Effective charge saturation in colloidal suspensions

Colloidal Stability of PFSA-Ionomer Dispersions. Part I. Single-Ion Electrostatic Interaction Potential Energies

Charged colloidal particles neutralized by a single counterion are increasingly important for many emerging technologies. Attention here is paid specifically to hydrogen fuel cells and water electrolyzers whose catalyst layers are manufactured from a perfluorinated sulfonic acid polymer (PFSA) suspended in aqueous/alcohol solutions. Partially dissolved PFSA aggregates, known collectively as ionomers, are stabilized by the electrostatic repulsion of overlapping diffuse double layers consisting of only protons dissociated from the suspended polymer. We denote such double layers containing no added electrolyte as "single ion". Size-distribution predictions build upon interparticle interaction potential energies from the Derjaguin-Landau-Verwey-Overbeek (DLVO) formalism. However, when only a single counterion is present in solution, classical DLVO electrostatic potential energies no longer apply. Accordingly, here a new formulation is proposed to describe how single-counterion diffuse double layers interact in colloidal suspensions. Part II (Srivastav, H.; Weber, A. Z.; Radke, C. J. Langmuir 2024 DOI: 10.1021/acs.langmuir.3c03904) of this contribution uses the new single-ion interaction energies to predict aggregated size distributions and the resulting solution pH of PFSA in mixtures of n-propanol and water. A single-counterion diffuse layer cannot reach an electrically neutral concentration far from a charged particle. Consequently, nowhere in the dispersion is the solvent neutral, and the diffuse layer emanating from one particle always experiences the presence of other particles (or walls). Thus, in addition to an intervening interparticle repulsive force, a backside osmotic force is always present. With this new construction, we establish that single-ion repulsive pair interaction energies are much larger than those of classical DLVO electrostatic potentials. The proposed single-ion electrostatic pair potential governs dramatic new dispersion behavior, including dispersions that are stable at a low volume fraction but unstable at a high volume fraction and finite volume-fraction dispersions that are unstable with fine particles but stable with coarse particles. The proposed single-counterion electrostatic pair potential provides a general expression for predicting colloidal behavior for any charged particle dispersion in ionizing solvents with no added electrolyte.

Energy-Scaled Debye-Hückel Theory for the Electrostatic Solvation Free Energy in Size-Asymmetric Electrolyte Solutions

In this report, an energy-scaled Debye-Hückel theory is developed for fast and accurate evaluation of the electrostatic solvation free energy in size-asymmetric electrolyte solutions. A size-asymmetric electrolyte solution is mapped to a dielectric continuum medium with Debye-Hückel-like response. Based on the scaling relation of the electrostatic energy of a spherical ion in the small and large size limits, a Padé polynomial is used to interpolate the electrostatic energy at finite size. The Padé polynomial is further interpreted as the electrostatic energy of an effective Debye-Hückel mean field model, depicted by a modified Debye parameter and a surface charge density due to the size asymmetry of the solvent ions. This theory can distinguish the electrostatic energies and the electrostatic solvation free energies of solutes with the same size but opposite charges. Application to charged hard and charged soft spheres demonstrates the accuracy of our approach.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Do Aqueous Suspensions of Smectite Clays Form a Smectic Liquid-Crystalline Phase?

Bottom-up strategies for the production of well-defined nanostructures often rely on the self-assembly of anisotropic colloidal particles (nanowires and nanosheets). These building blocks can be obtained by delamination in a solvent of low-dimensionality crystallites. To optimize particle availability, determination of the delamination mechanism and the different organization stages of anisotropic particles in dispersion is essential. We address this fundamental issue by exploiting a recently developed system of fluorohectorite smectite clay mineral that delaminates in water, leading to colloidal dispersions of single-layer, very large (≈20 μm) clay sheets at high dilution. We show that when the clay crystallites are dispersed in water, they swell to form periodic one-dimensional stacks of fluorohectorite sheets with very low volume fraction (<1%) and therefore huge (≈100 nm) periods. Using optical microscopy and synchrotron X-ray scattering, we establish that these colloidal stacks bear strong similarities, yet subtle differences, with a smectic liquid-crystalline phase. Despite the high dilution, the colloidal stacks of sheets, called colloidal accordions, are extremely robust mechanically and can persist for years. Moreover, when subjected to AC electric fields, they rotate as solid bodies, which demonstrates their outstanding internal cohesion. Furthermore, our theoretical model captures the dependence of the stacking period on the dispersion concentration and ionic strength and explains, invoking the Donnan effect, why the colloidal accordions are kinetically stable over years and impervious to shear and Brownian motion. Because our model is not system specific, we expect that similar colloidal accordions frequently appear as an intermediate state during the delamination process of two-dimensional crystals in polar solvents.

Structure of electrolyte solutions at nonuniformly charged surfaces on a variety of length scales

The structures of dilute electrolyte solutions close to nonuniformly charged planar substrates are systematically studied within the entire spectrum of microscopic to macroscopic length scales by means of a unified classical density functional theory approach. This is in contrast to previous investigations, which are applicable either to short or to long length scales. It turns out that interactions with microscopic ranges, e.g., due to the hard cores of the fluid molecules and ions, have a negligible influence on the formation of nonuniform lateral structures of the electrolyte solutions. This partly justifies the Debye-Hückel approximation schemes applied in previous studies of that system. In general, a coupling between the lateral and the normal fluid structures leads to the phenomenology that, upon increasing the distance from the substrate, fewer details of the lateral nonuniformities contribute to the fluid structure, such that ultimately only large-scale surface features remain relevant. It can be expected that this picture also applies to other fluids characterized by several length scales.

Thermodynamically Stable Colloidal Solids: Interfacial Thermodynamics from the Particle Size Distribution

True thermodynamic stability of a solid colloidal dispersion is generally unexpected, so much that thorough experimental validation of proposed stable systems remains incomplete. Such dispersions are under investigated and would be of interest due to their long-term stability and insensitivity to preparation pathway. We apply classical nucleation theory (CNT) to such colloidal systems, providing a relationship which links the size-dependent interfacial free energy density of the particles to their size distribution, and use this expression in the fitting of previously reported size distributions for putatively thermodynamically stable nanoparticles. Experimental data from a gold-thiol system exhibiting inverse coarsening or "digestive ripening" can be well-described in terms of a power-law dependence of the interfacial free energy γ on radius based on capacitive charging of the nanoparticles, going asr - 3 , as suggested by prior authors. Data from magnetite nanoparticles in highly basic solutions also can be well-fit using the CNT relation, but with γ going asr - 2 . Slightly better fits are possible if the power of the radius is non-integral, but we stress that more complex models of γ will require richer data sets to avoid the problem of overfitting. Some parameters of the fits are still robustly at odds with earlier models that implicitly assumed absolute thermodynamic stability: first, the extrapolated free energy density of the flat surface in these systems is small and positive, rather than strongly negative; second, the shape of the distributions indicates the solution phase to be supersaturated in monomer relative to the bulk, and thus that these two systems may only be metastable. For future work, we derive expressions for the important statistical thermodynamic and chemical parameters of the interface energy in terms of 1) the surfactant concentration, 2) the temperature dependence, and 3) the concentrations of particles in the tail of the distribution.

Dendritic polyelectrolytes with monovalent and divalent counterions: the charge regulation effect and counterion release

The charge regulation and the release of counterions are extremely important and substantial in determining the charge state of polyelectrolytes and the interaction between polyelectrolytes and proteins. Going beyond monovalent to multivalent cations, it is well-known that the effects of ions are qualitatively different. Therefore, the well-accepted descriptions of the charge regulation and the counterion release based on monovalent ions do not immediately apply to systems with multivalent ions. Here, we study the key structural and electrostatic features of charged dendrimers at hand of the pharmaceutically important dendritic polyglycerol sulfate (dPGS) macromolecule equilibrated with monovalent and divalent salts by molecular dynamics (MD) simulations. Following a simple but accurate scheme to determine its effective radius, the counterion condensed layer of the dPGS is determined with high accuracy and we observe the sequential replacement of condensed monovalent cations (MCs) to divalent cations (DCs) rendering a smaller dPGS effective charge versus the DC concentration. We resolve and track the release of counterions on the dPGS along its binding pathway with the plasma protein Human Serum Albumin (HSA). We find that the release of MCs remains favorable for the complexation leading to a considerable amount of release entropy as the driving force for complexation. The release of DCs only occurs above a certain DC concentration with a comparably smaller number of released ions than MCs. Its contribution to the binding free energy is small indicating a subtle cancellation between the entropy gain in releasing DCs and the enthalpy penalty from dissociating DCs from the dendrimer.

Fine tuning the structural colours of photonic nanosheet suspensions by polymer doping

Aqueous suspensions of nanosheets are readily obtained by exfoliating low-dimensional mineral compounds like H₃Sb₃P₂O₁₄. The nanosheets self-organize, at low concentration, into a periodic stack of membranes, i.e. a lamellar liquid-crystalline phase. Due to the dilution, this stack has a large period of a few hundred nanometres, it behaves as a 1-dimensional photonic material and displays structural colours. We experimentally investigated the dependence of the period on the nanosheet concentration. We theoretically showed that it cannot be explained by the usual DLVO interaction between uniform lamellae but that the particulate nature of nanosheet-laden membranes must be considered. Moreover, we observed that adding small amounts of 100 kDa poly(ethylene oxide) (PEO) decreases the period and allows tuning the colour throughout the visible range. PEO adsorbs on the nanosheets, inducing a strong reduction of the nanosheet charge. This is probably due to the Lewis-base character of the EO units of PEO that become protonated at the low pH of the system, an interpretation supported by theoretical modeling. Oddly enough, adding small amounts of 1 MDa PEO has the opposite effect of increasing the period, suggesting the presence of an additional intermembrane repulsion not yet identified. From an applied perspective, our work shows how the colours of these 1-dimensional photonic materials can easily be tuned not only by varying the nanosheet concentration (which might entail a phase transition) but also by adding PEO. From a theoretical perspective, our approach represents a necessary step towards establishing the phase diagram of aqueous suspensions of charged nanosheets.

Ion-Specific Adsorption on Bare Gold (Au) Nanoparticles in Aqueous Solutions: Double-Layer Structure and Surface Potentials

We study the solvation and electrostatic properties of bare gold (Au) nanoparticles (NPs) of 1-2 nm in size in aqueous electrolyte solutions of sodium salts of various anions with large physicochemical diversity (Cl^-, BF₄^-, PF₆^-, Nip^- (nitrophenolate), 3- and 4-valent hexacyanoferrate (HCF)) using nonpolarizable, classical molecular dynamics computer simulations. We find a substantial facet selectivity in the adsorption structure and spatial distribution of the ions at the AuNPs: while sodium and some of the anions (e.g., Cl^-, HCF^3-) adsorb more at the "edgy" (100) and (110) facets of the NPs, where the water hydration structure is more disordered, other ions (e.g., BF₄^-, PF₆^-, Nip^-) prefer to adsorb strongly on the extended and rather flat (111) facets. In particular, Nip^-, which features an aromatic ring in its chemical structure, adsorbs strongly and perturbs the first water monolayer structure on the NP (111) facets substantially. Moreover, we calculate adsorptions, radially resolved electrostatic potentials as well as the far-field effective electrostatic surface charges and potentials by mapping the long-range decay of the calculated electrostatic potential distribution onto the standard Debye-Hückel form. We show how the extrapolation of these values to other ionic strengths can be performed by an analytical Adsorption-Grahame relation between the effective surface charge and potential. We find for all salts negative effective surface potentials in the range from -10 mV for NaCl down to about -80 mV for NaNip, consistent with typical experimental ranges for the zeta potential. We discuss how these values depend on the surface definition and compare them to the explicitly calculated electrostatic potentials near the NP surface, which are highly oscillatory in the ±0.5 V range.

Coarse-Grained Molecular Dynamics (CG-MD) Simulation of the Encapsulation of Dexamethasone in PSS/PDDA Layer-by-Layer Assembled Polyelectrolyte Nanocapsules

Experimental studies have reported the fundamental and applied science aspects of polyelectrolyte (PE) layer-by-layer (LbL) self-assembly. LbL nanocoating is a simple and robust technique that can be used to modify the surface properties of nearly any material. These modifications take place by adsorption of mere nanometers of PE to impart previously absent properties to the nanocoated substrate. Paper manufacturing, drug delivery, and antimicrobial applications have since been developed. LbL self-assembly has become a very lucrative field of research. Computational modeling of LbL nanocoating has received limited attention. PE simulations often require significant computational resources and make computational modeling studies challenging. In this study, atomic-level PE and dexamethasone models are developed and then converted into coarse-grained (CG) models. This modeling study is based on experimental results that were previously reported. The CG models showed the effect of salt concentration and the number of PE layers on the LbL drug nanocapsule. The suitability of the model was evaluated and showed that this model can serve as a predictive tool for an LbL-nanocoated drug delivery system. It is suggested that this model can be used to simulate LbL drug delivery systems before the experimental evaluation of the real systems take place.

Antagonistic mixing in micelles of amphiphilic polyoxometalates and hexaethylene glycol monododecyl ether

HYPOTHESIS

Polyoxometalates (POMs) are metal oxygen clusters with a range of interesting magnetic and catalytic properties. POMs with attached hydrocarbon chains show amphiphilic behaviour so we hypothesised that mixtures of a nonionic surfactant and anionic surfactants with a polyoxometalate cluster as headgroup would form mixed micelles, giving control of the POM density in the micelle, and which would differ in size and shape from micelles formed by the individual surfactants. Due to the high charge and large size of the POM, we suggested that these would be nonideal mixtures due to the complex interactions between the two types of surfactants. The nonideality and the micellar composition may be quantified using regular solution theory. With supplementary information provided by small-angle neutron scattering (SANS), an understanding of this unusual binary surfactant system can be established.

EXPERIMENTS

A systematic study was performed on mixed surfactant systems containing polyoxometalate-headed amphiphiles (K₁₀[P₂W₁₇O₆₁OSi₂(C_nH_2n+1)₂], abbreviated as P₂W₁₇-2C_n, where n = 12, 14 or 16) and hexaethylene glycol monododecyl ether (C₁₂EO₆). Critical micelle concentrations (CMCs) of these mixtures were measured and used to calculate the interaction parameters based on regular solution theory, enabling prediction of micellar composition. Predictions were compared to micelle structures obtained from SANS. A phase diagram was also established.

FINDINGS

The CMCs of these mixtures suggest unusual unfavourable interactions between the two species, despite formation of mixed micelles. Micellar compositions obtained from SANS concurred with those calculated using the averaged interaction parameters for P₂W₁₇-2C_n/C₁₂EO₆ (n = 12 and 14). We attribute the unfavourable interactions to a combination of different phenomena: counterion-mediated interactions between P₂W₁₇ units and the unfolding of the ethylene oxide headgroups of the nonionic surfactant, yet micelles still form in these systems due to the hydrophobic interactions between surfactant tails.

Self-assembly of charged colloidal cubes

In this work, we show how and why the interactions between charged cubic colloids range from radially isotropic to strongly directionally anisotropic, depending on tuneable factors. Using molecular dynamics simulations, we illustrate the effects of typical solvents to complement experimental investigations of cube assembly. We find that in low-salinity water solutions, where cube self-assembly is observed, the colloidal shape anisotropy leads to the strongest attraction along the corner-to-corner line, followed by edge-to-edge, with a face-to-face configuration of the cubes only becoming energetically favorable after the colloids have collapsed into the van der Waals attraction minimum. Analysing the potential of mean force between colloids with varied cubicity, we identify the origin of the asymmetric microstructures seen in experiment.

Charge Regulation of Colloidal Particles: Theory and Simulations

To explore charge regulation (CR) in physicochemical and biophysical systems, we present a model of colloidal particles with sticky adsorption sites which account for the formation of covalent bonds between the hydronium ions and the surface functional groups. Using this model and Monte Carlo simulations, we find that the standard Ninham and Parsegian (NP) theory of CR leads to results which deviate significantly from computer simulations. The problem with the NP approach is traced back to the use of a bulk equilibrium constant to account for surface chemical reactions. To resolve this difficulty we present a new theory of CR. The fundamental ingredient of the new approach is the sticky length, which is nontrivially related to the bulk equilibrium constant. The theory is found to be in excellent agreement with computer simulations, without any adjustable parameters. As an application of the theory we calculate the effective charge of colloidal particles containing carboxyl groups, as a function of pH and salt concentration.

Long-range forces and charge inversions in model charged colloidal dispersions at finite concentration

In charged colloidal dispersion systems the interest is in finding their stability conditions, phase transitions, and transport properties, either in bulk or confinement, among other physicochemical quantities, for which the knowledge of the dispersions' molecular structure and the associated macroion-macroion forces is crucial. To investigate these phenomena simple models have been proposed. Most of the theoretical and simulation studies on charged particles suspensions are at infinite dilution conditions. Hence, these studies have been focused on the electrolyte structure around one or two isolated central particle(s), where phenomena as charge reversal, charge inversion and surface charge amplification have been shown to be relevant. However, experimental studies at finite volume fraction exhibit interesting phenomenology which imply very long-range correlations. A simple, yet useful, model is the Colloidal Primitive Model, in which the colloidal dispersion is modeled as a mixture of size (and charge) asymmetrical hard spheres, at finite volume fraction. In this paper we review recent integral equations solutions for this model, where very long-range attractive-repulsive forces, as well as new long-range, giant charge inversions are reported. The calculated macroions radial distribution functions, charge distributions, and macroion-macroion forces are qualitatively consistent with existing experimental results, and Monte Carlo and molecular dynamics simulations.

Jellium and cell model for titratable colloids with continuous size distribution

A good understanding and determination of colloidal interactions is paramount to comprehend and model the thermodynamic and structural properties of colloidal suspensions. In concentrated aqueous suspensions of colloids with a titratable surface charge, this determination is, however, complicated by the density dependence of the effective pair potential due to both the many-body interactions and the charge regulation of the colloids. In addition, colloids generally present a size distribution which results in a virtually infinite combination of colloid pairs. In this paper, we develop two methods and describe the corresponding algorithms to solve this problem for arbitrary size distributions. An implementation in Nim is also provided. The methods, inspired by the seminal work of Torres et al., [J. Chem. Phys. 128, 154906 (2008)] are based on a generalization of the cell and renormalized jellium models to polydisperse suspensions of spherical colloids with a charge regulating boundary condition. The latter is described by the one-pK-Stern model. The predictions of the models are confronted to the equations of state of various commercially available silica dispersions. The renormalized Yukawa parameters (effective charges and screening lengths) are also calculated. The importance of size and charge polydispersity as well as the validity of these two models is discussed in light of the results.

Charge and hydration structure of dendritic polyelectrolytes: molecular simulations of polyglycerol sulphate

Macromolecules based on dendritic or hyperbranched polyelectrolytes have been emerging as high potential candidates for biomedical applications. Here we study the charge and solvation structure of dendritic polyglycerol sulphate (dPGS) of generations 0 to 3 in aqueous sodium chloride solution by explicit-solvent molecular dynamics computer simulations. We characterize dPGS by calculating several important properties such as relevant dPGS radii, molecular distributions, the solvent accessible surface area, and the partial molecular volume. In particular, as the dPGS exhibits high charge renormalization effects, we address the challenges of how to obtain a well-defined effective charge and surface potential of dPGS for practical applications. We compare implicit- and explicit-solvent approaches in our all-atom simulations with the coarse-grained simulations from our previous work. We find consistent values for the effective electrostatic size (i.e., the location of the effective charge of a Debye-Hückel sphere) within all the approaches, deviating at most by the size of a water molecule. Finally, the excess chemical potential of water insertion into dPGS and its thermodynamic signature are presented and rationalized.

Electrolyte solutions at heterogeneously charged substrates

The influence of a chemically or electrically heterogeneous distribution of interaction sites at a planar substrate on the number density of an adjacent fluid is studied by means of classical density functional theory (DFT). In the case of electrolyte solutions the effect of this heterogeneity is particularly long ranged, because the corresponding relevant length scale is set by the Debye length which is large compared to molecular sizes. The DFT used here takes the solvent particles explicitly into account and thus captures phenomena, inter alia, due to ion-solvent coupling. The present approach provides closed analytic expressions describing the influence of chemically and electrically nonuniform walls. The analysis of isolated δ-like interactions, isolated interaction patches, and hexagonal periodic distributions of interaction sites reveals a sensitive dependence of the fluid density profiles on the type of the interaction, as well as on the size and the lateral distribution of the interaction sites.

Evidence of electrostatic-enhanced depletion attraction in the structural properties and phase behavior of binary charged colloidal suspensions

In this paper we study the structure and phase behavior of binary mixtures of charged particles at low ionic strength. Due to the large size asymmetry between both species, light scattering measurements give us access only to the partial static structure factor that corresponds to the big particles. We observe that the addition of small charged colloids produces a decrease of the main peak of the measured static structure factor and a shift to larger scattering vector values. This finding is in agreement with theory based on integral equations with the Hypernetted-Chain Closure (HNC) relation. The effective interaction between two big particles due to the presence of small particles is obtained by a HNC inversion scheme and used in numerical simulations that adequately reproduce the experiments. We find that the presence of small particles induces an electrostatic depletion screening among the big colloids, creating around them an exclusion zone for the small charged colloids greater than that caused in the case of neutral small colloids, which in turn augments the depletion effect.

Controlled assembly of single colloidal crystals using electro-osmotic micro-pumps

We assemble charged colloidal spheres at deliberately chosen locations on a charged unstructured glass substrate utilizing ion exchange based electro-osmotic micro-pumps. Using microscopy, a simple scaling theory and Brownian dynamics computer simulations, we systematically explore the control parameters of crystal assembly and the mechanisms through which they depend on the experimental boundary conditions. We demonstrate that crystal quality depends crucially on the assembly distance of the colloids. This is understood as resulting from the competition between inward transport by the electro-osmotic pump flow and the electro-phoretic outward motion of the colloids. Optimized conditions include substrates of low and colloids of large electro-kinetic mobility. Then a sorting of colloids by size is observed in binary mixtures with larger particles assembling closer to the ion exchanger beads. Moreover, mono-sized colloids form defect free single domain crystals which grow outside a colloid-free void with facetted inner crystal boundaries centered on the ion exchange particle. This works remarkably well, even with irregularly formed ion exchange resin splinters.

Drastic Swelling of Lipid Oligobilayers by Polyelectrolytes: A Potential Molecular Model for the Internal Structure of Lubricating Films in Mammalian Joints

Osteoarthritis is the most common arthropathy in western civilization. It is primarily caused by the degeneration of lipid-coated cartilage, leading to increased friction in joints. Hyaluronic acid (HA), a negatively charged polysaccharide and the main component of the synovial fluid, is held responsible for joint lubrication. It is believed that HA, adsorbed to the lipid-coated cartilage, forms a protective layer against wear. Studies have shown that the concentration and molecular weight (MW) of HA are reduced in joints suffering from osteoarthritis. On the basis of these observations, local joint injections of HA or mixtures of HA and surface-active phospholipids (SAPLs) have been applied as medical cures to restore the functionality of the joints in a procedure called viscosupplementation. However, this cure is still disputed, and no consensus has been reached with respect to optimum HA concentration and MW. To provide detailed insight in the structural rearrangement of lipid films upon contact with HA or polymeric analogues, we studied the interaction of the polyelectrolyte poly(allylamine hydrochloride) (PAH) with surface-bound oligobilayers of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) by neutron reflectivity (NR) and ellipsometry. Using this model system, we found a drastic swelling of the lipid films as a function of PAH concentration, whose strength compares to that in previous studies on HA incubation. In contrast, no significant dependence of film thickness on PAH MW was observed. A detailed picture of the film architecture was developed which inter alia shows that charged PAH is adsorbed to the lipid headgroups, leading to electrostatic repulsion. The swelling behavior is well explained by the equilibrium of Coulomb and van der Waals interactions in a DLVO-based model. Our detailed structural analysis of the PAH/lipid interfacial layer may help to elucidate the mechanisms of viscosupplementation and derive a structure-function relationship for the lubricating interface in mammalian joints.

Planar screening by charge polydisperse counterions

We study how a neutralising cloud of counterions screens the electric field of a uniformly charged planar membrane (plate), when the counterions are characterised by a distribution of charges (or valence), [Formula: see text]. We work out analytically the one-plate and two-plate cases, at the level of non-linear Poisson-Boltzmann theory. The (essentially asymptotic) predictions are successfully compared to numerical solutions of the full Poisson-Boltzmann theory, but also to Monte Carlo simulations. The counterions with smallest valence control the long-distance features of interactions, and may qualitatively change the results pertaining to the classic monodisperse case where all counterions have the same charge. Emphasis is put on continuous distributions [Formula: see text], for which new power-laws can be evidenced, be it for the ionic density or the pressure, in the one- and two-plates situations respectively. We show that for discrete distributions, more relevant for experiments, these scaling laws persist in an intermediate but yet observable range. Furthermore, it appears that from a practical point of view, hallmarks of the continuous [Formula: see text] behaviour are already featured by discrete mixtures with a relatively small number of constituents.

Counterion-Release Entropy Governs the Inhibition of Serum Proteins by Polyelectrolyte Drugs

Dendritic polyelectrolytes constitute high potential drugs and carrier systems for biomedical purposes. Still, their biomolecular interaction modes, in particular those determining the binding affinity to proteins, have not been rationalized. We study the interaction of the drug candidate dendritic polyglycerol sulfate (dPGS) with serum proteins using isothermal titration calorimetry (ITC) interpreted and complemented with molecular computer simulations. Lysozyme is first studied as a well-defined model protein to verify theoretical concepts, which are then applied to the important cell adhesion protein family of selectins. We demonstrate that the driving force of the strong complexation, leading to a distinct protein corona, originates mainly from the release of only a few condensed counterions from the dPGS upon binding. The binding constant shows a surprisingly weak dependence on dPGS size (and bare charge) which can be understood by colloidal charge-renormalization effects and by the fact that the magnitude of the dominating counterion-release mechanism almost exclusively depends on the interfacial charge structure of the protein-specific binding patch. Our findings explain the high selectivity of P- and L-selectins over E-selectin for dPGS to act as a highly anti-inflammatory drug. The entire analysis demonstrates that the interaction of proteins with charged polymeric drugs can be predicted by simulations with unprecedented accuracy. Thus, our results open new perspectives for the rational design of charged polymeric drugs and carrier systems.

Triple Junction at the Triple Point Resolved on the Individual Particle Level

At the triple point of a repulsive screened Coulomb system, a fcc crystal, a bcc crystal, and a fluid phase coexist. At their intersection, these three phases form a liquid groove, the triple junction. Using confocal microscopy, we resolve the triple junction on a single-particle level in a model system of charged PMMA colloids in a nonpolar solvent. The groove is found to be extremely deep and the incommensurate solid-solid interface to be very broad. Thermal fluctuations hence appear to dominate the solid-solid interface. This indicates a very low interfacial energy. The fcc-bcc interfacial energy is quantitatively determined based on Young's equation and, indeed, it is only about 1.3 times higher than the fcc-fluid interfacial energy close to the triple point.

Adsorption of Milk Proteins (β-Casein and β-Lactoglobulin) and BSA onto Hydrophobic Surfaces

Here, we study films of proteins over planar surfaces and protein-coated microspheres obtained from the adsorption of three different proteins ( β -casein, β -lactoglobulin and bovine serum albumin (BSA)). The investigation of protein films in planar surfaces is performed by combining quartz crystal microbalance (QCM) and atomic force microscopy (AFM) measurements with all-atomic molecular dynamics (MD) simulations. We found that BSA and β -lactoglobulin form compact monolayers, almost without interstices between the proteins. However, β -casein adsorbs forming multilayers. The study of the electrokinetic mobility of protein-coated latex microspheres shows substantial condensation of ions from the buffer over the complexes, as predicted from ion condensation theories. The electrokinetic behavior of the latex-protein complexes is dominated by the charge of the proteins and the phenomenon of ion condensation, whereas the charge of the latex colloids plays only a minor role.

Numerical evidence for thermally induced monopoles

Electric charges are conserved. The same would be expected to hold for magnetic charges, yet magnetic monopoles have never been observed. It is therefore surprising that the laws of nonequilibrium thermodynamics, combined with Maxwell's equations, suggest that colloidal particles heated or cooled in certain polar or paramagnetic solvents may behave as if they carry an electric/magnetic charge. Here, we present numerical simulations that show that the field distribution around a pair of such heated/cooled colloidal particles agrees quantitatively with the theoretical predictions for a pair of oppositely charged electric or magnetic monopoles. However, in other respects, the nonequilibrium colloidal particles do not behave as monopoles: They cannot be moved by a homogeneous applied field. The numerical evidence for the monopole-like fields around heated/cooled colloidal particles is crucial because the experimental and numerical determination of forces between such colloidal particles would be complicated by the presence of other effects, such as thermophoresis.

Interactions regulating the head-to-tail directed assembly of biological Janus rods

We show that the directed assembly of microtubule filaments is governed by a careful balance of long- and short-range interactions.

Osmotic Bulk Modulus of Charged Colloids Measured by Ensemble Optical Trapping

The optical-bottle technique is used to measure osmotic bulk moduli of colloid suspensions. The bulk modulus is determined by optically trapping an ensemble of nanoparticles and invoking a steady-state force balance between confining optical-gradient forces and repulsive osmotic-pressure forces. Osmotic bulk moduli are reported for aqueous suspensions of charged polystyrene particles in NaCl solutions as a function of particle concentration and ionic strength, and are compared to those determined by turbidity measurements under the same conditions. Effective particle charges are calculated from the bulk moduli and are found to increase as a function of ionic strength, consistent with previously reported results.

The persistence length of adsorbed dendronized polymers

The persistence length of cationic dendronized polymers adsorbed onto oppositely charged substrates was studied by atomic force microscopy (AFM) and quantitative image analysis. One can find that a decrease in the ionic strength leads to an increase of the persistence length, but the nature of the substrate and of the generation of the side dendrons influence the persistence length substantially. The strongest effects as the ionic strength is being changed are observed for the fourth generation polymer adsorbed on mica, which is a hydrophilic and highly charged substrate. However, the observed dependence on the ionic strength is much weaker than the one predicted by the Odijk, Skolnik, and Fixman (OSF) theory for semi-flexible chains. Low-generation polymers show a variation with the ionic strength that resembles the one observed for simple and flexible polyelectrolytes in solution. For high-generation polymers, this dependence is weaker. Similar dependencies are found for silica and gold substrates. The observed behavior is probably caused by different extents of screening of the charged groups, which is modified by the polymer generation, and to a lesser extent, the nature of the substrate. For highly ordered pyrolytic graphite (HOPG), which is a hydrophobic and weakly charged substrate, the electrostatic contribution to the persistence length is much smaller. In the latter case, we suspect that specific interactions between the polymer and the substrate also play an important role.

Poisson-Boltzmann thermodynamics of counterions confined by curved hard walls

We consider a set of identical mobile pointlike charges (counterions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are considered: a pair of parallel plates, the cylinder, and the sphere. The particle system in thermal equilibrium is assumed to be described by the nonlinear Poisson-Boltzmann theory. While the effectively one-dimensional plates and the two-dimensional cylinder have already been solved, the three-dimensional sphere problem is not integrable. It is shown that the contact density of particles at the charged surface is determined by a first-order Abel differential equation of the second kind which is a counterpart of Enig's equation in the critical theory of gravitation and combustion or explosion. This equation enables us to construct the exact series solutions of the contact density in the regions of small and large surface charge densities. The formalism provides, within the mean-field Poisson-Boltzmann framework, the complete thermodynamics of counterions inside a charged sphere (salt-free system).

Exploring the charging mechanisms in non-aqueous multiphase surfactant solutions, emulsions and colloidal systems via conductivity behaviors predicted with eyring's rate process theory

The schematic diagram shows charge separation induced and stabilized by an electric field and inverse micelles charged in the end.

Interplay of anisotropy in shape and interactions in charged platelet suspensions

Motivated by the intriguing phase behavior of charged colloidal platelets, we investigate the structure and dynamics of charged repulsive disks by means of Monte Carlo simulations. The electrostatic interactions are taken into account through an effective two-body potential, obtained within the nonlinear Poisson-Boltzmann formalism, which has the form of anisotropic screened Coulomb potential. Recently, we showed that the original intrinsic anisotropy of the electrostatic potential in competition with excluded volume effects leads to a rich phase behavior that not only includes various liquid-crystalline phases but also predicts the existence of novel structures composed of alternating nematic-antinematic sheets. Here, we examine the structural and dynamical signatures of each of the observed structures for both translational and rotational degrees of freedom. Finally, we discuss the influence of effective charge value and our results in relation to experimental findings on charged platelet suspensions.

Strong effect of weak charging in suspensions of anisotropic colloids

Suspensions of hard colloidal particles frequently serve as model systems in studies on fundamental aspects of phase transitions. But often colloidal particles that are considered as "hard" are in fact weakly charged. If the colloids are spherical, weak charging has only a weak effect on the structural properties of the suspension, which can be easily corrected for. However, this does not hold for anisotropic particles. We introduce a model for the interaction potential between charged ellipsoids of revolution (spheroids) based on the Derjaguin approximation of Debye-Hückel theory and present a computer simulation study on aspects of the system's structural properties and phase behaviour. In line with previous experimental observations, we find that even a weak surface charge has a strong impact on the correlation functions. A likewise strong impact is seen on the phase behaviour, in particular, we find stable cubatic order in suspensions of oblate ellipsoids.

Order of wetting transitions in electrolyte solutions

For wetting films in dilute electrolyte solutions close to charged walls we present analytic expressions for their effective interface potentials. The analysis of these expressions renders the conditions under which corresponding wetting transitions can be first- or second-order. Within mean field theory we consider two models, one with short- and one with long-ranged solvent-solvent and solvent-wall interactions. The analytic results reveal in a transparent way that wetting transitions in electrolyte solutions, which occur far away from their critical point (i.e., the bulk correlation length is less than half of the Debye length) are always first-order if the solvent-solvent and solvent-wall interactions are short-ranged. In contrast, wetting transitions close to the bulk critical point of the solvent (i.e., the bulk correlation length is larger than the Debye length) exhibit the same wetting behavior as the pure, i.e., salt-free, solvent. If the salt-free solvent is governed by long-ranged solvent-solvent as well as long-ranged solvent-wall interactions and exhibits critical wetting, adding salt can cause the occurrence of an ion-induced first-order thin-thick transition which precedes the subsequent continuous wetting as for the salt-free solvent.