Session P35: Polyelectrolyte Complexation: Thermodynamics and Self-Assembly

Modeling of complexation of oppositely charged polyelectrolytes in aqueous solutions

The association of oppositely charged polyelectrolytes in aqueous solutions can lead to formation of polyelectrolyte complexes (PECs) whose properties are governed by many physiochemical parameters. PECs can be divided into overcharged complexes, where one type of polyelectrolyte charge is present in excess, and neutral ones, which contain equimolar ratios of polyanion and polycation. Using a theory, which captures the effects of chain connectivity and ion-specificy of charged species, here we rationalize why in non-stoichiometric mixtures, excess polyelectrolyte appears in the PEC and we pinpoint theoretical underpinnings of the overcharging phenomenon. Further, using the same theory, we investigate “doping” of stoichiometric PECs, in which salt concentration is increased, leading to the breaking of ion-pairs between oppositely charged groups of polyelectrolytes and their replacement with counterions. We find that the predictions of the level of counterion replacement during doping follow a similar trend to data from doping experiments. The development of such theories to could lead to methods of rational design of practical applications of PECs.   

``Looping-back'' complexation in stoichiometrically assymmetric polyelectrolyte solutions

The complexation of ionic polymers is typically studied in model systems lacking compositional heterogeneity that is often unavoidable in realistic systems. We address this by examining the coacervation behavior of synthetic, homologous polyions over a range of stoichiometric asymmetry between polyanions and polycations. An unexpected, narrow ``looping-back'' coexistence window is observed at low salt concentrations, and is captured by a theoretical model incorporating reversible ion-binding and chain connectivity, revealing the importance of the competition between charge neutrality and mixing entropy. Partitioning of both small ions and polyions between the supernatant and coacervate phases is measured, and theoretically analyzed.   

Created by kT

The first report on a synthetic polyelectrolyte, polyacrylic acid, was published by W. Kern (1939). Ten years later, Fuoss and Sadek reported the first complex between two synthetic, oppositely-charged polyelectrolytes. At the time, it seemed evident that “strong electrostatic interactions…would lead to mutual precipitation.” However, Michaels could not measure an enthalpy of complexation and concluded it was driven by entropy or the “escaping tendency of microions.” With more sensitive calorimetric measurements, complexation enthalpies were again ascribed to the coulombic forces assembling the component polyelectrolytes. In this talk I will show how polyelectrolyte coacervates, complexes and multilayers rely on the loss of counterions, an entropic driving force, to assemble. This overall driving force is moderated by an enthalpic contribution attributed to changes in the structure of water around counterion-compensated polyelectrolyte repeat units. The experimentally-determined relative ion concentrations within and external to a PEC are predicted by the Donnan equilibrium.
  

Polyelectrolyte micellar complexes

Polyelectrolyte complexation opens new territory for polymer self-assembly. Micelles with complex cores are formed from neutral-charged block copolymers complexing with oppositely charged homopolymers and copolymers. The resulting objects bear a physical resemblance to micelles formed from solvophobic self-assembly of block copolymers. However, the details of formation, exchange, dissociation and scalling laws are all different. These characteristics will be discussed. The cores of these micelles can be used as depots and delivery vehicles for oppositely charged macromolecules. When these macromolecules are biologically active, such as proteins and nucleic acids, polyelectrolyte complex micelles can be used as therapeutic delivery vehicles. We have studied such micelles with nucleic acid-containing cores in detail with some unexpected results. At high concentrations of these micelles, when they begin to impinge on one another, they form as series of ordered phases with varying strucutures from bcc to hexagonal to lamellar. This set of structures and their associated properties will be discussed at length.   

Kinetics of phase separation of polyelectrolyte complex coacervates exhibiting lower critical solution temperature

Measurements on a common linear oppositely-charged polyelectrolyte complex, potassium-poly(styrene sulfonate) and poly(diallyl dimethyl ammonium bromide), shows liquid-liquid phase separation upon heating, or lower critical solution temperature behavior. The experimental accessibility of the binodal temperature occurs for a narrow range of monovalent salt concentration. We will report new results on the kinetics of phase separation studied by scattering techniques as a function of quench depth from the binodal. The growth rate of concentration fluctuations will be discussed and compared to available theories.   

Quantification of the lower critical solution temperature phase diagram of polyelectrolyte complex coacervates

Measurements on a common aqueous oppositely-charged polyelectrolyte complex, potassium-poly(styrene sulfonate) and poly(diallyl dimethyl ammonium bromide), shows liquid-liquid phase separation upon heating, or lower critical solution temperature behavior. The experimental accessibility of the apparent critical temperatures occurs for a narrow range of monovalent KBr salt concentration. We will show new static and dynamic light scattering and small-angle neutron scattering results and discuss how the correlation length, osmotic compressibility, and relaxation times change as the coexistence curve is approached by increasing temperature. The measurements of the binodal and spinodal curves from these associating polyelectrolyte solutions are compared to available mean field models.   

An Anomalous Small Angle X-ray Scattering Study of Counterion Distribution around Macroion

Counterion condensed around marcoion is important for solution behavior. While other techniques can hardly achieve, anomalous small angle X-ray scattering (ASAXS) can provide numbers and spatial distribution of counterions around macroion. {Mo₁₃₂}, a negetively charged sphere of ~3 nm diameter, was used as model of macroions to investigated by ASAXS. The result shows: 1. Extra Rb⁺ can neutralize most of negative charges and induce coagulation. 2. Extra Sr²⁺ can effectively screen the electrostatic interaction between macroions, while contrary to DLVO or Debye-Huckel theory, it only loosely associate with macroion and cannot induce coagulation. While the Coulomb force dominate the interactions between macroions and counterions in most cases, the energy penalty of break the hydration shell of divalent cation upon counterion-macroion association is important.   

Polymer chain conformation in polyelectrolyte complexes

The Complexation of oppositely charged polyelectrolytes through electrostatic interaction is ubiquitous in both natural and synthetic systems. One of the microscopic properties of interest in polyelectrolyte complexes (PEC) is the polymer chain conformation of a labeled chain. Recent literature studies on polycation/polyanion chain conformation in PEC’s using small-angle neutron scattering reported Gaussian chain statistics. Such scaling behavior is unlike polymer chains dissolved in good solvents, which show Gaussian statistics only at very high polymer concentrations (semidilute state). This behavior appears to be independent of chain length, salt concentration, and polymer concentration. We performed coarse-grained Langevin dynamics simulations of symmetric and flexible PECs and counterions, with and without salt added. As we gradually increase polymer concentration, the polymer chains transition from a globule-like state and level off to a Gaussian chain conformation. Qualitatively, similar behavior was also observed in the presence of salt. The polycations and polyanions have been observed to be highly overlapped in both cases. Such a qualitative agreement with experiments is observed because of the strong electrostatic driving force for complexation.   

Constraint Release in Entangled Liquid Coacervates Made from Oppositely Charged Polyelectrolytes

Mixtures of oppositely charged polyelectrolytes can phase separate to form a polymer rich coacervate phase, important in many technological applications and biological systems. Many studies focus on formation of the coacervate, but less work has focused on predicting their dynamics. We developed a scaling theory predicting the dynamics of unentangled and entangled liquid coacervates, finding that the structure of asymmetric coacervates results in a dynamic coupling between the high and low charge density polymers. The high charge density polymer can either reptate along the tube formed by other high charge density chains or along the tube formed by low charge density chains. In the latter, topological constraints imposed by the low charge density chains onto the high charge density chains vary with time by reptation of low charge density chains through the process called constraint release. In this work, we develop a scaling model to predict the effects of constraint release on entangled asymmetric coacervates, finding that the dynamic coupling broadens regimes dominated by tube rearrangement as compared to symmetric coacervates. Furthermore, constraint release weakens the concentration dependence of viscosity in regimes dominated by reptation of the high charge density chains.   

Solid-to-Liquid Phase Transition in Polyelectrolyte Complexes: Structural Evolution, Dynamics, and Phase Behavior

The physical states of polyelectrolyte complexes (PECs), formed by mixing together solutions of oppositely charged polyelectrolytes, can span from glassy solids to low viscosity liquids. Transformation between these two states can be readily achieved by altering salt concentration and temperature, but our understanding towards this process is still incomplete. To fill this gap, we here study a model PEC system comprising two controllably synthesized styrenic polyelectrolytes. We first employed rheology to determine phase and evaluate mechanical properties of this PEC under different conditions. Surprisingly, we detected a counterintuitive trend that in the solid regime, these complexes became stiffer as temperature and salt concentration increased. Above certain threshold, viscoelastic liquid responses appeared. Next, we used small-angle X-ray scattering and cryogenic electron microscopy to unveil the structural evolution of this PEC. Additionally, thermogravimetric analysis was adopted to quantitatively probe water composition and phase behavior. Together, structures, dynamics and phase behavior demonstrated excellent agreement and dictated an integrated mechanism for the physical responses of this PEC system during solid-to-liquid phase transition.   

Free Energy Profile of Complexation of two oppositely charged Polyelectrolytes

We report a study of the complexation process of two oppositely charged polyelectrolyte (PE) chains in dilute solution interacting through screened Coulomb potential within the DLVO framework. The two PE chains, as well as the neutral complex, are considered to be hypothetical spheres whose radii quantitatively denote the sizes of the respective chains, and the system is characterized by its free energy, calculated within the uniform spherical expansion approximation. Detailed comparative study of the effect of entropy gain of free counterions due to complexation and enthalpy change due to the reorganization of ion-pairs into two types-both of the monomer-counterion type and oppositely charged monomer-monomer type is shown. We have looked into both salt-free and salty conditions and how it affects the complex formation process. Several factors drive the mutual adsorption of the two PEs to form a neutral coacervate. The full free energy profile of complexation, including the intermediate stages, is found to be monotonic at all conditions. A free energy landscape for the pathway of the complexation process may also be employed in studying the quantitative time scales in the kinetics of complex coacervation of two PEs.   

Scaling relation of Complex Coacervate Core Micelles

Complex coacervation is a liquid-liquid phase separation when two oppositely charged polyelectrolytes are mixed in an aqueous solution. Because of the nature of electrostatic interaction, the coacervates are highly responsive to solution condition such as ionic strength. In this study, complex coacervate core micelles (C3Ms) are prepared by simple mixing of AB and A’B diblock copolyelectrolyte solutions in an aqueous solution where A and A’ are oppositely charged blocks, and B is PEO block. Owing to the coacervate cores, C3Ms have been used for stimuli-responsive vehicles in the field of food, cosmetics and biomedical industry. For wider utilization of C3Ms, understanding the scaling relation is significant. We have developed the scaling relation for C3Ms such as core dimension as a function of charged block length and ionic strength, and compared to experimental data obtained by light, x-ray, and neutron scattering measurements. These results are discussed in terms of current understanding of complex coacervates including free energy and interfacial tension.   

Ionic-group-dependent phase behavior of polyelectrolyte coacervates

Complex coacervates are polymer-rich phases generated by liquid-liquid phase separation when oppositely charged polyelectrolytes are mixed in aqueous solutions. Since the previous Voorn-Overbeek model does not account for the chain connectivity and chemistry-specific details, advanced models have been suggested up to now. However, experimental data of well-defined model system is rare to compare with the theoretical description. In this study, 4 polyelectrolytes are prepared (e.g., strong/weak and polyanion/polycation) from identical parent polymer using anionic polymerization, and thus 4 pairs of polyelectrolyte complex coacervates are investigated to map out the phase diagrams as a function of the pair of ionic group. It is found that the phase diagram shows distinctive features including salt resistance, the area of a two-phase region and the shape of binodal curves depending on the pairs of polyelectrolytes. In addition, atomistic MD simulations give molecular-level insight into the interaction of two charged moieties and especially show a clear difference in the ability to form hydrogen bonds. We believe chemistry specific parameters play an important role in control phase behavior and these findings shed new light on the biologically important topic of complex coacervation.