Diffuse Electric Double Layer Research Articles

Fines migration characteristics of illite in clayey silt sediments induced by pore water under the depressurization of natural gas hydrate

Marine gas hydrate is widely distributed in clayey silt sediments, which have high clay content and low permeability. The decomposition of natural gas hydrate will cause the mechanical failure of the reservoir and the decrease of pore water salinity, inducing the migration of clay minerals to clog the pore throat, which has a significant impact on the production efficiency of natural gas hydrate. In this work, the migration behaviour of illite in clayey silt sediments driven by pore water under the depressurization of hydrate was studied through pressure difference, pore throat and content changes. We studied the migration process of silt, excluding the interference of synergistic migration of silt and illite, and then studied the migration of illite under the change of flow rate and salinity. The results show that illite will migrate before silt and that critical flow rate and critical salinity exist. The flow rate mainly affects the torque generated by the forces detaching the illite particles. Illite particle detachment will occur if the flow rate exceeds the critical value and the torque balance is disrupted, and then the pore throat is clogged. There are two effects of salinity decrease on illite migration. Above the critical salinity, the expansion of the pore throat due to decomposition has a significant effect on illite migration. Below the critical salinity, the increase of the diffuse electric double layer thickness and the electrostatic repulsion will lead to an increase of the particle concentration in the pore water, making clogging more likely to occur even at low flow rates. This work suggests that clay migration has a complex impact on the development of clayey silt hydrate, and helps to consider the reasonable combination of saturation and production rate when designing a development plan to reduce the impact of permeability decline due to continuous pore throat clogging on development efficiency.

Effect of nanomaterials functionality on the acidic crude oil: Wettability and oil recovery studies

Chemical enhanced oil recovery often involves the injection of chemicals, such as surfactants, polymers, nanoparticles, and macromolecules. These chemicals are to alter the rock-oil-water interactions and mobilize the oil towards the production well. However, they often pose considerable challenges in the harsh environment of the oil-wet reservoirs, such as chemical instability, and high retention/adsorption of chemicals in the near-wellbore. Herein, we investigated the effect of functionalized silica nanofluids on improving oil recovery in the carbonate reservoir as a function of the oil acidity. To do so, we synthesized two types of silica nanofluids functionalized with sulfonate and carboxylate groups. We used two crude oils with different total acid numbers (TAN) of 0.4 and 5.7 mg/KOH. All experiments were ran at 100 °C and salinity of 67–240 kppm to simulate the harsh reservoir conditions of the Saudi Arabia. Spontaneous imbibition oil recovery studies were conducted to assess their effects on oil recovery. Contact angle and interfacial tension were performed at different conditions to examine the oil recovery mechanism. Further, in order to corroborate the previous research and comprehend the principles underlying the oil recovery, we also examined the electrokinetic zeta potential in parallel. Also, to better understand how oil and nanofluid functional groups interact, we conducted a surface complexation model study. In addition, molecular simulation (density functional theory and molecular dynamics) are employed to gain atomistic insights on the implicated molecular interactions between nanosilica particles with calcite surface in seawater brine. DFT simulations predicted that both functionalized nanosilica can form thermodynamically stable complexes with a dry and hydrated calcite surface. Further, MD simulations reveal that a good amount of both functionalized nanosilica are interacting with calcite surface in the diffuse electric double layer of the calcite-brine interface. However, the carboxylated functionalized nanosilica particles interact with rock stronger than sulfonated ones. Further, the carboxylated nanosilica could form stable complexes with naphthenic acids mediated by calcium ions, which supports the synergy effect observed experimentally. The results shed light on much more complex mechanisms behind the oil recovery rather than the common peripheral understanding. This work provides a good insight into the applicability of nanofluids for enhanced oil recovery for further research and field trials.

The regulation of protein crystallization using choline chloride precipitant and its mechanism

Inorganic salts are the most commonly used precipitants in protein crystallization. However, due to their strong ability to destroy the hydration shell and diffuse electric double layer of proteins, the use of inorganic salts can easily cause protein precipitation. This work studied protein crystallization using organic salt choline chloride (cc) as the precipitant. Compared with NaCl, crystallization, it was found that lysozyme could nucleate at a lower supersaturation and the single-crystal area was significantly enlarged with cc. Even at a high supersaturation of nearly 30, lysozyme crystals could still maintain a complete tetragonal morphology with no urchin-like crystals in cc solution. Furthermore, the average crystal size in cc solution was larger than that in NaCl solution even at a lower supersaturation. In addition, the quantitative efficiency of yield was about equal in cc and NaCl system. Combining Zeta potential, fluorescence spectrum and MD simulation, it was found that cc could interact with lysozyme through hydrogen bond, which weakened the damage of Cl− to diffuse electric double layer of proteins and increased the stability of lysozyme. DLS revealed that the presence of cc could promote the formation of large protein aggregates, which was favorable for crystal growth. In addition, CD spectra and lysozyme activity showed that the presence of cc did not affect the secondary structure and activity of lysozyme. This work proved that cc could be used as a substitute precipitant to grow protein crystals with large size and improve the stability of protein crystallization.

Prediction of electrostatic properties of reservoir rock in low salinity water injection into carbonate reservoirs

Geochemical modeling along with chemical reactions is one of the challenges in modeling of low salinity water injection. The most important issue in the geochemical model is to determine the correct electrical charge distribution model and its tuning parameters. The composition of the rock as well as the candidate water used is effective in determining the type of model and its parameters, so that the tuning parameters are determined based on the history of zeta potential experiments. In this study, in order to determine the correct model of electrical charge distribution and its tuning parameters in carbonate rock samples, first, equilibrium samples of Candidate water with crushed rock are subjected to static zeta potential tests. Then, the diffuse electrical double layer model is used to determine the electrical charge of the rock/water and water/oil surfaces and to predict the zeta potential. In the following, by adjusting the tuning parameters of the model to match the prediction results of the model with the history of the laboratory data, the density of the carbonate rock surface, the equilibrium constants and the kinetics of the governing reactions are determined. The obtained results show that the range of error in zeta potential prediction by the model compared to the laboratory data is from 2 to 20%, which is within the acceptable range of the performance of electrical charge distribution models. Moreover, it could be observed that the error of prediction using DLM model is significantly less than the conventional models (CD-MUSIC and BSM) for different candidate water. Finally, the effect of calculated zeta potential changes is used to calculate the contact angle changes of low salinity water injection based on the coupling of DLVO theory and geochemical model. The results of the study prove that the prediction error is less than 5% compared to the results of the static wettability tests. Based on this, according to the good match between the model and the laboratory results, it is possible to determine the properties of surface sites in surface complexation models of carbonate samples using the proposed approach and the subsequent tuning data of the geochemical model.

Determination of -potential of nanofluids based on electrolyte solutions from the measurements by the methods of electrical spectroscopy and laser correlation spectroscopy

The work discusses the problem of measurement of the -potential for electrolyte-based suspensions of nanoparticle. A theory is presented for the effect of the diffuse electric double layer, including the interphase (stagnant) layer, on the effective conductivity of such suspensions. The theory is based on the method of compact groups of inhomogeneities applied to a model system of hard-core–penetrable-shell particles embedded together with the base liquid in a uniform host of the conductivity . The cores represent the particles. The shells are electrically inhomogeneous in the radial direction, their conductivity profile being a continuous function σ2(r). The overlapping components obey the rule of dominance, according to which the local conductivity value is determined by the distance from the point to the center of to the nearest particle. This model is possible to analyze rigorously in the static limit. The desired conductivity is found from the integral relation which allows us to express the electrical conductivity in the terms of the -potential, thickness of the stagnant layer, matrix molarity, etc. The theory reveals the existence of different scenarios of behavior of the conductivity depending on the geometrical and electrical parameters of the stagnant layer. It is shown that the functional dependence between the thickness and -potential can be obtained from the rate of change of the conductivity with concentration for diluted suspensions; this rate can be measured experimentally. It is pointed out that the hydrodynamic radius of a nanoparticle can be obtained from the Smoluchowski-Einstein diffusion coefficient, which can be measured by the method of laser correlation spectroscopy. We give all necessary estimates and relations to demonstrate the opportunity of measuring the -potential by analyzing together the results obtained by the indicated methods. Namely, in order to find the-potential, it is necessary to simultaneously do a series of independent measurements: find the slope of the conductivity and estimate the thickness of the stagnant layer.

Activated Carbon Aerogel as an Electrode with High Specific Capacitance for Capacitive Deionization

In this study, carbon aerogels (CAs) were synthesized by the sol-gel method, using environmentally friendly glucose as a precursor, and then they were further activated with potassium hydroxide (KOH) to obtain activated carbon aerogels (ACAs). After the activation, the electrochemical performance of the ACAs was significantly improved, and the specific capacitance increased from 19.70 F·g−1 to 111.89 F·g−1. Moreover, the ACAs showed a stronger hydrophilicity with the contact angle of 118.54° compared with CAs (69.31°). When used as an electrode for capacitive deionization (CDI), the ACAs had not only a better diffuse electric double layer behavior, but also a lower charge transfer resistance and intrinsic resistance. Thus, the ACA electrode had a faster CDI desalination rate and a higher desalination capacity. The unit adsorption capacity is three times larger than that of the CA electrode. In the desalination experiment of 100 mg·L−1 sodium chloride (NaCl) solution using a CDI device based on the ACA electrode, the optimal electrode spacing was 2 mm, the voltage was 1.4 V, and the flow rate was 30 mL·min−1. When the NaCl concentration was 500 mg·L−1, the unit adsorption capacity of the ACA electrode reached 26.12 mg·g−1, much higher than that which has been reported in many literatures. The desalination process followed the Langmuir model, and the electro-sorption of the NaCl was a single layer adsorption process. In addition, the ACA electrode exhibited a good regeneration performance and cycle stability.

Nonlinear electric response of the diffuse double layer to an abrupt charge displacement inside a biological membrane

In order to elucidate the old, still unsolved problem of how the diffuse electric double layer responds to an abrupt, intramolecular charge displacement inside a biological membrane, we investigated the fastest components of the light-induced electric signals of bacteriorhodopsin and its mutants, in numerous ionic and buffer solutions. The obtained data for temperature and solute concentration dependence were interpreted as a consequence of changes in the capacity of the diffuse double layer surrounding the purple membrane. The possible physiological consequences of this so far not demonstrated phenomenon are discussed.

A Model for the Deposition of Scale Crystals on the Surface of Clay Particles

Deposition and aggregation of scale on microbial surface leads to poor stabilization of the treatment of oilfield high-scale oily wastewater. To study the deposition characteristics of scale on the surface of microbial particles, we perform the deposition and aggregation of calcium sulfate on the surface of clay particles as simulators of microbes and establish the deposition-aggregation process model. According to the theory of crystal growth, the diffuse electric double layer theory for clay, and the charged colloid theory, the scale deposition model can be divided into induction period, formative period of scale crystal nucleation, and crystal growth period. When calcium sulfate crystals deposit and aggregate on the surface of clay particles, the zeta potential and the average particle size on the surface of the clay particles increase continuously over time and tend to increase and decrease in cycles. The scale crystals are wrapped divergently around the surface of the clay particles in a needle-like form, such that the clay suspension is in a state of high aggregation. Logarithmic value of the conductivity in the formation of scale crystal has a good linear relationship with time, which conforms to the first-order rate equation. Conductivity curves can better reflect the deposition course of scale crystal on the surface of clay particles, which is divided into the induction period (6 min), transition period (1.5 min), formative period of scale crystal nucleation (10.75 min), rapid growth period of scale crystal (8.5 min), slow growth period of scale crystal (14.75 min), and stationary phase (4.75 min), and with the formation of the scale crystal, the deposition rate constant decreases gradually from 0.00945 min−1 to 0.0001 min−1. The results uncovered that Deposition and aggregation rules of scale on the surface of clay particles and the basis for further studying on microbial surface.

Transition from periodic to chaotic AC electroosmotic flows near electric double layer

AbstractElectroosmotic flows (EOFs) on insulated interfacial surface commonly exists as interfacial flows. Previously theoretical studies indicate that EOFs of Newtonian fluids on the insulated interfacial surface are steady in microchannels with symmetric zeta potentials (Suresh and Homsy, Physics of Fluids, 2004, 16, 2,349). Restricted by flow diagnostic methods in microfluidics, few velocity measurements of instantaneous EOFs have been reported, and the existence of unsteady EOFs on the insulated surface remains unclear. In this investigation, the velocity fluctuations of EOFs generated under AC electric field (named as ACFEOF) overlapped on a steady pressure‐driven flow are measured by laser induced fluorescence photobleaching anemometer, at the diffuse electric double layer (EDL) on the bottom wall far from electrodes. Chaotic velocity fluctuations according to unsteady ACFEOF has been, for the first time, observed. Stokes number (St) and electrical Reynolds number (ReE) related to oscillation and electro‐inertial effect are suggested to control chaotic ACFEOF.

Improving dielectric properties of poly(arylene ether nitrile) composites by employing core-shell structured BaTiO3@polydopamine and MoS2@polydopamine interlinked with poly(ethylene imine) for high-temperature applications

For organic film capacitors, the dielectric materials with high-k, flexible and high heat-resistance are desired. Herein, a kind of hybrid particles were fabricated via self-polymerization and crosslinking reaction, containing core-shell structured BaTiO3@polydopamine (BT@PDA) and MoS2@polydopamine (MoS2@PDA) interlinked with poly(ethylene imine) (PEI) to perserve better interfacial interaction and uniform dispersion in poly(arylene ether nitrile) (PEN) composites. The results suggest that the designed PEN-based composites demonstrate remarkable dielectric responses. The incorporation of hybrid particles endows the polymer composites with high relative dielectric constant and comparable low dielectric loss due to the construction of diffuse electrical double layer and more micro-capacitor networks in PEN-based composites. Particularly, the dielectric constant of composite loaded with 15 wt% hybrid particles is about 254% higher than that of PEN matrix at 1 kHz, while maintaining a relatively low dielectric loss (＜0.03). More importantly, the PEN-based composites maintain their dielectric constants from room temperature to 160 °C, thus exhibiting outstanding permittivity-temperature stability, which can better meet the requirements of high temperature applications. In conclusion, this is a feasible way to incorporate hybrid particles containing core-shell structured BT@PDA and MoS2@PDA into polymer matrix to design dielectric composites with excellent permittivity-temperature stability.

Apparent kinetics of hydrogen production with water-slurried aluminum delivery in aqueous sodium hydroxide solutions

Kinetic models were fit to experimental hydrogen production data from a stirred microspherical aluminum corrosion reactor, one model for each of two Al initial conditions prior to immersion in aqueous sodium hydroxide at pH 13.17–13.48: (i) air-dry, and (ii) water-suspended for 0.5–2 h, of which the latter has not been studied. Data fitting was fairly precise (R2>0.97), and results were confirmed by comparison to shrinking core models of the reaction time. Key findings were a low reaction order in hydroxide (0.46 for slurry and 0.55 for dry based reactions), along with relatively lower apparent activation energy and frequency factor for the slurry reactions (60.15, versus 64.75 kJ/mol for initially dry Al, with SE≈2.5kJ/mol), and just a slight effect of Al delivery mode on overall rates. Explanatory rate-limiting mechanisms were hypothesized following a model of a dissolving film over the corroding Al with analysis of diffuse electric double layer charging and transport resistance effects.

Influence of Salt Concentration on Charge Transfer When a Water Front Moves across a Junction between a Hydrophobic Dielectric and a Metal Electrode.

An energy-harvesting device based on water moving across the junction between a hydrophobic dielectric and a metal electrode is demonstrated. The charge transfer due to contact electrification as the junction is dipped vertically into water is investigated. Experiments combined with finite element simulations reveal how the electrode voltage changes during the dipping process. Moreover, the charge transfer observed for a range of salt concentrations is studied, and it is found that there exists an optimal salt concentration which allows maximum charge transfer. It is suggested that these results can be understood because of the additional charge removal from the diffuse electrical double layer at the hydrophobic surface. It is demonstrated that by tuning the salt concentration, one can harvest more than 3 times the electrical power as compared with pure water.

Quantifying the thickness of the electrical double layer neutralizing a planar electrode: the capacitive compactness.

The spatial extension of the ionic cloud neutralizing a charged colloid or an electrode is usually characterized by the Debye length associated with the supporting charged fluid in the bulk. This spatial length arises naturally in the linear Poisson-Boltzmann theory of point charges, which is the cornerstone of the widely used Derjaguin-Landau-Verwey-Overbeek formalism describing the colloidal stability of electrified macroparticles. By definition, the Debye length is independent of important physical features of charged solutions such as the colloidal charge, electrostatic ion correlations, ionic excluded volume effects, or specific short-range interactions, just to mention a few. In order to include consistently these features to describe more accurately the thickness of the electrical double layer of an inhomogeneous charged fluid in planar geometry, we propose here the use of the capacitive compactness concept as a generalization of the compactness of the spherical electrical double layer around a small macroion (González-Tovar et al., J. Chem. Phys. 2004, 120, 9782). To exemplify the usefulness of the capacitive compactness to characterize strongly coupled charged fluids in external electric fields, we use integral equations theory and Monte Carlo simulations to analyze the electrical properties of a model molten salt near a planar electrode. In particular, we study the electrode's charge neutralization, and the maximum inversion of the net charge per unit area of the electrode-molten salt system as a function of the ionic concentration, and the electrode's charge. The behaviour of the associated capacitive compactness is interpreted in terms of the charge neutralization capacity of the highly correlated charged fluid, which evidences a shrinking/expansion of the electrical double layer at a microscopic level. The capacitive compactness and its first two derivatives are expressed in terms of experimentally measurable macroscopic properties such as the differential and integral capacity, the electrode's surface charge density, and the mean electrostatic potential at the electrode's surface.

A strong inhibition of polyethyleneimine as shale inhibitor in drilling fluid

In this paper, the inhibition property of polyethyleneimine (PEI) in montmorillonite solution was studied. The inhibition property was evaluated by linear swelling test and rolling recovery test. Compared with other inhibitors, the addition of PEI resulted in the lowest swelling height in drilling fluid. In rolling recovery rate study, the addition of PEI resulted in the highest recovery rate after rolled at 120 °C.More importantly, PEI was environmental friendly inhibitor. The inhibition mechanism was investigated by Fourier transform infrared spectroscopy, X-ray diffraction, Transmission electron microscope, Scanning electron microscopy, Atomic force microscope, Zeta potential and Particle-size analyzer. The spectrums and images showed that the negative charge in the surface of montmorillonite (MMT) was neutralized by the positive charge in amino group of PEI. PEI was adsorbed in the surface and intercalated into interlayer of MMT, which reduced the hydration repulsion of diffuse electric double layer and prevented the invasion of water. Hydrogen bonding between hydroxyl in the surface of clay and amino groups in the backbone and side chain of PEI can be formed in the process. The adsorption and intercalation of PEI in the surface and interlayer of MMT was the major factor to prevent water molecules from invading into the gallery of clay. There were a quantity of positive ions in solution because of the protonation of nitrogen in water. More positive ions resulted in the stronger force between inhibitor and clay.

Experimental corroboration of general phenomenological theory for dynamics of EDL in viscous medium on rough heterogeneous electrode

The phenomenological theory for the anomalous electric double layer (EDL) impedance response (see J. Phys. Chem. C 118, 2014, 5122-5133) for rough heterogeneous electrodes is simplified for roughness features larger than the electrolyte screening length. The electrochemical impedance responses (EIS) of moderately rough polycrystalline Pt electrodes in NaNO3 electrolyte dissolved in aqueous and viscous media are analyzed and interpreted with the phenomenological theory. Experiments support predictions of theory for the EDL relaxation on rough and heterogeneous electrode, and also emphasize that the dynamics can be decomposed into compact layer and diffuse layer processes. Influence of viscosity is used to unravel the characteristic high frequency diffuse EDL dynamics through NaNO3 solution in 90% glycerol (by volume). These experiments also contrast the influence of concentration on EDL dynamics in aqueous and viscous media. EIS identifies four phenomenological regimes along with their characteristics frequencies. Finally, this phenomenological theory brings in significant physical insight and provides a useful method for interpreting experimental results.

The effect of surface transport on water desalination by porous electrodes undergoing capacitive charging

Capacitive deionization (CDI) is a technology in which water is desalinated by ion electrosorption into the electric double layers (EDLs) of charging porous electrodes. In recent years significant advances have been made in modeling the charge and salt dynamics in a CDI cell, but the possible effect of surface transport within diffuse EDLs on these dynamics has not been investigated. We here present theory which includes surface transport in describing the dynamics of a charging CDI cell. Through our numerical solution to the presented models, the possible effect of surface transport on the CDI process is elucidated. While at some model conditions surface transport enhances the rate of CDI cell charging, counter-intuitively this additional transport pathway is found to slow down cell charging at other model conditions.

Studies of electrochemical interfaces by broadband sum frequency generation

We present a perspective on the use of potential-dependent broadband multiplex vibrational sum-frequency generation spectroscopy (hereafter SFG) to study electrochemical systems. In SFG, a broadband mid-infrared (IR) pulse is combined with a narrowband visible pulse, generating a pulse at the sum frequency, which contains a spectrum that, due to the principles of nonlinear optics, originates solely from the electrified interface. Our SFG spectrometer can obtain one hundred or more spectra during a routine cyclic voltammetry (CV) measurement. We used SFG to study a model for a Li-ion battery anode and a low-overpotential CO2 reduction reactor based on a room-temperature ionic liquid (RTIL). SFG spectra from these complex systems were difficult to interpret, in part due to the organic electrolytes that have a forest of infrared vibrational transitions. Here we discuss a rubric for experimental measurement and interpretation with such systems. We describe the electrified interface, or double layer, as consisting of the electrode surface, a region of adsorbed molecules and an outer diffuse electric double layer. We combined resonant SFG, where the IR pulses were tuned to vibrational transitions of adsorbates, with nonresonant SFG where the IR pulses were tuned away from all vibrational transitions. The former provides information about chemistry on the electrode surface and the latter about the potential-dependent response of the double layer. We show how this rubric can be used to understand solid-electrolyte interphase formation on a model for the Li-ion electrode, and how low-overpotential CO2 reduction on Ag is controlled by potential-driven structural transitions of the RTIL electrolyte.

Simulations of charged droplet collisions in shear flow

Collisions of charged droplets in the shear flow of an electrolyte were simulated to investigate the effects of surface charges and double layers on the critical conditions for coalescence. A lattice Boltzmann method phase field flow solver was coupled with an iterative finite-difference solver for the linearized Poisson–Boltzmann equation describing electric double layers. The simulations resolve both the phase field diffuse interface and electric double layer. The critical capillary numbers for coalescence were determined under varying strengths of the electric interactions. Critical capillary numbers between 0.03 and 0.2 were found for droplet radii spanning 25–50 lattice nodes (12.5–25 times the characteristic interface thickness), with lower critical values for larger droplets. The droplet interfaces had a constant potential. Once electric repulsion becomes comparable to the viscous shear force on the drops, the critical capillary numbers decrease, and the decrease is smaller for longer Debye lengths. Though the ratio of droplet size and Debye length that can be achieved in the simulations is constrained by high computational demands, the simulations provide insight into the effects of surface charge on the interactions between interfaces in multiphase flows.

Polyethyleneimine as shale inhibitor in drilling fluid

In this paper, the inhibition property of polyethyleneimine (PEI) in drilling fluid was studied. The inhibition property was evaluated by linear swell test and roll recovery. The addition of PEI70000 resulted in the lowest swelling height, compared with the others inhibitor. Especially PEI was environmental and friendly. The inhibition mechanism was investigated by Fourier transform infrared spectroscopy, X-ray diffraction, X-ray photoelectron spectroscopy, Scanning electron microscopy, Zeta potential and Surface area analyzer. The negative charge in the surface of montmorillonite (Mt) was neutralized by the positive charge of PEI. PEI was adsorbed in the surface of Mt and intercalated into the interlayer of Mt, which reduced the hydration repulsion of diffuse electric double layer and leaded to inhibit the hydration of clay. Hydrogen bonding between amino groups in PEI and hydroxyl in the surface of Mt can be formed in the process. The coordination of electrostatic interaction and hydrogen bonding presented water molecules from the interlayer space of Mt, which resulted from the adsorption and intercalation of PEI in the surface and interlayer space of Mt. There was an amount of nitrogen in the backbone and side of PEI, leading to more positive ion than chitosan quaternary ammonium salt (HTCC). The more positive ion resulted in the stronger force between inhibitor and clay due to the protonation of nitrogen in water. The molecular weight of PEI has great influence on inhibition property. The larger molecular weight of PEI performed the better inhibition property except for PEI1800. Indicating the molecular weight of PEI was not the sole factor to control the inhibition property. What was more, the larger molecular weight of PEI leaded to the worse water-solubility.

Diffuse electric double layer in planar nanostructures due to Fermi-Dirac statistics

A double nanocapacitor modelled by two equally charged planar surfaces that confine oppositely charged quanta subjected to Fermi-Dirac statistics is considered theoretically. A global thermodynamic equilibrium was found by minimization of the Helmholtz free energy satisfying constraints that require electroneutrality and fixed total number of confined quanta. The solution obtained by using the Euler–Lagrange method yields self–consistent quantities: distribution of quanta within the pore, electric potential, equilibrium free energy and differential capacitance. Within real values, a rigorous numerical solution and an approximate analytical solution for electrons in the low temperature limit was found. The Fermi–Dirac constraints on the wave functions in the nanopore induced an effect of a diffuse electrical double layer near both charged surfaces. This effect is comparable to the corresponding effect of entropy at finite temperatures and for classical particles, as described by the acknowledged Poisson–Boltzmann theory. At small distances and small surface charges, the electrons are almost evenly distributed within the pore, while at larger distances they condense to the charged surfaces, shielding the electric field. The force between the charged surfaces is repulsive and monotonously decreases with increasing distance between surfaces. The energies stored in the nanocapacitor are up to ≃ 50eV/nm2.