# Polymer desorption under pulling: first order phase transition without phase coexistence

## TL;DR

This paper demonstrates that a self-avoiding polymer chain pulled from a surface undergoes a first-order phase transition without phase coexistence, supported by analytical theory and Monte Carlo simulations in different ensembles.

## Contribution

It provides the first analytical and computational evidence of a first-order desorption transition without phase coexistence in polymer-surface systems.

## Key findings

- Desorption transition is first-order with no phase coexistence.
- Force fluctuations are large at critical force in the f-ensemble.
- Structural distributions of loops, trains, and tails are analytically derived.

## Abstract

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.