Using the complex Langevin sampling strategy, field theoretic simulations are performed to study the equilibrium phase behavior and structure of symmetric polycation-polyanion mixtures without salt in good solvents. Static structure factors for the segment density and charge density are calculated and used to study the role of fluctuations in the electrostatic and chemical potential fields beyond the random phase approximation. We specifically focus on the role of charge density and molecular weight on the structure and complexation behavior of polycation-polyanion solutions. A demixing phase transition to form a ``complex coacervate'' is observed in strongly charged systems, and the corresponding spinodal and binodal boundaries of the phase diagram are investigated.
We investigate the complexation of a highly charged sphere with a long flexible polyelectrolyte, \textit{both negatively charged} in salt free environment. Electroneutrality is insured by the presence of divalent counterions. Using molecular dynamics (MD) within the framework of the primitive model, we consider different Coulomb coupling regimes. At strong Coulomb coupling we find that the adsorbed chain is always confined to the colloidal surface but forms different conformations that depend on the linear charge density of the chain. A mechanism involving the polyelectrolyte \textit{overcharg…
We consider the phase behavior of polymeric systems by calculating the structure factors beyond the Random Phase Approximation. The effect of this correction to the mean-field RPA structure factor is shown to be important in the case of coulombic systems. Two examples are given: simple electrolytes and mixtures of incompatible oppositely charged polyelectrolytes. In this last case, all former studies predicted an enhancement of compatibility for increasing charge densities; we also describe the complexation transition between the polyelectrolytes. We determine a phase diagram of the polyelectr…
How Topology Shapes the Phase Behavior of Polyelectrolytes
Institute for Computational Physics, University of Stuttgart（斯图加特大学计算物理研究所）；Department of Theoretical and Computational Biophysics, Max Planck Institute for Multidisciplinary Sciences（马克斯·普朗克多学科科学研究所理论计算生物物理学系）；Division of Chemistry and Chemical Engineering, California Institute of Technology（加州理工学院化学与化学工程系）
Complexation in symmetric solutions of oppositely charged polyelectrolytes is studied theoretically. We include polyion crosslinking due to formation of thermoreversible ionic pairs. The electrostatic free energy is calculated within the Random Phase Approximation taking into account the structure of thermoreversible polyion clusters. The degree of ion association is obtained self-consistently from a modified law of mass action, which includes long-range electrostatic contributions. We analyze the relative importance of the three complexation driving forces: long-range electrostatics, ion asso…
We characterize the role of charge correlations in the adsorption of a short, rod-like anionic polyelectrolyte onto a similarly charged membrane. Our theory reveals two different mechanisms driving the like-charge polyelectrolyte-membrane complexation: in weakly charged membranes, repulsive polyelectrolyte-membrane interactions lead to the interfacial depletion and a parallel orientation of the polyelectrolyte with respect to the membrane; while in the intermediate membrane charge regime, the interfacial counterion excess gives rise to an attractive "salt-induced" image force. This furthermore…
Complex coacervation, known as the liquid-liquid phase separation of solutions with oppositely charged polyelectrolytes, has attracted substantial interest in recent years. We study the effect of the charge regulation (CR) mechanism on the complex coacervation by including short-range interactions between the charged sites on the polymer chains as well as an association-dissociation energy parameter in the CR mechanism. We investigate the phase diagrams of two CR models: (i) the hopping CR model (HCR) and (ii) the asymmetric CR model (ACR). It is shown that during the phase separation that the…
We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particular, the first application of field-theoretic simulations to polyelectrolyte systems is reported. The polyelectrolyte ch…
We study a simple model of DNA divalent cationic surfactant complexation. We find that the combination of electrostatic and hydrophobic effects leads to a cooperative phenomenon in which as the amphiphile is added to the solution containing DNA, a large fraction of the DNA's charge is neutralized by the condensed divalent cationic surfactants, forming the surfoplex. This binding transition occurs for concentrations that are lower for divalent than for monovalent surfactants. Since the electrostatic strength is larger in the first case and the amount of surfactant lower, we suggest that multiva…
We investigated the fundamental electrical properties of microbubbles (MBs) that are directly encapsulated by the addition of oppositely charged polyelectrolytes (PEs). Charge-reversal of the MB-PE complex particles has been observed by the microscopic electrophoresis method, revealing unusual overcharging behaviors in MB-PE complex solutions, as follows. The critical concentrations of cationic PEs added for overcharging were not only independent of their chain lengths and molecular species, but also much larger than stoichiometric neutralization points. Thus, we provide a theoretical sketch t…
Interplay of Coulomb interaction energy, free ion entropy, and conformational elasticity is a fascinating aspect in polyelectrolytes (PEs). We develop a theory for complexation of two oppositely charged PEs, a process known to be the precursor to the formation of complex coacervates in PE solutions, to explore the underlying thermodynamics of complex formation, at low salts. Explicit calculation of the free energy of complexation and its components indicates that the entropy of free counterions and salt ions and the Coulomb enthalpy of bound ion-pairs dictate the equilibrium of PE complexation…
Complexation of a long flexible polyelectrolyte (PE) molecule with oppositely charged spherical particles such as colloids, micelles, or globular proteins in a salty water solution is studied. PE binds spheres winding around them, while spheres repel each other and form almost periodic necklace. If the total charge of PE is larger than the total charge of spheres, repulsive correlations of PE turns on a sphere lead to inversion of the net charge of each sphere. In the opposite case, we predict another correlation effect: under-screened by PE spheres bind to PE in such a great number that they …
We consider the complexation of highly charged semiflexible polyelectrolytes with oppositely charged macroions. On the basis of scaling arguments we discuss how the resulting complexes depend on the persistence length of the polyelectrolyte, the salt concentration, and the sizes and charges of the chain and the macroions. We study first the case of complexation with a single sphere and calculate the wrapping length of the chain. We then extend our considerations to complexes involving many wrapped spheres and study cooperative effects. The mechanical properties of such a complex under an exter…
In systems of highly charged linear polyelectrolytes and oppositely charged colloidal particles, long-lived clusters of polyelectrolyte-decorated particles form in an interval of concentrations around the isoelectric point, where reentrant condensation connected to charge inversion of cluster is observed. The mechanisms that drive the aggregation and stabilize, at the different polymer/particle ratios, a well defined size of the aggregates are not completely understood. Moreover, a central question still remains unanswered, i.e., whether the clusters are true equilibrium or metastable aggregat…
The association between polyelectrolytes (PEs) of the same size but opposite charge is systematically studied in terms of the potential of mean force (PMF) along their center-of-mass reaction coordinate via coarse-grained, implicit-solvent, explicit-salt computer simulations. The focus is set on the onset and the intermediate, transient stages of complexation. At conditions above the counterion-condensation threshold, the PE association process exhibits a distinct sliding-rod-like behavior where the polymer chains approach each other by first stretching out at a critical distance close to thei…
We report on the electrostatic complexation between polyelectrolyte-neutral copolymers and oppositely charged 6 nm-crystalline nanoparticles. For two different dispersions of oxide nanoparticles, the electrostatic complexation gives rise to the formation of stable nanoparticle clusters in the range 20 - 100 nm. It is found that inside the clusters, the particles are pasted together by the polyelectrolyte blocks adsorbed on their surface. Cryo-transmission electronic microscopy allows to visualize the clusters and to determine the probability distributions functions in size and in aggregation n…
Complexation of a Thermoresponsive Brush-Type Polyelectrolyte with an Oppositely Charged Surfactant: Effect of Temperature and Surfactant Concentration
The phase separation of oppositely-charged polyelectrolytes in solution is of current interest . In this work we study the driving force for polyelectrolyte complexation using molecular dynamics simulations. We calculate the potential of mean force between poly(lysine) and poly(glutamate) oligomers using three different forcefields, an atomistic force field and two coarse-grained force fields. There is qualitative agreement between all forcefields, i.e., the sign and magnitude of the free energy and the nature of the driving force are similar, which suggests that the molecular nature of water …
In this study, we investigated the thermodynamic features of a system based on oppositely charged polyelectrolytes, sodium alginate, and poly(diallyldimethylammonium chloride) (PDADMAC) at different pH values. Additionally, a comparison of the effects of the thermodynamic parameters on the growth of the layers based on the same polymers is presented. For this investigation, different techniques were combined to compare results from the association in solution and co-assembled layers at the silicon surface. Dynamic light scattering (DLS) and isothermal titration calorimetry (ITC) were used for …
Phase separation in salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations. Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the mixtures are carried out and demonstrate that electrostatic interactions favor nematic ordering. Coexistence curves for the symmetric mixtures are also constructed and are used to examine the effects of linear charge density and electrostatic interaction strength on rodlike polyelectrolyte complexation. It is found that the counterions are uni- formly dist…
Complexation between anionic and cationic polyelectrolytes results in solid-like precipitates or liquid-like coacervate depending on the added salt in the aqueous medium. However, the boundary between these polymer-rich phases is quite broad and the associated changes in the polymer relaxation in the complexes across the transition regime are poorly understood. In this work, the relaxation dynamics of complexes across this transition is probed over a wide timescale by measuring viscoelastic spectra and zero-shear viscosities at varying temperatures and salt concentrations for two different sal…
Based on extensive Monte Carlo simulations and analytical considerations we study the electrostatically driven adsorption of flexible polyelectrolyte chains onto charged Janus nanospheres. These net-neutral colloids are composed of two equally but oppositely charged hemispheres. The critical binding conditions for polyelectrolyte chains are analysed as function of the radius of the Janus particle and its surface charge density, as well as the salt concentration in the ambient solution. Specifically for the adsorption of finite-length polyelectrolyte chains onto Janus nanoparticles, we demonstr…
Polyelectrolyte-surfactant complexes (PESCs) have long been employed as oil-in-water (o/w) emulsions stabilizers, but never in the structure of colloidal complex coacervates providing a Pickering effect. The complexed state of PESCs could make them unsuitable o/w Pickering emulsifiers, which instead require a balance between colloidal structure and stability, amphiphilicity and wettability. Here we hypothesize that PESCs coacervates are efficient Pickering stabilizers. Instead of classical surfactants, we employ sophorolipid (SL) biosurfactants, atypical anionic/neutral stimuli-responsive bios…
The electrostatic complexation between DOTAP-DOPC unilamellar liposomes and an oppositely charged polyelectrolyte (NaPA) has been investigated in a wide range of the liposome surface charge density. We systematically characterized the "reentrant condensation" and the charge inversion of polyelectrolyte-decorated liposomes by means of dynamic light scattering and electrophoresis. We explored the stability of this model polyelectrolyte/colloid system by fixing each time the charge of the bare liposomes and by changing two independent control parameters of the suspensions: the polyelectrolyte/col…
The structure and stability of strongly charged complex fibers formed by complexation of a single long semi-flexible polyelectrolyte (PE) chain and many oppositely charged spherical macroions are investigated numerically at the ground-state level using a chain-sphere cell model. The model takes into account chain elasticity as well as electrostatic interactions between charged spheres and chain segments. Using a numerical optimization method based on a periodically repeated unit cell, we obtain fiber configurations that minimize the total energy. The optimal configurations exhibit a variety of…
