Article pubs.acs.org/Macromolecules
High Charge Density Coacervate Assembly via Hybrid Monte Carlo Single Chain in Mean Field Theory Tyler K. Lytle,† Mithun Radhakrishna,§ and Charles E. Sing*,‡ †
Department of Chemistry and ‡Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United States § Department of Chemical Engineering, Indian Institute of Technology (IIT) Gandhinagar, Gujarat, India S Supporting Information *
ABSTRACT: Oppositely charged polyelectrolytes in aqueous solution can undergo associative phase separation into a liquid-like complex coacervate phase that is polyelectrolyte-rich and an aqueous supernatant phase that is polyelectrolyte-deficient. This same complex coacervation motif can be used to drive self-assembly of block copolyelectrolytes via electrostatic interactions and can be controlled using e.g. ionic strength, pH, temperature, and polymer architecture. While there has been a large amount of research studying this self-assembly, the ability of theory to accurately capture the disparate length scales that govern the appropriate physics is limited. This is especially true when the coacervates have a high charge density; examples include biopolymers such as heparin or DNA as well as synthetic polymers such as poly(styrenesulfonate) or poly(acrylic acid). We incorporate molecular-level Monte Carlo simulations into single chain in mean field simulations, leading to a multiscale, coarse-grained description of such systems. These two length scales are connected using standard Widom insertion methods at the molecular Monte Carlo level, which provides the thermodynamic information needed to construct free energy landscapes used in the single chain in mean field calculations necessary to understand coacervate-driven self-assembly. We compare the results of our simulations to classical theories of complex coacervation and experiment. Our method demonstrates interesting behaviors in coacervate-forming diblock copolyectrolytes that reflect molecular details included into the model, such as morphological coexistence, interfacial excess of salt, and counterintuitive salt-induced ordering.
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INTRODUCTION
Assembly using complex coacervate motifs has been extensively studied in a number of situations, all involving pairs of oppositely charged block copolymers that can selfassemble into nanostructured morphologies.30,42−52 Early research focused on coacervation or complexation-driven micelles,43,45,46 which have been promising as drug-delivery vehicles and can encapsulate hydrophilic, charged drugs (in contrast to micelles formed by dispersive or hydrophobic interactions, which can only deliver hydrophobic drugs).50,52 Increasing the concentration of these micelles, or synthesizing triblock copolymers, has been shown to form gel materials that can demonstrate elastic material properties and responsiveness to the charge environment (via pH or salt concentration).42,44,47−49,53 Similar self-assembly motifs can lead to stimuli-responsive sensors that change color due to swelling and deswelling coacervate materials.44 Concurrent with this emerging interest in coacervationdriven assembly, theoretical and simulation work has aspired to provide prediction and ultimately guidance for materials design. Most theoretical efforts have focused on understanding the fundamentals of homopolymer coacervation.3,5,6,11−13,17,54−65 A
Self-assembly can be driven by a wide variety of interactions, including dispersive, hydrogen bonding, π−π stacking, and the hydrophobic effect.1 Electrostatic self-assembly has emerged as a common motif that has unique behaviors contrasting alternate methods; due to its sensitivity to solvent, pH, and salt concentration, as well as the long-ranged nature of the interactions, electrostatics has proven to be a versatile tool to drive assembly in a variety of soft materials.1 One important class of self-assembled charge materials are known as “complex coacervates”.2−6 These materials use oppositely charged polyelectrolytes or colloids that can form complexes. In contrast to similar self-assembly methods such as layer-bylayer7−9 or direct complexation or precipitation,10−15 coacervates are distinguished by their highly dynamic, liquid state.2 A large experimental literature has explored coacervation in a number of synthetic and natural polymer systems;2,4,6,13−30 high salt concentrations are typically used to screen the electrostatic interactions, leading to materials that are essentially “transient gels” that are electrostatically cross-linked. These materials have found use in a wide range of applications, such as food additives and encapsulants,31−33 tissue engineering scaffolds and protein encapsulants,34,35 adhesives,36−39 and model systems for membrane-less organelles.40,41 © 2016 American Chemical Society
Received: October 5, 2016 Revised: November 28, 2016 Published: December 12, 2016 9693
DOI: 10.1021/acs.macromol.6b02159 Macromolecules 2016, 49, 9693−9705
Article
Macromolecules
Figure 1. Schematic of the hybrid MC-SCMF scheme. (a) Molecular MC simulates solutions of polymer (polycation, orange; polyanion, blue; neutral polymer, cyan) and salt (cation, red; anion, purple). The RPM is used, with charged species represented as hard spheres of diameter σ in a dielectric solvent medium with ϵr = 78.5. Spatial coordinate is r. Widom insertion of salt/polymer species (dark red arrows) yields μEXC,i of species i. (b) μEXC,i is an input into the calculation of the free energy landscape f EXC(ϕS,ϕA,ϕB); see eq 8. (c) SCMF simulations consider coarse-grained representions of (for example) block copolymers. g monomers make up individual coarse-grained beads, which are connected by Gaussian springs (eq 10). In our scheme, polycation versus polyanion beads are indistinguishable. (d) f EXC from (b) contributes to a nonbonded Hamiltonian /NB (see full eq 11) calculated by assigning beads to grid points (blue arrows). Grid has coordinate x and informs MC updates of coarse-grained polymers. These chains do not interact except through the contribution of each coarse-grained bead to the ϕA or ϕB at a given grid point. The f EXC informs the distribution of SCMF chains, which set the values of ϕi at a grid point x used to calculate f EXC, establishing consistency between the two simulation methods.
computational methods capable of describing the large length scales in self-assembled coacervate materials. In principle, full field theoretic approaches such as those from Popov et al. should be capable of calculating these systems but to date have not been used for this purpose.60,61 Instead, a similar approach from Audus et al. has embedded the one-loop RPA into a selfconsistent field theory (SCFT) in order to capture both the charge-driven portion of the assembly and the large-scale morphological features.42 Initial work on this has shown matching with some experimental results.42 This is the only approach currently capable of treating these systems. This method has an important limitation; the one-loop RPA is known to break down in highly charge-dense scenarios, which are often used in coacervate-based assembly.57,60,61 New methods are needed to address the physical features present in these systems. In particular, the challenge is to describe both local charge structure (features such as counterion condensation and highly correlated polyanion−polycation interactions) that occurs at the
