Electrical Double Layer Interaction Research Articles

Nonlinear charge regulation for the deposition of silica nanoparticles on polystyrene spherical surfaces

HypothesisWe describe the deposition behavior of monodispersed silica nanoparticles on polystyrene spherical particles by using modified pairwise DLVO (Derjaguin-Landau-Verwey-Overbeek) interaction force profiles at pH values between two and twelve. Our modified model contains a new nonlinear charge regulation parameter that considers redistribution of ions, which allows us to realistically express the electrical double layer (EDL) interaction forces. ExperimentsSilanol-terminated silica nanoparticles (7.6 ± 0.4 nm), l-lysine-covered silica nanoparticles (7.8 ± 0.4 nm), and polyallylamine hydrochloride-covered polystyrene (PAH/PS) particles (348 ± 1 nm) were synthesized. Then, each type of silica nanoparticle was deposited on the PAH/PS particles at a range of pH values. FindingsOur new regulation parameter describes the realistic redistribution of charges governed by pH, total salt concentration, ionic strength of solution, and separation distance of particles. We find that this regulation parameter can be roughly approximated from the absolute values of theoretically calculated surface charge density and potential distributions, as well as experimentally measured ζ-potentials. Morphological analysis using electron microscopy of the experimental systems shows that the modified pairwise DLVO interaction forces exceptionally describe the deposition behavior of the silica nanoparticles physically adsorbed on the PAH/PS particle substrates.

Steric Interaction of Polyglycerol-Functionalized Detonation Nanodiamonds.

Detonation nanodiamonds have found numerous potential applications in a diverse array of fields such as biomedical imaging and drug delivery. Here, we systematically characterized non-functionalized and polyglycerol-functionalized detonation nanodiamond particles (DNPs) dispersed in aqueous suspensions at different ionic strengths (∼1.0 × 10-7 to 1.0 × 10-2 M) via dynamic light scattering and cryogenic transmission electron microscopy. For these colloidal suspensions, the total potential energies of interactions between a pair of DNPs were theoretically calculated using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory plus the fitting of the Boltzmann distribution to the interparticle spacing distribution of the colloidal DNPs. These investigations revealed that the non-functionalized DNPs are dispersed in aqueous media through the long-range (>10 nm) and weak (<7 kBT) electrical double-layer repulsive interaction, while the driving force on dispersion of polyglycerol-functionalized DNPs is mostly derived from the short-range (<2 nm) and strong (∼55 kBT) steric repulsive potential barrier generated by the polyglycerol. Moreover, our results show that the truly monodispersed and individually dispersed DNP colloids, forming no aggregates in aqueous suspensions, are available by both functionalizing DNPs by polyglycerol and increasing ionic strength of suspending media to ≳1.0 × 10-2 M.

Interfacial Polyelectrolyte-Surfactant Complexes Regulate Escape of Microdroplets Elastically Trapped in Thermotropic Liquid Crystals.

Polyelectrolytes adsorbed at soft interfaces are used in contexts such as materials synthesis, stabilization of emulsions, and control of rheology. Here, we explore how polyelectrolyte adsorption to aqueous interfaces of thermotropic liquid crystals (LCs) influences surfactant-stabilized aqueous microdroplets that are elastically trapped within the LCs. We find that adsorption of poly(diallyldimethylammonium chloride) (PDDA) to the interface of a nematic phase of 4-cyano-4'-pentylbiphenyl (5CB) triggers the ejection of microdroplets decorated with sodium dodecylsulfate (SDS), consistent with an attractive electrical double layer interaction between the microdroplets and LC interface. The concentration of PDDA that triggers release of the microdroplets (millimolar), however, is three orders of magnitude higher than that which saturates the LC interfacial charge (micromolar). Observation of a transient reorientation of the LC during escape of microdroplets leads us to conclude that complexes of PDDA and SDS form at the LC interface and thereby regulate interfacial charge and microdroplet escape. Poly(sodium 4-styrenesulfonate) (PSS) also triggers escape of dodecyltrimethylammonium bromide (DTAB)-decorated aqueous microdroplets from 5CB with dynamics consistent with the formation of interfacial polyelectrolyte-surfactant complexes. In contrast to PDDA-SDS, however, we do not observe a transient reorientation of the LC when using PSS-DTAB, reflecting weak association of DTAB and PSS and slow kinetics of formation of PSS-DTAB complexes. Our results reveal the central role of polyelectrolyte-surfactant dynamics in regulating the escape of the microdroplets and, more broadly, that LCs offer the basis of a novel probe of the structure and properties of polyelectrolyte-surfactant complexes at interfaces. We demonstrate the utility of these new insights by triggering the ejection of microdroplets from LCs using peptide-polymer amphiphiles that switch their net charge upon being processed by enzymes. Overall, our results provide fresh insight into the formation of polyelectrolyte-surfactant complexes at aqueous-LC interfaces and new principles for the design of responsive soft matter.

The role of small separation interactions in ferrofluid structure

Interparticle interactions in colloids are traditionally modeled by means of the DLVO theory, which includes van der Waals and electrical double layer (EDL) interactions However, the validity range limitations become critical in biocompatible magnetic colloids, requiring a more detailed description of the interactions, especially at small intersurface separations. As magnetic colloids, ferrofluids require an extended DLVO (XDLVO) model that includes magnetic interactions. Moreover, the nanoparticles of biocompatible ferrofluids are usually ionic-surfacted, such that their charged surfactants interact both electrically and sterically. In some of such particles, the charge is usually not located at the surface, but at the outer extremities of the surfactant molecules, and this feature restricts the EDL model validity to larger separation distances. We addressed this problem by means of a model proposed by Schnitzer and Morozov, which employs a generalized Derjaguin approximation that makes the EDL repulsion expression valid for all separations. The van der Waals expression of the DLVO theory is also problematic because it shows an unphysical divergence as the intersurface separation tends to zero, a problem that was circumvented by replacing the expression at small separations with another expression based on cohesion energy and the Born-Mayer repulsion. The modifications proposed here are of interest for research on colloids in general and our Monte Carlo simulations show that they acquire even greater importance when it comes to ferrofluids. The influence of magnetic interparticle interactions on the colloid structure is better gauged using these modifications, which prevent magnetic interactions from being obfuscated by artificially large van der Waals and EDL interactions. This conclusion makes the small separation treatment particularly important for the study of magnetic colloids.

Research progress on oil-water-rock interface interaction in micro-nano porous medium

Low/ultra-low permeability reservoirs have small pores, and the proportion of crude oil directly contacting with the rock and bound by the rock wall is much higher than that of conventional reservoirs, resulting in a large number of oil films difficult to be stripped. This seriously restricts the efficient development of low/ultra-low permeability reservoirs. The traditional adhesion work theory has limitations. A large number of crude oil in micro-nano pore throats is bound by the strong force of rock wall, and the adhesion force between oil film and rock becomes the main factor restricting the oil film peeling effect. This paper introduces the methods of analyzing oil-water-rock microscopic interaction by nanomechanics, such as atomic force microscope and molecular dynamics simulation. Focusing on oil-solid interface, the strong interaction between them is summarized. Nanomechanical analysis of the microscopic interface interactions among oil-water-rock shows that there are not only typical Derjaguin-Landau-Verwey Overbeek (DLVO) interactions (i.e., van der Waals and electrical double-layer interactions), but also non-DLVO interactions, such as hydrophobic and ion bridging interactions. This review focuses on the oil-rock interface interactions, summarizes recent research progress of the adhesion mechanism and the strong interaction between oil-rocks, discusses the challenges faced by efficient stripping of oil film and improving oil recovery in low permeability reservoirs. Finally, challenges and future prospects of this field are discussed.

Two-dimensional colloidal particle assembly in ionic surfactant solutions under an oscillatory electric field

Assembling colloidal particles under oscillatory electric field (OEF) has become an emerging bottom-up technique to synthesize advanced materials and fabricate micro/nano devices. Surfactants have often been used in colloidal dispersions to improve their stability. However, the precise role of surfactants in particle assembly processes under OEF is unknown. Here, we systematically study the effects of ionic surfactants on the colloidal particle assembly process subject to a fixed OEF, by using an anionic surfactant (sodium dodecyl sulfate) and a cationic surfactant (cetyltrimethylammonium bromide). In the concentration range below the critical micelle concentration (CMC), the particles tend to form three different aggregate structures, including randomly close-packed, hexagonally close-packed crystals, and randomly non close-packed structures. In the concentration range at CMC and above, the particles cannot assemble into any aggregate structures under the given OEF. With increasing surfactant concentration, the average interparticle separation distance within the aggregate can be regulated in a wide range. We qualitatively interpret the observed variation of particle assembly behaviors in different surfactant solutions based on the particle/particle interaction energy, implying that the repulsive electric double-layer interaction is significantly enhanced with increasing ionic surfactant concentration and hinders the particles approaching close to the high-energy barrier. These results suggest that the particle aggregate structure and interparticle separation distance of the two-dimensional colloidal assembly can be manipulated by controlling the ionic surfactant concentration according to the requirements of practical applications.

Electrokinetic Mechanisms and Synergistic Effect on Ion-Tuned Wettability in Oil-Brine-Rock Systems

Wettability alteration has been recognized as the dominant mechanism of ion-tuned waterflooding, where the ionic composition of injecting brine is modified to improve oil recovery. Yet mechanisms of ion-tuned wettability have not been fully understood, and there are ongoing debates over the effectiveness and relative contribution of each mechanism. In this paper, ion-tuned wettability in variable oil-brine-rock (OBR) systems over a wide range of ionic compositions is theoretically investigated, with focuses on two electrokinetic mechanisms, double layer expansion (DLE) and multicomponent ion exchange (MIE). Results indicate that the qualitative features of ion-tuned wettability in terms of DLE and MIE in various OBR systems with different surface properties can be divided into two typical types, depending on the electrical double layer (EDL) interaction being repulsive or attractive. With attractive EDL force, both DLE and MIE do not contribute to the water-wetness. While with repulsive EDL force, DLE only takes effect at relatively high concentration and MIE has a significantly larger impact at a low percentage of divalent cation. In addition, DLE and MIE can have a synergistic effect, where one mechanism alone has a negligible effect on wettability but two mechanisms combined have a big impact.

Electroosmotic flow: From microfluidics to nanofluidics.

Electroosmotic flow (EOF), a consequence of an imposed electric field onto an electrolyte solution in the tangential direction of a charged surface, has emerged as an important phenomenon in electrokinetic transport at the micro/nanoscale. Because of their ability to efficiently pump liquids in miniaturized systems without incorporating any mechanical parts, electroosmotic methods for fluid pumping have been adopted in versatile applications—from biotechnology to environmental science. To understand the electrokinetic pumping mechanism, it is crucial to identify the role of an ionically polarized layer, the so‐called electrical double layer (EDL), which forms in the vicinity of a charged solid–liquid interface, as well as the characteristic length scale of the conducting media. Therefore, in this tutorial review, we summarize the development of electrical double layer models from a historical point of view to elucidate the interplay and configuration of water molecules and ions in the vicinity of a solid–liquid interface. Moreover, we discuss the physicochemical phenomena owing to the interaction of electrical double layer when the characteristic length of the conducting media is decreased from the microscale to the nanoscale. Finally, we highlight the pioneering studies and the most recent works on electro osmotic flow devoted to both theoretical and experimental aspects.

Colloid Interaction Energies for Surfaces with Steric Effects and Incompressible and/or Compressible Roughness

Colloid aggregation and retention in the presence of macromolecular coatings (e.g., adsorbed polymers, surfactants, proteins, biological exudates, and humic materials) have previously been correlated with electric double layer interactions or repulsive steric interactions, but the underlying causes are not fully resolved. An interaction energy model that accounts for double layer, van der Waals, Born, and steric interactions as well as nanoscale roughness and charge heterogeneity on both surfaces was extended, and theoretical calculations were conducted to address this gap in knowledge. Macromolecular coatings may produce steric interactions in the model, but non-uniform or incomplete surface coverage may also create compressible nanoscale roughness with a charge that is different from the underlying surface. Model results reveal that compressible nanoscale roughness reduces the energy barrier height and the magnitude of the primary minimum at separation distances exterior to the adsorbed organic layer. The depth of the primary minimum initially alters (e.g., increases or decreases) at separation distances smaller than the adsorbed organic coating because of a decrease in the compressible roughness height and an increase in the roughness fraction. However, further decreases in the separation distance create strong steric repulsion that dominates the interaction energy profile and limits the colloid approach distance. Consequently, adsorbed organic coatings on colloids can create shallow primary minimum interactions adjacent to organic coatings that can explain enhanced stability and limited amounts of aggregation and retention that have commonly been observed. The approach outlined in this manuscript provides an improved tool that can be used to design adsorbed organic coatings for specific colloid applications or interpret experimental observations.

Ionic liquid assisted synthesis of h-MoO3 hollow microrods and their application for electrochemical sensing of Imidacloprid pesticide in vegetables

Herein, we demonstrate the ionic liquid (1-butyl-3-methylimidazolium bromide [BMIM]+ [Br]−) assisted solvo-hydrothermal synthesis of novel hexagonal MoO3 hollow microrods (h-MoO3 HRs). The h-MoO3 HRs were preferentially obtained through the formation of electric double layer and strong electrostatic interactions of ionic liquids with colloidal particles, including the electrons and ions. As-synthesized h-MoO3 HRs were further anchored on glassy carbon electrode (h-MoO3 HRs/GCE) and directly employed as a working electrode towards the electrochemical sensing of Imidacloprid (IMD) pesticide. The electrochemical response of IMD at h-MoO3 HRs/GCE was verified by cyclic voltammetry (CV) and differential pulse voltammetry (DPV). The h-MoO3 HRs/GCE electrode exhibited two distinct quasireversible redox couple towards IMD. From the CV and DPV, the sensitivity was calculated to be 2.02 × 10−1 A L mol−1 cm−2 and 1.39 × 10−1 A L mol−1 cm−2, respectively. Under optimal conditions, h-MoO3 HRs/GCE sense IMD with wide linear range of CV from 38.7 to 114 μM and from DPV 38.7 to 132 μM. The estimated detection limits from CV and DPV was calculated as 8.3 and 5.9 μM, respectively. In view of practical application, the proposed electrochemical sensor h-MoO3 HRs/GCE is successfully applied for the detection of IMD at low levels in vegetable samples.

Intermolecular and Surface Interactions in Engineering Processes

Interactions involving chemical reagents, solid particles, gas bubbles, liquid droplets, and solid surfaces in complex fluids play a vital role in many engineering processes, such as froth flotation, emulsion and foam formation, adsorption, and fouling and anti-fouling phenomena. These interactions at the molecular, nano-, and micro scale significantly influence and determine the macroscopic performance and efficiency of related engineering processes. Understanding the intermolecular and surface interactions in engineering processes is of both fundamental and practical importance, which not only improves production technologies, but also provides valuable insights into the development of new materials. In this review, the typical intermolecular and surface interactions involved in various engineering processes, including Derjaguin–Landau–Verwey–Overbeek (DLVO) interactions (i.e., van der Waals and electrical double-layer interactions) and non-DLVO interactions, such as steric and hydrophobic interactions, are first introduced. Nanomechanical techniques such as atomic force microscopy and surface forces apparatus for quantifying the interaction forces of molecules and surfaces in complex fluids are briefly introduced. Our recent progress on characterizing the intermolecular and surface interactions in several engineering systems are reviewed, including mineral flotation, petroleum engineering, wastewater treatment, and energy storage materials. The correlation of these fundamental interaction mechanisms with practical applications in resolving engineering challenges and the perspectives of the research field have also been discussed.

Measurements and analysis of xanthate chain length effect on bubble attachment to galena surfaces

Although available flotation experiments show that sulphide flotation recovery increases with increasing xanthate chain length, quantitative analysis to reveal the underlying mechanisms is missing. Herein, we investigate the chain length effect by using a recently developed attachment apparatus and an advanced theory to determine and validate the attachment time of air bubbles to galena surfaces in solutions of ethyl, propyl, butyl and amyl xanthate collectors. Specifically, the attachment time was accurately determined from either transient force curves or transient film thickness of the bubble-surface attachment. The theory was based on the film drainage theory and colloidal forces, which include the advanced multilayer dispersion (van der Waals) interactions and the electrical double-layer interaction. The multilayer dispersion theory has allowed us to describe the effect of galena hydrophobicity induced by the xanthate chain length in terms of interfacial gas enrichment (IGE) on the bubble-surface attachment. The experimental results show that the attachment time is greatly affected by both the hydrophobicity and the bubble size, and agree with the theoretical results. Critically, it was possible to accurately quantify the attachment time of the hydrophobised galena surfaces to bubbles using the measured transient force curves and the advanced multilayer dispersion theory incorporating the IGE layer. Finally, this study made it possible to explain the effect of the hydrophobicity and bubble size on attachment time and provides the principle for the attachment mechanism of hydrophobic minerals to air bubbles.

Electrical double layer interactions between soil colloidal particles: Polarization of water molecule and counterion

The electrical double layer (EDL) interactions strongly affect aggregation and dispersion of soil colloidal particles. In this research a modified model taking the polarization of water molecule and counterion into account was proposed based on nonlinear Poisson-Boltzmann theory to describe electrostatic interaction. The polarizations of both the counterion and the water molecule can increase the interaction between ion/water and soil particle surface, and then decrease the surface potential. Particle surface potential also depends on the surface separation when the EDL overlaps. The midpoint potential between colloidal particles decreases with increase of ion polarization but increases in the presence of water polarization through the change of the double layer thickness. Both the electrostatic repulsive pressure between soil particles and its force range increase markedly in the presence of the polarization of water molecules, but decrease with increase of counterion polarization. The water molecule polarization, rather than the counterion polarization, contributes more to EDL interactions. The counterion polarization is the origin of Hofmeister effects of the EDL interactions, which is affected by water polarization. The theoretical predicted force curve between clay particles by the modified model was verified by the experimental determination of surface force. In addition, the hydration force, fitted to a double exponential decay function, can be estimated by subtraction of the electrostatic interaction force based on DLVO theory from that based on the present model.

The Interaction between Cations in Saline Water and Calcium Bentonite in Copper Flotation

In this study, the effect of cations, Na+ and Mg2+, in saline water on copper flotation in the presence of calcium bentonite was investigated. It was found that as the concentration of NaCl was increased, the copper recovery initially decreased and then increased to above 99%, while the copper grade initially increased and then decreased. In contrast, as the concentration of MgCl2 was increased, the copper recovery continuously increased, while the copper grade continuously decreased. The variation of copper recovery and grade was mainly attributed to the synergistic effect of pulp rheology and flotation solution chemistry. The underpinning mechanisms are the compressing electrical double layer and ion-exchange interaction between saline water and bentonite, which occur at the same time. Using saline water slightly affected the pulp rheology with a decrease in copper recovery at low NaCl concentration. Increasing the concentration of cations in saline water might even facilitate the flowing out of exchangeable cations, especially divalent cations, from the interlayer space of bentonite to the solution, resulting in the decrease of copper grade at high salt concentration.

The Effect of Dissolved Gases on the Short-Range Attractive Force between Hydrophobic Surfaces in the Absence of Nanobubble Bridging.

The short-range attractive forces between hydrophobic surfaces are key factors in a wide range of areas such as protein folding, lipid self-assembly, and particle-bubble interaction such as in industrial flotation. Little is certain about the effect of dissolved (well-controlled) gases on the interaction forces, in particular in those systems where the formation of surface nanobubble bridges is suppressed. Here, we probe the short-range attractive force between hydrophobized silica surfaces in aqueous solutions with varying but well-controlled isotherms of gas solubility. The first contact approach force measurement method using AFM shows that decreasing gas solubility results in a decrease of the force magnitude as well as shortening of its range. The behavior was found to be consistent across all four aqueous systems and gas solubilities tested. Using numerical computations, we corroborate that attractive force can be adequately explained by a multilayer dispersion force model, which accounts for an interfacial gas enrichment (IGE), that results in the formation of a dense gas layer (DGL) adjacent to the hydrophobic surface. We found that the DGL on the hydrophobic surface is affected only by the concentration of dissolved gases and is independent of the salt type, used to control the gas solubility, which excludes the effect of electrical double-layer interactions on the hydrophobic force.

Gypsum-brine-dolomite interfacial interactions in the presence of scale inhibitor

The underlying mechanisms upon which chemical scale inhibitors (SIs) mitigate inorganic scale formation, as a major drawback of waterflooding, are of practical implications. The present study investigates interactions between gypsum precursors in contact with dolomite rock and brine from experimental, simulation, and theoretical stands point of view. The influence of various dominant parameters such as the presence of inhibitor, dolomite rock and brine salinity on the intermolecular interaction energies is investigated. The results show that with the use of SI, the electrical double-layer and Lewis acid-base interaction energies decrease whereas Lifshitz-van der Waals increases approximately one order of magnitude. Furthermore, based on the works of cohesion and adhesion, the used SI retards gypsum from getting precipitated then deposited almost 77% and 90%, respectively. In most cases also, the gypsum-scaled dolomite rock compared to the bare rock would be more prone to gypsum scaling.

ANALYSIS OF ELECTROSTATIC PROPERTIES OF POLYSTYRENE FOAM FILTRATION MEDIA

The relevance of research. The analysis of the aqueous suspension filtration initial stage through clean polystyrene foam filtration media carried out. Such feature of its work as hydro-sorting is considered. The degree of imbalance and interaction with other electrostatic systems in aqueous suspension determines the layer of potential-forming ions, which is formed around the core of the system. It determines system’s sign and most of the electrical double layer charge. It is usually determined using a physical quantity such as electrostatic or ζ-potential. The aim of this work is to determine the electrostatic properties of polystyrene foam granules and the degree of influence on the process of retaining various nature colloidal particles on their surface when filtering an aqueous suspension through them.&#x0D; Research results. The relationship between the sizes of polystyrene foam granules and the concentrations of electrostatic charge on their surface analyzed. Using the Poison-Boltzmann theory, a relationship between an electrostatic charge and an electric double layer of polystyrene foam granules in aqueous suspension showed. The importance of the ζ-potential researching for controlling of colloidal suspensions filtering process substantiated. The electrostatic properties of different morphology colloids studied. Analysis of research data confirms the hypothesis of a very close connection between the various morphologies colloids ζ-potential magnitude and their electric double layer interaction force with electric double layer of polystyrene foam granules in an aqueous suspension. This means that the polystyrene foam filter “charging” time is closely connected to the values of colloids ζ-potential in the filtered aqueous suspension.&#x0D; Conclusions. The initial filtration stage through clean polystyrene foam media is significantly different from the main stage of filtration due to the electrostatic interaction forces predominance. The time difference of the colloidal crusts complete formation completion on polystyrene foam granules of different diameters is so insignificant that it can be neglected and this time is considered the same for polystyrene foam granules of different diameters. Regardless of the origin nature, the retention intensity of the colloids by polystyrene foam filtration media granules and, consequently, the polystyrene filter “charging” time is directly depends on their z-potential value.&#x0D;

Revert Banding in One-Dimensional Periodic Precipitation of the (AgNO3 + KBr) System in Agar Gel.

A periodically precipitating system wherein interband distance successively decreases is known as revert Liesegang banding. The phenomenon is rare, and the underlying mechanism is implicit. In the present paper, the Liesegang system comprising of AgNO3 and KBr as the outer and inner electrolyte pair showing revert banding in agar gel by employing a 1D experimental setup is studied under varying concentrations of participating species. Revert banding was observed under all the experimental conditions. The concentrations of inner and outer electrolytes were found to play a major role in reverting since they build the ionic strength inside Liesegang tubes. We hypothesize that the band reverting is the interplay of van der Waals and electrical double-layer interactions, and hence classical DLVO (Derjaguin–Landau–Verwey–Overbeek) theory can be applied to interpret reverting. We propose that revert deposition of precipitates is the outcome of flocculation and peptization of sols, which is the manifestation of balancing attractive and repulsive interactions acting on colloidal particles responsible for band formation.

Pressure of active system under the electric double layer interaction

Self-driven particle systems consist of particles that can extract energy from the environment and transform into active motion, and thus are significantly different from the classical passive particle systems. For such an active system, the question of whether there is a classical equation of state (EOS) has caused spreading concern. Recent studies analyzed the validity of the EOS of an active system under the harmonic potential (Solon et. al, 2015 &lt;i&gt;Nature Physics&lt;/i&gt;, &lt;b&gt;11&lt;/b&gt; 673). In contrast, this paper explores the conditions for and the specific forms of the EOS of an active system under electric double-layer interaction between the wall and the particles. The results show that the wall pressure is related to the shape of the active particles. When a wall exerts a moment on the active particles, the particles orientation turns to the equilibrium state parallel to the wall surface under the action of the moment, and the increase of the wall-particle interaction strength enhances the parallel-orientation trend, which reduces the system pressure. The association of pressure and wall means that the active system does not have a general equation of state. In the case where the wall-particle interaction intensity is extremely small or extremely large, by defining the effective temperature, the active system has an equation of state similar to that of the ideal gas. In addition, it is found that the extent of the shape of particles deviating from the rotational symmetry is a key factor affecting the pressure of active particles. The research results provide a reference for the study of the current active system equilibrium properties, and provide a basis for studying the thermodynamic properties of active systems under more complex interaction potentials.

Enzyme Immobilization Behavior on the Surface of Hydroxyapatite Capsules under Alkaline Condition

We prepared hydroxyapatite (HA) capsules encapsulating maghemite particles. In order to evaluate enzyme immobilization behavior of the HA capsules under alkaline condition, we immobilized five kinds of enzymes with different isoelectric point in carbonate/bicarbonate buffer (CBB, pH 10.0). When the enzymes in CBB were moderately charged, immobilization efficiency on the HA capsules showed the highest value. It was suggested that immobilization efficiency was affected according to both pI of enzyme and pH of the surrounding solution and that enzyme immobilized on the HA capsules by not only electrical double layer interactions but also ion interaction and other interactions.