Soft particle analysis of electrokinetics of biological cells and their model systems

Interfacial Electrokinetic Phenomena of Thermoresponsive Microgels with a Spatial Gradient of Charged Groups

When functional microgels are synthesized via radical copolymerization, spatial gradients of functional groups often form due to a difference in reactivity ratios between monomer and comonomer. In this study, we systematically investigated the effect of a decreasing gradient of charged groups from the core to the shell of microgels on their surface properties, which are crucial for colloidal particles, through the analysis of interfacial electrokinetic phenomena using Ohshima's equation. A series of electrophoretic analyses combined with dynamic light scattering revealed that the surface of the microgels undergoes a multistep collapse during the particle-size reduction due to dehydration upon increasing the temperature. Furthermore, the more complicated hierarchical gradient of charged groups within the microgels was elucidated by quantitatively evaluating changes in surface properties during precipitation polymerization based on interfacial electrokinetic phenomena.

Physicochemical surface properties of Chlorella vulgaris: a multiscale assessment, from electrokinetic and proton uptake descriptors to intermolecular adhesion forces

Given the growing scientific and industrial interests in green microalgae, a comprehensive understanding of the forces controlling the colloidal stability of these bioparticles and their interactions with surrounding aqueous microenvironment is required. Accordingly, we addressed here the electrostatic and hydrophobic surface properties of Chlorella vulgaris from the population down to the individual cell levels. We first investigated the organisation of the electrical double layer at microalgae surfaces on the basis of electrophoresis measurements. Interpretation of the results beyond zeta-potential framework underlined the need to account for both the hydrodynamic softness of the algae cells and the heterogeneity of their interface formed with the outer electrolyte solution. We further explored the nature of the structural charge carriers at microalgae interfaces through potentiometric proton titrations. Extraction of the electrostatic descriptors of interest from such data was obscured by cell physiology processes and dependence thereof on prevailing measurement conditions, which includes light, temperature and medium salinity. As an alternative, cell electrostatics was successfully evaluated at the cellular level upon mapping the molecular interactions at stake between (positively and negatively) charged atomic force microscopy tips and algal surface via chemical force microscopy. A thorough comparison between charge-dependent tip-to-algae surface adhesion and hydrophobicity level of microalgae surface evidenced that the contribution of electrostatics to the overall interaction pattern is largest, and that the electrostatic/hydrophobic balance can be largely modulated by pH. Overall, the combination of multiscale physicochemical approaches allowed a drawing of some of the key biosurface properties that govern microalgae cell-cell and cell-surface interactions.

Investigation of the Electrokinetic Properties of HIV-Based Virus-Like Particles

The antigen density on the surface of HIV-based virus-like particles (VLPs) plays a crucial role in the improvement of HIV vaccine potency. HIV VLPs consist of a dense protein core, which is surrounded by a lipid bilayer and whose surface is usually decorated with antigenic glycoproteins. The successful downstream processing of these particles is challenging, and the high-resolution and cost-efficient purification of HIV-based VLPs has not yet been achieved. Chromatography, one of the major unit operations involved in HIV VLP purification strategies, is usually carried out by means of ion exchangers or ion-exchange membranes. Understanding the electrokinetic behavior of HIV-based VLPs may help to improve the adjustment and efficiency of the corresponding chromatographic processes. In this study, we investigated the electrokinetics and aggregation of both undecorated and decorated VLPs and interpreted the data from the perspective of the soft particle model developed by Ohshima (OSPM), which fails to fully predict the behavior of the studied VLPs. Post-Ohshima literature, and particularly the soft multilayer particle model developed by Langlet et al., provides an alternative theoretical framework to overcome the limits of the OSPM. We finally hypothesized that the electrophoretic mobility of HIV-based VLPs is controlled by an electrohydrodynamic interplay between envelope glycoproteins, lipid bilayer, and Gag envelope.

Noble Metal Nanoparticles with Nanogel Coatings: Coinage Metal Thiolate-Stabilized Glutathione Hydrogel Shells

Developing biocompatible nanocoatings is crucial for biomedical applications. Noble metal colloidal nanoparticles with biomolecular shells are thought to combine diverse chemical and optothermal functionalities with biocompatibility. Herein, we present nanoparticles with peptide hydrogel shells that feature an unusual combination of properties: the metal core possesses localized plasmon resonance, whereas a few-nanometer-thick shells open opportunities to employ their soft framework for loading and scaffolding. We demonstrate this concept with gold and silver nanoparticles capped by glutathione peptides stacked into parallel β-sheets as they aggregate on the surface. A key role in the formation of the ordered structure is played by coinage metal(I) thiolates, i.e., Ag(I), Cu(I), and Au(I). The shell thickness can be controlled via the concentration of either metal ions or peptides. Theoretical modeling of the shell's molecular structure suggests that the thiolates have a similar conformation for all the metals and that the parallel β-sheet-like structure is a kinetic product of the peptide aggregation. Using third-order nonlinear two-dimensional infrared spectroscopy, we revealed that the ordered secondary structure is similar to the bulk hydrogels of the coinage metal thiolates of glutathione, which also consist of aggregated stacked parallel β-sheets. We expect that nanoparticles with hydrogel shells will be useful additions to the nanomaterial toolbox. The present method of nanogel coating can be applied to arbitrary surfaces where the initial deposition of the seed glutathione monolayer is possible.

Bactericidal Ability of Well-Controlled Cationic Polymer Brush Surfaces and the Interaction Analysis by Quartz Crystal Microbalance with Dissipation

In this study, cationic poly(2-(methacryloyloxy)ethyl) trimethylammonium chloride) (PMTAC) brush surfaces were prepared by surface-initiated atom transfer radical polymerization (SI-ATRP), and their properties were systematically investigated to discuss the factors affecting their bactericidal properties and interactions with proteins. Model equations for the analysis of electrophoretic behaviors were considered for accurate parameter estimation to indicate the charge density at the interface. The zeta potential dependency of the PMTAC brushes was successfully analyzed using Smolchowski's equation and the Gouy-Chapman model, which describes the diffusive electric double layer. The analysis of the quartz crystal microbalance with dissipation (QCM-D) indicated that the electrostatic interaction promoted protein adsorption, with a large quantity of a negatively charged protein, bovine serum albumin (BSA), being adsorbed. The bactericidal efficiency of the high-graft-density polymer brush (0.45 chains nm-2) was higher than that of the low-graft-density polymer brush (0.06 chains nm-2). To investigate the mechanism of this phenomenon, we applied the dissipation change (ΔD) of QCM-D analysis. The BSA was likewise adsorbed when the brush structure was changed; however, the negative ΔD indicated that the BSA-adsorbed, high-graft-density PMTAC brush became a rigid state. In the bacteria culture media, the behaviors were the same as BSA adsorption, and the high-graft-density polymer brush was also estimated to be more rigid than the low-graft-density polymer brush. Moreover, for S. aureus adhesion after incubating in TSB, a small slope of ΔD/ΔF plots considered initial adsorption of bacteria on the high-graft-density polymer brush strongly interacted compared to that of the low-graft-density polymer brush. The scattered value of the slope of ΔD/ΔF on the high-graft-density polymer brush was considered to be due to the dead bacteria between the bacteria and the polymer brush interface. These investigations for a well-defined cationic polymer brush will contribute to the design of antibacterial surfaces.

Microalgae as Soft Permeable Particles

The colloidal stability of non-motile algal cells in water drives their distribution in space. An accurate description of the interfacial properties of microalgae is therefore critical to understand how microalgae concentrations can change in their biotope or during harvesting processes. Here, we probe the surface charges of three unicellular algae─Chlorella vulgaris, Nannochloropsis oculata, and Tetraselmis suecica─through their electrophoretic mobility. Ohshima's soft particle theory describes the electrokinetic properties of particles covered by a permeable polyelectrolyte layer, a usual case for biological particles. The results appear to fit the predictions of Ohshima's theory, proving that all three microalgae behave electrokinetically as soft particles. This allowed us to estimate two characteristic parameters of the polyelectrolyte external layer of microalgae: the volume charge density and the hydrodynamic penetration length. Results were compared with transmission electron microscopy observations of the algal cells' surfaces, and in particular of their extracellular polymeric layer, which was identified with the permeable shell evidenced by electrophoretic measurements. Noticeably, the algal surface potentials estimated from electrophoretic mobility using the soft particle theory are less negative than the apparent zeta potentials. This finding indicates that electrostatics are expected to play a minor role in phenomena of environmental and industrial importance, such as microalgae aggregation or adhesion.

Design of biointerfaces composed of soft materials using controlled radical polymerizations

Soft interface materials have an immense potential for the improvement of biointerfaces, which are the interface of biological and artificially designed materials. Controlling the chemical and physical structures of the interfaces at the nanometer level plays an important role in understanding the mechanism of the functioning and its applications. Controlled radical polymerization (CRP) techniques, including atom transfer radical polymerization (ATRP) and reversible addition-fragmentation chain-transfer (RAFT) polymerization, have been developed in the field of precision polymer chemistry. It allows the formation of well-defined surfaces such as densely packed polymer brushes and self-assembled nanostructures of block copolymers. More recently, a novel technique to prepare polymers containing biomolecules, called biohybrids, has also been developed, which is a consequence of the advancement of CRP so as to proceed in an aqueous media with oxygen. This review article summarizes recent advances in CRP for the design of biointerfaces.

Space Electroosmotic Thrusters in Ion Partitioning Soft Nanochannels

Space electroosmotic thrusters (EOTs) are theoretically investigated in a soft charged nanochannel with a dense polyelectrolyte layer (PEL), which is considered to be more realistic than a low-density PEL. When the PEL is dense, its permittivity is smaller than the one of the electrolyte solution layer, leading to rearrangement of ions in the channel, which is denoted as the ion partitioning effect. It is noted that fluid viscosity becomes high within the PEL owing to the hydration effect. An analytical solution for electroosmotic velocity through the channel is obtained by utilizing the Debye-Hückel linearization assumption. Based on the fluid motion, thruster performances, including thrust, specific impulse, thrust-to-power ratio, and efficiency, are calculated. The ion partitioning effect leads to enhancement of the thruster velocity, while increase of the dynamic viscosity inside the PEL reduces the flow rate of the fluid. Therefore, these performances are further impacted by the dense soft material, which are discussed in detail. Moreover, changes or improvements of the thruster performances from the dense PEL to the weak PEL are presented and compared, and distributions of various energy items are also provided in this study. There is a good result whereby the increase in electric double layer thickness promotes the development of thruster performances. Ultimately, the simulated EOTs produce thrust of about 0 to 20 μN and achieve thruster efficiency of 90.40%, while maintaining an appropriate thrust-power ratio of about 1.53 mN/W by optimizing all design parameters.

Modern bio and chemical sensors and neuromorphic devices based on organic semiconductors

This review summarizes and highlights the current state-of-the-art of research on chemical sensors and biosensors in liquid environment and neuromorphic devices based on electrolyte-gated organic transistors with the active semiconductor layer of organic π-conjugated materials (small molecules, oligomers and polymers). The architecture and principles of operation of electrolyte-gated organic transistors and the main advantages and drawbacks of these devices are considered in detail. The criteria for the selection of organic semiconductors for these devices are presented. The causes of degradation of semiconductor layers and ways of their elimination are discussed. Examples of the use of electrolyte-gated organic transistors as bio and chemical sensors, artificial synapses and computing devices are given.

The bibliography includes 132 references.

Determination of Protein Charge in Aqueous Solution Using Electrophoretic Light Scattering: A Critical Investigation of the Theoretical Fundamentals and Experimental Methodologies

Studies are reported of the measurement of electrophoretic mobilities of bovine serum albumin (BSA) in aqueous potassium chloride solutions as a function of ionic strength and pH using electrophoretic light scattering (ELS). It is demonstrated that the use of palladium or platinum electrodes should be avoided and that platinized platinum electrodes are necessary to avoid interference from unwanted electrochemical phenomena at the electrode-liquid interface. Potentiometric acid titration was performed to quantify the amount of protonic charge per protein molecule at the same pH values as the electrophoretic mobility measurements. It is shown that appropriate selection of an electrokinetic model yields excellent agreement between predicted and experimental electrophoretic mobilities across the ranges of pH and ionic strength studied in accordance with the protonic charge values obtained by titration. The experimental results are explained in terms of protonation, chloride counterion binding, and protein molecule permeability. This work highlights specific requirements of using ELS for confident analysis of proteins in aqueous solutions.

Influence of slip velocity at the core of a diffuse soft particle and ion partition effects on mobility

Nonlinear effects on the electrophoresis of a soft particle, consisting of a rigid hydrophobic core coated with a diffuse polymer layer (PEL) suspended in an electrolyte medium, are studied. The impact of the ion partitioning effect arising due to the Born energy difference between the PEL and the electrolyte is approximated based on the equilibrium Boltzmann equation, with which the ion distribution and hence, the charge density is modified. The equations describing the electrokinetic transport comprising the Darcy-Brinkman extended Navier-Stokes equations which includes the ion partitioning effect coupled with the modified Nernst-Planck equations and Poisson equations for electric field are solved numerically. The present numerical model for the soft particle compares well with the existing theoretical solutions and experimental results in the limiting cases. A deviation from existing simplified models based on the Boltzmann distribution of ions occurs when the Debye layer polarization, relaxation and the electroosmosis induced by the PEL immobile charge become significant. The hydrophobicity of the inner core strongly influences the nonlinear electrokinetic effects by modifying the Debye layer, electroosmotic flow in the PEL and surface conduction. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of the soft particle by attenuating the shielding effect. When the Debye layer is in the order of the particle size the hydrophobicity of the core surface and the ion partitioning effect manifest the surface conduction, which implies that the Boltzmann distribution of ions is no longer valid. The core hydrophobicity and ion partitioning effect have influence on the condensation of the PEL immobile charge, which creates a significant impact on the mobility.

Wall teichoic acids govern cationic gold nanoparticle interaction with Gram-positive bacterial cell walls

Molecular-level understanding of nanomaterial interactions with bacterial cell surfaces can facilitate design of antimicrobial and antifouling surfaces and inform assessment of potential consequences of nanomaterial release into the environment. Here, we investigate the interaction of cationic nanoparticles with the main surface components of Gram-positive bacteria: peptidoglycan and teichoic acids. We employed intact cells and isolated cell walls from wild type Bacillus subtilis and two mutant strains differing in wall teichoic acid composition to investigate interaction with gold nanoparticles functionalized with cationic, branched polyethylenimine. We quantified nanoparticle association with intact cells by flow cytometry and determined sites of interaction by solid-state 31P- and 13C-NMR spectroscopy. We find that wall teichoic acid structure and composition were important determinants for the extent of interaction with cationic gold nanoparticles. The nanoparticles interacted more with wall teichoic acids from the wild type and mutant lacking glucose in its wall teichoic acids than those from the mutant having wall teichoic acids lacking alanine and exhibiting more restricted molecular motion. Our experimental evidence supports the interpretation that electrostatic forces contributed to nanoparticle-cell interactions and that the accessibility of negatively charged moieties in teichoic acid chains influences the degree of interaction. The approaches employed in this study can be applied to engineered nanomaterials differing in core composition, shape, or surface functional groups as well as to other types of bacteria to elucidate the influence of nanoparticle and cell surface properties on interactions with Gram-positive bacteria.

Heat Transport of Electrokinetic Flow in Slit Soft Nanochannels

Soft nanochannels are defined as nanochannels with a polyelectrolyte layer (PEL) on the rigid walls. In the present study, the thermal transport properties of the fluids through slit soft nanochannels are investigated under the combined influences of pressure-driven and streaming potential. Based on the analytical solutions of electric potential and velocity distributions, a dimensionless temperature of electrolyte solution in soft nanochannels is obtained by resolving the energy equation. Then, a finite difference method is used to compute the energy equation and test the validity of the analytical solution. Results show that the temperature increases with the decrease of dimensionless velocity and the heat transfer rate for rigid nanochannel are higher than that for the soft one. Moreover, we find the total entropy generation decreases with the increases of the ratio K_λ of the electrical double layer (EDL) thickness in PEL to the EDL thickness on the solid wall.

Efficient electrochemomechanical energy conversion in nanochannels grafted with end-charged polyelectrolyte brushes at medium and high salt concentration

We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.

Softness Induced Enhancement in Net Throughput of Non-Linear Bio-Fluids in Nanofluidic Channel under EDL Phenomenon

In this article, we describe the electro-hydrodynamics of non-Newtonian fluid in narrow fluidic channel with solvent permeable and ion-penetrable polyelectrolyte layer (PEL) grafted on channel surface with an interaction of non-overlapping electric double layer (EDL) phenomenon. In this analysis, we integrate power-law model in the momentum equation for describing the non-Newtonian rheology. The complex interplay between the non-Newtonian rheology and interfacial electrochemistry in presence of PEL on the walls leads to non-intuitive variations in the underlying flow dynamics in the channels. As such, we bring out the variations in flow dynamics and their implications on the net throughput in the channel in terms of different parameters like power-law index (n), drag parameter (α), PEL thickness (d) and Debye length ratio (κ/κ_PEL) are discussed. We show, in this analysis, a relative enhancement in the net throughput through a soft nanofluidic channel for both the shear-thinning and shear-thickening fluids, attributed to the stronger electrical body forces stemming from ionic interactions between polyelectrolyte layer and electrolyte layer. Also, we illustrate that higher apparent viscosity inherent with the class of shear-thickening fluid weakens the softness induced enhancement in the volumetric flow rate for the shear-thickening fluids, since the viscous drag offered to the f low f ield becomes higher for the transport of shear-thickening fluid.

Ion size effect on electrostatic and electroosmotic properties in soft nanochannels with pH-dependent charge density

We report a theoretical study of the ion size effect on various properties in a soft nanochannel with pH-dependent charge density.

Dielectric analysis based on spherical-shell model for cationic and anionic spherical polyelectrolyte brushes

We report here a dielectric study on cationic and anionic spherical polyelectrolyte brush (SPB) (consisting of a polystyrene (PS) core and poly (2-aminoethylmethacrylate hydrochloride (PAEMH) chains or poly (acrylic acid) (PAA) chains grafted onto the core) suspensions over a frequency range of 40 Hz-110 MHz. The relaxation behavior of the suspensions shows significant changes in the brush layer properties when changing the particle mass fraction or pH of the system. After eliminating the electrode polarization effect at a low frequency, two definite relaxations related to interfacial polarization, around 100 kHz and 10 MHz respectively, are observed. Based on a single layer spherical-shell model, we developed a curve-fitting procedure to analyze such dielectric spectra for soft particles, and then calculated the dielectric properties of the components of the SPBs (such as the permittivities and conductivities of the layer and solution phase), especially the layer thickness d _s of the polyelectrolyte chain (PE) layer. We also found a larger confinement degree of counterions in the PAEMH brush due to the protonation of the amino group. Moreover, the repulsive force between the SPB particles is evaluated by using the d _s combined with the relative theoretical formulas. We conclude that by raising (reducing) the acidity of the system, the stability of the PAEMH-SPB (PAA-SPB) suspension was improved. An increase in particle concentration can also improve the stability of these two dispersions.

Dielectric spectroscopy of ionic microgel suspensions

The determination of the net charge and size of microgel particles as a function of their concentration, as well as the degree of association of ions to the microgel backbone, has been pursued in earlier studies mainly by scattering and rheology. These methods suffer from contributions due to inter-particle interactions that interfere with the characterization of single-particle properties. Here we introduce dielectric spectroscopy as an alternative experimental method to characterize microgel systems. The advantage of dielectric spectroscopy over other experimental methods is that the polarization due to mobile charges within a microgel particle is only weakly affected by inter-particle interactions. Apart from electrode polarization effects, experimental spectra on PNIPAM-co-AA [poly(N-isopropylacrylamide-co-acrylic acid)] ionic microgel particles suspended in de-ionized water exhibit three well-separated relaxation modes, which are due to the polarization of the mobile charges within the microgel particles, the diffuse double layer around the particles, and the polymer backbone. Expressions for the full frequency dependence of the electrode-polarization contribution to the measured dielectric response are derived, and a theory is proposed for the polarization resulting from the mobile charges within the microgel. Relaxation of the diffuse double layer is modeled within the realm of a cell model. The net charge and the size of the microgel particles are found to be strongly varying with concentration. A very small value of the diffusion coefficient of ions within the microgel is found, due to a large degree of chemical association of protons to the polymer backbone.

Electrostatic interaction of soft particles

Theories of the electrostatic interaction between two soft particles (i.e., particles covered with an ion-penetrable surface layer of polyelectrolytes) in an electrolyte solution are reviewed. Interactions of soft particles after contact of their surface layers are particularly discussed. Interaction in a salt-free medium and the discrete-charge effect are also treated.

Polyelectrolyte brushes: theory, modelling, synthesis and applications

Polyelectrolyte (PE) brushes are a special class of polymer brushes (PBs) containing charges. Polymer chains attain "brush"-like configuration when they are grafted or get localized at an interface (solid-fluid or liquid-fluid) with sufficiently close proximity between two-adjacent grafted polymer chains - such a proximity triggers a particular nature of interaction between the adjacent polymer molecules forcing them to stretch orthogonally to the grafting interface, instead of random-coil arrangement. In this review, we discuss the theory, synthesis, and applications of PE brushes. The theoretical discussion starts with the standard scaling concepts for polymer and PE brushes; following that, we shed light on the state of the art in continuum modelling approaches for polymer and PE brushes directed towards analysis beyond the scaling calculations. A special emphasis is laid in pinpointing the cases for which the PE electrostatic effects can be de-coupled from the PE entropic and excluded volume effects; such de-coupling is necessary to appropriately probe the complicated electrostatic effects arising from pH-dependent charging of the PE brushes and the use of these effects for driving liquid and ion transport at the interfaces covered with PE brushes. We also discuss the atomistic simulation approaches for polymer and PE brushes. Next we provide a detailed review of the existing approaches for the synthesis of polymer and PE brushes on interfaces, nanoparticles, and nanochannels, including mixed brushes and patterned brushes. Finally, we discuss some of the possible applications and future developments of polymer and PE brushes grafted on a variety of interfaces.

Electrostatics of soft charged interfaces with pH-dependent charge density: effect of consideration of appropriate hydrogen ion concentration distribution

Explicit consideration of hydrogen ion concentration for describing the electrostatics of grafted polyelectrolyte layers with pH-dependent charge density exhibits the necessity of considering a non-uniform depth dependent monomer distribution.

Effect of finite ion sizes in electric double layer mediated interaction force between two soft charged plates

A new theory quantifies the effect of finite ion size in osmotic pressure (Πosm) between two soft charged plates.

Mobility reversal of polyelectrolyte-grafted colloids in monovalent salt solutions

We present molecular dynamics simulations on the electrophoresis of a negative colloid grafted with positive polyelectrolytes. Net-neutral colloids show a varying mobility in monovalent salt. For colloids with negative net charge the mobility is negative at low and positive at high salt concentrations. This mobility reversal is an electrokinetic effect, and thus different from that observed in multivalent salt. Our results agree with numerical calculations based on the Darcy-Brinkman formalism, with which we predict the mobility reversal to also occur for experimentally accessible colloids.

Effect of finite ion sizes in an electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution

We provide a theory to analyze the impact of finite ion sizes (or steric effect) in electrostatic potential distribution for a charged soft surface in contact with an electrolyte solution. The theory is based on a free energy model that appropriately accounts for the contribution of finite ion sizes as well as the structural characteristics of a soft interface, represented by a combination of a rigid surface and a fixed charge layer (FCL), with the FCL being in contact with an electrolyte solution forming an electric double layer (EDL). This FCL contains a particular kind of ion which is impermeable to the electrolyte solution, and this impermeability is quantified in terms of the corresponding Donnan potential of the "membrane" represented by the FCL-electrolyte interface. We find that consideration of the finite ion size increases the magnitude of this Donnan potential, with the extent of increase being dictated by three length scales, namely, the thickness of the FCL, the thickness of the electrolyte EDL, and the thickness of an equivalent EDL within the FCL. Such regulation of the Donnan potential strongly affects the distribution of the permeable electrolyte ions within the FCL, which in turn will have significant implications in several processes involving "soft" biological membranes.