Dielectric Saturation Effects Research Articles

Improving the Born equation: Origin of the Born radius and introducing dielectric saturation effects

Improving the Born equation: Origin of the Born radius and introducing dielectric saturation effects

Nanofiltration through cylindrical nanopores end-grafted with polyelectrolytes

Taking account of the effects of polyelectrolytes friction, osmotic pressure, and dielectric saturation, a continuum model is adopted to investigate the rejection and permeability of cylindrical nanopores end-grafted with pH-regulated polyelectrolytes (PEs). In addition to a detailed simulation for the behavior of the system considered under various conditions, the intriguing phenomena and underlying mechanisms are also discussed. The results gathered suggest that end-grafted nanopores show a better rejection than the corresponding bare nanopores, and the real rejection is dictated by the mean volumetric flux. Complete coverage of PEs over the cross section of a nanopore will not improve its rejection due to the hindrance in flow rate. However, both partial grafting of nanopore feed side and reducing membrane thickness can promote permeability and maintain the level of rejection. The rejection for the case where the subunits of a PE layer are localized near the outer ring of a nanopore cross section is better than that for the case where they are localized near its inner ring. The former also shows a higher permeability than the latter. By end-grafting a nanopore with 8-nm radius, its rejection for 100 mM KCl is comparable to that for a bare nanopore with 2-nm radius, although the flow rate in the former is one-order-of-magnitude larger than in the latter. This reveals that end-grafting has the potential for enlarging nanopore, thereby opening a new avenue of raising permeability while maintaining rejection simultaneously.

Effect of Dielectric Saturation on Ion Activity Coefficients in Ion Exchange Membranes.

Polymeric ion exchange membranes are used in water purification processes to separate ions from water. The distribution and transport of ionic species through these membranes depend on a variety of factors, including membrane charge density, morphology, chemical structure, and the specific ionic species present in the fluid. The electrical potential distribution between membranes and solutions is typically described using models based on Donnan theory. An extension of the original theory is proposed to account for the nonideal behavior of ions both in the fluid and in the membrane as well to provide a more robust description of interactions of solutes with fixed charge groups on the polymer backbone. In this study, the variation in dielectric permittivity in the membrane medium with electric field strength is taken into account in a model based on Gouy–Chapman double-layer theory to provide a more accurate description of ion activity coefficients in an ion exchange membrane. A semianalytical model is presented that accounts for the variation in dielectric permittivity of water in a charged polymer membrane. A comparison of this model with Manning’s counterion condensation model clearly demonstrates that by incorporating changes in water dielectric permittivity with electric field strength, much better agreement with experiments can be obtained over a range of salt concentrations for different ions.

Strong increase of correlations in liquid glycerol observed by nonlinear dielectric techniques.

Nonlinear dielectric measurements are an important tool to access material properties and dynamics concealed in their linear counterparts, but the available data are often intermittent and, on occasion, even contradictory. Employing and refining a recently developed technique for high ac field dielectric measurements in the static limit, we ascertain nonlinear effects in glycerol over a wide temperature range from 230 to 320K. We find that the temperature dependence of the Piekara factor a, which quantifies the saturation effect, changes drastically around 290K, from ∂a/∂T = +1.4 to -130 in units of 10-18V2m-2K-1. These high values of |a| quantify not only elevated dielectric saturation effects but also indicate a temperature driven increase in higher-order orientational correlations and considerable correction terms with respect to the central limit theorem. No signature of this feature can be found in the corresponding low field data.

Static permittivity of environmentally relevant low-concentration aqueous solutions of NaCl, NaNO3, and Na2SO4.

In this paper, the result of a systematic study and molecular mechanisms governing the dielectric spectra of aqueous solutions of NaCl, NaNO3, and Na2SO4 with environmentally relevant concentrations (∼mmol/l) are presented, for frequencies from 200 MHz up to 20 GHz and at temperature 25.00 ± 0.01 °C. The measured spectra were fitted with a Debye relaxation model using a non-linear, weighted, least-squares analysis. Conductivity was measured independently to reduce uncertainty in obtaining other parameters by spectral fitting. Careful experimentation provided dielectric data of sufficiently low uncertainty to enable observation of polarization mechanisms that emerge only in the low-concentration regime. The data were fitted by a concentration-dependent parametric model that includes terms accounting for internal depolarizing fields and the solvent dilution effect (mixture relation), the kinetic depolarization effect, the dielectric saturation effect, and the Debye-Falkenhagen effect that accounts for the contribution of ionic atmosphere polarization. It has been shown that, in NaCl and NaNO3 solutions at sufficiently low concentrations, the static permittivity increases due to the Debye-Falkenhagen effect. It has also been shown that, to calculate the number of irrotationally bound water molecules ZIB, the measured static permittivity values should be corrected to account for the contributions of kinetic depolarization and Debye-Falkenhagen effects. Otherwise, unrealistic values of ZIB are obtained. An explanation for the different strengths of the Debye-Falkenhagen effect observed for the different electrolyte solutions, essentially due to the electrophoretic effect and coordination number, is also presented.

Principles of surface potential estimation in mixed electrolyte solutions: Taking into account dielectric saturation

The dielectric properties between in-particle/water interface and bulk solution are significantly different, which are ignored in the theories of surface potential estimation. The analytical expressions of surface potential considering the dielectric saturation were derived in mixed electrolytes based on the nonlinear Poisson-Boltzmann equation. The surface potentials calculated from the approximate analytical and exact numerical solutions agreed with each other for a wide range of surface charge densities and ion concentrations. The effects of dielectric saturation became important for surface charge densities larger than 0.30 C/m \begin{document}$ ^2 $\end{document} . The analytical models of surface potential in different mixed electrolytes were valid based on original Poisson-Boltzmann equation for surface charge densities smaller than 0.30 C/m \begin{document}$ ^2 $\end{document} . The analytical model of surface potential considering the dielectric saturation for low surface charge density can return to the result of classical Poisson-Boltzmann theory. The obtained surface potential in this study can correctly predict the adsorption selectivity between monovalent and bivalent counterions.

Experimental study on effective microwave heating/fracturing of coal with various dielectric property and water saturation

Microwave heating is a promising technology in coal processing and coal seam permeability enhancement. It is vital to investigate the influencing factors for microwave heating of coal to ensure the optimal heating effect and the best energy efficiency. To address this, different types of coal samples with various water saturation were treated with various microwave powers and irradiation times. Thermocouple and infrared thermal image system were used to measure the temperature of coal samples during and after microwave treatment. Through analysing the temperature, the effects of dielectric property and water saturation of coal, microwave power and treatment time on microwave heating were investigated. It was found the heating rate of coal samples increases with the loss factor at the initial heating period, which then changes as the composition changes under microwave irradiation. It was also found that coal samples with low water saturation have much better microwave heating effects. Moisture not only impedes microwave heating but also facilitates uniformed heating, which impedes the formation of thermal fractures. Additionally, the experiment results suggest the average temperature increases with microwave power and irradiation time. However, extending the microwave irradiation time is more effective when the microwave power increases to a certain extent.

The effects of dielectric decrement and finite ion size on differential capacitance of electrolytically gated graphene

We analyze the effects of dielectric decrement and finite ion size in an aqueous electrolyte on the capacitance of a graphene electrode, and make comparisons with the effects of dielectric saturation combined with finite ion size. We first derive conditions for the cross-over from a camel-shaped to a bell-shaped capacitance of the diffuse layer. We show next that the total capacitance is dominated by a V-shaped quantum capacitance of graphene at low potentials. A broad peak develops in the total capacitance at high potentials, which is sensitive to the ion size with dielectric saturation, but is stable with dielectric decrement.

Impact of Nano- and Mesoscales on Macroscopic Cation Conductivity in Perfluorinated-Sulfonic-Acid Membranes

A mean-field local-density theory is outlined for ion transport in perfluorinated-sulfonic-acid (PFSA) membranes. A theory of molecular-level interactions predict nanodomain and macroscale conductivity. The effects of solvation, dielectric saturation, dispersion forces, image charge, finite size, and confinement are included in a physically consistent 3D-model domain geometry. Probability-distribution profiles of aqueous cation concentration at the domain-scale are in agreement with atomistic simulations using no explicit fitting parameters. Measured conductivities of lithium-, sodium-, and proton-form membranes with equivalent weights of 1100, 1000, and 825 g/mol(SO3) validate the macroscale predictions using a single-value mesoscopic fitting parameter. Cation electrostatic interactions with pendant sulfonate groups are the largest source of migration resistance at the domain-scale. Tortuosity of ionically conductive domains is the largest source of migration resistance at the macroscale. Our proposed tr...

The role of Stern layer in the interplay of dielectric saturation and ion steric effects for the capacitance of graphene in aqueous electrolytes

Nano-scale devices continue to challenge our theoretical understanding of microscopic systems. Of particular interest is the characterization of the interface electrochemistry of graphene-based sensors. Typically operated in a regime of high ion concentration and high surface charge density, dielectric saturation and ion crowding become non-negligible at the interface, complicating continuum treatments based upon the Poisson-Boltzmann equation. Using the Poisson-Boltzmann equation, modified with the Bikerman-Freise model to account for non-zero ion size and the Booth model to account for dielectric saturation at the interface, we characterize the diffuse layer capacitance of both metallic and graphene electrodes immersed in an aqueous electrolyte. We find that the diffuse layer capacitance exhibits two peaks when the surface charge density of the electrode is increased, in contrast with experimental results. We propose a self-consistent (and parameter-free) method to include the Stern layer which eliminates the spurious secondary peak in the capacitance and restores the correspondence of the model with experimental observations. This study sheds light on the interplay between the ion steric effects and the dielectric saturation in solvent, exposes the importance of quantum capacitance when graphene is used as an electrode, and demonstrates the importance of a self-consistent treatment of the Stern layer in continuum models of the electrode-electrolyte interface. Furthermore, the theoretical foundation provides a base upon which more detailed models of graphene-based sensors can be built.

Decoupling the Influences of Molecular- and Mesoscales on Macroscopic Transport Properties in Perfluorosulfonic-Acid Membranes

Performance of polymer-electrolyte-fuel-cells (PEFCs) links strongly to thermodynamic and mass-transport properties of the polymer membrane. The quintessential PEFC-membrane material is perfluorosulfonic-acid (PFSA) polymer, which phase separates into nanoscale hydrophilic water-filled domains through which ions and water transport and into hydrophobic polymer-matrix domains that provide structural integrity and durability. Although considerable progress has been made to reduce reactant mass-transport limitations in PFSA membranes, mass-transport is still a critical area of concern. Aqueous electrolyte transport across a phase-separated membrane is inherently a multiscale problem with aqueous-dissolved species moving through nanoscale domains that are connected to form a transport network at the intermediate mesoscale. To guide the optimization of PEFC material design and operation, we decouple the impact of micro and macro length-scale on mass transport in PEFC membranes. Specifically, molecular-scale interactions between aqueous-electrolyte and polymer in hydrophilic domains of PFSA membranes are modeled with mean-field local-density theory aligned with an experimentally consistent 3D domain geometry. Our molecular-scale description of membrane conductivity accounts for solvation, electrostatics, solvent dielectric saturation, finite size, and confinement effects. The microscale framework is validated against atomistic simulations and, subsequently, up-scaled to predict macroscale conductivity and solvent absorption by accounting for the interconnectedness of the hydrophilic domains. Excellent agreement is found with experimental data, as shown in Figure 1. Our proposed multiscale model for membrane conductivity and solvent sorption provides a new tool to explore potential avenues for improving PFSA membrane performance. Acknowledgements This work was funded by the Assistant Secretary for Energy Efficiency and Renewable Energy, Fuel Cell Technologies Office, of the U. S. Department of Energy under contract number DE-AC02-05CH11231 and by the National Science Foundation Graduate Research Fellowship under Grant No. DGE 1106400 Figure 1.3M PFSA membrane conductivity of proton-form membranes as a function of water content as determined from the model (open) and experiments (filled, with lines to guide the eyes) for equivalent weights of 1100 (circles), 1000 (squares), and 825 g/mol (SO3-) (diamonds) Figure 1

Molecular-Based Theory for Electron-Transfer Reorganization Energy in Solvent Mixtures.

Using statistical-field techniques, we develop a molecular-based dipolar self-consistent-field theory (DSCFT) for charge solvation in liquid mixtures under equilibrium and nonequilibrium conditions, and apply it to compute the solvent reorganization energy of electron-transfer reactions. In addition to the nonequilibrium orientational polarization, the reorganization energy in liquid mixtures is also determined by the out-of-equilibrium solvent composition around the reacting species due to preferential solvation. Using molecular parameters that are readily available, the DSCFT naturally accounts for the dielectric saturation effect and the spatially varying solvent composition in the vicinity of the reacting species. We identify three general categories of binary solvent mixtures, classified by the relative optical and static dielectric permittivities of the solvent components. Each category of mixture is shown to produce a characteristic local solvent composition profile in the vicinity of the reacting species, which gives rise to the distinctive composition dependence of the reorganization energy that cannot be predicted using the dielectric permittivities of the homogeneous solvent mixtures.

Static dielectric permittivity of ice from first principles.

The static permittivity of ice is computed from first principles as a function of the electric field, together with the generalized Kirkwood factor. The molecular dipole in ice is unambiguously obtained by an original method combining a slab approach and Berry phase calculations, and the fluctuations of the polarization are sampled by Monte Carlo runs using first-principles model Hamiltonians for different proton configurations. Common approximations in the exchange-correlation functionals overestimate the dielectric permittivity and enhance ferroelectric configurations and the Kirkwood factor, whereas dielectric saturation effects compare well with experiment.

Capacitance of graphene in aqueous electrolytes: The effects of dielectric saturation of water and finite size of ions

We present a theoretical model for electrolytically top-gated graphene, in which we analyze the effects of dielectric saturation of water due to possibly strong electric fields near the surface of a highly charged graphene, as well as the steric effects due to the finite size of salt ions in an aqueous electrolyte. By combining two well-established analytical models for those two effects, we show that the total capacitance of the solution-gated graphene is dominated by its quantum capacitance for gating potentials $\ensuremath{\lesssim}1\phantom{\rule{0.28em}{0ex}}\mathrm{V}$, which is the range of primary interest for most sensor applications of graphene. On the other hand, at the potentials $\ensuremath{\gtrsim}1\phantom{\rule{0.28em}{0ex}}\mathrm{V}$ the total capacitance is dominated by a universal capacitance of the electric double layer in the electrolyte, which exhibits a dramatic decrease of capacitance with increasing gating potential due to the interplay of a fully saturated dielectric constant of water and ion crowding near graphene.

Molecular Dynamics Study of Nanoconfined Water Flow Driven by Rotating Electric Fields under Realistic Experimental Conditions

In our recent work, J. Chem. Phys. 2013, 138, 154712, we demonstrated the feasibility of unidirectional pumping of water, exploiting translational-rotational momentum coupling using nonequilibrium molecular dynamics simulations. Flow can be sustained when the fluid is driven out of equilibrium by an external spatially uniform rotating electric field and confined between two planar surfaces exposing different degrees of hydrophobicity. The permanent dipole moment of water follows the rotating field, thus inducing the molecules to spin, and the torque exerted by the field is continuously injected into the fluid, enabling a steady conversion of spin angular momentum into linear momentum. The translational-rotational coupling is a sensitive function of the rotating electric field parameters. In this work, we have found that there exists a small energy dissipation region attainable when the frequency of the rotating electric field matches the inverse of the dielectric relaxation time of water and when its amplitude lies in a range just before dielectric saturation effects take place. In this region, that is, when the frequency lies in a small window of the microwave region around ∼20 GHz and amplitude ∼0.03 V Å(-1), the translational-rotational coupling is most effective, yielding fluid velocities of magnitudes of ∼2 ms(-1) with only moderate fluid heating. In this work, we also confine water to a realistic nanochannel made of graphene giving a hydrophobic surface on one side and β-cristobalite giving a hydrophilic surface on the other, reproducing slip-and-stick velocity boundary conditions, respectively. This enables us to demonstrate that in a realistic environment, the coupling can be effectively exploited to achieve noncontact pumping of water at the nanoscale. A quantitative comparison between nonequilibrium molecular dynamics and analytical solutions of the extended Navier-Stokes equations, including an external rotating electric field has been performed, showing excellent agreement when the electric field parameters match the aforementioned small energy dissipation region.

A Continuum Solvent Model of the Partial Molar Volumes and Entropies of Ionic Solvation

Continuum solvent models of electrolyte solutions are extremely useful. However, before we can use them with confidence, it is important to test them by comparison with a range of experimental properties. Here, we have adapted our recently developed1,2 simple continuum solvent model of ionic solvation free energies to calculate the solvation entropies and partial molar volumes of a group of monovalent and monatomic ions. This procedure gives good quantitative agreement for larger ions, and reproduces key qualitative features, such as the shift to positive entropies of solvation for iodide and the shift to negative partial molar volumes for small cations. Small ions require a correction to account for dielectric saturation effects, which brings them also into good agreement with experiment. We argue that this model does not require ad hoc corrections, and uses parameters that have good external physical justification. This work therefore establishes that our continuum solvent model can provide a satisfactory understanding of ionic solvation. It can thus serve as a foundation for improved models that explain and predict more complex ion specific effects.

Diffusion Modeling in Compacted Bentonite Based on Modified Gouy-Chapman Model

ABSTRACTThe integrated sorption and diffusion (ISD) model has been developed to quantify radionuclide transport in compacted bentonite. The current ISD model, based on averaged pore aperture and the Gouy-Chapman electric double layer (EDL) theory can quantitatively account for diffusion of monovalent cations and anions under a wide range of conditions (e.g., salinity, bentonite density). To improve the applicability of the current ISD model for multivalent ions and complex species, the excluded volume effect and the dielectric saturation effect were incorporated into the current model, and the modified Poisson-Boltzmann equations were numerically solved. These modified models had little effect on the calculation of effective diffusivity of Sr2+/Cs+/I−. On the other hand, the model, modified considering the effective electric charge of hydrated ions, calculated using the Gibbs free energy of hydration, agreed well with the diffusion data including those of Sr2+.

Understanding physical properties of solutions using equation of state: Electrolyte systems

An exact solution to the Poisson–Boltzmann equation is proposed with the assumption of a new potential of mean force. As a possible candidate for this purpose, a logarithmic potential of mean force changes the non-linear differential equation to a linear one, while achieving the same results as those with the original Debye–Hückel theory. The effect of dielectric saturation is discussed with respect to the radial distribution function. From the proposed potential function, a simple perturbed equation of state for a non-primitive model was developed using statistical mechanics and other equations to derive the activity and osmotic coefficients. These equations correspond to the Lewis–Randall framework. The problem of deriving a closed form for the compressibility factor is bypassed using an approximate function. The present work is compared with the original Debye–Hückel (DH) theory and the mean spherical approximation (MSA) theory using the simulation data of activity coefficient for restricted primitive 1:1, 2:1 and 2:2 electrolyte systems. Individual ionic activity coefficient data from aqueous NaCl solution at 298.15K were examined with our proposed theory, with which the results including other thermodynamic properties were in better agreement with the experimental data than were those from DH and MSA, especially for high-valent ions. Two model parameters for each ion were used at a fixed temperature and an additional parameter was needed for variable temperatures. The use of closed equations for thermodynamic properties of electrolyte solutions should foster research examining electrolyte solutions for increased thermodynamic accessibility.

Dielectric Nanodroplets: Structure, Stability, Thermodynamics, Shape Transitions and Electrocrystallization in Applied Electric Fields

The response and properties of a dielectric nanodroplet with a 10 nm diameter made of formamide placed in a uniform electric field are explored with molecular dynamics simulations and an analytic free energy formulation. Increasing fields cause the initially spherical liquid droplet to undergo gradual prolate spheroidal elongation along the field direction that culminates in a shape instability and a first-order shape transition to a slender liquid needle at a field of ∼0.50 V/nm. This transition is accompanied by enhanced reorientation of the molecular dipoles along the field direction, with the elongated droplets exhibiting a field-induced ferroelectric state, unlike the state of the droplet under field-free conditions. For larger fields, we find further gradual enhancement of the molecular dipole reorientation and the onset of a first-order electro-crystallization transition at a field of 1.4375 V/nm. This transition is portrayed by a sharp increase in the positional order parameter, a significant decrease in the molecular diffusion, and further preferential reorientation of the dipoles. Both transitions exhibit hysteresis as the change in the electric field is reversed, that is, for decreasing fields. Data from the molecular dynamics simulation were used for determination of the field-dependent dielectric permittivity of the formamide droplet. An analytic dielectric continuum model is developed, and a free energy expression which includes polarization, surface, and saturation terms is formulated, yielding results for the variation of the droplet shape as a function of the applied field, or electric Bond number, in agreement with the results obtained from the molecular dynamics simulations. Proper inclusion of dielectric saturation effects in the continuum model, expressed in terms of an electric field-dependent dielectric permittivity, is found to play an important role.

High electric field effects on gigahertz dielectric properties of water measured with microwave microfluidic devices

Silicon microstrip line devices with 260 nm planar microfluidic channels are fabricated and used to investigate water dielectric saturation effects. Microwave scattering parameter measurements are conducted from 1 to 16 GHz under different uniform dc electric fields. When the applied dc field is increased to approximately 1 MV/cm, the measured transmission coefficient S(21) is increased up to 18 dB, which indicates a large change in water dielectric properties. Extracted water permittivity (epsilon=epsilon'+jepsilon") shows that epsilon' and epsilon" are changed up to 70% and 50%, respectively.