Surface Charge Strength Research Articles

Effective electrostatic interaction between columnar colloids: roles of solvent steric hindrance, polarity, and surface geometric characteristics

In the present work, coupling between the electrostatic interaction and solvent steric hindrance, and solvent polarity are studied by classical density functional theory with emphasis on their influence on the effective electrostatic potential between two similarly charged and parallel cylinder surfaces immersed in electrolyte solution.Several conclusions are confirmed. First, solvent steric hindrance always enhances the effective electrostatic potential curve oscillation and its first potential well depth or induces the potential well formation even in +1:−1 electrolyte; the enhancing effects are positively correlated with the solvent packing fraction. The curve oscillation is weakened anomalously with the surface charge density strength. Second, with a certain packing fraction of the crowding agent, its diameter has no distinct effect on the oscillation intensity of the effective electrostatic potential curves, but the oscillation period is always equal to the diameter. Third, influences of solvophilicity or solvophobicity of counter- and co-ions on the effective electrostatic potential are different in strength and mode. Strong counter-ion solvophobicity greatly raises the like-charge attraction strength with a simultaneously weakening of the effective electrostatic potential oscillation, and vice versa; solvophobicity or solvophilicity of co-ion influences the effective electrostatic potential curve in a less obvious way by translating it up/down, respectively; more specifically, the curve morphology is rarely changed. Fourth, it is illustrated that high counter-ion valence and high surface charge are not necessary conditions (confirmed in previous literature) of the surface charge reversal occurrence; counter-ion solvophobicity induces the charge reversal at far milder conditions: univalent counter-ion, lower bulk concentration, and lower surface charge strength. Fifth, by comparing with previous two works on the effects of solvent granularity on the effective electrostatic potential in flat and spherical slits, we conclude that the flat slit contact potential is always repulsive, the spherical slit contact potential can be very attractive, and the present cylinder slit contact potential is between the two.

Nanofiltration Membranes Modified with a Clustered Multiquaternary Ammonium-Based Ionic Liquid for Improved Magnesium/Lithium Separation.

Lithium separation is of great significance to overcome the lithium supply shortage resulting from a heightened demand in the energy sector. The low selectivity of polymer nanofiltration membranes for lithium extraction from concentrated Mg/Li mixtures caused by miniaturized pore structures and weak and unstable positive surface charges limits their practical implementation. To address the surface charge strength and stability, a novel ionic liquid monomer, N1-(6-aminohexyl)-N1,N1,N6,N6,N6-pentamethylhexane-1,6-diaminium bromide (denoted as DABIL), is first synthesized and covalently anchored on a pristine polyamide thin-film composite (TFC) membrane via a secondary amidation reaction for improved selective lithium separation from Mg/Li mixtures. DABIL modification of the polyamide network contributes to increased surface hydrophilicity, an enlarged membrane pore structure, and reinforced Donnan exclusion effects. Molecular dynamics simulation confirmed that the difference of the interaction energies between water and the multication groups dominates the surface properties. The DABIL membrane exhibits sixfold enhancement of water permeability compared to the unmodified membrane and outperforms the recently reported state-of-the-art positively charged membranes. It presents an improved Li+/Mg2+ selectivity of 26.49, suggesting the membranes' potential for lithium recovery. Moreover, the membrane shows efficient antibacterial activity for mitigating biofilm formation. We establish that functionalization of TFC membranes with ionic liquids containing multication side chains could be a promising approach to achieve improved and sustainable permselectivity for the recovery of critical metal resources.

Effective electrostatic forces between two neutral surfaces with surface charge separation: valence asymmetry and dielectric constant heterogeneity

Based on CDFT calculations, we study new features of surface electrostatic force (SEF) between two face-to-face overall neutral surfaces, each of which is comprised of atomic scale strip shape charge distribution and is immersed in +2:−1 electrolyte. Dielectric constant of near surface fluid is lower than that of distant fluid. Ion valence and dielectric constant heterogeneity effects are reflected in the following aspects. (i) For asymmetrical configuration of the strip shape charge distribution, if the coexistence bulk mole concentration is high like , one repulsion peak of the SEF appears at approximately two times the ion diameter and the peak height increases obviously with the ion valence and the strip shape domain width ; however, for low value, like , the ion valence almost does not cause any effect on the SEF shape and strength at small distances except that the higher valence ion causes a higher decaying rate of the SEF with the surface separation. (ii) For the case of the asymmetrical configuration and bivalent ion, strength of the small distance attractive SEF always reduces with the value, and is positively correlated with the value except when the value is high and the domain surface charge strength is low. (iii) The symmetrical strip shape charge distribution is an efficient way in inducing the attractive SEF in presence of bivalence ions even if the value is low down to ; the attraction strength is positively correlated with the value. (iv) The ion adsorption, playing a key role in influencing the SEF for the present overall neutral two-surface system, generally increases with the value, and far higher than that relevant to two similarly charged surfaces with equal value. (v) The lower surface fluid dielectric constant accords both the force and potential curves with new features like alternative mode of attraction and repulsion even in low bulk concentration, big strength in comparison with the average thermal energy, and large insensitivity to the surface charge distribution patterns and ion valence.

Surface electrostatic force in presence of dimer counter-ion

Combining classical density functional theory with modified interfacial statistical associating fluid theory, we investigate the surface electrostatic force (SEF) between two negatively and similarly charged planar surfaces immersed in electrolyte solution consisting of monomer anion and dimer cation. The dimer cation is comprised of two hard spheres (HSs) tangentially bonded together and freely rotating on the top of each other; one of the two HS sites is positively charged and the other is neutral. New findings about novel properties of the SEF caused by the dimer counter-ion are summarized below. (i) In the presence of only univalent counter-ion, the SEF always becomes more and more repulsive with increasing of the dimer counter-ion neutral site size, whether the bulk electrolyte solution is dense or not, and the surface charge strength is small, moderate, or large; repulsion strength of the SEF always reduces with the bulk concentration, and at equal surface distance rapidly increases with the surface charge strength. (ii) In the presence of bivalent counter-ion of monomer or dimer, rather complex SEF behavior emerges. Specifically, (a) at low surface charge strength, the dimer counter-ion with small neutral site size induces one obvious like-charge attraction (LCA) at lower bulk concentrations; whereas at higher bulk concentrations, a repulsive SEF emerges instead, whose strength monotonously decreases with the neutral site size. (b) For high surface charge strengths, the SEF curves exhibit oscillatory structure with the LCA feature; moreover, the dimer counter-ion always induces larger LCA position and strength than the monomer counter-ion does; the LCA strength decreases with the counter-ion neutral site size, and the LCA position always reduces with increase of the surface charge strength. (c) Dependence of the LCA strength on the bulk concentration is conditional on the surface charge strengths considered; to speak specifically, for very high surface charge strength, the LCA strength reduces with the bulk concentration, whereas for not so high value, the opposite is true. The above observations can be analyzed from fluctuation and balance of the three factors: osmotic pressure difference between inside and outside the plates; hard sphere repulsion in congested space, and “hydrogen bond” formation.

A statistical mechanics study on relationship between nanopore size and energy storage in supercapacitors

By applying classical density functional theory approach, one study is done on the impacts of the relative size (compared to that of the salt ions) of the cylindrical pore electrode on the curves of differential electrical capacitance Cd vs surface charge strength |σ| and energy storage density E vs applied voltage U, main conclusions are summarized as follows. (i) Solvent granularity always tries to facilitate a change of the Cd - σ curve from bell-shaped to camel shape; given that the cylindrical pore is shallow with reduced radius such as R∗=1.5 and in the presence of symmetrical and higher valence ion the Cd - σ curve always assumes camel shape, whatever the electrolyte bulk concentration is. (ii) For sufficiently small cylindrical pore such as R∗=1.5, symmetrical high valence electrolyte induces one extremely high peak of the camel-shaped Cd - σ curve at both sides of zero surface charge. (iii) Symmetrical high valence (2:2 and 3:3) electrolytes help in raising the E value, which is almost independent on the electrolyte bulk concentration, whatever the cylindrical pore radius is. (iv) Influence of the pore size on the single pore E value becomes observable only when the applied voltage exceeds some lower limit voltage, which is positively correlated with the ion valence. After exceeding the lower limit voltage, the curve of E versus U display saturation trend only for smaller pore such as R∗=1.5; whereas for larger pore, increase rate of E with U becomes faster and faster. The deep reason for the small pore saturation phenomena is that the co-ion adsorption capacities go to zero when the σ value exceeds some critical value after which the surface potential increases steeply with the σ value.

Inter-surface effective electrostatic interactions in the presence of surface charge discreteness and solvent granularity

Effects of relative arrangement of discrete surface charges and solvent granularity on the effective potential of mean force (EPMF) are studied. Main conclusions are summarized as follows: (i) With consideration of the solvent granularity the EPMF always becomes more attractive, and one like charge attraction always appears even if the counter-ion is univalent. Moreover, with transition from asymmetrical to symmetrical surface charge distributions of similar surface charge compactness, attraction strength of the EPMF always rises; with increase of the counter-ion valence the EPMF attraction strength rises unless the surface charge configuration is asymmetrical and less compact and the counter-ion high-valence. (ii) Whether the surface charge distribution is asymmetrical or symmetrical, the EPMF tends to become more attractive in the compactness charge configuration than in the non-compactness charge configuration. (iii) The correlation between the EPMF attraction strength and bulk mole concentration can be positive or negative depending on the counter-ion valence, compactness of surface charge distribution, and average surface charge strength. Highly taking value of each of the three quantities helps in inducing one negative correlation and vice versa. (iv) Co-ion size has almost no influence on the EPMF, increasing or decreasing the counter-ion size inhibits or enhances the solvent granularity effect.

How Ion Size influences Energy Storage in Cylindrical Nanoporous Supercapacitors

The present study is performed on the way and mechanism by which ion size changes curves of differential electrical capacitance (Cd) vs surface charge strength |σ| and energy storage density E vs a...

Role of neutral and non-hard sphere interaction in differential capacitance of electrical double-layer

Classical density functional theory is combined with the extended primitive model and solvent primitive model to investigate how differential capacitance Cd of electrical double-layer formed inside cylindrical pore is influenced by solvent granularity, bulk concentration, counter-ion diameter, and neutral and non-hard sphere (HS) potential utail_αβ(r) between ion species, between solvent and counter-ion (and co-ion). Several main conclusions are drawn. (i) The Cd−surface charge strength (|σ|) curve generally rises as a result of consideration of the solvent granularity. (ii) An interionic attractive utail_αβ(r) helps in raising the Cd curve whereas a repulsive utail_αβ(r) tends to lower the Cd curve. Moreover, a secondary Cd peak appears when |σ| increases to an appropriately large value, and becomes increasingly evident with the strength of the attractive utail_αβ(r) and eventually disappears as the attractive utail_αβ(r)reduces in attraction or changes into repulsion at all. (iii) The Cd − |σ| curve is raised by increasing the repulsion between the solvent and counter-ion; however, both counter-ion diameter and bulk concentration cause obvious changes of the Cd − |σ∗| curve morphology. Concretely speaking, the Cd peak height and the peak position rise with the counter-ion size decreasing. Moreover, changing the utail_αβ(r) between solvent and counter-ion from attraction to repulsion facilitates a transition from bell-shaped curve to camel-shaped curve. (iv) Effects of all of the factors considered in influencing the Cd curve diminish increasingly with |σ|. All of the above observations can be explained by considering the interionic depletion potential induced by the solvent and its changes with the system parameters.

Effects of interionic non-hard sphere neutral interaction and solvent crowding on differential capacitance curve of electrical double layer

By using classical density functional theory, we study the effects of interionic nonhard sphere neutral interaction (NHSNI) and solvent crowding on curve of differential electrical capacitance (Cd) vs surface charge strength |σ| of an electrical double layer (EDL) formed inside a cylindrical pore electrode. Main new findings are summarized as follows. (i) Increasing the intercounterion neutral attractive interaction helps in raising the Cd − |σ| curve and vice versa; the lowering or enhancing effect continues until rather high |σ|, such as |σ| = 1 C m−2. (ii) Attractive NHSNI between coion and counterion lowers the Cd − |σ| curve and vice versa; the lowering or enhancing effect quickly becomes very weak with |σ|. (iii) The lowering or enhancing effect strength of the intercounterion NHSNI potential range is negatively correlated with the bulk electrolyte concentration, whereas the correlation becomes positive for the potential range of the NHSNI between coion and counterion. (iv) Whether the bulk concentration is high or low, one stronger intercounterion attractive NHSNI tends to induce one more obvious peak of the Cd − |σ| curve at higher |σ|; only after this peak, the intercounterion NHSNI does not influence the Cd − |σ| curve obviously. However, the peak does not come with one intercounterion repulsive NHSNI and any kind of NHSNI between coion and counterion. (v) The solvent crowding induced by its granularity generally raises the Cd curve when |σ| is low and moderate, but the enhancing effect tends to become unobservable with further rising of |σ|. The above findings are explained reasonably by analyzing the ions local distributions in the EDL, their adsorption capacities, and the peak of change rate of the total ion adsorption capacity with |σ|.

Solvent granularity in the differential electrical capacitance of supercapacitor and mechanism analysis

In this work, we study how solvent granularity influences the differential electrical capacitance (Cd) of supercapacitor using aqueous electrolyte and molecular mechanism modulating the curve morphology of Cd versus surface charge density σ. Main new findings and conclusions are summarized into several points: (i) the solvent granularity helps to raise the Cd value, and the effect tends to weaken as the surface charge strength σ increases; particularly, the threshold σ, beyond which the solvent granularity effect begins to become graphically unobservable, rises obviously with the pore size. (ii) The bulk electrolyte concentration and pore size evidently influence the transition between camel-shaped and bell-shaped Cd−σ curves; a smaller pore and/or a higher bulk concentration help to facilitate the change from camel-shaped into bell-shaped curve, and the two factors are cooperative. (iii) Whether the Cd−σ curve is camel-shaped or bell-shaped, and the counter-ion is univalent or multivalent, the Cd value always tends to drop with the σ value as the latter one is sufficiently large; particularly, under conditions of very small pore the Cd value eventually approaches zero as the σ is approximately over 0.7C/m2. (iv) High counter-ion valence causes rising of the Cd value and the threshold σ corresponding to the Cd peak in the case of the camel-shaped curve. (iv) A new concept is introduced: change rate of the whole ion adsorption capacity with the surface charge strength, which, combined with the crowding effect, co-ion exclusion effect, discloses the mechanism of action by which all factors considered influence Cd by changing the electrostatic screening environment in the EDL.

Capacitance of electrical double layer formed inside a single infinitely long cylindrical pore

By using classical density functional theory, we investigate the capacitance of a primitive model and an extended primitive model electrical double layer (EDL) formed in a single infinitely long cylindrical pore. We obtain dependencies of the EDL differential capacitance on the parameters characterizing the electrolyte-electrode system. It is shown that (i) high electrical valence and small size of counter-ions help to raise the and the two factors have a synergistic effect; the increases with the co-ion size at high bulk concentrations, but is not sensitive to the co-ion size at lower concentrations. (ii) The curve of the versus (surface charge density) moves upwards completely with the cylindrical pore radius regardless of the electrolyte types and bulk concentrations and whether the curve is a camel-shaped or bell-shaped curve. (iii) At low concentrations, the curve is camel shaped regardless of the electrolyte types and pore sizes, and a transition from a camel-shaped to bell-shaped curve will eventually occur when the bulk concentration rises to an appropriate value. Moreover, the high electrical valence tends to delay the transition and raise the transition concentration. (iv) In the case of the camel-shaped curve, the tends to decrease with the after the curve goes beyond its maximal value; the surface charge strength (corresponding to the maxima) increases with the counter-ion valence and pore size, but decreases with the bulk concentration. However, the concentration effect is very small in the presence of only one valence counter-ion, whereas it will become obvious with the presence of two valence counter-ions. (v) In determining the shape of the curve, increasing the strength of an attractive interionic neutral and non-HS interaction has the same effect as decreasing the bulk concentration, i.e. it makes the characteristics of the camel-shaped curve more obvious. Conversely, the incorporation of a repulsive interionic neutral and non-HS interaction transforms an originally not obvious camel-shaped curve into a bell-shaped curve. The above observations can be explained self-consistently by analyzing the adsorption of salt ions and the resulting screening effect and their influencing factors.

Change of electrostatic potential of mean force between two curved surfaces due to different salt composition, ion valence and size under certain ionic strength

Change of an electrostatic potential of mean force (EPMF) between two cylindrical rod surfaces with salt composition, ion valence, and ion size at a constant ionic strength of 0.3M is studied by a classical density functional theory (CDFT) in a primitive model electrolyte solution. Several novel observations are made: (i) strength of a so-called like charge attraction (LCA) reduces in an invariable manner with the salt solution changing from single 2:1 electrolyte to mixture of 2:1 and 1:1 type electrolytes of varying concentration ratios; the change is even over entire range of the composition variation under low surface charge strength, and tends to be insensitive to the composition variation in the presence of the divalent counter-ion, and more and more drastic at a critical point the divalent counter-ion disappears, respectively, as the surface charge strength becomes big enough. (ii) Both monovalent counter-ion and co-ion diameters have only a marginal effect on both the LCA strength and equilibrium distance, and the former “abnormally” affects less than the latter. (iii) Depending on the surface charge strength considered, the divalent counter-ion diameter influences the LCA strength in solution comprised of 2:1 type and 1:1 type electrolytes, monotonously or non-monotonously. All of these findings provide forceful support for a recently proposed hydrogen-bonding style mechanism explaining the LCA.