Variation of Surface Propensity of Halides with Droplet Size and Temperature: The Planar Interface Limit

The radial number density profiles of halide and alkali ions in aqueous clusters with equimolar radius ≲1.4 nm, which correspond to ≲255 H2O molecules, have been extensively studied by computations. However, the surface abundance of Cl-, Br-, and I- relative to the bulk interior in these smaller clusters may not be representative of the larger systems. Indeed, here we show that the larger the cluster is, the lower the relative surface abundance of chaotropic halides is. In droplets with an equimolar radius of ≈2.45 nm, which corresponds to ≈2000 H2O molecules, the polarizable halides show a clear number density maximum in the droplet's bulk-like interior. A similar pattern is observed in simulations of the aqueous planar interface with halide salts at room temperature. At elevated temperature the surface propensity of Cl- decreases gradually, while that of I- is partially preserved. The change in the chaotropic halide location at higher temperatures than the room temperature may considerably affect photochemical reactivity in atmospheric aerosols, vapor-liquid nucleation and growth mechanisms, and salt crystallization via solvent evaporation. We argue that the commonly used approach of nullifying parameters in a force field in order to find the factors that determine the ion location does not provide transferable insight into other force fields.

Quantifying uncertainty in nanofiltration transport models for enhanced metals recovery

To decarbonize our global energy system, sustainably harvesting metals from diverse sourcewaters is essential. Membrane-based processes have recently shown great promise in meeting these needs by achieving high metal ion selectivities with relatively low water and energy use. An example is nanofiltration, which harnesses steric, dielectric, and Donnan exclusion mechanisms to perform size- and charge-based fractionation of metal ions. To further optimize nanofiltration systems, multicomponent models are needed; however, conventional methods necessitate large amounts of data for model calibration, introduce substantial uncertainty into the characterization process, and often yield poor results when extrapolated. In this work, we develop a new computational architecture to alleviate these concerns. Specifically, we develop a framework that: (1) reduces the data requirement for model calibration to only charged species measurements; (2) eliminates uncertainty propagation problems present in conventional characterization processes; (3) enables exploration of pH optimization for enhancing metal ion selectivities; and (4) enables uncertainty quantification to assess the sensitivity of partition coefficients and ion driving forces to learned pore size distributions. Our framework captures eight independent datasets comprising over 500 measurements to within ±15%. Our studies also suggest that the expectation-maximization algorithm can effectively learn pore size distributions and that optimizing pH can improve metal ion selectivities by a factor of 3-10×. Our findings also reveal that image charges appear to play a less pronounced role in dielectric exclusion under the studied conditions and that ion driving forces are more sensitive to pore size distributions than partition coefficients.

Lithium Concentration from Salt-Lake Brine by Donnan-Enhanced Nanofiltration

Membranes offer a scalable and cost-effective approach to ion separations for lithium recovery. In the case of salt-lake brines, however, the high feed salinity and low pH of the post-treated feed have an uncertain impact on nanofiltration's selectivity. Here, we adopt experimental and computational approaches to analyze the effect of pH and feed salinity and elucidate key selectivity mechanisms. Our data set comprises over 750 original ion rejection measurements, spanning five salinities and two pH levels, collected using brine solutions that model three salt-lake compositions. Our results demonstrate that the Li⁺/Mg²⁺ selectivity of polyamide membranes can be enhanced by 13 times with acid-pretreated feed solutions. This selectivity enhancement is attributed to the amplified Donnan potential from the ionization of carboxyl and amino moieties under low solution pH. As feed salinities increase from 10 to 250 g L^-1, the Li⁺/Mg²⁺ selectivity decreases by ∼43%, a consequence of weakening exclusion mechanisms. Further, our analysis accentuates the importance of measuring separation factors using representative solution compositions to replicate the ion-transport behaviors with salt-lake brine. Consequently, our results reveal that predictions of ion rejection and Li⁺/Mg²⁺ separation factors can be improved by up to 80% when feed solutions with the appropriate Cl^-/SO₄^2- molar ratios are used.

Permittivity Threshold and Thermodynamics of Integer Charge-Transfer Complexation for an Organic Donor-Acceptor Pair

Molecular charge doping involves the formation of donor-acceptor charge-transfer complexes (CTCs) through integer or partial electron transfer; understanding how local chemical environment impacts complexation is important for controlling the properties of organic materials. We present steady-state and temperature-dependent spectroscopic investigations of the p-dopant 2,3,5,6-tetrafluoro-7,7,8,8-tetracyanoquinodimethane (F₄TCNQ) complexed with the electron donor and hole transport material N,N'-diphenyl-N,N'-di-p-tolylbenzene-1,4-diamine (MPDA). Equilibrium formation constants (K_CT) were determined for donor-acceptor pairs dissolved in a series of solvents covering a range of values of permittivity. A threshold for highly favorable complex formation was observed to occur at ϵ ∼ 8-9, with large (>10⁴) and small (<10³) values of K_CT obtained in solvents of higher and lower permittivity, respectively, but with chloroform (ϵ = 4.81) exhibiting an anomalously high formation constant. Temperature-dependent formation constants were determined in order to evaluate the thermodynamics of complex formation. In 1,2-dichloroethane (ϵ = 10.36) and chlorobenzene (ϵ = 5.62), complex formation is both enthalpically and entropically favorable, with higher enthalpic and entropic stabilization in the solvent with higher permittivity. Complexation in chloroform is exothermic and entropically disfavored, indicating that specific, inner-shell solvent-solute interactions stabilize the charge-separated complex and result in a net increase in local solution structure. Our results provide insight into how modification to the chemical environment may be utilized to support stable integer charge transfer for molecular doping applications and requiring only modest changes in local permittivity.

The Contribution of the Ion-Ion and Ion-Solvent Interactions in a Molecular Thermodynamic Treatment of Electrolyte Solutions

Developing molecular equations of state to treat electrolyte solutions is challenging due to the long-range nature of the Coulombic interactions. Seminal approaches commonly used are the mean spherical approximation (MSA) and the Debye-Hückel (DH) theory to account for ion-ion interactions and, often, the Born theory of solvation for ion-solvent interactions. We investigate the accuracy of the MSA and DH approaches using each to calculate the contribution of the ion-ion interactions to the chemical potential of NaCl in water, comparing these with newly computer-generated simulation data; the ion-ion contribution is isolated by selecting an appropriate primitive model with a Lennard-Jones force field to describe the solvent. A study of mixtures with different concentrations and ionic strengths reveals that the calculations from both MSA and DH theories are of similar accuracy, with the MSA approach resulting in marginally better agreement with the simulation data. We also demonstrate that the Born theory provides a good qualitative description of the contribution of the ion-solvent interactions; we employ an explicitly polar water model in these simulations. Quantitative agreement up to moderate salt concentrations and across the relevant range of temperature is achieved by adjusting the Born radius using simulation data of the free energy of solvation. We compute the radial and orientational distribution functions of the systems, thereby providing further insight on the differences observed between the theory and simulation. We thus provide rigorous benchmarks for use of the MSA, DH, and Born theories as perturbation approaches, which will be of value for improving existing models of electrolyte solutions, especially in the context of equations of state.

Computing the Work of Solid-Liquid Adhesion in Systems with Damped Coulomb Interactions via Molecular Dynamics: Approaches and Insights

Recently, the dry-surface method [Langmuir2016, 31, 8335−8345] has been developed to compute the work of adhesion of solid–liquid and other interfaces using molecular dynamics via thermodynamic integration. Unfortunately, when long-range Coulombic interactions are present in the interface, a special treatment is required, such as solving additional Poisson equations, which is usually not implemented in generic molecular dynamics software, or as fixing some groups of atoms in place, which is undesirable most of the time. In this work, we replace the long-range Coulombic interactions with damped Coulomb interactions, and explore several thermal integration paths. We demonstrate that regardless of the integration path, the same work of adhesion values are obtained as long as the path is reversible, but the numerical efficiency differs vastly. Simple scaling of the interactions is most efficient, requiring as little as 8 sampling points, followed by changing the Coulomb damping parameter, while modifying the Coulomb interaction cutoff length performs worst. We also demonstrate that switching long-range Coulombic interactions to damped ones results in a higher work of adhesion by about 10 mJ/m² because of slightly different liquid molecule orientation at the solid–liquid interface, and this value is mostly unchanged for surfaces with substantially different Coulombic interactions at the solid–liquid interface. Finally, even though it is possible to split the work of adhesion into van der Waals and Coulomb components, it is known that the specific per-component values are highly dependent on the integration path. We obtain an extreme case, which demonstrates that caution should be taken even when restricting to qualitative comparison.

In Situ Characterization of Dehydration during Ion Transport in Polymeric Nanochannels

The transport of hydrated ions across nanochannels is central to biological systems and membrane-based applications, yet little is known about their hydrated structure during transport due to the absence of in situ characterization techniques. Herein, we report experimentally resolved ion dehydration during transmembrane transport using modified in situ liquid ToF-SIMS in combination with MD simulations for a mechanistic reasoning. Notably, complete dehydration was not necessary for transport to occur across membranes with sub-nanometer pores. Partial shedding of water molecules from ion solvation shells, observed as a decrease in the average hydration number, allowed the alkali-metal ions studied here (lithium, sodium, and potassium) to permeate membranes with pores smaller than their solvated size. We find that ions generally cannot hold more than two water molecules during this sterically limited transport. In nanopores larger than the size of the solvation shell, we show that ionic mobility governs the ion hydration number distribution. Viscous effects, such as interactions with carboxyl groups inside the membrane, preferentially hinder the transport of the mono- and dihydrates. Our novel technique for studying ion solvation in situ represents a significant technological leap for the nanofluidics field and may enable important advances in ion separation, biosensing, and battery applications.

Renormalized site density functional theory for models of ion hydration

The development of accurate statistical mechanics models of molecular liquid systems is a problem of great practical and fundamental importance. Site-density functional theory (SDFT) is one of the promising directions in this area, but its success hinges upon the ability to efficiently reconcile the co-existence of two distinct intra- and inter-molecular interaction regimes in a molecular liquid. The renormalized formulation of SDFT (RSDFT), which we have recently developed, resolves this problem by introducing an additional potential field variable that decouples two interaction scales and maps the molecular liquid problem onto the effective simple liquid mixture. This work provides a critical assessment of RSDFT for the hydrated ion system-a problem that historically has always been one of the most difficult cases for SDFT applications. Using a two-site model of water, we perform a comprehensive analysis of hydrated alkali metal and halogen ions, including both structural and free energy based characteristics. The results indicate that RSDFT provides a significant improvement over conventional three-dimensional reference interaction site model implementations and may prove useful in coarse grained simulations based on two-site solvent models.

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes

Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined.In this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion-ion, ion-water, and water-water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions.DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air-water interface, ions in bulk, and at the air-water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.