Adsorption of a Gaussian random copolymer chain at an interface

Abstract

We consider the adsorption of an isolated, Gaussian, random, and quenched copolymer chain at an interface. We first propose a simple analytical method to obtain the adsorption/depletion transition, by averaging over the disorder the partition function instead of the free energy. The adsorption thresholds obtained by previous authors at a solid/liquid and at a liquid/liquid interface for multicopolymer chains can be rederived using this method. We also compare the adsorption thresholds obtained for bimodal and for Gaussian disorder; they only agree for small disorder. We focus on the specific case of an ideally flat asymmetric liquid/liquid interface, and consider the situation where the chain is composed of monomers of two different chemical species A and B. The replica method is developed for this case. We show that the Hartree approximation, coupled to a replica symmetry assumption, leads to the same adsorption thresholds as obtained from our general method. In order to describe the properties of the adsorbed (or depleted) chain, we develop a new approximation for long chains, within the framework of the replica theory. In most cases, the behavior of a random copolymer chain can be mapped onto that of a homopolymer chain at an asymmetric attractive interface. The values of the effective adsorption energy are different for a random and a periodic copolymer chain. Finally, we consider the case of uncorrelated annealed disorder. The behavior of an annealed chain can be mapped onto that of a homopolymer chain at an asymmetric non attractive interface; hence, an annealed chain cannot adsorb at an asymmetric interface. PACS. 05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems -68.10.-m Fluid surfaces and fluid-fluid interfaces -82.65.Dp Thermodynamics of surfaces and interfaces List of notations a size of a monomer, D length defined by equation (A.10), D eff length defined by D eff ≡ a/ 6|∆χ eff |, f fraction of charged monomers, i discrete curvilinear coordinate along the chain, s continuous curvilinear coordinate along the chain, u operator defined by u ≡ n α=1 θ(z α ), u(s) real number defined by u(s) ≡ n α=1 θ z α (s) , U energy of adsorption per monomer,potential acting on a monomer located at a position z, z position with respect to the interface (z < 0 in the water phase), δ length defined by δ ≡ a/ ∆χ/6, θ(z) Heaviside function, defined by θ(z < 0) = 0 and θ(z > 0) = 1, ξ(s) parameter describing the chemical nature of the sth monomer: ξ(s) = χ A in the case of a A monomer and ξ(s) = −χ B for a B monomer, a

Field-Driven Translocation of Regular Block Copolymers through a Selective Liquid−Liquid Interface

“…As is well-known from experiment, − in the presence of selective interfaces for which the energy gain for a monomer in the favored solvent is large, the hydrophobic and polar blocks of a copolymer chain try to stay on different sides of the boundary between the two solvents, leading thus to a major reduction of the interfacial tension which has important technological applications, i.e., for compatilizers, thickeners, or emulsifiers. Not surprisingly, during the past two decades the problem has gained a lot of attention also from theory − as well as from computer experiment. − While in earlier studies attention has been mostly focused on diblock copolymers 6,8 due to their relatively simple structure, the scientific interest shifted later to random HP copolymers at penetrable interfaces. − , In contrast, our investigations have focused mainly on the impact of block size M on the static properties and localization kinetics of regular multiblock copolymers at the phase boundary between the two immiscible solvents. We showed that these are well described by a simple scaling theory 1,3 in terms of the total copolymer length N (the number of repeating units in the chain), the block size M (the number of consecutive monomers of the same kind), and the selectivity parameter χ, that is, the energy gained by a monomer when moving into the more favorable solvent.…”

Kinetics of Copolymer Localization at a Selective Liquid−Liquid Interface

“…For strongly selective interfaces, when the energy gain for a monomer in the favored solvent is large, the hydrophobic and polar blocks of a copolymer chain try to stay on different sides of the interface leading thus to a major reduction of the interfacial tension between the immiscible liquids or melts which has important technological applications, e.g., for compatilizers, thickeners or emulsifiers. Not surprisingly, during the last two decades the problem has gained a lot of attention from experiment − and theory − as well as from computer experiment. − While in earlier studies attention has been mostly focused on diblock copolymers 2,4 due to their relatively simple structure, the scientific interest shifted later to random HP-copolymers at penetrable interfaces. − , Until recently though, the properties of regular multiblock copolymers, especially with emphasis on their dependence on block length M , have remained largely unexplored. This has been a driving force for our research, since experimentalists are now able to synthesize polymers with an increased variety of controlled structures.…”

Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment

“…Not surprisingly, during the last two decades the problem has gained a lot of attention from experiment [1][2][3][4], theory [5][6][7][8][9] as well as from computer experiment [10][11][12][13][14]. While in earlier studies attention has been mostly focused on diblock copolymers [2,4] due to their relatively simple structure, the scientific interest shifted later to random HP copolymers at penetrable interfaces [6][7][8][9]14]. Until recently though, the properties of regular multiblock copolymers (i.e.…”