Adsorption of Copolymer Chains at Liquid-Liquid Interfaces: The Effect of Sequence Distribution
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ADSORPTION OF COPOLYMER CHAINS AT LIQUID-LIQUID INTERFACES: THE EFFECT OF SEQUENCE DISTRIBUTION C. YEUNG÷, ANNA C. BALAZS
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AND DAVID JASNOW÷
'Department of Physics and Astronomy, University of Pittsburgh, 'Pittsburgh, PA 15260. °Materials Science and Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261. INTRODUCTXON
The presence of copolymers at an interface between two immiscible fluids is crucial to such processes as emulsion stabilization and microemulsion formation [1]. Recently Marques and Joanny [2] and Garel et al. [3] have studied the behavior of a random copolymer at a liquid-liquid interface. However, the arrangement or sequence distribution of the monomers in a copolymer can vary widely from random to blocky or purely alternating. In this paper, we use both analytic arguments and molecular dynamics simulations to determine how the sequence distribution affects the adsorption and conformation of a single macromolecule at the boundary between two immiscible fluids [4]. In particular, we derive an expression for the free energy of a copolymer at the interface and compare the resulting predictions with the outcome of the simulations. Our findings yield design criteria for fabricating polymers that display the desired interfacial properties. THE MODEL
As in the previous studies [2,3] we will assume that the liquid-liquid interface remains fixed in space and is perfectly sharp. The polymer is represented by a Gaussian chain composed of two different monomers, A and B. The monomer-solvent interaction energies are taken to be symmetric: -A for a monomer in the favorable solvent and +A in the unfavorable one. We neglect interactions between the monomers along the chain. Let the variables PA and P8 be the fraction of A and B sites, respectively, in a single polymer chain. Given a site A in the chain, the parameter PA-a yields the conditional probability that the next site is a B site. We now introduce the parameter f, which characterizes the sequence distribution in the chain. The value of f is defined through the following equation: PA PA- R
(PA PB)f,(1)
where f lies between 0 and 1. For the sake of simplicity, we will study the symmetric case where PA = P8 = 0.5. In this limit, Garel et. al [3] have shown that as the chain length approaches infinity, a random copolymer will always be localized at the interface. By altering the value of f, we can determine the behavior of other symmetric copolymers at this penetrable surface.
For example, for PA = Pa = 0.5, f = 1 corresponds to an
Mat. Res. Soc. Symp. Proc. Vol. 248. 01992 Materials Research Society
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SIMULATIONS' To test these prediction, we have performed a series of molecular dynamics simulations. In these simulations, we consider a one dimensional Gaussian chain near an interface. We need only consider a one dimensional chain since the other dimensions will not be effected by the interface. The configuration of the N-monomer chain is given by {Z7},.LN. The interface is located at Z = 0 and the A type monomers favor the Z > 0 r
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