Reduction Of Surface Potential Research Articles

Osteogenic Potential and Long-Term Enzymatic Biodegradation of PHB-based Scaffolds with Composite Magnetic Nanofillers in a Magnetic Field.

Millions of people worldwide suffer from musculoskeletal damage, thus using the largest proportion of rehabilitation services. The limited self-regenerative capacity of bone and cartilage tissues necessitates the development of functional biomaterials. Magnetoactive materials are a promising solution due to clinical safety and deep tissue penetration of magnetic fields (MFs) without attenuation and tissue heating. Herein, electrospun microfibrous scaffolds were developed based on piezoelectric poly(3-hydroxybutyrate) (PHB) and composite magnetic nanofillers [magnetite with graphene oxide (GO) or reduced GO]. The scaffolds' morphology, structure, mechanical properties, surface potential, and piezoelectric response were systematically investigated. Furthermore, a complex mechanism of enzymatic biodegradation of these scaffolds is proposed that involves (i) a release of polymer crystallites, (ii) crystallization of the amorphous phase, and (iii) dissolution of the amorphous phase. Incorporation of Fe3O4, Fe3O4-GO, or Fe3O4-rGO accelerated the biodegradation of PHB scaffolds owing to pores on the surface of composite fibers and the enlarged content of polymer amorphous phase in the composite scaffolds. Six-month biodegradation caused a reduction in surface potential (1.5-fold) and in a vertical piezoresponse (3.5-fold) of the Fe3O4-GO scaffold because of a decrease in the PHB β-phase content. In vitro assays in the absence of an MF showed a significantly more pronounced mesenchymal stem cell proliferation on composite magnetic scaffolds compared to the neat scaffold, whereas in an MF (68 mT, 0.67 Hz), cell proliferation was not statistically significantly different when all the studied scaffolds were compared. The PHB/Fe3O4-GO scaffold was implanted into femur bone defects in rats, resulting in successful bone repair after nonperiodic magnetic stimulation (200 mT, 0.04 Hz) owing to a synergetic influence of increased surface roughness, the presence of hydrophilic groups near the surface, and magnetoelectric and magnetomechanical effects of the material.

The effect of ions on liquid-solid interface investigated by charge sensitive direct current droplet-based electricity generator

The contact electrification (CE) between DI water and SiO2 or fluorinated polymer has been proven to be mainly due to electron transfer, which is significantly influenced by ions in solution. However, how these ions in water affect the charge transfer at the liquid-solid (L-S) interface is still unresolved, especially for the already charged friction layer. Here, a direct current droplet-based electricity generator (DC-DEG) which is sensitive to the change of charge transfer at the L-S interface is adopted to detect the effects of ions in the neutral salt solution on the charged PTFE surface. The distribution of ions on the charged L-S interface (the change of electric potential on the solid surface) and its effects on the output of DC-DEGs have been studied. The results indicate that the charge transfer of droplets and then the output of DC-DEGs are closely related to the concentrations of salt solutions. Anions can enhance the surface potential of PTFE due to their adsorptions on PFTE while cations can reduce it due to their screen effect. At low ionic concentrations, the surface potential enhancement caused by anion adsorption is larger than that surface potential reduction caused by screen effect from cations. At high ionic concentrations, the electrostatic screen effect of cations increases a lot to weaken the surface potential and reducing the charge separation of droplets induced by electrostatic induction (EI). This work explains the redistribution process of ions at the L-S interface and also provides a clever solution for improving the electrical output performance of DEGs.

Guanidinium-Functionalized Polymer Dielectrics for Triboelectric Bacterial Detection.

Development of rapid detection strategies that target potentially pathogenic bacteria has gained increasing attention due to the increasing awareness for better health and safety. In this study, we evaluate an intrinsically antimicrobial polymer, 2Gdm, which is a poly(norbornene)-based functional polymer featuring guanidinium groups as side chains, for bacterial detection by the means of triboelectric nanogenerators (TENGs) and triboelectric nanosensors (TENSs). Attachment of bacteria to the sensing layer is anticipated to alter the overall triboelectric properties of the underlying polymer layer. The positively charged guanidinium functional groups can interact with the negatively charged phospholipid bilayer of bacteria and lead to bacterial death, which can then be detected by optical microscopy, X-ray photoelectron microscopy, and more advanced self-powered sensing techniques such as TENGs and TENSs. The double bonds present along the poly(norbornene) backbone allow for thermally induced cross-linking to obtain X-2Gdm and thus rendering materials remain stable in water. By monitoring the change in voltage output after immersion in various concentrations of Gram-negative Escherichia coli (E. coli) and Gram-positive Streptococcus pneumoniae (S. pneumoniae), we have demonstrated the utility of X-2Gdm as a new polymer dielectric for autonomous bacterial detection. As the bacterial concentration increases, the amount of adsorbed bacteria also increases, resulting in a decrease in the surface potential of the X-2Gdm thin film; this reduction in surface potential can cause a decrease in the triboelectric output for both TENGs and TENSs, which serves as a key working mechanism for facile bacterial detection. TENG and TENS systems are capable of detecting E. coli and S. pneumoniae within a range of 4 × 105 to 4 × 108 CFU/mL with a limit of detection of 106 CFU/mL. This report highlights the promising prospects of employing TENGs and TENSs as innovative sensing technologies for rapid bacterial detection by leveraging the electrostatic interactions between bacterial cell membranes and cationic groups present on polymer surfaces.

Rapid Escherichia coli Cloned DNA Detection in Serum Using an Electrical Double Layer-Gated Field-Effect Transistor-Based DNA Sensor.

In this study, a rapid diagnosis platform was developed for the detection of Escherichia coli O157:H7. An electrical double layer (EDL)-gated field-effect transistor-based biosensor (BioFET) as a point-of-care testing device is demonstrated with its high sensitivity, portability, high selectivity, quick response, and ease of use. The specially designed ssDNA probe was immobilized on the extended gate electrode to bind the target complementary DNA segment of E. coli, resulting in a sharp drain current change within minutes. The limit of detection for target DNA is validated to a concentration of 1 fM in buffer solution and serum. Meanwhile, the results of a Kelvin probe force microscope were shown to have reduced surface potential of the DNA immobilized sensors before and after the cDNA detection, which is consistent with the decreased drain current of the BioFET. A 1.2 kb E. coli duplex DNA synthesized in plasmid was sonicated and detected in serum samples with the sensor array. Gel electrophoresis was used to confirm the efficiency of sonication by elucidating the length of DNA. Those results show that the EDL-gated BioFET system is a promising platform for rapid identification of pathogens for future clinical needs.

Chemical Dopant‐Free Doping by Annealing and Electron Beam Irradiation on 2D Materials

AbstractDoping is a key technique for forming complementary metal‐oxide‐semiconductor (CMOS) that is a basic building block for current state‐of‐the‐art semiconductor devices. However, conventional doping methods such as ion implantation are unsuitable for 2D materials due to their ultra‐thinness to accommodate substitutionally doped atomic structures and vulnerability to high energy ion bombardment. Chemical doping methods have been widely used for 2D materials to induce a charge exchange transfer; however, they are subjected to surface contamination which can be detrimental for high quality semiconductor device processing. In this work, the authors reveal the effects of chemicals‐free doping in which annealing induces a p‐doping effect by physisorption and substitution of oxygen atoms while electron beam irradiation selectively n‐dopes MoTe2, based on the results obtained by electrical characterization and Kelvin probe force microscopy. The annealing increases work‐function of MoTe2 which undergoes oxidation as observed in the reduction of surface potential and the transition of transfer curves toward the p‐type behavior. Electrical measurements and a significant reduction in surface potential after electron beam irradiation indicate the generation of trapped charges which is responsible for the n‐doping effect. Subsequently, the authors fabricate a CMOS inverter consisting of distinctively p‐ and n‐doped areas of MoTe2.

Field emission of GaN nanofilms on Si substrates enhanced by hydrogen plasma treatment

The (002) oriented GaN nanostructured films prepared by pulsed laser deposition (PLD) on n-type Si (100) substrates were treated by H- and O-plasma, finding both treatments do not make the sizable changes in crystalline structure and morphology of GaN nanofilms. However, the field emission (FE) performance of GaN nanofilms is considerably improved by H-plasma treatment (H-GaN) but deteriorated by O-plasma treatment (O-GaN). The turn-on fields, Eon, for H- and O-plasma treated GaN nanofilms are determined to be 0.52 and 1.79 V μm−1, respectively, in contrast with that of pristine GaN nanofilms, 0.95 V μm−1. The improvement of FE performance by the H-plasma treatments could be attributed to the reasons of the reduced surface potential barrier, the increased electron concentration, the increased surface conductivity, and the increased effective emission area. The first-principles calculations represents that the experimental and theoretical work function results have the same trend with the descending sequence of O-plasma treated GaN > pristine GaN > the H-plasma treated GaN.

Uncovering topographically hidden features in 2D MoSe2 with correlated potential and optical nanoprobes

Developing characterization strategies to better understand nanoscale features in two-dimensional nanomaterials is of crucial importance, as the properties of these materials are many times driven by nanoscale and microscale chemical and structural modifications within the material. For the case of large area monolayer MoSe2 flakes, kelvin probe force microscopy coupled with tip-enhanced photoluminescence was utilized to evaluate such features including internal grain boundaries, edge effects, bilayer contributions, and effects of oxidation/aging, many of which are invisible to topographical mapping. A reduction in surface potential due to n-type behavior was observed at the edge of the flakes as well as near grain boundaries. Potential phase mapping, which corresponds to the local dielectric constant, depicted local biexciton and trion states in optically-active regions of interest such as grain boundaries. Finally, nanoscale surface potential and photoluminescence mapping was performed at several stages of oxidation, revealing that various oxidative states can be evaluated during the aging process. Importantly, all of the characterization performed in this study was non-destructive and rapid, crucial for quality evaluation of an exciting class of two-dimensional nanomaterials.

Charge transfer in SnS2/Na0.9Mg0.45Ti3.55O8 heterojunction in photocatalytic process

SnS2/Na0.9Mg0.45Ti3.55O8 (SNMTO) composite photocatalyst was synthesized by a hydrothermal method. The chemical combination in lattice scale between SnS2 and Na0.9Mg0.45Ti3.55O8 (NMTO) was observed by high-resolution transmission electron microscopy, indicating that heterojunctions were obtained between SnS2 and NMTO. The photocatalytic activity of SNMTO heterojunctions was improved in comparison with that of pure NMTO and SnS2 for the photocatalytic degradation of methylene blue and Rhodamine B. Electrons were excited in n-type semiconductors NMTO and SnS2 under light illumination, and a part of them moved to the interface, determined with the surface potential reduction observed directly by Kelvin probe force microscopy. The charge redistribution in the composite illustrates a high density of interface states between SnS2 and NMTO, which attract lots of photoelectrons, as a result enhancing the photocatalytic performance. This finding is very different from the speculation that the photogenerated electrons and holes migrate from one part to another because it is difficult for charge carriers to travel through the interface with high energy.

Study of surface complexation modeling on a novel hybrid enhanced oil recovery (EOR) method; smart-water assisted foam-flooding

This contribution focuses on surface complexes in the calcite-brine-surfactant system. This is relevant for the recovery of oil when using a new hybrid enhanced oil recovery (EOR) method, which combines smart-water (i.e., ionically modified brine) and foam-flooding (SWAF) of light oil with dissolved carbon dioxide (CO2) at high pressure in carbonate (i.e., calcite) reservoirs. Using this new hybrid EOR-method (i.e., the SWAF-process) is not only economically attractive (i.e., it reduces opex costs) but also enhances the effectiveness of the production process, and thus reduces the environmental impact. Ionically modified brine (i.e., low-salinity) has a dual improvement effect. It not only leads to more stable foam lamellae, but also helps to change the carbonate rock wettability, leading for some conditions to more favorable relative permeability behavior. The mechanism for the modified permeability behavior in the presence of ionically modified brine is only partly understood. Therefore, we study this process initially in a zero dimensional (thermodynamics) setting, which can be used for the one dimensional (1D) displacement process with an oleic phase that contains carbon dioxide (CO2) and an aqueous phase that contains both carbon dioxide (CO2) and all the ionic substances. Using DLVO theory and surface complexation modeling to better understand the mechanism(s) of ionically modified brine as wettability modifier and foam stabilizer. We perform simulations using both (NaCl) and (MgCl2) to show the effect of a divalent ion at the high-salinity (8500 mmol/kg-w) and low-salinity (0.4 mmol/kg-w) for both ambient-conditions at (25°C) and at the reservoir-conditions (80°C). We confine our analysis to a description that uses the Dzombak-Morel model of surface complexes, which is based on the Debye-Hückel theory (i.e., valid up to ionic strength of 0.3 (mol/kilogram of water)). We also investigate the effect of carbon dioxide (CO2) on the stability of low-salinity foam-laminae. We model the foam-laminae, which contain as surface complex a (cationic) surfactant in an aqueous phase. We use the PHREEQC-software to calculate the surface charge and the surface potential. The presence of a carbon dioxide (CO2) phase leads to dissolution of four valent C(IV) compounds in the aqueous film. PHREEQC also calculates the equilibrium concentrations and surface potential and allows the study of the effect of salinity and the carbon dioxide (CO2) gas pressure. For the soap-film (foam-film) in a carbon dioxide (CO2) atmosphere we do use Pitzer activity coefficients (i.e., valid up to 6 (mol/kilogram of water)). As our aim is to show the methodology and the versatility of this approach, we leave more realistic choices of these parameters for future work.sFor the conditions considered we can qualitatively state that, in the presence of (NaCl i.e., at pH > 10) and (MgCl2 i.e., pH > 10.3), the low-salinity case shows a more stable water-film behavior at (25°C) and at (80°C) than the high-salinity case for both (25°C) and (80°C). Moreover, high carbon dioxide (CO2) pressures have a destabilizing effect on the film, as they reduce the surface potential. A reduced surface potential leads to a decreasing electrostatic double layer repulsion and thus destabilizes the foam-film, whereas low-salinity leads to less screening of the surface potential and thus improves the stability of the foam-film. The low-salinity flow is characterized by a high residual oil saturation and low end-point permeability for the two phase oil-water flow. This leads to a more favorable mobility ratio and thus a more favorable displacement process. For the calcite surface an enhanced stability helps to stabilize the water film on the calcite surface if the oil-water surface charge has the same sign as the surface charge on the calcite surface. Our calculations show the pH range where the sign of these charges is the same or opposite at low-salinity and high-salinity conditions. Admittedly these calculations only show trends, but can be used to delineate optimal conditions for the application of “Smart Water Assisted Foam (SWAF) Flooding”. It is expected that the SWAF-process under the optimum conditions will make the proposed new hybrid Enhanced Oil Recovery (EOR) process environmentally and economically attractive.

Tunable Optoelectronic Properties of WS2 by Local Strain Engineering and Folding

AbstractLocal strain engineering is an exciting approach to tune optoelectronic properties of materials. Two‐dimensional (2D) materials such as 2D transition metal dichalcogenides (TMDs) are particularly well‐suited for this purpose due to their high flexibility and deformability. Local strain engineering in 2D TMDs is typically achieved via strained wrinkles. Wrinkles on thick TMD layers have been reported to show interesting photoluminescence enhancement due to bandgap modulation and funneling effect. However, the wrinkles in ultrathin TMDs are not investigated because they can easily fall down to form folds. Both wrinkles and folds are achieved simultaneously in 1–3L tungsten disulfide (WS2) using a new fabrication technique. A layer‐dependent reduction in surface potential is found for both folded layers and perfect packed layers due to the dominant interlayer screening effect. The strain produced from the wrinkles modulates the semiconductive junction properties significantly. Thermoionic modeling suggests that strained (1.6%) wrinkles can lower the Schottky barrier height (SBH) by 20%. Upon illumination, SBH reduces significantly due to photogenerated carriers. This is an important advance toward controlling the optoelectronic properties of 2D TMDs via strain engineering, with applications for electronics and optoelectronics devices.

Oxidation facilitated antimicrobial ability of laser micro-textured titanium alloy against gram-positive Staphylococcus aureus for biomedical applications

Micro-textures were engineered on titanium samples by a rapid, highly repeatable, and cost effective nanosecond laser texturing process. The controlled and repeatable micro-texture was effective in the reduction of adhesion and proliferation of Staphylococcus aureus. However, the adhesion and proliferation of human bone marrow mesenchymal stem cells were found unaffected. The authors observed time-delayed saturation of oxidation on laser micro-textured Ti6Al4V as compared to pristine material yielding a super-hydrophobic surface (contact angle of ∼158.2°). An in-house setup was designed to expose a three-dimensionally laser micro-textured Ti6Al4V sample to S. aureus-spiked nutrient broth for 24 h in a closed loop continuous flow system. The authors observed a 50% reduction of S. aureus adhesion and proliferation over the laser micro-textured surface compared to pristine samples. In vitro tests confirmed that blood coagulation remains largely unaffected, while protein adsorption was decreased by fourfold on the micro-textured surfaces, a desirable property for surgical tools. Nanosecond laser micro-textured surfaces were effective in reducing S. aureus adhesion and its proliferation due to phase evolution, oxidative transformation of Ti6Al4V, and reduction of surface potential. In addition, laser based micro-texturing is a nontoxic, environment friendly green process that is also a cost effective alternative to conventional surface modification techniques such as mechanical micromachining and chemical treatments.

Вплив температури та іонної сили середовища на поверхневий потенціал еритроцитів людини

During freezing of cell suspensions the ionic strength of extracellular and, subsequently, intracellular media is responsible for the changes in membrane potential of cells. In this research we revealed the temperature and concentration dependencies of the surface potential of human erythrocytes during freezing of the cell suspension at the points corresponding to the values of temperature and 1:1 concentration of the electrolyte according to the phase diagram of a water-NaCl binary system. The concentrations of sodium ions on the surface of erythrocytes depending on concentration and temperature of the bulk solution were determined. It has been shown that the concentration of sodium ions on the surface of cells was 1.5 times higher than that in the bulk solution. The kink of surface potential temperature dependence for human erythrocytes for 0.15 and 0.3 M concentrations of 1:1 electrolyte within 8...12°C temperature range was of special interest. This temperature dependence feature of the surface potential calculated for the charged surface with a particular surface charge density from the purely physical considerations without taking into account the structure and composition of the surface could be one of the causes of rearrangements in membrane at these temperatures. Misbalance of electrostatic interactions on the surface of membrane outer monolayer appeared as a result of an increased concentration of counterions on the surface of cells and correspondingly the reduced surface potential might trigger the rearrangements and changes in relationships between membrane protein and lipid components.Probl Cryobiol Cryomed 2017; 27(1): 19–28Â

Direct observation of localized surface plasmon field enhancement by Kelvin probe force microscopy

A surface plasmon (SP) is a fundamental excitation state that exists in metal nanostructures. Over the past several years, the performance of optoelectronic devices has been improved greatly via the SP enhancement effect. In our previous work, the responsivity of GaN ultraviolet detectors was increased by over 30 times when using Ag nanoparticles. However, the physics of the SP enhancement effect has not been established definitely because of the lack of experimental evidence. To reveal the physical origin of this enhancement, Kelvin probe force microscopy (KPFM) was used to observe the SP-induced surface potential reduction in the vicinity of Ag nanoparticles on a GaN epilayer. Under ultraviolet illumination, the localized field enhancement induced by the SP forces the photogenerated electrons to drift close to the Ag nanoparticles, leading to a reduction of the surface potential around the Ag nanoparticles on the GaN epilayer. For an isolated Ag nanoparticle with a diameter of ~200 nm, the distribution of the SP localized field is located within 60 nm of the boundary of the Ag nanoparticle. For a dimer of Ag nanoparticles, the localized field enhancement between the nanoparticles was the strongest. The results presented here provide direct experimental proof of the localized field enhancement. These results not only explain the high performance of GaN detectors observed with the use of Ag nanoparticles but also reveal the physical mechanism of SP enhancement in optoelectronic devices, which will help us further understand and improve the performance of SP-based optoelectronic devices in the future.

NC60 deposition kinetics: the complex contribution of humic acid, ion concentration, and valence

The demonstrated toxicity coupled with inevitable environmental release of nC60 raise serious concerns about its environmental fate and transport, therefore it is crucial to understand how nC60 will interact with subsurface materials including attached phase soil and sediment organic matter (AP-SOM). This study investigated the attachment of nC60 onto a Harpeth humic acid (HHA) coated silica surface under various solution conditions using a quartz crystal microbalance with dissipation monitoring. The HHA coating greatly enhanced nC60 attachment at low ion concentrations while hindering attachment at high ion concentrations in the presence of both mono and divalent cations. At low ion concentrations, the HHA greatly reduced the surface potential of the silica, enhancing nC60 deposition through reduction in the electrostatic repulsion. At high ion concentrations however, the reduced surface potential became less important due to the near zero energy barrier to deposition and therefore non-DLVO forces dominated, induced by compaction of the HHA layer, and leading to hindered attachment. In this manner, observed contributions from the HHA layer were more complex than previously reported and by monitoring surface charge and calculated DLVO interaction energy alongside attachment experiments, this study advances the mechanistic understanding of the variable attachment contributions from the humic acid layer.

Foamability of sodium dodecyl sulfate solutions: Anomalous effect of dodecanol unexplained by conventional theories

Conventional theories indicate that surfactant solutions with low surface tension, fast adsorption kinetics, and high interfacial viscoelasticity increase foamability. These theories are applicable to single surfactants of pre-CMC. Here, we examine whether these theories are applicable for surfactant mixtures. Specifically, we investigated the foamability of sodium dodecyl sulfate (SDS)-dodecanol (DOH) solutions. We found that the foamability of SDS–DOH solutions exhibited ‘anomalies’ that were unexplained by conventional theories. The remarkable decrease in the foamability of SDS solutions caused by the addition of DOH could not be easily explained by the theories of surface tension and surface viscoelasticity. Instead, we proposed alternative mechanisms to resolve these unexpected results. Below the DOH solubility limit, the replacement of SDS molecules by DOH molecules at the air–water interface results in a reduced surface potential, leading to a lower foamability. The antifoam effects of DOH droplets can account for the reduced foamability above this limit. This paper highlights the complex effect of surfactant mixtures on foamability.

Fabrication and X-ray photoemission characteristics of Au spherical shell photocathodes

Gold spherical shell photocathode was prepared by seed-mediated growth on polystyrefle template and dispersed on the aluminum substrates by spin-coating procedure. Polystyrefle template was then removed by heat treatment. SEM surface morphology shows that Au spherical shell of ～10 μm in diameter can be self-supported after polystyrefle substrate is removed. The thickness of Au shell is about 70-90 nm and the grain size on the surface is about 30-60 nm. X-ray photoemission characteristics of Au reflection photocathodes in the 400-1400 eV photon energy region are obtained, indicating that the Au shell photocathodes can emit 3 times more photoelectrons than the plane Au photocathode; this results from the special surface morphology of Au spherical shell and the reduction of surface potential.

Modified surface chemistry, potential, and optical properties of polar gallium nitride via long chained phosphonic acids

Surface potential, chemistry, topography, and optical properties were modulated utilizing the attachment of phosphonic acids (11-mercaptoundecylphosphonic acid, 1H,1H,2H,2H-perfluorooctanephosphonic acid, and 1,8-octanediphosphonic acid) with phosphoric acid to polar (c-plane) GaN. These changes were identified using X-ray photoelectron spectroscopy (XPS), atomic force microscopy (AFM) with kelvin probe force microscopy (KPFM), photoluminescence (PL), and water contact angle. The results indicated that the attachment of phosphonic groups to gallium nitride strongly depends on the formation of a native oxide layer and subsequent passivation. It was seen that a fluorine terminated phosphonic acid increased the overall surface oxide versus other groups, as well as reduced the surface potential and improved the photoluminescence relative to other treatments. Sulfur terminated phosphonic acid demonstrated a similar reduction in surface potential and oxide formation to fluorine based phosphonic acid; however, improvements of optical luminescence on the same scale were not achieved.

Influence of Various Conducting and Inorganic Dielectric Drift Barriers on the Charge Decay in Parylene-C Electret Layers

This paper reports on an attempt to improve the charge carrier life time in electret layers made of Parylene-C by implementing a patterned drift barrier close to the surface. Using various, differently structured metals and inorganic materials as a drift barrier, the initial surface potential directly after charging was increased by about 11.5% compared to electret layers made of pure Parylene-C. Furthermore, a higher charging efficiency was achieved. The charge carrier distribution has a higher homogeneity and the usually observed surface potential reduction at the rim of the electret layer was less pronounced. Against expectations, the long-term stability did not improve among the chosen materials and patterns. Regarding side effects observed with unstructured drift barriers, the electret layers with a structured drift barrier do not suffer from the horizontal discharging.

Approximate analytic solution of the nonlinear Poisson–Boltzmann equation for spherical colloidal particles immersed in a general electrolyte solution

By means of polynomial approximation and iteration procedure using linearization solution as initial solution, the non-linear Poisson–Boltzmann equation describing a spherical colloidal particle immersed in an arbitrary valence and mixed electrolyte solution is solved analytically, and analytical expressions for electrical potential distribution ψ(r) and surface charge density/surface potential relationship (σ/ψ 0) are acquired. The σ/ψ 0 expression performs very well for the entire range of a reduced colloidal radius x 0 only if a reduced surface potential y 0 is lower than 15.5; particularly, in the case of x 0 >10, the σ/ψ 0 expression applies over the entire range of y 0, and maximum of the absolute value of percent relative error (PRE) is not larger than 2 if one does not come across a parameter combination as of an extreme case of x 0 < 0.9 and y 0 > 15.5. The ψ(r) expression outperforms the linearization solution greatly and performs very well for the domain of x 0 ≤ 1.5 and y 0 ≤ 4.5 with maximum of the absolute value of PRE not larger than 3, whereas that of the linearization solution may stand 22 for the same parameter range. It is concluded that the present σ/ψ 0 expression is the first one valid for entire range of x 0, given that y 0 is not unreasonably high, and the present paper proposes, to some extent, a “universal” way for solving nonlinear differential equations.

Approximate analytical expressions for electrical potential distribution and surface charge density/surface potential relationship for planar, cylindrical, and spherical entities immersed in a general electrolyte solution

New analytical expressions for electrical potential distribution and surface charge density/surface potential relationship ( σ/ ψ 0) are derived by approximately solving a Poisson–Boltzann equation describing the electrical potential distribution around a colloidal particle with planar, cylindrical, or spherical shape and immersed in a general electrolyte solution. Application scopes of these new expressions are limited to small reduced radius of the colloidal particle, and are complementary with those of previous expressions available in literature, which advisably apply for larger reduced radius without solitary exception. For the new expressions for σ/ ψ 0 relationship, the accuracy is summarized as follows: in the case of the cylindrical colloidal particle and if top limit of a reduced surface potential is fixed as 5.5, top limits of a reduced colloidal radius are respectively not larger than 0.1, 0.034 and 0.008 for 3:1, 2:1 and 1:1 type electrolyte solutions; whereas in the case of the spherical colloidal particle and if top limit of the reduced surface potential is fixed as 6.5, top limits of the reduced colloidal radius are, respectively, not larger than 0.49, 0.39, and 0.29 for 3:1, 2:1 and 1:1 type electrolyte solutions. In the case of the planar colloidal particle immersed in a general electrolyte solution, an exact expression for ( σ/ ψ 0) relationship is obtained.