Nanoparticle Adsorption on a Weak Polyelectrolyte. Stiffness, pH, Charge Mobility, and Ionic Concentration Effects Investigated by Monte Carlo Simulations

Mechanism of nanoplastics capture by jellyfish mucin and its potential as a sustainable water treatment technology

The accumulation of nanoplastics (NPs) in the environment has raised concerns about their impact on human health and the biosphere. The main aim of this study is to understand the mechanism that governs the capture of NPs by jellyfish mucus extracted from the jellyfish Aurelia sp. (A.a.) and compare the capture/removal efficiency to that of conventional coagulants and mucus from other organisms. The efficacy of A.a mucus to capture polystyrene and acrylic NPs (∼100 nm) from spiked wastewater treatment plant (WWTP) effluent was evaluated. The mucus effect on capture kinetics and destabilization of NPs of different polymer compositions, sizes and concentrations was quantified by means of fluorescent NPs, dynamic light scattering and zeta potential measurements and visualized by scanning electron microscopy. A dosing of A.a. mucus equivalent to protein concentrations of ∼2-4 mg L^-1 led to a rapid change in zeta potential from a baseline of -30 mV to values close to 0 mV, indicating a marked change from a stable to a non-stable dispersion leading to a rapid (<10 min) and significant removal of NPs (60 %-90 %) from a stable suspension. The A.a. mucus outperformed all other mucus types (0-37 %) and coagulants (0 %-32 % for ferric chloride; 23-40 % for poly aluminum chlorohydrate), highlighting the potential for jellyfish mucus to be used as bio-flocculant. The results indicate a mucus-particle interaction consisting of adsorption-bridging and "mesh" filtration. Further insight is provided by carbohydrate composition and protein disruption analysis. Total protein disruption resulted in a complete loss of the A.a. mucus capacity to capture NPs, while the breaking of disulfide bonds and protein unfolding resulted in improved capture capacity. The study demonstrates that natural jellyfish mucin can capture and remove NPs in water and wastewater treatment systems more efficiently than conventional coagulants, highlighting the potential for development of a new type of bio-flocculant.

Accelerated simulation method for charge regulation effects

The net charge of solvated entities, ranging from polyelectrolytes and biomolecules to charged nanoparticles and membranes, depends on the local dissociation equilibrium of individual ionizable groups. Incorporation of this phenomenon, charge regulation (CR), in theoretical and computational models requires dynamic, configuration-dependent recalculation of surface charges and is therefore typically approximated by assuming constant net charge on particles. Various computational methods exist that address this. We present an alternative, particularly efficient CR Monte Carlo method (CR-MC), which explicitly models the redistribution of individual charges and accurately samples the correct grand-canonical charge distribution. In addition, we provide an open-source implementation in the large-scale Atomic/Molecular Massively Parallel Simulator molecular dynamics (MD) simulation package, resulting in a hybrid MD/CR-MC simulation method. This implementation is designed to handle a wide range of implicit-solvent systems that model discreet ionizable groups or surface sites. The computational cost of the method scales linearly with the number of ionizable groups, thereby allowing accurate simulations of systems containing thousands of individual ionizable sites. By matter of illustration, we use the CR-MC method to quantify the effects of CR on the nature of the polyelectrolyte coil-globule transition and on the effective interaction between oppositely charged nanoparticles.

Inducing pH control over the critical micelle concentration of zwitterionic surfactants via polyacids adsorption: Effect of chain length and structure

HYPOTHESIS

The critical concentration above which micelles form from zwitterionic surfactant solutions and their thermodynamic stability is affected by the interaction with weak Brønsted polyacid chains (A_n) via the formation of charged hydrogen bonds between the latter and anionic moieties.

EXPERIMENTS

The interaction between zwitterionic micelles and polyacids capable of forming hydrogen bonds, and its dependence on the environmental pH and polymer structure, has been studied with constant-pH simulations and a restricted primitive model for all electrolytes.

FINDINGS

At low pH, the formation of polyacid/micelle complexes is witnessed independently of the polymer size or structure, so that the concentration above which micelles form is substantially decreased compared to polyacid-free cases. Upon rising pH, polymer desorption takes place within a narrow range of pH values, its location markedly depending on the size and structure of polyacids, and on the relative disposition between headgroup charged moieties. Thus, the desorption onset for long linear polyacids (A₆₀) interacting with sulphobetainic headgroups is roughly two pH units higher than for six decameric chains (6A₁₀) adsorbed onto micelles bearing phosphorylcholinic headgroups. This effect, together with the preferential desorption of chain ends at intermediate pH, may be exploited for drug delivery purposes or building advanced metamaterials.

On the distribution of hydrophilic polyelectrolytes and their counterions around zwitterionic micelles: the possible impact on the charge density in solution

Despite their charge neutrality, micelles composed of surfactants with zwitterionic headgroups selectively accumulate anions at their hydrophobic core/solution interphase due to electrostatic interactions if headgroup positive moieties are the innermost. This tendency may be markedly enhanced if polyions substitute simple ions. To investigate this possibility, solutions composed of zwitterionic micelles and hydrophilic polyanions have been investigated with Monte Carlo simulations representing the studied systems via primitive electrolyte models. Structural and energetic properties are obtained to highlight the impact of connecting simple ions into polyions on the interactions between electrolytes and micelles. Despite the latter, polyanions conserve their conformational properties. A marked increase in the concentration of charged species inside the micellar corona is, instead, found when polyions are present independently of their charge sign or the headgroup structure. Thus, polyelectrolytes act as "shuttle" for all charged species, with the potential of increasing reactions rates involving the latter due to mass effects. Besides, results for the polyions/micelles mixing free energy and Helmholtz energy profiles indicate that the critical micelle concentration is impacted minimally by hydrophilic polyelectrolytes, an outcome agreeing with experiments. This finding is entirely due to weak enthalpic effects while mixing hydrophilic polyions and micelles. A strong reduction in the screening of the micelle negative charge, acquired following the adsorption of anions in the corona and due to counterions layering just outside it (the so called "chameleon effect"), is forecasted when polyanions substitute monovalent anions.

Heteroprotein complex coacervation: Focus on experimental strategies to investigate structure formation as a function of intrinsic and external physicochemical parameters for food applications

Proteins are important components of foods, because they are one of the essential food groups, they have many functional properties that are very useful for modifying the physicochemical and textural properties of processed foods and possess many biological activities that are beneficial to human health. The process of heteroprotein complex coacervation (HPCC) combines two or more proteins through long-range coulombic interaction and specific short-range forces, creating a liquid-liquid colloid, with highly concentrated protein in the droplet phase and much more diluted-protein in the bulk phase. Coacervates possess novel, modifiable, physicochemical characteristics, and often exhibit the combined biological activities of the protein components, which makes them applicable to formulated foods and encapsulation carriers. This review discusses research progress in the field of HPCC in three parts: (1) the basic and innovative experimental methods and simulation tools for understanding the physicochemical behavior of these heteroprotein supramolecular architectures; (2) the influence of environmental factors (pH, mixing ratio, salts, temperature, and formation time) and intrinsic factors (protein modifications, metal-binding, charge anisotropy, and polypeptide designs) on HPCC; (3) the potential applications of HPCC materials, such as encapsulation of nutraceuticals, nanogels, emulsion stabilization, and protein separation. The wide diversity of possible combinations of proteins with different properties, endows HPCC materials with great potential for development into highly-innovation functional food ingredients.

Monte Carlo study of the effects of macroion charge distribution on the ionization and adsorption of weak polyelectrolytes and concurrent counterion release

HYPOTHESIS

Adsorption of weak polyelectrolytes onto charged nanoparticles, and concurrent effects such as spatial partitioning of ions may be influenced by details of the polyelectrolyte structure (linear or star-like) and size, by the mobility of the nanoparticle surface charge, or the valence of the nanoparticle counterions.

EXPERIMENTS

Ionization and complexation of weak polyelectrolytes on spherical macroions with monovalent and divalent countrions has been studied with constant-pH Monte Carlo titrations and primitive electrolyte models for linear and star-like polymers capable, also, of forming charged hydrogen bonds. Nanoparticles surface charge has been represented either as a single colloid-centered total charge (CCTC) or as surface-tethered mobile monovalent spherical charges (SMMSC).

FINDINGS

Differences in the average number of adsorbed polyelectrolyte arms and their average charge, and in the relative amount of macroion counterions (m-CI's) released upon polymer adsorption are found between CCTC and SMMSC nanoparticles. The amount of the counterions released also depends on the polymer structure. As CCTC adsorbs a lower number of star-like species arms, the degree of condensation of polymer counterions (p-CI's) onto the polyelectrolyte is also substantially higher for the CCTC colloid, with a concurrent decrease of the osmotic coefficient values.

DEAE-dextran hydrochloride behaviour in aqueous solution-The effect of ionic strength and concentration

DEAE-dextran hydrochloride is a positively charged biocompatible polyelectrolyte. Its behaviour in aqueous solutions - the changes in its colloidal characteristics and resulting conformation changes - were investigated using a combination of light scattering, densitometry and ultrasound spectrometry. The results indicated the formation of a voluminous, hydrated and coiled conformation of chains having average particle sizes in the range of units of microns at low ionic strength. This phenomenon was supported by an increase in DEAE-dextran hydrochloride concentration in the solution. The increase in ionic strength caused the shielding of DEAE-dextran hydrochloride charges on its chain, resulting in the destabilization of the conformation arrangement of the polyelectrolyte and the formation of denser, more compact and stiffer structures having smaller particle sizes. The proposed model of DEAE-dextran hydrochloride density in the studied environments (distilled water, NaCl solutions) showed the possibility of using a single equation model to calculate the overall density of the system.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Explicit Ion Effects on the Charge and Conformation of Weak Polyelectrolytes

The titration behavior of weak polyelectrolytes is of high importance, due to their uses in new technologies including nanofiltration and drug delivery applications. A comprehensive picture of polyelectrolyte titration under relevant conditions is currently lacking, due to the complexity of systems involved in the process. One must contend with the inherent structural and solvation properties of the polymer, the presence of counterions, and local chemical equilibria enforced by background salt concentration and solution acidity. Moreover, for these cases, the systems of interest have locally high concentrations of monomers, induced by polymer connectivity or confinement, and thus deviate from ideal titration behavior. This work furthers knowledge in this limit utilizing hybrid Monte Carlo⁻Molecular Dynamics simulations to investigate the influence of salt concentration, pK a , pH, and counterion valence in determining the coil-to-globule transition of poorly solvated weak polyelectrolytes. We characterize this transition at a range of experimentally relevant salt concentrations and explicitly examine the role multivalent salts play in determining polyelectrolyte ionization behavior and conformations. These simulations serve as an essential starting point in understanding the complexation between weak polyelectrolytes and ion rejection of self-assembled copolymer membranes.

A Monte Carlo study of the electrical double layer of a shape-asymmetric electrolyte around a spherical colloid

In this paper, we present a Monte Carlo simulation study on the structure of the electrical double layer around a spherical colloid surrounded by a binary electrolyte composed of spherical and non-spherical ions. Results are provided for the radial distribution functions between the colloid and ions, the orientation correlations between the colloid and non-spherical particles, and the integrated charge. Work is reported mainly for non-spherical particles modeled as spherocylinders, although a particular comparison is made between spherocylindrical particles and dimers. For the conditions investigated here, spherocylinders and dimers produce essentially the same structural information. Additionally, it is shown that spherocylinders mostly orient tangentially to the colloid at its surface; this preferred orientation disappears for larger distances. We also evidence that, near the colloid, the integrated charge attenuates monotonically when the macroparticle is highly charged, whereas for intermediate and low charged states of the colloid, the integrated charge can display charge reversal, overcharging, or both, with magnitudes that are sensitive to the salt concentration and to the localization of charge inside the spherocylinders.

pH-Dependent Polyelectrolyte Bridging of Charged Nanoparticles

Systems comprised of polyelectrolytes and charged nanoparticles are of great technological interest, being common components in formulations among other uses. The colloidal stability of formulations is an important issue, and thus a lot of effort has been made to study the interactions of individual components in these systems. Here, the complexation and adsorption of an annealed (pH-dependent) polyelectrolyte to two spherical nanoparticles has been studied using coarse-grained Monte Carlo simulations. This has been done mainly by varying the solution pH and separation distance (concentration) between the nanoparticles. The polyelectrolyte charge distribution is seen to vary with nanoparticle separation distance, and its ability to bridge both nanoparticles changes with pH. The flexible polyelectrolyte creates compact, multilink bridges at short nanoparticle separation distances and evolves to a stretched single-link bridge at longer distances, where a larger fraction of the polyelectrolyte wraps around the nanoparticles. The annealed polyelectrolyte is also compared with a quenched polyelectrolyte of similar fixed fractional charge. Here, a difference is found in the adsorption ability at low pH/ionization due to the ability of the annealed polyelectrolytes to concentrate charges in the vicinity of the nanoparticle. At intermediate polyelectrolyte charge fractions and with increasing nanoparticle separation distances, the annealed system is able to link nanoparticles at larger distances as compared to the quenched, in good agreement with experimental observations. The results in this work contribute to the understanding of the effect of annealed polyelectrolytes and pH variations in the phase behavior of polyelectrolyte-nanoparticle systems, potentially aiding in the design and optimization of pH-responsive systems.

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.

Accumulation of nanoparticles in "jellyfish" mucus: a bio-inspired route to decontamination of nano-waste

The economic and societal impacts of nano-materials are enormous. However, releasing such materials in the environment could be detrimental to human health and the ecological biosphere. Here we demonstrate that gold and quantum dots nanoparticles bio-accumulate into mucus materials coming from natural species such as jellyfish. One strategy that emerges from this finding would be to take advantage of these trapping properties to remove nanoparticles from contaminated water.

Surface charging behavior of nanoparticles by considering site distribution and density, dielectric constant and pH changes – a Monte Carlo approach

Monte Carlo simulations are used to describe the charging behavior of metal oxide nanoparticles thus enabling a novel and original approach to predict nanoparticle reactivity and the possible interactions with biological and environmental molecules.

Adsorption of pH-responsive polyelectrolyte chains onto spherical macroions

The adsorption of pH-responsive polyelectrolyte chains onto oppositely charged spherical macroions is investigated through Metropolis Monte Carlo simulations and the Weighted Histogram Analysis Method. In this case, the polymer charge density is susceptible to the solution conditions, such as salt concentration and pH, as well as the presence of other charged species. Thus, the pH and ionic strength variations leads to abrupt variations of the conformational and electric properties of the chain, as a result of first-order-like transition between the adsorbed and desorbed states. The diagram of states as a function of ionic strenght and p H is provided. Despite the inhomogeneities in the polyelectrolyte charge distribution induced by the macroion presence and its dependence on ionic strength, the scaling relation between the macromolecular charge densities and the critical Debye length is obtained in agreement with experimental investigations.

Stabilization of lead sulfide nanoparticles by polyamines in aqueous solutions. A structural study of the dispersions

Lead sulfide (PbS) nanoparticles have been synthesized in aqueous solutions by a reaction between inorganic lead salts and sodium sulfide and stabilized using the cationic polyelectrolytes branched poly(ethylenimine) (PEI), poly(allylamine hydrochloride) (PAH), and poly(diallyldimethylammonium chloride) (PDDA). The structures of the polyamine-stabilized nanoparticle dispersions were examined in detail using UV-vis spectroscopy, small-angle X-ray scattering (SAXS), static and dynamic electrophoretic mobility measurements, and transmission electron microscopy (TEM). Considerable differences were found between the stabilizing efficiencies of these polyelectrolytes, which cannot be attributed to their charge densities or their persistence lengths. Small monodisperse nanoparticles of PbS with a tight stabilizing shell were consistently found only when PEI was used as a stabilizer even at high pH values, although its charge density is then very low. The excellence of PEI as a stabilizer is mainly due to the extensive branching of the chains and the presence of uncharged secondary and tertiary amine groups, which apparently serve as good anchoring points at the nanoparticle surfaces. None of the polyelectrolytes examined here provide long-term protection of the nanoparticles toward oxidation by air, showing that a need for more complex multipurpose stabilizers exists for aqueous PbS dispersions.

Multiple scale reorganization of electrostatic complexes of poly(styrenesulfonate) and lysozyme

We report on a SANS investigation into the potential for these structural reorganization of complexes composed of lysozyme and small PSS chains of opposite charge if the physicochemical conditions of the solutions are changed after their formation. Mixtures of solutions of lysozyme and PSS with high matter content and with an introduced charge ratio [-]/[+](intro) close to the electrostatic stoichiometry lead to suspensions that are macroscopically stable. They are composed at local scale of dense globular primary complexes of radius approximately 100 A; at a higher scale they are organized fractally with a dimension 2.1. We first show that the dilution of the solution of complexes, all other physicochemical parameters remaining constant, induces a macroscopic destabilization of the solutions but does not modify the structure of the complexes at submicronic scales. This suggests that the colloidal stability of the complexes can be explained by the interlocking of the fractal aggregates in a network at high concentration: dilution does not break the local aggregate structure, but it does destroy the network. We show, second, that the addition of salt does not change the almost frozen inner structure of the cores of the primary complexes, although it does encourage growth of the complexes; these coalesce into larger complexes as salt has partially screened the electrostatic repulsions between two primary complexes. These larger primary complexes remain aggregated with a fractal dimension of 2.1. Third, we show that the addition of PSS chains up to [-]/[+](intro) approximately 20, after the formation of the primary complex with a [-]/[+](intro) close to 1, only slightly changes the inner structure of the primary complexes. Moreover, in contrast to the synthesis achieved in the one-step mixing procedure where the proteins are unfolded for a range of [-]/[+](intro), the native conformation of the proteins is preserved inside the frozen core.

Understanding the protonation behavior of linear polyethylenimine in solutions through Monte Carlo simulations

The success of polyethyleneimine (PEI) as a nonviral-based gene delivery vector has been attributed to its proton buffering capacity. Despite the great interest in PEI for its use in nonviral-based gene delivery, the protonation behavior of PEI in solution is not well understood. Earlier experimental studies have reported inconsistent values of the protonation state of PEI. In this work, we report our investigation of the protonation behavior of a realistic linear PEI (lPEI) with computational approaches. Reported experimental pK(a) values of several diamine compounds are first examined. A screened Coulombic interaction with a distance dependence dielectric is shown to reproduce the shifted pK(a) values of the model diamine compounds. Then atomistic molecular dynamic simulations of lPEI chain with 20 repeating units are performed and the results are used to provide parameters for a coarse-grained polyamine model. The screened Coulombic interaction is then incorporated in the coarse-grained lPEI chain and computational titrations are performed. The obtained computational titration curves of lPEI in solutions were found to be in best agreement with experimental results by Smits et al., but the computational titration curves have too strong of a dependence on salt concentration compared to the experimental results by Smits et al. Disregarding the discrepancy in the salt dependence, our computational titrations reveal that approximately 55% of the lPEI amine groups are protonated under physiological conditions in solution with a nearly alternating arrangement of protonated and nonprotonated amines. Titrations of lPEI in the presence of a polyanion are also performed to determine how the charge state of lPEI could be affected by complexation with DNA in gene therapy preparations. While the presence of the polyanion increases the degree of protonation of the PEI, many of PEI amines remain unprotonated under physiological conditions, providing evidence that PEI complexed with DNA could still have proton buffering capacity. Potential sources of error that have resulted in the inconsistency of previously reported protonation states of PEI were also discussed.

Finite size and inner structure controlled by electrostatic screening in globular complexes of proteins and polyelectrolytes

We present an extended structural study of globular complexes made by mixing a positively charged protein (lysozyme) and a negatively charged polyelectrolyte (PSS). We study the influence of all the parameters that may act on the structure of the complexes (charge densities and concentration of the species, partial hydrophobicity of the polyion chain, ionic strength). The structures on a scale range lying from 10 Å to 1000 Å are measured by SANS. Whatever the conditions, the same structure is found, based on the formation of dense ∼100 Å globules with a neutral core and a volume fraction of organic species (compacity) of ∼0.3. On the larger scale, the globules are arranged into fractal aggregates. Zetametry measurements show that the globular complexes have a total positive charge when the charge ratio of species introduced in the mixture [-]/[+]intro > 1 and a total negative charge when [-]/[+]intro < 1. This comes from the presence of charged species in slight excess in a layer at the surface of the globules. The globule finite size is determined by the Debye length 1/κ however the physicochemical parameters are modified in the system, as long as chain-protein interactions are of a simple electrostatic nature. The mean number of proteins per primary complex Nlyso_comp grows exponentially on a master curve with 1/κ. This enables to picture the mechanisms of formation of the complexes. There is an initial stage of formation where the growth of the complexes is only driven by attractions between opposite species associated with counterion release. During the growth of the complexes, the globules progressively repel themselves by electrostatic repulsion because their charge increases. When this repulsion becomes dominant in the system, the globules stop growing and behave like charged colloids: they aggregate with a RLCA process, which leads to the formation of fractal aggregates of dimension 2.1.

A Monte Carlo Study of Weak Polyampholytes: Stiffness and Primary Structure Influences on Titration Curves and Chain Conformations

The conformation and titration curves of weak polyampholytes are examined using Monte Carlo simulations with screened Coulomb potentials in the Grand Canonical ensemble. Two different types of monomers are considered. Depending on the solution pH, monomers A are weak acidic sites that can either be negatively charged or uncharged (as carboxylic groups), whereas monomers B are weak basic sites that can either be positively charged or uncharged (as amino groups). The influence of the chain stiffness, primary structure, and ionic concentration on the acid/base properties of the polyampholyte chains are systematically investigated. By adjusting the pH values, titration curves and then the fractions of positively and negatively ionized charged monomers are calculated. Stiffness influence is estimated by comparing two models of chain: a fully flexible and a rod-like polyampholyte. Different primary structures such as statistical (diblock, octablock, and alternating) and random polyampholytes are also considered. We demonstrate that the primary structure plays important roles in the acid/base properties as well as the charge distribution along the polymer backbone of a statistical rod-like polyampholyte. When flexible polyampholytes are considered, polyampholyte conformations promote the attractive electrostatic interactions between positively and negatively charged monomers, hence leading to more or less compact conformations and acid/base properties relatively different in comparison to the rod-like polyampholytes. Various conformations such as extended, globular, and pearl-necklace conformations are found in good agreement with the literature by adjusting the interaction parameter between monomers and monomer stoichiometry.