In this work, we explore the statistical physics of colloidal particles that interact with electrolytes via ion-specific interactions. Firstly we study particles interact weakly with electrolyte using linear response theory. We find that the mean potential around a particle is linearly determined by the {\em effective charge distribution} of the particle, which depends both on the bare charge distribution and on ion-specific interactions. We also discuss the effective interaction between two such particles and show that, in far field regime, it is bilinear in the effective charge distributions of two particles. We subsequently generalize the above results to the more complicated case where particles interact strongly with the electrolyte. Our results indicate that in order to understand the statistical physics of non-dilute electrolytes, both ion-specific interactions and ionic correlations have to be addressed in a single unified and consistent framework.
By using the recently generalized version of Newton Shell Theorem analytical equations are derived to calculate the electric interaction energy between two separated charged spheres surrounded outside and inside by electrolyte. This electric interaction energy is calculated as a function of the electrolyte ion concentration, temperature, distance between the spheres and size of the spheres. At the same distance between the spheres the absolute value of the interaction energy decreases with increasing electrolyte ion concentration and increases with increasing temperature. At zero electrolyte i…
Artifacts arise in the simulations of electrolytes using periodic boundary conditions (PBC). We show the origin of these artifacts are the periodic image charges and the constraint of charge neutrality inside the simulation box, both of which are unphysical from the view point of real systems. To cure these problems, we introduce a multi-scale Monte Carlo method, where ions inside a spherical cavity are simulated explicitly, whilst ions outside are treated implicitly using continuum theory. Using the method of Debye charging, we explicitly derive the effective interactions between ions inside …
By using the recently generalized version of Newton Shell Theorem [3] analytical equations are derived to calculate the electric interaction energy between two charged spheres, a small one is located within a larger one, and each sphere is surrounded outside and inside by electrolyte. This electric interaction energy is calculated as a function of the electrolyte ion concentration, temperature, distance between the centers and size of the spheres. At the same distance between the centers of the spheres the absolute value of the interaction energy decreases with increasing electrolyte ion conce…
A novel integral equations approach is applied for studying ion pairing in the restricted primitive model (RPM) electrolyte, i. e., the three point extension (TPE) to the Ornstein-Zernike integral equations. In the TPE approach, the three-particle correlation functions $g^{[3]}({\bf r}_{1},{\bf r}_{2},{\bf r}_{3})$ are obtained. The TPE results are compared to molecular dynamics (MD) simulations and other theories. Good agreement between TPE and MD is observed for a wide range of parameters, particularly where standard integral equations theories fail, i. e., low salt concentration and high io…
Extensive Monte Carlo simulations and scaling arguments are used to study the colloidal charge reversal. The critical colloidal surface charge density $σ_c$ at which the reversal first appears is found to depend strongly on the ionic size. We find that $σ_c$ has an inflection point as a function of the electrolyte concentration. The width of the plateau region in the vicinity of the inflection point depends on the temperature and the ionic radius $a$. In agreement with the theoretical predictions it is found that the critical colloidal charge above which the electrophoretic mobility becomes re…
Water-in-salt electrolytes (WiSEs) are a class of super-concentrated electrolytes that have shown much promise in replacing organic electrolytes in lithium-ion batteries. At the extremely high salt concentrations of WiSEs, ionic association is more complicated than the simple ion pair description. In fact, large branched clusters can be present in WiSEs, and past a critical salt concentration, an infinite percolating ionic network can form spontaneously. In this work, we simplify our recently developed thermodynamic model of reversible ionic aggregation and gelation, tailoring it specifically …
We report the ion transport mechanisms in succinonitrile (SN) loaded solid polymer electrolytes containing polyethylene oxide (PEO) and dissolved lithium bis(trifluoromethane)sulphonamide (LiTFSI) salt using molecular dynamics simulations. We investigated the effect of temperature and loading of SN on ion transport and relaxation phenomenon in PEO-LiTFSI electrolytes. It is observed that SN increases the ionic diffusivities in PEO-based solid polymer electrolytes and makes them suitable for battery applications. Interestingly, the diffusion coefficient of TFSI ions is an order of magnitude hig…
The classical Debye-Huckel (DH) theory clearly accounts for the origin of screening in electrolyte solutions and works rather well for dilute electrolyte solutions. While the Debye screening length decreases with the ion concentration and is independent of ion size, recent surface-force measurements imply that for concentrated solutions, the screening length exhibits an opposite trend; it increases with ion concentration and depends on the ionic size. The screening length is usually defined by the response of the electrolyte solution to a test charge, but can equivalently be derived from the c…
The concept of the partial osmotic pressure of ions in an electrolyte solution is critically examined. In principle these can be defined by introducing a solvent-permeable wall and measuring the force per unit area which can certainly be attributed to individual ions. Here I demonstrate that although the total wall force balances the bulk osmotic pressure as required by mechanical equilibrium, the individual partial osmotic pressures are extra-thermodynamic quantities dependent on the electrical structure at the wall, and as such they resemble attempts to define individual ion activity coeffic…
We studied ion concentration profiles and the charge density gradient caused by electrode reactions in weak electrolytes by using the Poisson--Nernst--Planck equations without assuming charge neutrality. In weak electrolytes, only a small fraction of molecules is ionized in bulk. Ion concentration profiles depend on not only ion transport but also the ionization of molecules. We considered the ionization of molecules and ion association in weak electrolytes and obtained analytical expressions for ion densities, electrostatic potential profiles, and ion currents. We found the case that the tota…
The self-consistent field theory (SCFT) is used to study the mean potential near a charged plate inside a $m:-n$ electrolyte. A perturbation series is developed in terms of $g = 4 πb/\ell_{\rm {\scriptscriptstyle DB}}$, where $b, \ell_{\rm{\scriptscriptstyle DB}}$ are Bjerrum length and {\em bare} Debye length respectively. To the zeroth order, we obtain nonlinear Poisson-Boltzmann theory. For asymmetric electrolytes ($m \neq n$), the first order (one-loop) correction to mean potential contains a {\em secular term}, which indicates the breakdown of regular perturbation method. Using a renormal…
By using the generalized version of the Shell Theorem analytical equations are derived to calculate the electric energy of a charged sphere and the field energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the ion concentration of the electrolyte. The work needed to build up the charged sphere (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the screening effect of the electrolyte on the charge-charge interaction. The energy needed to build up the charged spher…
Long-range ion induced water-water correlations were recently observed in femtosecond elastic second harmonic scattering experiments of electrolyte solutions. To further the qualitative understanding of these correlations, we derive an analytical expression that quantifies ion induced dipole-dipole correlations in a non-interacting gas of dipoles. This model is a logical extension of Debye-Hückel theory that can be used to qualitatively understand how the combined electric field of the ions induces correlations in the orientational distributions of the water molecules in an aqueous solution. T…
An important question in understanding the structure of ionic liquids is whether ions are truly "free" and mobile which would correspond to a concentrated ionic melt, or are rather "bound" in ion pairs, that is a liquid of ion pairs with a small concentration of free ions. Recent surface force balance experiments from different groups have given conflicting answers to this question. We propose a simple model for the thermodynamics and kinetics of ion pairing in ionic liquids. Our model takes into account screened ion-ion, dipole-dipole and dipole-ion interactions in the mean field limit. The r…
The propensity for ion-pairing can often dictate the thermodynamic and kinetic properties of electrolyte solutions. Fast and accurate estimates of ion-pairing can thus be extremely valuable for supplementing design and screening efforts for novel electrolytes. Here, we introduce an efficient cluster model to estimate the local ion-pair potential-of-mean-force (PMF) between ionic solutes in electrolytes. The model incorporates an ion-pair and a few layers of explicit solvent in a gas-phase cluster and leverages an enhanced sampling approach to achieve high efficiency and accuracy. We employ har…
A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical sol…
The replica Ornstein-Zernike equations for an electrolyte adsorbed in a charged, disordered matrix were applied to a model, where both subsystems consisted of points carrying a single (positive or negative) charge. While the system as a whole was electroneutral, each of the subsytems had a net charge. The results of this study are compared with the ones previously obtained, where the interactions in such a system were considered to be the same as in the case of electroneutral subsystems.
We calculate the ion distributions around an interface in fluid mixtures of highly polar and less polar fluids (water and oil) for two and three ion species. We take into account the solvation and image interactions between ions and solvent. We show that hydrophilic and hydrophobic ions tend to undergo a microphase separation at an interface, giving rise to an enlarged electric double layer. We also derive a general expression for the surface tension of electrolyte systems, which contains a negative electrostatic contribution proportional to the square root of the bulk salt density. The amplit…
The study of the electrical double layer lies at the heart of colloidal and interfacial science. The standard mean-field Poisson-Boltzmann (PB) theory is incapable of modeling many phenomena originated from ion correlation. An important example is charge inversion or overcharging of electrical double layers in multivalent electrolyte solutions. Existing theories aiming to include correlations cannot capture the nonmonotonic dependence of charge inversion on salt concentration because they have not systematically accounted for the inhomogeneous nature of correlations from surface to the bulk an…
The electrostatic screening length predicted by Debye-Hückel theory decreases with increasing ionic strength, but recent experiments have found that the screening length can instead increase in concentrated electrolytes. This phenomenon, referred to as underscreening, is believed to result from ion-ion correlations and short-range forces such as excluded volume interactions among ions. We use Brownian Dynamics to simulate a version of the Restrictive Primitive Model for electrolytes over a wide range of ion concentrations, ionic strengths, and ion excluded volume radii for binary electrolytes.…
The lithium transport mechanism in ternary polymer electrolytes, consisting of PEO/LiTFSI and various fractions of the ionic liquid N-methyl-N-propylpyrrolidinium bis(trifluoromethane)sulfonimide, are investigated by means of MD simulations. This is motivated by recent experimental findings [Passerini et al., Electrochim. Acta 2012, 86, 330-338], which demonstrated that these materials display an enhanced lithium mobility relative to their binary counterpart PEO/LiTFSI. In order to grasp the underlying microscopic scenario giving rise to these observations, we employ an analytical, Rouse-based…
We present an extensive molecular dynamics (MD) simulation study of the lithium ion transport in ternary polymer electrolytes consisting of poly(ethylene oxide) (PEO), lithium-bis(trifluoromethane)sulfonimide (LiTFSI) and the ionic liquid N-methyl-N-propylpyrrolidinium bis(trifluoromethane)sulfonimide (PYR13TFSI). In particular, we focus on two different strategies by which the ternary electrolytes can be devised, namely by (a) adding the ionic liquid to PEO20LiTFSI, and (b) substituting the PEO chains in PEO20LiTFSI by the ionic liquid. In order to grasp the changes of the overall lithium tra…
The ion distribution of electrolytes near interfaces with dielectric contrast has important consequences for electrochemical processes and many other applications. To date, most studies of such systems have focused on geometrically simple interfaces, for which dielectric effects are analytically solvable or computationally tractable. However, all real surfaces display nontrivial structure at the nanoscale and have, in particular, nonuniform local curvature. Using a recently developed, highly efficient computational method, we investigate the effect of surface geometry on ion distribution and i…
The interaction between charged objects in an electrolyte solution is a fundamental question in soft matter physics. It is well-known that the electrostatic contribution to the interaction energy decays exponentially with object separation. Recent measurements reveal that, contrary to the conventional wisdom given by classic Poisson-Boltzmann theory, the decay length increases with ion concentration for concentrated electrolytes and can be an order of magnitude larger than the ion diameter in ionic liquids. We derive a simple scaling theory that explains this anomalous dependence of the decay …
Ion-pairing is commonly considered as a culprit for the reduced ionic conductivity in polymer electrolyte systems. However, this simple thermodynamic picture should not be taken literally, as ion-pairing is a dynamical phenomenon. Here we construct model PEO-LiTFSI systems with different degree of ion-pairing by tuning solvent polarity, and examine the relation between the cation-anion distinct conductivity $σ^\rm{d}_{+-}$ and the lifetime of ion-pairs $τ_{+-}$ using molecular dynamics simulations. It is found that there exist two distinct regimes where $σ^\rm{d}_{+-}$ scales with $1/τ_{+-}$ a…
According to classical electrolyte theories interactions in dilute (low ion density) electrolytes decay exponentially with distance, with the Debye screening length the characteristic length-scale. This decay length decreases monotonically with increasing ion concentration, due to effective screening of charges over short distances. Thus within the Debye model no long-range forces are expected in concentrated electrolytes. Here we reveal, using experimental detection of the interaction between two planar charged surfaces across a wide range of electrolytes, that beyond the dilute (Debye-Huucke…
A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) dynamic structure factor of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics (BD) with implicit water molecules and molecular dynamics (MD) method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding dy…
We study, using Monte Carlo simulations, the interaction between infinite heterogeneously charged surfaces inside an electrolyte solution. The surfaces are overall neutral with quenched charged domains. An average over the quenched disorder is performed to obtain the net force. We find that the interaction between the surfaces is repulsive at short distances and is attractive for larger separations.
A desktop experiment has been done to show the nonlinearity in the I-V characteristics of an ion conducting electrochemical micro-system. Its chaotic dynamics is being reported for the first time which has been captured by an electronic circuit. Polyvinylidene fluoride-co-hexafluoropropene (PVdF-HFP) gel electrolyte comprising of a combination of plasticizers (ethylene carbonate and propylene carbonate) and salts have been prepared to study the exchange of ions through porous poly ethylene terephthalate (PET) membranes. The nonlinearity of this system is due to the ion exchange of the polymer …
In the present work, we study an electrolyte solution confined between planar surfaces with nonopatterned charged domains, which has been connected to a bulk ionic reservoir. The system is investigated through an improved Monte Carlo (MC) simulation method, suitable for simulation of electrolytes in the presence of modulated surface charge distributions. We also employ a linear approach in the spirit of the classical Debye-Hückel approximation, which allows one to obtain explicit expressions for the averaged potentials, ionic profiles, effective surface interactions and the net ionic charge co…
Grand canonical simulations designed to resolve critical universality classes are reported for $z$:1 hard-core electrolyte models with diameter ratios $λ{=} a_+/a_- {\lesssim} 6$. For $z {=} 1$ Ising-type behavior prevails. Unbiased estimates of $T_c(λ)$ are within 1% of previous (biased) estimates but the critical densities are $\sim $5 % lower. Ising character is also established for the 2:1 and 3:1 equisized models, along with critical amplitudes and improved $T_c$ estimates. For $z {=} 3$, however, strong finite-size effects reduce the confidence level although classical and O$(n {\geq} 3)…
The electric field in an extended phase of a liquid electrolyte exposed to a temperature gradient is attributed to different thermophoretic mobilities of the ion species. As shown herein, such Soret-type ion thermodiffusion is not required to induce thermoelectricity even in the simplest electrolyte if it is confined between charged walls. The space charge of the electric double layer leads to selective ion diffusion driven by a temperature-dependent electrophoretic ion mobility, which -- for narrow channels -- may cause thermo-voltages larger in magnitude than for the classical Soret equilibr…
Lithium chloride LiCl is widely used as a prototype system to study the strongly dissociated 1-1 electrolyte solution. Here, we combined experimental measurements and classical molecular dynamics simulations to study the ion conduction in this system. Ionic conductivities were reported at both 20$^\circ$C and 50$^\circ$C from experiments and compared to results from molecular dynamics simulations. The main finding of this work is that transference numbers of Li$^+$ and Cl$^-$ become comparable at high concentration. This phenomenon is independent of the force fields employed in the simulation …
Grand canonical Monte Carlo simulation results are reported for an electric double layer modelled by a planar charged hard wall, anisotropic shape cations, and spherical anions at different electrolyte concentrations and asymmetric valencies. The cations consist of two tangentially tethered hard spheres of the same diameter, $d$. One sphere is charged while the other is neutral. Spherical anions are charged hard spheres of diameter $d$. The ion valency asymmetry 1:2 and 2:1 is considered, with the ions being immersed in a solvent mimicked by a continuum dielectric medium at standard temperatur…
Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective…
We use molecular dynamics simulations of the primitive model of electrolytes to study the ionic structure in aqueous monovalent electrolyte solutions confined by charged planar interfaces over a wide range of electrolyte concentration, interfacial separation, surface charge density, and ion size. The investigations are inspired by recent experiments that have directly measured the increase in the decay length for highly-concentrated electrolytes with increase in concentration. The behavior of ions in the nanoconfinement created by the interfaces is probed by evaluating the ionic density profil…
Ion transport in concentrated electrolytes plays a fundamental role in electrochemical systems such as lithium ion batteries. Nonetheless, the mechanism of transport amid strong ion-ion interactions remains enigmatic. A key question is whether the dynamics of ion transport can be predicted by the local static structure alone, and if so what are the key structural motifs that determine transport. In this paper, we show that machine learning can successfully decompose global conductivity into the spatio-temporal average of local, instantaneous ionic contributions, and relate this ``local molar c…
We study the ionic equilibria and interactions of neutral semi-permeable spherical shells immersed in electrolyte solutions, including polyions. Although the shells are uncharged, only one type of ions of the electrolyte can permeate them, thus leading to a steric charge separation in the system. This gives rise to a charge accumulation inside the shell and a build up of concentration- dependent shell potential, which converts into a disjoining pressure between the neighboring shells. These are quantified by using the Poisson-Boltzmann and integral equations theory. In particular, we show that…
Ion distribution in aqueous electrolytes near the interface plays critical roles in electrochemical, biological and colloidal systems and is expected to be particularly significant inside nanoconfined regions. Electroneutrality of the total charge inside nanoconfined regions is commonly assumed a priori in solving ion distribution of aqueous electrolytes nanoconfined by uncharged hydrophobic surfaces with no direct experimental validation. Here, we use a quantitative nuclear magnetic resonance approach to investigate the properties of aqueous electrolytes nanoconfined in graphitic-like nanopor…
University of Cambridge（剑桥大学）；University of Freiburg（弗莱堡大学）
Electrolytes play an important role in a plethora of applications ranging from energy storage to biomaterials. Notwithstanding this, the structure of concentrated electrolytes remains enigmatic. Many theoretical approaches attempt to model the concentrated electrolytes by introducing the idea of ion pairs, with ions either being tightly `paired' with a counter-ion, or `free' to screen charge. In this study we reframe the problem into the language of computational statistics, and test the null hypothesis that all ions share the same local environment. Applying the framework to molecular dynamic…
Distribution of a two component electrolyte mixture between the model adsorbent and a bulk aqueous electrolyte solution was studied using the replica Ornstein-Zernike theory and the grand canonical Monte Carlo method. The electrolyte components were modelled to mimic the HCl/NaCl and HCl/CaCl_2 mixtures, respectively. The matrix, invaded by the primitive model electrolyte mixture, was formed from monovalent negatively charged spherical obstacles. The solution was treated as a continuous dielectric with the properties of pure water. Comparison of the pair distribution functions (obtained by the…
The addition of filler particles to polymer electrolytes is known to increment their ionic conductivity (IC). A detailed understanding of how the interactions between the constituent materials are responsible for the enhancement, remains to be developed. A significant contribution is ascribed to an increment of the polymer amorphous fraction, induced by the fillers, resulting in the formation of higher ionic conductivity channels in the polymer matrix. However, the dependence of IC on the particle weight load and its composition on the polymer morphology is not fully understood. This work inve…
The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-Hückel models to calculate activity coefficients of aqueous mixtures of most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-Hückel theory that does not take steric and correlation effects of ions and water into account. In contrast, the Poisson-Fermi theory developed in recent years treats ions and water molecules as nonuniform hard spheres of any size with interstitial voids and includes ion-water and…
Polymer electrolytes typically exhibit diminished ionic conductivity due to the presence of correlation effects between the cations and anions. Microscopically, transient ionic aggregates, e.g. {\it ion-pairs}, {\it ion-triplets} or higher order ionic clusters, engender ionic correlations. Employing {\it all-atom} simulation of a model polymer electrolyte comprising of poly(ethylene oxide) and lithium iodide, the ionic correlations are explored through construction of elementary functions between pairs of the ionic species that qualitatively explains the spatio-temporal nature of these correla…
