Recent advances in the electric double layer in colloid science

On the Validity of Constant pH Simulations

Constant pH (cpH) simulations are now a standard tool for investigating charge regulation in coarse-grained models of polyelectrolytes and colloidal systems. Originally developed for studying solutions with implicit ions, extending this method to systems with explicit ions or solvents presents several challenges. Ensuring proper charge neutrality within the simulation cell requires performing titration moves in sync with the insertion or deletion of ions, a crucial aspect often overlooked in the literature. Contrary to the prevailing views, cpH simulations are inherently grand-canonical, meaning that the controlled pH is that of the reservoir. The presence of the Donnan potential between the implicit reservoir and the simulation cell introduces significant differences between titration curves calculated for open and closed systems; the pH of an isolated (closed) system is different from the pH of the reservoir for the same protonation state of the polyelectrolyte. To underscore this point, in this paper, we will compare the titration curves calculated using the usual cpH algorithm with those from the exact canonical simulation algorithm. In the latter case, titration moves adhere to the correct detailed balance condition, and pH is calculated using the recently introduced surface Widom insertion algorithm. Our findings reveal a very significant difference between the titration isotherms obtained using the standard cpH algorithm and the canonical titration algorithm, emphasizing the importance of using the correct simulation approach when studying charge regulation of polyelectrolytes, proteins, and colloidal particles.

Canonical titration simulations

We present a Monte Carlo approach for performing titration simulations in the canonical ensemble. The standard constant pH (cpH) simulation methods are intrinsically grand canonical, allowing us to study the protonation state of molecules only as a function of pH in the reservoir. Due to the Donnan potential between a system and an (implicit) reservoir of a semi-grand canonical simulation, the pH of the reservoir can be significantly different from that of an isolated system, for an identical protonation state. The new titration method avoids this difficulty by using the canonical reactive Monte Carlo algorithm to calculate the protonation state of macromolecules as a function of the total number of protons present inside the simulation cell. The pH of an equilibrated system is then calculated using a new surface insertion Widom algorithm, which bypasses the difficulties associated with the bulk Widom particle insertion for intermediate and high pH values. To properly treat the long range Coulomb force, we use the Ewald summation method, showing the importance of the Bethe potential for calculating the pH of canonical systems.

A Gaussian field approach to the planar electric double layer structures in electrolyte solutions

In this work, the planar, electric, double-layer structures of non-polarizable electrodes in electrolyte solutions are studied with Gaussian field theory. A response function with two Yukawa functions is used to capture the electrostatic response of the electrolyte solution, from which the modified response function in the planar symmetry is derived analytically. The modified response function is further used to evaluate the induced charge density and the electrostatic potential near an electrode. The Gaussian field theory, combined with a two-Yukawa response function, can reproduce the oscillatory decay behavior of the electric potentials in concentrated electrolyte solutions. When the exact sum rules for the bulk electrolyte solutions and the electric double layers are used as constraints to determine the parameters of the response function, the Gaussian field theory could at least partly capture the nonlinear response effect of the surface charge density. Comparison with results for a planar electrode with fixed surface charge densities from molecular simulations demonstrates the validity of Gaussian field theory.

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.

Unveiling the detection kinetics and quantitative analysis of colorimetric sensing for sodium salts using surface-modified Au-nanoparticle probes

Rapid, reliable, and sensitive colorimetric detection has been regarded as a highly potential technique for visually monitoring the cation ions. Yet, insight into detection kinetics and quantitative analysis for colorimetric sensing of sodium ions has rarely been revealed. Herein, in-depth kinetic investigations of colorimetric detection using surface-modified Au-nanoparticle (AuNP) probes were performed for interpreting the correlation of salt concentration, reaction duration, and light absorbance. To envision these undisclosed issues, modification of AuNP surfaces with ascorbic acid was found to be highly essential for boosting the detection sensitivity due to adjusting the zeta potential of AuNP colloids towards a slightly positive value. Next, modeling the light absorbance of AuNPs under various aggregation circumstances was employed, which visually elucidated the color change so that it was visible to the naked eye, due to the intense field localization on the edges of aggregated AuNPs. In addition, the involved activation energy of AuNP aggregation was found to follow the first-order Arrhenius formula, with the extracted value of 22.5 kJ mol^-1. Finally, quantitative visualization of colorimetric Na⁺ ion sensing was realized, and the experimental relation was obtained for explicitly determining the unknown concentration of Na⁺ ions in a visual manner.

Thermodynamics of Electrolyte Solutions Near Charged Surfaces: Constant Surface Charge vs. Constant Surface Potential

Electric double layers are ubiquitous in science and engineering and are of current interest, owing to their applications in the stabilization of colloidal suspensions and as supercapacitors. While the structure and properties of electric double layers in electrolyte solutions near a charged surface are well characterized, there are subtleties in calculating thermodynamic properties from the free energy of a system with charged surfaces. These subtleties arise from the difference in the free energy between systems with constant surface charge and constant surface potential. In this work, we present a systematic, pedagogical framework to properly account for the different specifications on charged bodies in electrolyte solutions. Our approach is fully variational---that is, all free energies, boundary conditions, relevant electrostatic equations, and thermodynamic quantities are systematically derived using variational principles of thermodynamics. We illustrate our approach by considering a simple electrolyte solution between two charged surfaces using the Poisson--Boltzmann theory. Our results highlight the importance of using the proper thermodynamic potential and provide a general framework for calculating thermodynamic properties of electrolyte solutions near charged surfaces. Specifically, we present the calculation of the pressure and the surface tension between two charged surfaces for different boundary conditions, including mixed boundary conditions.

Pseudo-Laminarization of Mixed Microbubble Water and Complex Fluids in Capillary Flows

Symmetry in fluid flow is determined by external factors such as magnetic or electric fields. Owing to the electrical properties of fluids, liquids containing fine bubble or ionic surfactant molecules differ from the normal fluid flow. Therefore, the pressure drop and frictional coefficient in a pipe are measured and estimated for water alone, for mixed microbubble water (MB), and for complex fluids (anionic surfactant solution and polymer solution) in capillary flow with constant flow rate. For water alone, good agreement is obtained between the experimental and theoretical values for laminar Hagen–Poiseuille flow and the Blasius expression in turbulent flow. For the MB, pseudo-laminarization is suggested up to a Reynolds number of 4.2×103. Both the anionic surfactant solution and the polymer solution exhibit the same tendency as that of the MB. In explaining these behaviors, elasticity and electrical interaction are discussed, and electrical interaction on the capillary wall is strongly suggested to be a contributing factor. Additionally, surface tension is investigated and supports the discussion.

Kinetic Evidence That the Solvent Barrier for Electron Transfer Is Absent in the Electric Double Layer

Classical capacitance studies have revealed that the first layer of water present at an aqueous metal-electrolyte interface has a dielectric constant less than 1/10th of that of bulk water. Modern theory indicates that the barrier for electron transfer will decrease substantially in this layer; yet, this important prediction has not been tested experimentally. Here, we report the interfacial electron transfer kinetics for molecules positioned at variable distances within the electric double layer of a transparent conductive oxide as a function of the Gibbs free energy change. The data indicate that the solvent reorganization is indeed near zero and increases to bulk values only when the molecules are positioned greater than 15 Å from the conductive electrode. Consistent with this conclusion, lateral intermolecular electron transfer, parallel to a semiconducting oxide electrode, was shown to be more rapid when the molecules were within the electric double layer. The results provide much needed feedback for theoretical studies and also indicate a huge kinetic advantage for aqueous electron transfer and redox catalysis that takes place proximate to a solid interface.

Unraveling Chiral Selection in the Self-assembly of Chiral Fullerene Macroions: Effects of Small Chiral Components Including Counterions, Co-ions, or Neutral Molecules

Lactic acid-functionalized chiral fullerene (C₆₀) molecules are used as models to understand chiral selection in macroionic solutions involving chiral macroions, chiral counterions, and/or chiral co-ions. With the addition of Zn²⁺ cations, the C₆₀ macroions exhibit slow self-assembly behavior into hollow, spherical, blackberry-type structures, as confirmed by laser light scattering (LLS), transmission electron microscopy (TEM), and atomic force microscopy (AFM) techniques. Chiral counterions with high charge density show no selection to the chirality of AC₆₀ macroions (LAC₆₀ and DAC₆₀) during their self-assembly process, while obvious chiral discrimination between the assemblies of LAC₆₀ and DAC₆₀ is observed when chiral counterions with low charge density are present. Compared with chiral counterions, chiral co-ions show weaker effects on chiral selection with larger amounts needed to trigger the chiral discrimination between LAC₆₀ and DAC₆₀. However, they can induce a higher degree of discrimination when abundant chiral co-ions are present in solution. Furthermore, the self-assembly of chiral AC₆₀ macroions is fully suppressed by adding significant amounts of neutral molecules with opposite chirality. Thermodynamic parameters from isothermal titration calorimetry (ITC) reveal that chiral selection is controlled by the ion pairing and the destruction of solvent shells between ions, and meanwhile originates from the delicate balance between electrostatic interaction and molecular chirality.

Structure of electric double layers in capacitive systems and to what extent (classical) density functional theory describes it

Ongoing scientific interest is aimed at the properties and structure of electric double layers (EDLs), which are crucial for capacitive energy storage, water treatment, and energy harvesting technologies like supercapacitors, desalination devices, blue engines, and thermocapacitive heat-to-current converters. A promising tool to describe their physics on a microscopic level is (classical) density functional theory (DFT), which can be applied in order to analyze pair correlations and charge ordering in the primitive model of charged hard spheres. This simple model captures the main properties of ionic liquids and solutions and it predicts many of the phenomena that occur in EDLs. The latter often lead to anomalous response in the differential capacitance of EDLs. This work constructively reviews the powerful theoretical framework of DFT and its recent developments regarding the description of EDLs. It explains to what extent current approaches in DFT describe structural ordering and in-plane transitions in EDLs, which occur when the corresponding electrodes are charged. Further, the review briefly summarizes the history of modeling EDLs, presents applications, and points out limitations and strengths in present theoretical approaches. It concludes that DFT as a sophisticated microscopic theory for ionic systems is expecting a challenging but promising future in both fundamental research and applications in supercapacitive technologies.

Bimodal behaviour of charge carriers in graphene induced by electric double layer

A theoretical investigation is performed into the electronic properties of graphene in the presence of liquid as a function of the contact area ratio. It is shown that the electric double layer (EDL) formed at the interface of the graphene and the liquid causes an overlap of the conduction bands and valance bands and increases the density of state (DOS) at the Fermi energy (E_F). In other words, a greater number of charge carriers are induced for transport and the graphene changes from a semiconductor to a semimetal. In addition, it is shown that the dependence of the DOS at E_F on the contact area ratio has a bimodal distribution which responses to the experimental observation, a pinnacle curve. The maximum number of induced carriers is expected to occur at contact area ratios of 40% and 60%. In general, the present results indicate that modulating the EDL provides an effective means of tuning the electronic properties of graphene in the presence of liquid.

Dye synthesis in the Pechmann reaction: catalytic behaviour of samarium oxide nanoparticles studied using single molecule fluorescence microscopy

Photochemically prepared samarium oxide nanoparticles (Sm₂O₃NP) efficiently catalyze the formation of coumarin 153 via the Pechmann trans-esterification and condensation process. The formation of the fluorescent coumarin allowed the catalytic process to be monitored in real time at the single molecule level using Total Internal Reflection Fluorescence Microscopy (TIRFM). Benchtop experiments conducted in parallel demonstrated that the observed catalysis occurred in solution rather than by pure heterogeneous catalysis and is due to a mobile population of small Sm₂O₃NP released from a polydisperse original sample containing larger particles. TIRFM provided unique insights by demonstrating that catalysis by these smaller colloidal particles is in fact a surface process, while the larger particles are merely suppliers of the small catalytic nanostructures. We refer to this behaviour as a semi-heterogeneous catalytic system. This work showcases the opportunity that single molecule fluorescence techniques can offer in terms of understanding and ultimately improving benchtop and scaled-up synthesis. This specific example highlights the general applicability of this approach to the study of widely-utilized chemical reactions and lays the groundwork for researchers to adopt similar strategies in other systems.

Tailor-Made Core-Shell CaO/TiO2-Al2O3 Architecture as a High-Capacity and Long-Life CO2 Sorbent

CaO-based sorbents are widely used for CO2 capture, steam methane reforming, and gasification enhancement, but the sorbents suffer from rapid deactivation during successive carbonation/calcination cycles. This research proposes a novel self-assembly template synthesis (SATS) method to prepare a hierarchical structure CaO-based sorbent, Ca-rich, Al2O3-supported, and TiO2-stabilized in a core-shell microarchitecture (CaO/TiO2-Al2O3). The cyclic CO2 capture performance of CaO/TiO2-Al2O3 is compared with those of pure CaO and CaO/Al2O3. CaO/TiO2-Al2O3 sorbent achieved superior and durable CO2 capture capacity of 0.52 g CO2/g sorbent after 20 cycles under the mild calcination condition and retained a high-capacity and long-life performance of 0.44 g CO2/g sorbent after 104 cycles under the severe calcination condition, much higher than those of CaO and CaO/Al2O3. The microstructure characterization of CaO/TiO2-Al2O3 confirmed that the core-shell structure of composite support effectively inhibited the reaction between active component (CaO particles) and main support (Al2O3 particles) by TiO2 addition, which contributed to its properties of high reactivity, thermal stability, mechanical strength, and resistance to agglomeration and sintering.

Effects of image charges on double layer structure and forces

The study of the electrical double layer lies at the heart of soft matter physics and biophysics. Here, we address the effects of the image charges on the double layer structure and forces. For electrolyte solutions between two neutral plates, we show that depletion of the salt ions by the image charge repulsion results in short-range attractive and long-range repulsive forces. If cations and anions are of different valency, the asymmetric depletion leads to the formation of an induced electrical double layer. In comparison to a 1:1 electrolyte solution, both the attractive and the repulsive parts of the interaction are stronger for the 2:1 electrolyte solution. For two charged plates, the competition between the surface charge and the image charge effect can give rise to like-charge attraction and charge inversion. These results are in stark contrast with predictions from the Poisson-Boltzmann theory.

Block-copolymer-induced long-range depletion interaction and clustering of silica nanoparticles in aqueous solution

Small-angle neutron scattering (SANS) has been carried out to examine the block-copolymer-induced depletion interaction of charged silica nanoparticles in aqueous solution. The measurements have been performed on fixed concentrations (1 and 10 wt. %) of anionic Ludox silica nanoparticles having sizes of 8 and 16 nm in the presence of 0.1M NaCl and varying concentration of polyethylene oxide-polypropylene oxide-polyethylene oxide P85 [(EO)(26)(PO)(39)(EO)(26)] block copolymer. The presence of the block copolymer induces an attractive depletion interaction between charge-stabilized nanoparticles. The effective interaction of silica nanoparticles is modeled by a combination of two Yukawa potentials accounting for attractive depletion and repulsive electrostatic forces. The depletion interaction is found to be a long-range attraction whose magnitude and range increase with block-copolymer concentration. The depletion interaction is further enhanced by tuning the self-assembly of the block copolymer through the variation of temperature. The increase of the depletion interaction ultimately leads to clustering of nanoparticles and is confirmed by the presence of a Bragg peak in the SANS data. The positioning of the Bragg peak suggests simple-cubic-type packing of particles within the clusters. The scattering from the clusters in the low-Q region is governed by the Porod scattering, indicating that clusters are quite large (order of microns). The depletion interaction is also found to be strongly dependent on the size of the nanoparticles.

Dynamic Light Scattering Based Microelectrophoresis: Main Prospects and Limitations

Microelectrophoresis based on the dynamic light scattering (DLS) effect has been a major tool for assessing and controlling the conditions for stability of colloidal systems. However, both the DLS methods for characterization of the hydrodynamic size of dispersed submicron particles and the theory behind the electrokinetic phenomena are associated with fundamental and practical approximations that limit their sensitivity and information output. Some of these fundamental limitations, including the spherical approximation of DLS measurements and an inability of microelectrophoretic analyses of colloidal systems to detect discrete charges and differ between differently charged particle surfaces due to rotational diffusion and particle orientation averaging, are revisited in this work. Along with that, the main prospects of these two analytical methods are mentioned. A detailed review of the role of zeta potential in processes of biochemical nature is given too. It is argued that although zeta potential has been used as one of the main parameters in controlling the stability of colloidal dispersions, its application potentials are much broader. Manipulating surface charges of interacting species in designing complex soft matter morphologies using the concept of zeta potential, intensively investigated recently, is given as one of the examples. Branching out from the field of colloid chemistry, DLS and zeta potential analyses are now increasingly finding application in drug delivery, biotechnologies, physical chemistry of nanoscale phenomena and other research fields that stand on the frontier of the contemporary science. Coupling the DLS-based microelectrophoretic systems with complementary characterization methods is mentioned as one of the prosperous paths for increasing the information output of these two analytical techniques.

Additional considerations about the role of ion size in charge reversal

The effect of the ion size on the charge reversal process is studied via canonical Monte Carlo simulation. To this end, a primitive model of electrolyte is used to analyze the electric double layer formed by an asymmetric electrolyte in the presence of a charged planar wall. Different values of ion diameters and surface charge densities are used so as to determine the conditions at which the charge reversal first occurs. For each case, the apparent surface charge density is calculated as a function of the distance from the charged wall for the different electrolyte concentrations in order to establish the minimal salt concentration required for the charge reversal. We will refer to this electrolyte concentration as the reversal concentration and will show how it depends on the surface charge density and on the ion size. From the apparent surface charge density profiles, the distance from the wall at which the charge reversal arises as well as its intensity can be also inferred.

Attraction between weakly charged silica spheres at a water-air interface induced by surface-charge heterogeneity

We report an optical and atomic force microscopic (AFM) study of interactions between weakly charged silica spheres at a water-air interface. Attractive interactions are observed at intermediate interparticle distances and the amplitude of the attraction increases with the amount of salt (NaCl) added into the water phase. AFM images obtained in the salty water show the formation of patchy charge domains of size approximately 100 nm on the silica surface. The experiment suggests that surface heterogeneity produced during ionization plays an important role in the generation of attractions between like-charged particles at the interface.

Isn't self-assembly a misnomer? Multi-disciplinary arguments in favor of co-assembly

Self-assembly is a ubiquitous physicochemical phenomenon. It is inherent to molecular recognition effects in the biological domain, and thus presents a basis for understanding the constitution and dynamic organization of living beings. However, it is argued in this paper that the very notion of self-assembly presents an incorrect and misleading one for the physical effects that it stands for. Self-assembly presents a misnomer as each self-assembly process not only depends on, but also includes a certain degree of ordering in the immediate surrounding of the 'self-assembling' entities. Claims are provided to support the idea that every self-assembly process is, in fact, a co-assembly event, as it implies mutual changes and structuring of both the 'self-assembled' system and its nearest surrounding. This point of view is related to the systemic observation that there could be no physical qualities independent on the context of their existence. In order to illustrate that the concept of co-assembly presents only an instance of a more profound and systemic philosophy of life, the examples of the interplay between internal and external factors of development are provided from the fields of quantum and classical physics, biology, evolutionary theory and psychology.

Measured long-ranged attractive interaction between charged polystyrene latex spheres at a water-air interface

We report results of a systematic experimental study of interactions between charged polystyrene (PS) latex spheres at a water-air interface. Optical observations of stable bonded particle clusters and formation of circular chainlike structures at the interface demonstrate that the interaction potential is of dipole origin. Atomic force microscopy (AFM) is used to examine the distribution of charge groups on the colloidal surface. AFM phase images show patchy domains of size approximately 100 nm on the particle surface, indicating that the surface charge distribution of the PS spheres is not uniform, as is commonly believed. Such patchy charges can introduce fluctuating in-plane dipoles, leading to an attraction at short interparticle separations. A theoretical analysis is given to explain the mechanism for attractions between like-charged particles at the interface.

Like-charge attraction in confinement: myth or truth?

It is general wisdom that like-charged colloidal particles repel each other when suspended in liquids. This is in perfect agreement with mean field theories being developed more than 60 years ago. Accordingly, it was a big surprise when several groups independently reported long-ranged attractive components in the pair potential () of equally charged colloids. This so-called (LCA) was only observed in thin sample cells while the pair-interaction in unconfined suspensions has been experimentally confirmed to be entirely repulsive. Despite considerable experimental and theoretical efforts, LCA remains one of the most challenging mysteries in colloidal science. We experimentally reinvestigate the pair-potential () of charged colloidal particles with digital video microscopy and demonstrate that optical distortions in the particle's images lead to slightly erroneous particle positions. If not properly taken into account, this artefact pretends a minimum in () which was in the past misleadingly interpreted as LCA. After correcting optical distortions we obtain entirely repulsive pair interactions which show good agreement with linearized mean field theories.

Long-ranged attraction between charged polystyrene spheres at aqueous interfaces

We report an optical and atomic force microscopic study of interactions between charged polystyrene spheres at a water-air interface. Optical observations of bonded particle clusters and formation of circular chainlike structures at the interface demonstrate that the interaction potential is of dipole origin. Atomic force microscope phase images show patchy domains on the colloidal surface, indicating that the surface charge distribution is not uniform as is commonly believed. Such surface heterogeneity introduces in-plane dipoles, leading to an attraction at short interparticle distances.

Confinement-induced colloidal attractions in equilibrium

The Poisson-Boltzmann theory for colloidal electrostatic interactions predicts that charged colloidal spheres dispersed in water should repel each other, even when confined by charged surfaces. Direct measurements on highly charged polystyrene spheres, however, reveal strong, long-ranged confinement-induced attractions that have yet to be explained. We demonstrate that anomalous attractions also characterize the equilibrium pair potential for more weakly charged colloidal silica spheres sedimented into a monolayer above a glass surface. This observation substantially expands the range of conditions for which mean-field theory incorrectly predicts the sign of macroions' interactions, and provides new insights into how confinement induces long-ranged like-charge attractions.