Force-induced desorption of uniform block copolymers

Abstract

We investigate self-avoiding walk models of linear block copolymers adsorbed at a surface and desorbed by the action of a force. We rigorously establish the dependence of the free energy on the adsorption and force parameters, and the form of the phase diagram for several cases, including AB-diblock copolymers and ABA-triblock copolymers, pulled from an end vertex and from the central vertex. Our interest in block copolymers is partly motivated by the occurrence of a novel mixed phase in a directed walk model of diblock copolymers Iliev and Janse van Rensburg (2012 J. Stat. Mech. P01019) and we believe that this paper is the first rigorous treatment of a self-avoiding walk model of the situation.

Copolymeric stars adsorbed at a surface and subject to a force: a self-avoiding walk model

“…by definition of H * a . If λ(y 1/g ) > κ(a), then ψ(a, y 1/g ) = λ(y 1/g ), and by lemma 4 in reference [22], for almost every y > (λ −1 (κ(a))) g , lim n→∞ (H * a /n) = y d dy λ(y 1/g ) = β > 0. On the other hand, if λ(y 1/g ) < κ(a), then the right hand side of equation ( 32) is independent of y, and so one may assume, without loss of generality, that for arbitrary small ǫ > 0 there exists an N ǫ such that H * n < ǫn for all n > N ǫ .…”

“…The adsorption and desorption of block copolymers is interesting because of their application in steric stabilization of dispersions where one type of block tends to adsorb on the surface of the colloidal particle while the other type of block is in the surrounding medium [8,33] (in which the colloidal particle is dispersed). The properties of the adsorbed block copolymer were modelled using a self-avoiding walk model of linear diblock and triblock copolymers in reference [22]. The adsorbed copolymer is pulled from the surface with the force being applied at the end or at the centre of the polymer.…”

Copolymeric stars adsorbed at a surface and subject to a force: a self-avoiding walk model

“…The adsorption and desorption of block copolymers is interesting because of their application in steric stabilization of dispersions where one type of block tends to adsorb on the surface of the colloidal particle while the other type of block is in the surrounding medium [7,33] (in which the colloidal particle is dispersed). The properties of the adsorbed block copolymer were modelled using a self-avoiding walk model of linear diblock and triblock copolymers in reference [22]. The adsorbed copolymer is pulled from the surface with the force being applied at the end or at the centre of the polymer.…”

“…The adsorbed copolymer is pulled from the surface with the force being applied at the end or at the centre of the polymer. In reference [22] it is shown that the phase diagrams of these models have numerous phases, including free, adsorbed, and ballistic phases while some phases have a mixed adsorbed-ballistic character. Some of the results of this paper will be used here.…”

“…When two colloidal particles approach one another the extended blocks lose entropy resulting in stabilization of the dispersion. A self-avoiding walk model of linear diblock and triblock copolymers was considered in [22]. For a general review of the statistical mechanics of copolymers see for instance [35].…”