Complex Formation in Solutions of Oppositely Charged Polyelectrolytes at Different Polyion Compositions and Salt Content

Polyelectrolyte-multivalent molecule complexes: physicochemical properties and applications

The complexation of polyelectrolytes with other oppositely charged structures gives rise to a great variety of functional materials with potential applications in a wide spectrum of technological fields. Depending on the assembly conditions, polyelectrolyte complexes can acquire different macroscopic configurations such as dense precipitates, nanosized colloids and liquid coacervates. In the past 50 years, much progress has been achieved to understand the principles behind the phase separation induced by the interaction of two oppositely charged polyelectrolytes in aqueous solutions, especially for symmetric systems (systems in which both polyions have similar molecular weight and concentration). However, in recent years, the complexation of polyelectrolytes with alternative building blocks such as small charged molecules (multivalent inorganic species, oligopeptides, and oligoamines, among others) has gained attention in different areas. In this review, we discuss the physicochemical characteristics of the complexes formed by polyelectrolytes and multivalent small molecules, putting a special emphasis on their similarities with the well-known polycation-polyanion complexes. In addition, we analyze the potential of these complexes to act as versatile functional platforms in various technological fields, such as biomedicine and advanced materials engineering.

Self-Assembly of Miktoarm Star Polyelectrolytes in Solutions with Various Ionic Strengths

We studied the self-assembly of miktoarm star polyelectrolytes with different numbers of arms in solutions with various ionic strengths using coarse-grained molecular dynamic simulations. Spherical micelles are obtained for star polyelectrolytes with fewer arms, whereas wormlike clusters are obtained for star polyelectrolytes with more arms at a low ionic strength environment, with hydrophilic arms showing a stretched conformation. The number of clusters shows an overall decreasing tendency with increasing the number of arms in star polyelectrolytes due to strong electrostatic coupling between polycations and polyanions. The formation of wormlike clusters follows an overall stepwise pathway with an intermittent association-dissociation process for star polyelectrolytes with weak electrostatic coupling. These computational results can provide relevant physical insights to understand the self-assembly mechanism of star polyelectrolytes in solvents with various ionic strengths and to design star polyelectrolytes with functional groups that can fine-tune self-assembled structures for specific applications.

Coarse-grained Simulations of the Impact of Chain Length and Stiffness on the Formation and Aggregation of Polyelectrolyte Complexes

Polyelectrolyte complexes formed from nucleic acids and synthetic polycations have been studied because of their potential in gene delivery. Coarse-grained molecular dynamics simulations are performed to examine the impact of chain length and polyanion stiffness on polyplex formation and aggregation. Polyplexes containing single polyanion chain fall into three structural regimes depending on polyanion stiffness: flexible polyanions form collapsed complexes, semiflexible polyanions form various morphologies including toroids and hairpins, and stiff polyanions form rod-like structures. Polyplex size generally decreases as polycation length increases. Aggregation (i.e., formation of complexes containing multiple polyanions) is observed in some simulations containing multiple polyanions and an excess of short polycations. Aggregation is observed to only occur for semiflexible and stiff polyanions and is promoted by shorter polycation lengths. Simulations of short, stiff polyanions condensed by long polycations are used as a model for siRNA gene delivery complexes. These simulations show multiple polyanions are spaced out along the polycation with polyanion-polyanion interactions, usually limited to overlapping chain ends. These structures differ from aggregates of longer polyanions in which the polyanions are packed together in parallel, forming bundles.

Interpolyelectrolyte Complex Dissociation vs Polyelectrolyte Desorption from Oppositely Charged Surface upon Salt Addition

The structure of complexes formed by oppositely charged polyelectrolytes and adsorbed layers on charged surfaces is sensitive to low-molecular-weight salt. Furthermore, if the concentration exceeds some threshold value, the complexes and adsorbed chains can be "dissolved". This is due to the screening of the electrostatic interactions between charged units. In the current paper, we perform a comparative analysis of "dissolution" (dissociation) of complexes and layers upon addition of salt. For this, the conventional Brownian dynamics of computer simulations is used. We demonstrate that the complex based on linear chains dissociates at lower salt concentration than that required for desorption of equivalent chains from an oppositely charged surface. The physical reason is the difference in the symmetry of the electric field, which binds the chains into the complex (layer). In the salt-free regime, the intensity of the electric field (and attractive force) between two linear chains decays with the distance R between them, like for two spherical objects, ∼R^-2, if R is bigger than the characteristic size of the chain. On the contrary, the attractive force of the chain to the infinite surface does not depend on the distance to the surface (the electric field is constant). Therefore, if attractive forces in the condensed states of the two systems are equal, one needs to add more salt to screen the constant force than the decaying one. The computer simulation results on the adsorption of the chains were compared with the experimental data obtained for adsorption of cationic poly(4-vinylpyridine) on the surface of anionic liposomes. Good quantitative agreement was achieved.

Comparing water-mediated hydrogen-bonding in different polyelectrolyte complexes

All-atom molecular dynamics simulations are used to investigate the polyelectrolyte-specific influence of hydration and temperature on water diffusion in hydrated polyelectrolyte complexes (PECs). Two model PECs were compared: poly(allylamine hydrochloride) (PAH)-poly(sodium 4-styrenesulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA)-poly(acrylic acid) (PAA). The findings show that the strength of the hydrogen bonding i.e. polyelectrolyte water interaction has enormous influence on the water mobility, which has implications for PEC structure and properties. A 10-fold difference in the average water diffusion coefficient between PAH-PSS and PDADMA-PAA PECs at the same hydration level is observed. The vast majority of the water molecules hydrating the PDADMA-PAA PECs, for hydrations in the range of 26-38 wt%, are effectively immobilized, whereas for PAH-PSS PECs the amount of immobilized water decreases with hydration. This points to the polyelectrolyte-specific character of the PE-water hydrogen bonding relationship with temperature. PAA-water hydrogen bonds are found to be significantly less sensitive to temperature than for PSS-water. The polyelectrolyte-water interactions, investigated via radial distribution function, hydrogen bond distance and angle distributions, are connected with resulting structure of the PECs. The PDADMA-PAA and PAH-PSS PECs are prepared experimentally and the states of water at different hydration levels is determined using differential scanning calorimetry (DSC). Experiments confirm the differences between PDADMA-PAA and PAH-PSS PECs observed in the theoretical modelling. The results suggest that the initial predictions of the PEC's bonding with water can be based on simple molecular-level considerations.

Hydration and Temperature Response of Water Mobility in Poly(diallyldimethylammonium)-Poly(sodium 4-styrenesulfonate) Complexes

The combination of all-atom molecular dynamics simulations with differential scanning calorimetry (DSC) has been exploited to investigate the influence of temperature and hydration on the water distribution and mobility in poly(diallyldimethylammonium) (PDADMA) and poly(sodium 4-styrenesulfonate) (PSS) complexes. The findings show that the vast majority of the water molecules hydrating the polyelectrolyte complexes (PECs) with 18-30 wt % hydration are effectively immobilized due to the strong interactions between the PE charge groups and water. Temperature and hydration were found to decrease similarly the fraction of strongly bound water. Additionally, at low hydration or at low temperatures, water motions become dominantly local vibrations and rotations instead of translational motion; translation dominance is recovered in a similar fashion by increase of both temperature and hydration. DSC experiments corroborate the simulation findings by showing that nonfreezing, bound water dominates in hydrated PECs at comparable hydrations. Our results raise attention to water as an equal variable to temperature in the design and engineering of stimuli-responsive polyelectrolyte materials and provide mechanistic explanation for the similarity.

Mechanical properties of bulk graphene oxide/poly(acrylic acid)/poly(ethylenimine) ternary polyelectrolyte complex

Ternary complexes formed in a single pot process through the mixing of cationic (branched polyethylenimine, BPEI) and anionic (graphene oxide, GO, and poly(acrylic acid), PAA) aqueous solutions exhibit superior mechanical performance in comparison to their binary analogs. The composition of the ternary complex can be simply tuned through the composition of the anionic solution, which influences the water content and mechanical properties of the complex. Increasing the PAA content in the complex decreases the overall water content due to improved charge compensation with the BPEI, but this change also significantly improves the toughness of the complex. Ternary complexes containing ≤32 wt% PAA were too brittle to generate samples for tensile measurements, while extension in excess of 250% could be reached with 57 wt% PAA. From this work, the influence of GO and PAA on the mechanical properties of GO/PAA/BPEI complexes were elucidated with GO sheets acting to restrain the viscous flow and improve the mechanical strength at low loading (<12.6 wt%) and PAA more efficiently complexes with BPEI than GO to generate a less swollen and stronger network. This combination overcomes the brittle nature of GO-BPEI complexes and viscous creep of PAA-BPEI complexes. Ternary nanocomposite complexes appear to provide an effective route to toughen and strengthen bulk polyelectrolyte complexes.

50th Anniversary Perspective: A Perspective on Polyelectrolyte Solutions

From the beginning of life with the information-containing polymers until the present era of a plethora of water-based materials in health care industry and biotechnology, polyelectrolytes are ubiquitous with a broad range of structural and functional properties. The main attribute of polyelectrolyte solutions is that all molecules are strongly correlated both topologically and electrostatically in their neutralizing background of charged ions in highly polarizable solvent. These strong correlations and the necessary use of numerous variables in experiments on polyelectrolytes have presented immense challenges toward fundamental understanding of the various behaviors of charged polymeric systems. This Perspective presents the author's subjective summary of several conceptual advances and the remaining persistent challenges in the contexts of charge and size of polymers, structures in homogeneous solutions, thermodynamic instability and phase transitions, structural evolution with oppositely charged polymers, dynamics in polyelectrolyte solutions, kinetics of phase separation, mobility of charged macromolecules between compartments, and implications to biological systems.

From polyelectrolyte complexes to polyelectrolyte multilayers: Electrostatic assembly, nanostructure, dynamics, and functional properties

Polyelectrolyte complexes (PECs) are three-dimensional macromolecular structures formed by association of oppositely charged polyelectrolytes in solution. Polyelectrolyte multilayers (PEMs) can be considered a special case of PECs prepared by layer-by-layer (LbL) assembly that involves sequential deposition of molecular-thick polyelectrolyte layers with nanoscale control over the size, shape, composition and internal organization. Although many functional PEMs with novel physical and chemical characteristics have been developed, the current practical applications of PEMs are limited to those that require only a few bilayers and are relatively easy to prepare. The viability of such engineered materials can be realized only after overcoming the scientific and engineering challenges of understanding the kinetics and transport phenomena involved in the multilayer growth and the factors governing their final structure, composition, and response to external stimuli. There is a great need to model PEMs and to connect PEM behavior with the characteristics of the PEC counterparts to allow for prediction of performance and better design of multilayered materials. This review focuses on the relationship between PEMs and PECs. The constitutive interactions, the thermodynamics and kinetics of polyelectrolyte complexation and PEM formation, PEC phase behavior, PEM growth, the internal structure and stability in PEMs and PECs, and their response to external stimuli are presented. Knowledge of such interactions and behavior can guide rapid fabrication of PEMs and can aid their applications as nanocomposites, coatings, nano-sized reactors, capsules, drug delivery systems, and in electrochemical and sensing devices. The challenges and opportunities in future research directions are also discussed.

Application of Monte Carlo simulation in addressing key issues of complex coacervation formed by polyelectrolytes and oppositely charged colloids

This paper reviews the recent advance of Monte Carlo (MC) simulation in addressing key issues of complex coacervation between polyelectrolytes and oppositely charged colloids. Readers were first supplied with a brief overview of current knowledge and experimental strategies in the study of complex coacervation. In the next section, the general MC simulation procedures as well as representative strategies applied in complex coacervation were summarized. The unique contributions of MC simulation in either capturing delicate features, easing the experimental trials or proving the concept were then elucidated through the following aspects: i) identify phase boundary and decouple interaction contributions; ii) clarify composition distribution and internal structure; iii) predict the influences of physicochemical conditions on complex coacervation; iv) delineate the mechanisms for "binding on the wrong side of the isoelectric point". Finally, current challenges as well as prospects of MC simulation in complex coacervation are also discussed. The ultimate goal of this review is to provide readers with basic guideline for synergistic design of experiments in combination with MC simulation, and deliver convincing interpretation and reliable prediction for the structure and behavior in polyelectrolyte-macroion complex coacervation.

Modeling competitive substitution in a polyelectrolyte complex

We have simulated the invasion of a polyelectrolyte complex made of a polycation chain and a polyanion chain, by another longer polyanion chain, using the coarse-grained united atom model for the chains and the Langevin dynamics methodology. Our simulations reveal many intricate details of the substitution reaction in terms of conformational changes of the chains and competition between the invading chain and the chain being displaced for the common complementary chain. We show that the invading chain is required to be sufficiently longer than the chain being displaced for effecting the substitution. Yet, having the invading chain to be longer than a certain threshold value does not reduce the substitution time much further. While most of the simulations were carried out in salt-free conditions, we show that presence of salt facilitates the substitution reaction and reduces the substitution time. Analysis of our data shows that the dominant driving force for the substitution process involving polyelectrolytes lies in the release of counterions during the substitution.

Coarse-grained simulations of polyelectrolyte complexes: MARTINI models for poly(styrene sulfonate) and poly(diallyldimethylammonium)

We present simulations of aqueous polyelectrolyte complexes with new MARTINI models for the charged polymers poly(styrene sulfonate) and poly(diallyldimethylammonium). Our coarse-grained polyelectrolyte models allow us to study large length and long time scales with regard to chemical details and thermodynamic properties. The results are compared to the outcomes of previous atomistic molecular dynamics simulations and verify that electrostatic properties are reproduced by our MARTINI coarse-grained approach with reasonable accuracy. Structural similarity between the atomistic and the coarse-grained results is indicated by a comparison between the pair radial distribution functions and the cumulative number of surrounding particles. Our coarse-grained models are able to quantitatively reproduce previous findings like the correct charge compensation mechanism and a reduced dielectric constant of water. These results can be interpreted as the underlying reason for the stability of polyelectrolyte multilayers and complexes and validate the robustness of the proposed models.

Novel stabilisation of emulsions by soft particles: polyelectrolyte complexes

We put forward the concept of a novel particle stabiliser of oil–water emulsions, being the polyelectrolyte complex (PEC) formed between oppositely charged water-soluble polymers in cases where either polymer alone is incapable of stabilising an emulsion. Using poly(4-styrene sulfonate) sodium salt, PSSNa and poly(diallyldimethylammonium chloride), PDADMAC, of low polydispersity and similar molecular mass, we correlate the behaviour of their mixtures in water with that of emulsions after addition of oil. In aqueous mixtures, spherical particles of diameters between 100 and 150 nm are formed through electrostatic interactions between charged polymer chains. Around equal mole fractions of the two polymers, the zeta potential of the particles reverses in sign and emulsions of oil-in-water (o/w) for a range of oils can be prepared which are the most stable to coalescence and creaming. The effects of PEC concentration and the oil : water ratio have been examined. All emulsions are o/w and stability is achieved by close-packed particle layers at drop interfaces and particle aggregation in the continuous phase. Increasing the salt concentration initially causes destabilisation of the aqueous particle dispersion due to particle aggregation followed by dissolution of particles at high concentrations; the corresponding emulsions change from being stable to completely unstable and are then re-stabilised due to adsorption of uncharged individual polymer molecules.

Electrospinning polyelectrolyte complexes: pH-responsive fibers

Fibers were electrospun from a solution comprised of oppositely charged polyelectrolytes, in efforts to achieve highly confined macromolecular packaging. A stoichiometric ratio of poly(allylamine hydrochloride) and poly(acrylic acid) solution was mixed in an ethanol-water co-solvent. Differential scanning calorimetry (DSC) analysis of electrospun fibers demonstrated no indication of glass transition, Tg. Infrared spectroscopy (FTIR) analysis of the fibers as a function of temperature, demonstrated an amidation process at lower temperature compared to cast film. Polarized FTIR indicated a preference of the functional groups to be perpendicular to the fiber axis. These results imply formation of mixed phase fibers with enhanced conditions for intermolecular interactions, due to the highly aligned and confined assembly of the macromolecules. The tunable intermolecular interactions between the functional groups of the polyelectrolytes, impact pH-driven, reversible swelling-deswelling of the fibers. The degree of ionization of PAA at pH 5.5 and pH 1.8 varied from 85% to 18%, correspondingly, causing transformation of ionic interactions to hydrogen bonding between the functional groups. The chemical change led to a massive water diffusion of 500% by weight and to a marked increase of 400% in fiber diameter, at a rate of 0.50 μm s(-1). These results allow for manipulation and tailoring of key fiber properties for tissue engineering, membranes, and artificial muscle applications.

Phase behavior of electrostatically complexed polyelectrolyte gels using an embedded fluctuation model

Nanostructured, responsive hydrogels formed due to electrostatic interactions have promise for applications such as drug delivery and tissue mimics. These physically cross-linked hydrogels are composed of an aqueous solution of oppositely charged triblocks with charged end-blocks and neutral, hydrophilic mid-blocks. Due to their electrostatic interactions, the end-blocks microphase separate and form physical cross-links that are bridged by the mid-blocks. The structure of this system was determined using a new, efficient embedded fluctuation (EF) model in conjunction with self-consistent field theory. The calculations using the EF model were validated against unapproximated field-theoretic simulations with complex Langevin sampling and were found consistent with small angle X-ray scattering (SAXS) measurements on an experimental system. Using both the EF model and SAXS, phase diagrams were generated as a function of end-block fraction and polymer concentration. Several structures were observed including a body-centered cubic sphere phase, a hexagonally packed cylinder phase, and a lamellar phase. Finally, the EF model was used to explore how parameters that directly relate to polymer chemistry can be tuned to modify the resulting phase diagram, which is of practical interest for the development of new hydrogels.

Branched-linear polyion complexes investigated by Monte Carlo simulations

Complexes formed by one charged and branched copolymer with an oppositely charged and linear polyion have been investigated by Monte Carlo simulations. A coarse-grained description has been used, in which the main chain of the branched polyion and the linear polyion possess the same absolute charge and charge density. The spatial extension and other structural properties, such as bond-angle orientational correlation function, asphericity, and scaling analysis of formed complexes, at varying branching density and side-chain length of the branched polyion, have been explored. In particular, the balance between cohesive Coulomb attraction and side-chain repulsions resulted in two main structures of a polyion complex. These structures are (i) a globular polyion core surrounded by side chains appearing at low branching density and (ii) an extended polyion core with side chains still being expelled at high branching density. The globule-to-extended transition occurred at a crossover branching density being practically independent of the side chain length.

Adsorption and solution properties of bottle-brush polyelectrolyte complexes: effect of molecular weight and stoichiometry

Polyelectrolyte complexes (PECs) self-assembled from bottle-brush polyelectrolytes, having a cationic main chain and uncharged side chains, and linear anionic sodium polystyrenesulfonate (NaPSS) have been investigated with emphasis on (i) the charge density and side chain density of the bottle-brush polyelectrolyte, (ii) the molecular weight of NaPSS, and (iii) the charge stoichiometry of the mixture. Light scattering and electrophoretic mobility data demonstrate that small molecular complexes are formed when the PEO45 side chain density is sufficiently high to provide steric stabilization and prevent PEC aggregation. The adsorption of PECs on negatively charged silicon oxynitride was investigated using dual polarization interferometry, and the time evolution of the adsorbed amount and thickness was determined. Cationic, uncharged, and negatively charged complexes all adsorb to negatively charged silicon oxynitride, and maximum adsorption is achieved for positively charged complexes containing small amounts of PSS. The adsorbed amount and the kinetics of adsorption are reduced with increasing PSS content, and for any given stoichiometry with increasing PSS molecular weight. These findings are discussed in terms of the PEC structure and the ability of anionic polyelectrolytes to leave the PECs during adsorption.

Charge inversion, condensation and decondensation of DNA and polystyrene sulfonate by polyethylenimine

We study the formation and structure of stable electrostatic complexes between polyanions (DNA and poly(styrene-sulfonate)) and linear polyethylenimine. The charge ratio x of the mixture is tuned by varying the concentration of the polycation at constant concentration of polyanion. In agreement with recent theories, dynamic light scattering and electrophoretic mobility measurements show two distinct regimes of weak and strong complexation. At low polycation concentration, negatively charged small complexes involving a few polyanion chains are observed first. By further increasing x, these small complexes condense at a precise charge ratio x(c) < 1 to form large anionic aggregates. The inversion of the charge of the condensed complexes coincides with the maximum of complexation and precedes the dissolution of the aggregates which occurs at a well-defined decondensation threshold x(d) > 1. Above x(d), positively charged complexes containing again a few overcharged polyanion chains are observed. The macroscopic phase diagram is qualitatively well corroborated by AFM observation of the complexes. The influence of entropic effects is probed by varying parameters like concentration, polycation molecular weight and ionic strength. Structure of stable negatively charged complexes is investigated at higher concentration using Small Angle Neutron Scattering. In the condensed regime, we observe large soluble bundles with sharp interfaces where the local structure of the polyanions is preserved.

Coarse-grained molecular dynamics simulations of DNA condensation by block copolymer and formation of core-corona structures

Coarse-grained molecular dynamics simulations are used to study the condensation of single polyanion chains with block copolymers composed of cationic and neutral blocks. The simulations are an effort to model complexes formed with DNA and cationic copolymers such as polyethylenimine-g-polyethylene glycol which have been used in gene delivery. The simulations reveal that increases in the cationic block length of the copolymer result in greater condensation of the polyanion. The ability of the complexes to form core-corona structures, with the neutral blocks of the copolymers forming a corona around a dense core formed from the charged beads, is investigated. The core-corona structure is shown to be dependent on both condensation of the polyanion chain and the length of the neutral block of the copolymer. Increasing the length of the cationic and neutral blocks of the copolymer both result in improvement in the core-corona structure. The internal structure of the complex core is shown to be a function of the architecture of the copolymer. Complexes formed from linear diblock copolymers have homogeneous cores with similarly arranged cationic and anionic beads; however, complexes formed with star-shaped copolymers have a layered core structure, with anionic beads found in the center of the cores.

Polyelectrolyte condensation in bulk, at surfaces, and under confinement

In this review we discuss recent results from computer simulations based on coarse-grained polyion models representing aqueous solutions of polyelectrolytes. The focus will be directed to the conformation of the polyions and, in particular, their condensation in bulk, induced by multivalent ions and oppositely charged polyelectrolytes, at responsive surfaces and under confinement.

Molecular dynamics simulations of DNA-polycation complex formation

Complexes formed from DNA and polycations are of interest because of their potential use in gene therapy; however, there remains a lack of understanding of the structure and formation of DNA-polycation complexes at atomic scale. In this work, molecular dynamics simulations of the DNA duplex d(CGCGAATTCGCG) in the presence of polycation chains are carried out to shed light on the specific atomic interaction that result in complex formation. The structures of complexes formed from DNA with polyethylenimine, which is considered one of the most promising DNA vector candidates, and a second polycation, poly-L-lysine, are compared. After an initial separation of approximately 50 A, the DNA and polycation come together and form a stable complex within 10 ns. The DNA does not undergo any major structural changes on complexation and remains in the B-form. In the formed complex, the charged amine groups of the polycation mainly interact with DNA phosphate groups, with polycation intrusion into the major and minor grooves dependent on the identity and charge state of the polycation. The ability of the polycation to effectively neutralize the charge of the DNA phosphate groups and the resulting influence on the DNA helix interaction are discussed.

Conformational characteristics of single flexible polyelectrolyte chain

The behaviour of a flexible anionic chain of 150 univalent and negatively charged beads connected by a harmonic-like potential with each other in the presence of an equal number of positive and free counterions, is studied in molecular dynamics simulations with Langevin thermostat in a wide range of temperatures. Simulations were carried out for several values of the bending parameter, corresponding to fully flexible polyion, moderately and strongly stiff polyion as well as for the case when bend conformation is preferable to the straight one. We have found that in all cases three regimes can be distinguished, which can be characterized as "random coil", observed at high temperatures; "extended conformation" observed at moderate temperatures (of the order of 1 in reduced units), and compact "globular conformation" attained at low temperatures. While the transition between high-temperature random and extended conformations is gradual, the transition from the extended coil to the globular state, taking place at a temperature of about 0.2 in reduced units, is of abrupt character resembling a phase transition.

Formation and stability of water-soluble, molecular polyelectrolyte complexes: effects of charge density, mixing ratio, and polyelectrolyte concentration

The formation of complexes with stoichiometric (1:1) as well as nonstoichiometric (2:1) and (1:2) compositions between oppositely charged synthetic polyelectrolytes carrying strong ionic groups and significantly different molecular weights is reported in this contribution. Poly(sodium styrenesulfonate) (NaPSS) was used as polyanion, and a range of copolymers with various molar ratios of the poly(methacryloxyethyltrimethylammonium) chloride, poly(METAC), and the nonionic poly(ethylene oxide) ether methacrylate, poly(PEO45MEMA), were used as polycations. Formation and stability of PECs have been investigated by dynamic and static light scattering (LS), turbidity, and electrophoretic mobility measurements as a function of polyelectrolyte solution concentration, charge density of the cationic polyelectrolyte, and mixing ratio. The data obtained demonstrate that in the absence of PEO45 side chains the 100% charged polymer (polyMETAC) formed insoluble PECs with PSS that precipitate from solution when exact stoichiometry is achieved. In nonstoichiometric complexes (1:2) and (2:1) large colloidally stable aggregates were formed. The presence of even a relatively small amount of PEO45 side chains (25%) in the cationic copolymer was sufficient for preventing precipitation of the formed stoichiometric and nonstoichiometric complexes. These PEC's are sterically stabilized by the PEO45 chains. By further increasing the PEO45 side-chain content (50 and 75%) of the cationic copolymer, small, water-soluble molecular complexes could be formed. The data suggest that PSS molecules and the charged backbone of the cationic brush form a compact core, and with sufficiently high PEO45 chain density (above 25%) molecular complexes are formed that are stable over prolonged times.

Brownian dynamics simulations of copolymer-stabilized nanoparticles in the presence of an oil–water interface

We describe predictions of properties of copolymer-stabilized nanoparticles in the presence of an oil-water interface based on Brownian dynamics simulations. These simulations provide information regarding the equilibrium and diffusion properties of the stabilized particles. The hydrophilic part of the copolymer is modeled as a polyelectrolyte and is described at the Debye-Hückel level. Both block and random copolymers are considered. The surface area of particles at the fluid interface and the diffusion properties of the particles give some guidance into the copolymer architectures that may be most useful for stabilizing nanoparticles at fluid interfaces. We find based on our results that a conservative recommendation to enhance transportability in a water phase and attachment to an oil-water interface would be to design nanoparticles with a random copolymer attached to them.

H4 histone tail mediated DNA-DNA interaction and effects on DNA structure, flexibility, and counterion binding. A molecular dynamics study

All-atom molecular dynamics (MD) simulations were performed during 30-45 ns for a system of three identical DNA 22-mers, 14 short fragments of the charged H4 histone tail peptide fragment (amino acids 5-12, KGGKGLGK) with K(+) counterions, and explicit water. The simulation setup mimics the crowded conditions of DNA in eukaryotic chromatin. To assess the influence of tail fragments on DNA structure and dynamics, a "control" 20 ns MD simulation was carried for a system with the same DNA and water content but in the absence of oligopeptides. Results of DNA interaction with the histone tail fragments, K(+), and water is presented. DNA structure and dynamics and its interplay with the histone tail fragments binding are described. The charged side chains of the lysines play a major role in mediating DNA-DNA attraction by forming bridges and coordinating to phosphate groups and electronegative sites in the minor groove. Binding of all species to DNA is dynamic. Some of the tail fragments while being flexible and mobile in each of its functional groups remain associated near certain locations of the DNA oligomer. The present work allows capturing typical features of the histone tail-counterion-DNA structure, interaction, and dynamics.

Interaction between colloids with grafted diblock polyampholytes

The interaction between composite colloidal particles composed of a spherical core and grafted AB-diblock polyampholytes (diblock copolymers with oppositely charged blocks) are investigated by using a coarse-grained model solved with Monte Carlo simulations. The B block is end-grafted onto the core of the colloid and its linear charge density is varied, whereas the linear charge density of the A block is fixed. The brush structure of a single colloid, the mean force between two colloids, and the structure of solutions of such colloids have been determined for different linear charge densities of the B blocks and block lengths. Many features of the present system are controlled by the charge of the B blocks. In the limit of uncharged B blocks, (i) the grafted chains are stretched and form an extended polyelectrolyte brush, (ii) a strong repulsive force is operating between two colloids, (iii) and the solution is thermodynamic stable and displays strong spatial correlation among the colloids. In the limit where the charges of the two types of blocks exactly compensate each other, (i) the chains are collapsed and form a polyelectrolyte complex surrounding the cores, (ii) an attractive force appears between two colloids, and (iii) strong colloid clustering appears in the solution. These features become more pronounced as the length of the polymer blocks is increased, and a phase instability occurs at sufficiently long chains. A comparison with properties for other related colloidal particles is also provided.

Structure of polyelectrolyte complexes by Brownian dynamics simulation: Effects of the bond length asymmetry of the polyelectrolytes

Brownian dynamics simulations were performed to study the structure of polyelectrolyte complexes formed by two flexible, oppositely charged polyelectrolyte chains. The distribution of monomers in the complex as well as the radius of gyration and structure factor of complexes and individual polyelectrolytes are reported. These structural properties were calculated for polyelectrolyte chains with equal number of monomers, keeping constant the bond length of the negative chain and increasing the bond length of the positive chain. This introduces an asymmetry in the length of the chains that modulates the final structure of the complexes. In the symmetric case the distribution of positive and negative monomers in the complex are identical, producing clusters that are locally and globally neutral. Deviations from the symmetric case lead to nonuniform, asymmetric monomer distributions, producing net charge oscillations inside the complex and large changes in the radius of gyration of the complex and individual chains. From the radius of gyration of the polyelectrolyte chains it is shown that the positive chain is much more folded than the negative chain when the chains are asymmetric, which is also confirmed through the scaling behavior of the structure factors.

Coil-globule coexistence and compaction of DNA chains

In this work we discuss different factors governing coil-globule coexistence in the compaction process of DNA. We initially analyse the role played by fluctuations in the degree of binding of an external compacting agent in the conformational behavior of the chain backbone. The analysis relies both on Monte Carlo simulation results and simple statistical approaches. Compacting agents of various binding characteristics are taken into consideration and the degree of charge neutralization upon the chain is related to conformational indicators. Selected model systems comprising stiff chains in the presence of multivalent ions are employed to assess intrinsic single-chain conformational fluctuation, in the presence of external agents but not resulting from differences in binding. It is shown that trends found for a variety of compacting agents, including the extension of the coil-globule coexistence regions, can be rationalised on the basis of this analysis.