Particles In Electrolyte Solution Research Articles

New charged aggregate mathematical models to predict the behavior, structural parameters, and geometrical features of microemulsions

Experimental characterization techniques can provide qualitative and quantitative information on the behavior and properties of microemulsion systems. However, they suffer from several inherent drawbacks that often restrict their application to research settings rather than routine practice in various industries. Also, the majority of theoretical studies on microemulsion systems have focused on nonionic surfactants and suffer from restrictive assumptions and limitations that can be violated under realistic conditions. Therefore, their practical applications to real-world problems such as surfactant-based enhanced oil recovery (EOR) processes require the exercise of extreme caution. This work is intended to fill existing research gaps and solve industrial challenges by developing new mathematical models for predicting micelle size besides other structural and geometrical parameters in ionic surfactant-induced oil-in-water (O/W) and water-in-oil (W/O) microemulsions. The main purpose of the present study is to derive novel models that are not only fitting-free, objective, independent of iterative algorithms and experimental data, and inclusive of intermicellar interactions, but also applicable to complex systems containing real crude oil, experiencing compositional changes, and under any thermodynamic conditions. First, a recently proposed surface charging model for dispersions of charged particles in electrolyte solutions is combined with the DLVO theory of colloidal interactions to develop a thermodynamic model for the structural description of O/W microemulsions. Then, upon coupling a surface charging model for non-electrolyte dispersions of charged aqueous cavities with the DLVO theory, another thermodynamic model is developed for W/O microemulsions. Next, the developed mathematical models are supplemented with an auxiliary material balance equation and an equilibrium condition to calculate the radius of micelles in each type of systems. After determining the radii of oil- and water-swollen micelles using the new models, other geometrical and structural parameters such as solubilized phase-to-surfactant molar ratio, aggregation number, the volumes of microemulsion and excess phases, intermicellar distance, and periodicity are readily calculated in an explicit manner using the derived relationships. Afterwards, some reliable complementary tools are discussed for calculations of the associated physical parameters to avoid the need for experimental measurements, thereby making the models more practical and operational. Finally, the validity of the developed models is verified using literature experimental data.

What in particle morphology determines the DLVO interaction energy between hematite particles in electrolyte solutions?

The experimental stability of hematite particles (radius: ∼74 nm) dispersed in solutions of varying salinity deviates considerably from predictions based on the Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. For untreated hematite particles, at pH = 6 and 10, the theoretical values could be matched to the experimental ones by modifying the particle radius used in calculations from 74 to 13 nm. For particles heat-treated at 350 °C for 1 h, the theoretical values at pH = 10 could also be matched to the experimental ones by modifying the particle radius to 7 nm. Atomic force microscopy measurements revealed that the radius of curvature for surface protrusions on the hematite particles was 14 nm on average for the untreated particles at pH = 6 and 10, which almost equals the aforementioned modified particle radius. For the heat-treated hematite particles at pH = 10, the average radius of curvature was 9 nm, which also matched the corresponding modified particle radius. Therefore, we argue that the interaction energy between hematite particles is governed by not the overall particle radius but the curvature radius for surface protrusions. This could account for the discrepancy between theory and experiment regarding the salinity-dependent stability ratio of these particle dispersions.

Theory of Charge Regulation of Colloidal Particles in Electrolyte Solutions

We present a theory that enables us to (i) calculate the effective surface charge of colloidal particles and (ii) efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution due to the presence of 1:1 electrolyte. It also accounts self-consistently for the electrostatic potential produced by the deprotonated surface groups. To examine the accuracy of the theory, we have performed extensive reactive Monte Carlo simulations, which show excellent agreement between theory and simulations without any adjustable parameters.

The effect of high-molecular compounds nature on the electroflotation removal of the metal compounds from electrolyte solutions

• Removal of heavy metal ions (Fe (III), Ni (II), Cu (II), Pb (II) and Zn (II)) as part of the multi-component system from electrolyte solutions by means of electroflotation and filtration with presence of the high-molecular compounds (HMC) of different nature. • Effect of solution pH, metal and electrolyte concentration on the dispersed properties and electrokinetic potential of the dispersed low-soluble metal compounds and efficiency of their electroflotation removal. • Effect of HMC (flocculants and surfactants) with the anionic, cationic, non-ionic and amphoteric nature upon the dispersed properties, electrokinetic potential and efficiency of electroflotation and electroflotation with subsequent filtration removal of the low-soluble metal compounds particles in electrolyte solutions. • The efficiency of electroflotation removal of heavy metals from concentrated electrolyte solutions with the anionic HMS runs to 98–99% for all components. The process of removal of heavy metal ions as part of the multi-component system from electrolyte solutions by means of electroflotation and filtration with presence of the high-molecular compounds (HMC) of different nature has been studied. Studies were performed in solutions with ions of iron (III), nickel (II), copper (II), lead (II) and zinc(II), as well as NaCl and Na 2 SO 4 (pH 9.5–10.5). It has been shown that addition of the sulphate and sodium chloride mixture in 50 g/L concentration to solutions containing metal ions with total 0.1 g/L concentration reduced the absolute value of dispersed phase ζ-potential from −2.5 mV to −6 mV. The dispersed phase size is getting smaller, two particle types appear in the solution − 54 µm (72% of the total particle quantity) and 5.0 µm (28%). Rise of the total metal ion concentration up to 0.2 g/L results in reduction of the dispersed phase size: 1.5 µm (63%) and 46 µm (37%) particles prevail, the ζ-potential is reduced slightly (-7.1 mV). In this case, the rate of removal of the studied metals by mean of electroflotation is not more than 32–46%. Addition of the anionic HMS (flocculants and surfactants) to the solutions with the total concentration of metal ions of 0.2 g/L and salts of 50 g/L results in rise of dispersed phase ζ-potential and tends its value to the isoelectric point (±0 mV). When the cationic surfactants are added, the particle surface is recharged, the ζ-potential acquires the + values (5.3–7.8 mV). It has been concluded, that the rate of electroflotation removal of heavy metals from concentrated electrolyte solutions with the anionic HMS runs to 98–99% for all components. Subsequent solution filtration with the anionic flocculant allows for reduction of the residual concentration to the following values: 0.5∙10 -4 g/L for Fe (III), Cu (II) and Pb (II) ions and. 0.1∙10 -4 g/L for for Ni (II), 0.14∙10 -3 g/L for Zn (II). Addition of the cationic, non-ionic and amphoteric surfactants does not result in increase of electroflotation process efficiency.

Effects of Modification Degrees on the Colloidal Stability of Amphiphilic Janus Graphene Oxide in Aqueous Solution with and without Electrolytes.

Colloidal stability of modified graphene oxide (GO) is fundamental for its practical applications. Meanwhile, most of the investigations mainly focused on the nanosheets modified by a certain amount of modifiers and neglected the effects of the modification degree, which could vary the physical and chemical properties of modified GO and significantly affect its stability in solution. To the best of our knowledge, this study initially investigated the impact of modification degrees on the colloidal stability of graphene-based amphiphilic Janus nanosheets (JGO) via both experimental and theoretical approaches. The prepared JGO, asymmetrically grafted by dodecylamine, exhibited a direct relation between the modification degree and nanosheet thickness, refractive index, electrostatic properties, hydrophobicity, and the ultimate colloidal stability. In addition, the ionic strength imposed distinctive influences on the aggregation behavior of JGO. Based on the comparison between experimental results and theoretical calculation, it was revealed that the JGO should be modeled as two-dimensional (2D) nanosheets in pure water and be treated as 3D spherical particles in electrolyte solutions for the prediction with the extended Derjaguin-Landau-Verwey-Overbeek theory.

Hybrid density-potential functional theory of electric double layers

We present a field theoretic derivation for the free energy of the electrolyte solution. A reference system is introduced to describe non-electrostatic interactions, notably hard-sphere interactions, between charged particles in the electrolyte solution. The reference system is described by the Bikerman theory — a local density approximation, and the fundamental measure theory (FMT) — a nonlocal density approximation. Combining the classical part for charged particles in electrolyte solution and a quantum mechanical part for interacting electrons, we obtain a hybrid density-potential functional for the grand canonical potential of the electric double layer (EDL). Variation analysis of the hybrid density-potential functional leads to two controlling equations in terms of the electron density and the electric potential, respectively. Numerical implementation of the developed model is demonstrated for a simple EDL without specific adsorption. Particularly, oscillating density of counterions occurs near the metal surface when the FMT is used for the reference system.

Diffusiophoresis in Suspensions of Charged Soft Particles

The diffusiophoresis in a suspension of charged soft particles in electrolyte solution is analyzed. Each soft particle is composed of a hard core of radius r0 and surface charge density σ and an adsorbed fluid-penetrable porous shell of thickness a−r0 and fixed charge density Q. The effect of particle interactions is considered by using a unit cell model. The ionic concentration, electric potential, and fluid velocity distributions in a unit cell are solved as power expansions in σ and Q, and an explicit formula for the diffusiophoretic velocity of the soft particle is derived from a balance between the hydrodynamic and electrostatic forces exerted on it. This formula is correct to the second orders of σ and Q and valid for arbitrary values of κa, λa, r0/a, and the particle volume fraction of the suspension, where κ is the Debye screening parameter and λ is the reciprocal of a length featuring the flow penetration into the porous shell. The effects of the physical characteristics and particle interactions on the diffusiophoresis (including electrophoresis and chemiphoresis) in a suspension of charged soft particles, which become those of hard particles and porous particles in the limits r0=a and r0=0, respectively, are significant and complicated.

Reentrant crystallization of like-charged colloidal particles in an electrolyte solution: Relationship between the shape of the phase diagram and the effective potential of colloidal particles

The reentrant crystallization of like-charged colloidal particles in electrolyte solutions was studied to clarify the relationship between the shape of the phase diagram and the particle-particle effective potential. Coexisting densities were calculated at various electrolyte concentrations using the thermodynamic perturbation expansion method with effective one-component models. The effective potentials were obtained using an integral equation theory for liquids. Some model effective potentials were examined. The calculated results indicated that the reentrant behaviors of various acidic protein solutions observed in the experiments required not only the nonmonotonic dependence of the short-range attraction on the electrolyte concentration, but also the absence of a long repulsive tail.

Ionic equilibria and swelling of soft permeable particles in electrolyte solutions

We discuss osmotic equilibria between soft permeable particles, of radius R and volume charge density ρ, and bulk electrolyte solutions of inverse Debye length κ. Existing models are based on a simplified assumption of weakly charged particles. Here we derive analytical approximations for the distribution of potentials, ions and pressure in a system, suitable even when ρ is quite large. Our theory is valid not only for "large" particles (κR≫ 1), where the central part is fully screened, but also for weakly screened "small" particles (κR≤ 1) with overlapping inner diffuse layers. Besides, we present novel coarse-grained simulations to validate the analysis and illustrate the variation of potential/ion profiles in response to changes in κR and ρ. Our simulations also allow us to argue that swelling of both "large" and "small" particles is uniform, although their inner non-uniform local pressure profiles are essentially and qualitatively different. These results are directly relevant for a variety of permeable charged objects, from polymer micro- and nanogels to more rigid porous colloids.

Electrophoresis of spherical soft particles in electrolyte solutions: A review.

Theories on the electrophoresis of spherical soft particles suspended in an electrolyte solution are thoroughly reviewed. The review predominantly covers studies on the electrophoresis in dilute and concentrated suspensions as well as bounded media, carried out mainly during the past two decades. Moreover, studies on the electrostatics of soft particles are also surveyed. Finally, the research gaps and prospects of the electrophoresis of soft particles are presented.

Protein Translational Diffusion and Intermolecular Interactions of Globular and Intrinsically Unstructured Proteins.

The study of intermolecular interactions of proteins has been an important problem for many years. This paper presents an approach to analyze different levels of protein interactions in solutions through a set of the second- and higher-order virial coefficients. The proposed approach is based on the diversified analysis of protein translational collective diffusion and self-diffusion obtained by dynamic light scattering and the pulsed-field gradient NMR (PFG NMR) spectroscopy experimental data. The experimental results were analyzed within the theoretical approach based on Vink's frictional formalism of nonequilibrium thermodynamics and the standard Derjaguin-Landau-Verwey-Overbeekb (DLVO) theory of interactions of colloid particles in electrolyte solutions. The second- and higher-order virial coefficients were obtained to estimate the pairwise and many-body intermolecular interactions in the solutions of globular α-chymotrypsin and intrinsically unstructured αS-casein. The second virial coefficients were calculated from the model of the protein-protein potential of mean force. The description of protein-protein interactions includes a set of interaction potentials: the attractive charge-dipole, dipole-dipole, the dispersion Hamaker, the mean force osmotic-attraction, and the repulsive charge-charge ones. It has been found that the major contribution to the intermolecular αS-casein interactions is made by the repulsive charge-charge potential, whereas for the case of α-chymotrypsin, the contributions from other types of interaction are of importance. It was determined that the model was well suited to describe the interactions of both globular and intrinsically disordered proteins. The suggested combination of Vink's approach and the DLVO theory is novel and holds much promise to make a profound analysis of the processes in systems containing various types of protein molecules.

Identifying Single Particles in Air Using a 3D-Integrated Solid-State Pore.

Solid-state micro- and nanopores are a versatile sensor platform capable of detecting single particles in electrolyte solution by cross-pore ionic current. Here we report on a use of this technology to identify airborne particulate matter. The detection concept lies in an electrophoretic control of air-floating particles captured in liquid to deliver them into a pore detector via microfluidic channels. We demonstrate resistive pulse measurements to machine-learning-based discriminations of intragranular contents of cypress and cedar pollens at a single-particle level. This all-electrical-sensor technique would pave a new venue toward real-time monitoring of single particles and molecules in air.

A theory to determine the surface potentials of clay particles in electrolyte solutions

Surface potential, an important parameter at the interface between water and charged particles (such as clays and clay minerals), has a significant effect on a number of chemical and physical properties of particles. The existing theories used to estimate surface potential assume that the double layer medium is a continuous dielectric and the dielectric properties depend on the strong electric field produced by the particle surface charges. In the present study, the analytical relationships between the electric field strength and surface potentials were established based on the nonlinear Poisson-Boltzmann equation to examine the dielectric saturation, and then a new method to determine the surface potential was proposed. Surface potential can be determined using the derived equations from the electric field strength at the particle surface, which was calculated from the surface charge density. For a particle with surface charge density of 0.2C m−2, the surface potentials in 0.001 mol L−1 1:1 and 2:1 electrolytes determined by Gouy-Chapman model were respectively −242 and − 121 mV while those determined by the present method were respectively-286 and -143 mV. The above analyses showed that, due to the influence of dielectric saturation, the surface potential was underestimated using the Gouy-Chapman model for a continuous dielectric medium. The aggregate stability experiments showed that the amount of released small particles for montmorillonite aggregates in different electrolytes was a function of surface electrical potentials calculated based on dielectric saturation. The surface potential was approximate −115 mV for a 3.7% of released <10 μm particles in both KCl and CaCl2 electrolytes when dielectric saturation was taken into account. The surface electrical potentials calculated based on the new method explained the differences between the aggregate stability of clays in different electrolyte solutions.

Nonlocal statistical field theory of dipolar particles in electrolyte solutions

We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard–Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson–Boltzmann–Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the ‘Yukawa’-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.

Ionic Specificity in Rapid Coagulation of Silica Nanoparticles

The Smoluchowski theory has been widely accepted as the basic theory to estimate the rapid coagulation rate of colloidal particles in electrolyte solutions. However, because the size and specificity of molecules and ions are not taken into account, the theory is applicable only if the particle size is large enough to neglect the effects caused by the structured layers composed of water molecules, ions, and hydrated ions adsorbed on the colloidal surface. In the present study, the rapid coagulation rates of silica nanoparticles in concentrated chloride and potassium solutions were measured by using a low-angle light-scattering apparatus, and the dependence of the experimental value of rapid coagulation rate, KER, on the particle diameter, Dp, and also on the Gibbs free energy of hydration of ions, ΔGhyd, was investigated extensively. The following were found. (1) When the particle size was small enough, the value of KER reduced exponentially not only with the decreasing particle size but also with the increasing value of (-ΔGhyd) of cations (counterions) in the case of chloride solutions and with that of anions (coions) in the case of potassium solutions. (2) Silica nanoparticles of Dp ≲ 70 nm in 1 M KNO3 and KSCN solutions did not coagulate at all, although they coagulated at Dp ≳ 100 nm as in the other potassium solutions. These unexpected phenomena were explained by the proposed mechanisms.

Many-body interactions between charged particles in a polymer solution: the protein regime.

We study the phase behavior of charged particles in electrolyte solutions wherein non-adsorbing polymers are added to provide an attractive depletion interaction. The polymer has a radius of gyration similar to that of the particle radius, which causes significant many-body effects in the effective polymer mediated interaction between particles. We use a recently developed analytical theory, which gives a closed expression for the full depletion interaction, accounting for all orders of many-body terms in the potential of mean force. We compare with simulations of an explicit polymer model and show that the potential of mean force provides an accurate and computationally efficient description for the charged particle/polymer mixture, over a range of electrolyte concentrations. Furthermore, we demonstrate that the usual pair potential approach is highly inaccurate for these systems. A simple simulation method is used to estimate the limits of stability of the mixture. The pair approximation is shown to predict a much greater region of instability compared with the many-body treatment, due to its overestimation of the polymer depletion effect.

Dissolution of commercial nanoscale silica particles in electrolyte solution: The importance of the solid-solvent-ratio to physical and chemical properties of the solid-liquid interface

Dissolution experiments of silica nanoparticles (NPs) were performed in an aqueous TRIS buffer system (pH=7.6) at 25°C and the effect of the particles to solvent ratio (PSR) was studied. Increasing the PSR distinctly promotes the kinetic size effect described previously, which leads to solute concentrations exceeding the thermodynamic saturation concentration under the respective conditions considerably. The striking experimental observations readily are rationalized by analysis of the Gibbs free energy (GFE) of the system. In the extended model approach the dissolution and Ostwald ripening is described using gradient curves of GFE, which have been calculated considering a variable interfacial tension of the solid-liquid-interface, γ. The GFE analysis provides size, RP, and concentration, ZP, of NPs as a function of dissolution time. The variation of the interfacial tension with particle size, γ(RP), is a consequence of the properties of the electric double layer, surface charge and surface potential, around the NPs. Suggestions are made how to predict the dissolution process from properties of the initial system solid-solution. Any meaningful report of dissolution experiments should include the saturation concentration of the material that forms the NPs as thermodynamic criterion, and the time necessary to obtain half of the saturation concentration in the system considered as kinetic criterion. Both aforementioned criteria are accessible from experiments without any model considerations.

Influence of extracellular polymeric substances on the aggregation kinetics of TiO2 nanoparticles

The early stage of aggregation of titanium oxide (TiO2) nanoparticles was investigated in the presence of extracellular polymeric substance (EPS) constituents and common monovalent and divalent electrolytes through time-resolved dynamic light scattering (DLS). The hydrodynamic diameter was measured and the subsequent aggregation kinetics and attachment efficiencies were calculated across a range of 1–500 mM NaCl and 0.05–40 mM CaCl2 solutions. TiO2 particles were significantly aggregated in the tested range of monovalent and divalent electrolyte concentrations. The aggregation behavior of TiO2 particles in electrolyte solutions was in excellent agreement with the predictions based on Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Divalent electrolytes were more efficient in destabilizing TiO2 particles, as indicated by the considerably lower critical coagulation concentrations (CCC) (1.3 mM CaCl2 vs 11 mM NaCl). The addition of EPS to the NaCl and low concentration CaCl2 (0.05–10 mM) solutions resulted in a dramatic decrease in the aggregation rate and an increase in the CCC values. For solutions of 11 mM NaCl (the CCC values of TiO2 in the absence of EPS) and above, the resulting attachment efficiency was less than one, suggesting that the adsorbed EPS on the TiO2 nanoparticles led to steric repulsion, which effectively stabilized the nanoparticle suspension. At high CaCl2 concentrations (10–40 mM), however, the presence of EPS increased the aggregation rate. This is attributed to the aggregation of the dissolved extracellular polymeric macromolecules via intermolecular bridging, which in turn linked the TiO2 nanoparticles and aggregates together, resulting in enhanced aggregate growth. These results have important implications for assessing the fate and transport of TiO2 nanomaterials released in aquatic environments.

On the maximum of the magnitude of the electrophoretic mobility of a spherical colloidal particle in an electrolyte solution

The magnitude of the electrophoretic mobility μ of a spherical colloidal particle in an electrolyte solution with κa > 3 (κ = the Debye-Huckel parameter of the electrolyte solution and a = particle radius), when plotted as a function of the particle zeta potential ζ, exhibits a maximum μmax at ζ = ζmax. Analytic expressions applicable for large κa (κa ≥ 30) are derived for μmax and ζmax for a spherical particle in a symmetrical electrolyte solution. Analytic expressions for μmax and ζmax are also derived for a spherical particle in a 2:1 or 1:2 electrolyte solution. Finally, it is to be noted that μmax and ζmax for a cylindrical particle of radius a when the particle is oriented perpendicular to the applied electric field are the same as those for a spherical particle of radius a for large κa (κa ≥ 30).

Electric Interfacial Layer of Modified Cellulose Nanocrystals in Aqueous Electrolyte Solution: Predictions by the Molecular Theory of Solvation

The X-ray crystal structure-based models of Iα cellulose nanocrystals (CNC), both pristine and containing surface sulfate groups with negative charge 0-0.34 e/nm(2) produced by sulfuric acid hydrolysis of softwood pulp, feature a highly polarized "crystal-like" charge distribution. We perform sampling using molecular dynamics (MD) of the structural relaxation of neutral pristine and negatively charged sulfated CNC of various lengths in explicit water solvent and then employ the statistical mechanical 3D-RISM-KH molecular theory of solvation to evaluate the solvation structure and thermodynamics of the relaxed CNC in ambient aqueous NaCl solution at a concentration of 0.0-0.25 mol/kg. The MD sampling induces a right-hand twist in CNC and rearranges its initially ordered structure with a macrodipole of high-density charges at the opposite faces into small local spots of alternating charge at each face. This surface charge rearrangement observed for both neutral and charged CNC significantly affects the distribution of ions around CNC in aqueous electrolyte solution. The solvation free energy (SFE) of charged sulfated CNC has a minimum at a particular electrolyte concentration depending on the surface charge density, whereas the SFE of neutral CNC increases linearly with NaCl concentration. The SFE contribution from Na(+) counterions exhibits behavior similar to the NaCl concentration dependence of the whole SFE. An analysis of the 3D maps of Na(+) density distributions shows that these model CNC particles exhibit the behavior of charged nanocolloids in aqueous electrolyte solution: an increase in electrolyte concentration shrinks the electric interfacial layer and weakens the effective repulsion between charged CNC particles. The 3D-RISM-KH method readily treats solvent and electrolyte of a given nature and concentration to predict effective interactions between CNC particles in electrolyte solution. We provide CNC structural models and a modeling procedure for studies of effective interactions and the formation of ordered phases of CNC suspensions in electrolyte solution.