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Full adsorption of flexible chains onto typical solid substrates occurs at a surface interaction energy of (5–10) kBT. The corresponding detachment force is in the range 10–50 pN. In contrast to “bare” solid substrates common to non-living materials, surfaces coated with brush-like polymer layers are very common in biological soft matter. We employ a simple mean-field approach to describe the effects of weak attraction between a floating long macromolecule and the brush. We show that even for a moderately thick brush a very small effective attraction is enough to produce complete binding of the long chain. The detachment force scales as , where W is the brush thickness. Hence the force could be 1 to 2 orders of magnitude smaller than in the case of typical solid substrates.

Phase transitions were recognized among the most fascinating phenomena in physics. Exactly solved models are especially important in the theory of phase transitions. A number of exactly solved models of phase transitions in a single polymer chain are discussed in this review. These are three models demonstrating the second order phase transitions with some unusual features: two-dimensional model of β-structure formation, the model of coil–globule transition and adsorption of a polymer chain grafted on the solid surface. We also discuss models with first order phase transitions in a single macromolecule which admit not only exact analytical solutions for the partition function with explicit finite-size effects but also the non-equilibrium free energy as a function of the order parameter (Landau function) in closed analytical form. One of them is a model of mechanical desorption of a macromolecule, which demonstrates an unusual first order phase transition with phase coexistence within a single chain. Features of first and second order transitions become mixed here due to phase coexistence which is not accompanied by additional interfacial free energy. Apart from that, there exist several single-chain models belonging to the same class (adsorption of a polymer chain tethered near the solid surface or liquid–liquid interface, and escape transition upon compressing a polymer between small pistons) that represent examples of a highly unconventional first order phase transition with several inter-related unusual features: no simultaneous phase coexistence, and hence no phase boundary, non-concave thermodynamic potential and non-equivalence of conjugate ensembles. An analysis of complex zeros of partition functions upon approaching the thermodynamic limit is presented for models with and without phase coexistence.