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At least 235 records · Page 13

Physically Based Modeling of PEMFC Cathode Catalyst Layers: Effective Microstructure and Ionomer Structure–Property Relationship Impacts

Abstract This work presents a pseudo-two-dimensional proton exchange membrane fuel cell (PEMFC) model incorporating Nafion ionomer structure–property relationships in the cathode catalyst layer (CL) to capture and explain losses at low Pt loading. Structural data from neutron reflectometry and thin film Nafion conductivity measurements predict variations in the oxygen diffusion coefficient and ionic conductivity with changing CL ionomer thickness and Pt loading. By including these structure–property relationships, predicted polarization curves agree closely with previously published experimental data from cells with Pt loadings between 0.025 and 0.2 mg/cm2. Results demonstrate that structure–property relationships based on physically measurable ionomer and CL properties provide a feasible interpretation of PEMFC CL phenomena for a range of Pt loadings and help explain previously unaccounted-for losses at low Pt. Results also show that simulations must account for surface species coverage variations in order to properly capture the kinetic losses. Finally, results suggest that an increase in ionomer thickness surrounding the C/Pt surfaces may lead to improved cell performance due to improved ionic conductivity.

Electrochemistry↗

Theoretical study of the bonding of Nb(2+) to CH2, C2H2, and C2H4

The bonding of Nb(2+) with CH2, C2H2, and C2H4 is studied by using electronic structure calculations that include high levels of electron correlation. The binding energy for NbCH2(2+) is in good agreement with the lower bound determined from the reaction with CH4 but is significantly smaller than the value determined from the binding energy and ionization potential of NbCH2(+). The calculations and a new interpretation of the experiment indicate that the larger value is in error primarily because the ionization potential of NbCH2(+) determined from bracketing charge-exchange reactions is too small. The computed binding energy of NbC2H2(2+) is in good agreement with experiment. The calculations show that the bonding is predominantly covalent in character for both NbCH2(2+) and NbC2H2(2+), whereas for NbC2H4(2+) the electronic states that are predominantly ionic and covalent are nearly degenerate. The trend in binding energies, CH2 greater than C2H2 greater than C2H4, is consistent with the energy required to prepare the ligands for bonding.

Bauschlicher, Charles W., Jr.↗

Methods of recovering an elemental rare earth metal, and methods of forming a rare earth metal

A method of recovering an elemental rare earth metal comprises placing a rare earth-containing material comprising a rare earth metal in a reaction solution comprising a reducing agent and a non-aqueous solvent comprising an ionic liquid or a eutectic mixture, reducing the rare earth metal with the reducing agent to form a metallic rare earth metal and cations of the reducing agent, transferring the cations of the reducing agent from the reaction solution to an electrochemical cell through an ion exchange membrane, and reducing the cations of the reducing agent in the electrochemical cell. Related methods of forming an elemental rare earth metal, and related systems are disclosed.

Case, Mary E.↗

Investigation into Na and Cs activity coefficients in high salt solutions to support Cs removal in Hanford tank waste

The treatment of Hanford tank waste is one of the most technically challenging environmental cleanup activities for the U.S. Department of Energy to date. To expedite the processing of liquid waste stored in underground tanks in southeastern Washington state, it is necessary to remove the significant dose contributor, 137 Cs. Toward this effort, ion exchange with crystalline silicotitanate (CST) has been employed as part of the Tank Side Cesium Removal system. The model used to predict Cs exchange onto CST was developed using activity coefficients calculated from the Bromley equation. A series of batch contact tests that varied in [Na] were conducted to look at the impact of Na concentration on Cs distribution. Experimental distribution ratios ( K d ) were compared to the distribution ratios predicted using three different activity coefficient models: (1) commercially available HSC software, (2) the Bromley equation, and (3) a simplified approach adapted from Marcos-Arroyo et al. Ultimately, the Bromley method underpredicted the effect of ionic strength on the Na activity coefficient ( γ Na+ ), HSC overestimated the impact of ionic strength on the expected performance due to the Cs activity coefficient ( γ Cs+ ), but the simplified approach predicted the experimental K d values quite well in a binary matrix. In conclusion, expansion of this approach in complex matrices is necessary for application to Hanford tank waste.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Elliptical-P cells in the avian perilymphatic interface of the Tegmentum vasculosum

Elliptical cells (E-P) are present at the perilymphatic interface lumen (PIL) of the lagena. The E-P cells often separate from the tegmentum vasculosum (TV) and have touching processes that form a monolayer between the K+ rich perilymph and the Na+ rich endolymph, similar to the mammalian Reissner's membrane. We examined the TV of chicks (Gallus domesticus) and quantitated the expression of anti-S100 alphaalphabetabeta and S100 beta. There was a 30% increase of S100 beta saturation in the light cells facing the PIL when compared to other TV light cells. We show that: (1) the dimer anti- S100 alphaalphabetabeta and the monomer anti-S100 beta are expressed preferentially in the light cells and the E-P cells of TV; (2) expression of S100 beta is higher in light cells facing the PIL than in adjacent cells; (3) the expression of the dimer S100 alphaalphabetabeta and monomer S100 beta overlaps in most inner ear cell types, including the cells of the TV, most S100 alphaalphabetabeta positive cells express S 100 beta, but S100 beta positive cells do not always express S100 alphaalphabetabeta; and (4) the S100 beta expression in light cells, the abundant Na+-K+ ATPase on dark cells of the TV, and previously demonstrated co-localization of S100 beta/GABA in sensory cells suggest that S100 beta could have, in the inner ear, a dual neurotrophic-ionic modulating function.

NASA Discipline Neuroscience↗

Manifestation of postcollision interaction in Krypton LMN Auger spectra following K-shell photoionization

In this work, we report on an experimental and theoretical study of post-collision interaction (PCI) effects on L 2 -M 4,5 N 2,3 Auger electrons measured above the Kr K-edge in which L 2 vacancies are primarily generated by KL 2 x-ray emission. Such cascade processes, in which a deep inner-shell vacancy decays first by x-ray emission followed by Auger electron emission, is a strong decay mode in heavy atoms. The L 2 -M 4,5 N 2,3 Auger electron peak is observed to become increasingly asymmetric with a shifting peak maximum as the absorbed x-ray energy approaches the K-shell ionization threshold. This is attributed to PCI energy exchanges of the Auger electron with the 1s photoelectron. To model the PCI effects, we have applied a semiclassical approach modified to account for the combined lifetimes of the K and L 2 hole states. In addition, our analysis treats several closely spaced Auger transitions with final ionic states having different terms and angular momenta.

74 ATOMIC AND MOLECULAR PHYSICS↗

Identifying electrochemical processes by distribution of relaxation times in proton exchange membrane electrolyzers

Distribution of relaxation time (DRT) is used to interpret electrochemical impedance spectroscopy (EIS) for proton exchange membrane (PEM) water electrolyzers, with an attempt to separate overlapped relaxation processes in Nyquist plots. By varying operating conditions and catalyst loadings, four main relaxation peaks arising from EIS can be identified and successfully separated from low to high frequencies as (P1) mass transport, (P2) oxygen evolution reaction kinetics, (P3) reaction kinetics (with faster time constant than P2), and (P4) ionic transport. Here, the shape, height, and frequency of the DRT peaks change with different membrane electrode assembly (MEA) configurations. Electron microscopy reveals distinct features from the cross-sectioned MEAs which verify critical DRT results in that increasing the iridium (Ir)-anode loading from 0.2 mgIr/cm 2 to 1.5 mgIr/cm 2 reduces kinetic losses due to higher site-access; a thick and compacted anode, however, also triggers higher ohmic resistances from membrane/catalyst layer hydration and increases transport losses due to longer ionomer pathways. DRT provides higher resolution to EIS for deconvoluting processes with different relaxation times and the quantification of DRT peaks improves the accounting of total losses from each process.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lignin Derived Ionic Liquids: Synthesis and Application for Biopolymer Processing (CRADA Final Report)

We have established a scalable and economically viable process to convert lignin into ionic liquids for use in biopolymer processing. We have studied the four main topics: 1) lignin depolymerization to produce vanillin through oxidation, 2) lignin reduction to produce guaiacols, 3) oxidation process scale up, and 4) ionic liquid synthesis and application for biopolymer processing. The main accomplishment is summarized below: A maximal vanillin yield of 4.9% (8.8% total product yield) was achieved under optimal oxidation conditions using design of experiments (DOE); Aminophenol with 94.5% purity was synthesized via reductive amination using vanillin isolated from ion-exchange chromatography; At a higher lignin loading (10%), the vanillin yield in the scale up reaction was lower than the bench scale reaction; The filtration-based downstream separation of the scale-up process was able to recover 76% of vanillin; A maximal lignin reduction product (guaiacols) yield of 6.5% was achieved in the presence of Ru/C, formic acid, and methanol; The lignin reduction product yield and composition were affected by the use of different solvent and catalytic reagents (methanol in combination of Ru/C and formic acid gives the highest product yield); Lignin oxidation and reduction products: vanillin, acetovanillone, guaiacols, and eugenol are successfully used for IL synthesis; XX based ILs showed cellulose solubility with up to xx%; Technoeconomic analysis results indicate the potential of producing affordable ILs from kraft lignin (MSP: $14/kg); Life-cycle assessment results show the potential to reduce GHG emissions by up to 85% relative to existing ILs ([Ch][Lys]) with GHG emission: 1.2 kg CO 2e /kg of IL produced.

09 BIOMASS FUELS↗

Radionuclide transport in fractured chalk under abrupt changes in salinity

Internationally, it has been agreed that geologic repositories for spent fuel and radioactive waste are considered the internationally agreed upon solution for intermediate and long-term disposal. In countries where traditional nuclear waste repository host rocks (e.g., clay, salt, granite) are not available, other low permeability lithologies must be studied. Here, chalk is considered to determine its viability for disposal. Despite chalk's low bulk permeability, it may contain fracture networks that can facilitate radionuclide transport. In arid areas, groundwater salinity may change seasonally due to the mixing between brackish groundwater and fresh meteoric water. Such salinity changes may impact the radionuclides' mobility. In this study, radioactive U(VI) and radionuclide simulant tracers (Sr, Ce and Re) were injected into a naturally fractured chalk core. The mobility of tracers was investigated under abrupt salinity variations. Two solutions were used: a low ionic strength (IS) artificial rainwater (ARW; IS ~0.002) and a high IS artificial groundwater (AGW; IS ~0.2). During the experiments, the tracers were added to ARW, then the carrier was changed to AGW, and vice versa. Ce was mobile only in colloidal form, while Re was transported as a conservative tracer. Both Re and Ce demonstrated no change in mobility due to salinity changes. In contrast, U and Sr showed increased mobility when AGW was introduced and decreased mobility when ARW was introduced into the core. These experimental results, supported by reactive transport modeling, suggest that saline groundwater solutions promote U and Sr release via ion-exchange and enhance their migration in fractured chalk. Here the study emphasizes the impact of salinity variations near spent fuel repositories and their possible impact on radionuclide mobility.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

Holistic design principles for flow batteries: Cation dependent membrane resistance and active species solubility

Cation dependent resistance of a commercial cation exchange membrane, Nafion™ 212, as well as the solubility of select active materials are investigated, demonstrating practical consequences of cation choice on redox flow battery (RFB) performance. The conductivity of alkali and methyl- or -alcohol substituted ammonium cations through pretreated Nafion™ 212 reveal that cation size is the dominant factor affecting ionic transport. Among the alkali series the resistance increases with larger ionic radii and similarly, with increasing steric bulk through substitution on ammonia. The solubility of ferrocyanide, a commonly used redox flow battery posolyte (or catholyte), as well as iron, cobalt, and chromium metal-organic compounds are determined for the same series of cations. Full cells are assembled using various cation mixtures and membrane pre-treatments to demonstrate practical effects of each variable. Here, we highlight the need to carefully select the correct cations for efficient electrolyte design, since certain cations may lead to high conductivity but low solubility, or vice versa, and provide design principles for RFBs using Nafion™ 212.

25 ENERGY STORAGE↗

Membrane–Electrolyte System Approach to Understanding Ionic Conductivity and Crossover in Alkaline Flow Cells

Membrane transport properties are crucial for electrochemical devices, and these properties are influenced by the composition and concentration of the electrolyte in contact with the membrane. We apply this general membrane-electrolyte system approach to alkaline flow batteries, studying conductivity and ferricyanide crossover of Nafion and E-620. We report undetectable crossover for as-received Nafion and E-620 after both sodium and potassium exchange, but high ferricyanide permeability of 10 –7 to 10 –8 cm2 s –1 for Nafion subjected to pre-treatment prevalent in the flow battery literature. We show how the electrolyte mass fraction in hydrated membranes regulates the influence of ion concentration on membrane conductivity, identifying that increasing electrolyte concentration may not increase 1 membrane conductivity even when it increases electrolyte conductivity. To illustrate this behavior we introduce a new metric, the membrane penalty, as the ratio of the conductivity of the electrolyte to that of the membrane equilibrated with the electrolyte. We discuss the tradeoff between flow battery volumetric capacity and areal power density that arises from these findings. Finally, we apply insights from this approach to provide recommendations for use of membranes in alkaline flow cells, and electrochemical reactors in general.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Guanidinium-Based Ionic Covalent-Organic Nanosheets for Sequestration of Cr(VI) and As(V) Oxoanions in Water

Chromium- and arsenic-based oxoanions are among the major highly toxic and carcinogenic inorganic pollutants present in groundwater, demanding fast and selective sequestration. Efficient capturing and removal of these highly mobile oxometallates at neutral pH presents a great challenge in groundwater cleanup. In this report, a series of guanidinium-based ionic organic covalent nanosheets (iCONs) with varying hydrogen bonding, steric, and electronic properties was studied to examine the structure–activity relationship in the adsorption and removal of chromium- and arsenic-based oxoanions in water. Structural modulations in iCONs were found to alter the guanidinium acidity, thus regulating the oxoanion uptake limits via ion exchange. The hydrogen bonding, steric, and electrostatic interactions at/near the guanidinium-based anion binding site in iCONs exerted heavy influences on the uptake efficiency and selectivity of arsenate but not on those of chromate. Further analyses revealed that the parallel bidentate hydrogen bonding interactions play a key role in the weak binding of arsenate to the protonated/positively charged guanidine motifs, whereas the strong ion–ion interactions between chromate and guanidinium appear to be more tolerant to the geometric and structural perturbation.

36 MATERIALS SCIENCE↗

Ion-Atom Cold Collisions and Atomic Clocks

Collisions between ultracold neutral atoms have for some time been the subject of investigation, initially with hydrogen and more recently with laser cooled alkali atoms. Advances in laser cooling and trapping of neutral atoms in a Magneto-Optic Trap (MOT) have made cold atoms available as the starting point for many laser cooled atomic physics investigations. The most spectacularly successful of these, the observation of Bose-Einstein Condensation (BEC) in a dilute ultra-cold spin polarized atomic vapor, has accelerated the study of cold collisions. Experimental and theoretical studies of BEC and the long range interaction between cold alkali atoms is at the boundary of atomic and low temperature physics. Such studies have been difficult and would not have been possible without the development and advancement of laser cooling and trapping of neutral atoms. By contrast, ion-atom interactions at low temperature, also very difficult to study prior to modern day laser cooling, have remained largely unexplored. But now, many laboratories worldwide have almost routine access to cold neutral atoms. The combined technologies of ion trapping, together with laser cooling of neutrals has made these studies experimentally feasible and several very important, novel applications might come out of such investigations . This paper is an investigation of ion-atom interactions in the cold and ultra-cold temperature regime. Some of the collisional ion-atom interactions present at room temperature are very much reduced in the low temperature regime. Reaction rates for charge transfer between unlike atoms, A + B(+) approaches A(+) + B, are expected to fall rapidly with temperature, approximately as T(sup 5/2). Thus, cold mixtures of atoms and ions are expected to coexist for very long times, unlike room temperature mixtures of the same ion-atom combination. Thus, it seems feasible to cool ions via collisions with laser cooled atoms. Many of the conventional collisional interactions, exploited as a useful tool at room temperature and higher, are greatly enhanced at low energy. For example, collisional spin transfer from one species of polarized atoms to another has long been a useful method for polarizing a sample of atoms where no other means was available. Because optical pumping cannot be used to polarize the nuclear spin of Xe-129 or He-3 (for use in nmr imaging of the lungs), the nuclear spins are polarized via collisions with an optically pumped Rb vapor in a cell containing both gases. In another case, a spin polarized thermal Cs beam was used to polarize the hyperfine states of trapped He(+)-3 ions in order to measure their hyperfine clock transition frequency. The absence of an x-ray light source to optically pump the ground state of the He(+)-3 ion necessitated this alternative state preparation. Similarly, Cd(+) and Sr(+) ions were spin-oriented via collisions in a cell with optically pumped Rb vapor. Resonant RF spin changing transitions in the ground state of the ions were detected by changes in the Rb resonance light absorption. Because cold collision spin exchange rates scale with temperature as T(sup -1/2) this technique is expected to be a far more powerful tool than the room temperature counterpart. This factor of 100 or more enhancement in spin exchange reaction rates at low temperatures is the basis for a novel trapped ion clock where laser cooled neutrals will cool, state select and monitor the ion clock transition. The advantage over conventional direct laser cooling of trapped ions is that the very expensive and cumbersome UV laser light sources, required to excite the ionic cooling transition, are effectively replaced by simple diode lasers.

Prestage, John D.↗

Synthesis and structure of Americium(III) diglycolate oxalate Trihydrate, Am(ODA)(C 2 O 4 )(H 2 O) 3

Improving f-element separations is important for actinide(III) (An 3+ ) and lanthanide(III) (Ln 3+ ) based technologies. Unfortunately, An 3+ and Ln 3+ ions are difficult to separate from one another because they have similar chemical characteristics. One successful separation method utilizes anion exchange chromatography. This approach exploits differences in An 3+ and Ln 3+ Lewis acidities and their varying abilities to attract anionic complexing agents, like oxalates (C 2 O 4 2– ) and diglycolates (ODA 2– ). The resulting negatively charged complexes are then separated using an anion exchange resin. To better understand how this anion exchange separation works, we reacted Am 3+ (aq) (aq designates Am 3+ dissolved in water) with the anion exchange complexing agents (H 2 C 2 O 4 and H 2 ODA). Here, the resulting Am(ODA)(C 2 O 4 )(H 2 O) 3 product was characterized using single crystal X-ray diffraction and UV-Vis-NIR spectroscopy. The Am(ODA)(C 2 O 4 )(H 2 O) 3 structure was similar to that established previously for Ln 3+ analogues, namely Ln(ODA)(C 2 O 4 )(H 2 O) x . These compounds were all isomorphous, had bridging C 2 O 4 2– and ODA 2– ligands, and crystallized as 2-dimensional extended solids. In addition, the Am 3 +–O bond distances could be predicted based on relative differences in Am 3+ and Ln 3+ 9-coordinate metal ionic radii. Overall, isolation of Am(ODA)(C 2 O 4 )(H 2 O) 3 showcased similarities in complexation and crystallization chemistry for Am 3+ and Ln 3+ .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Selective Sorbent Design: CaS Aerogel for Rapid Remediation of Aqueous Pb (II)

Heavy metals are a persistent environmental problem due to their high toxicity, even at very low concentrations (parts per billion, ppb). The removal of such diluted heavy metals is challenging because of the competition the counterions (Ca 2+ , Na + , Mg 2+ , etc.) present in natural water bodies. The design of sorbents capable of removing ions below the action limit (15 ppb for Pb 2+ ) requires a strong driving force for selective uptake and rapid removal. In this work, we report the synthesis of porous CaS aerogels (surface area = 143.6 m 2 /g) by oxidative assembly of CaS nanoparticles and describe their use in selective Pb 2+ ion remediation from water. Despite the presence of amorphous CaCO 3 (up to 50 wt %) in the gel network, the gels demonstrated a capacity of 17.1 mmol Pb/g aerogel (3543 mg/g), and this could be augmented to 22.5 mmol Pb/g aerogel (4593 mg/g) by modifying the synthesis to reduce CaCO 3 content to ca. 15 wt %. Moreover, the selectivity of CaS aerogels toward Pb 2+ ions is high, as evidenced by little-to-no change in the distribution constant (K d ∼ 10 4 ) in the presence of competing ions (1 M) such as Na + , Mg 2+ , and Ca 2+ . During remediation with low concentrations (100 ppb) of Pb 2+ with CaS aerogels, the level of Pb 2+ dropped to 5.4 ppb (below the 15 ppb EPA limit) within 1 h with a 95.4% removal efficiency. In contrast to the CO 2 supercritically dried aerogels, lower surface area ambient dried gels (xerogels) only remove 40% of the lead ions from a 100 ppb solution, saturating within 1 h. The efficiency and rapidity of selective Pb 2+ uptake using CdS aerogels arise from a combination of a strong thermodynamic driving force for cation exchange (K eq = 2.5 × 10 27 ) and chemisorption along with favorable kinetics associated with the high surface area porous architecture. These results show that formation of high surface area metal chalcogenide aerogels by oxidative assembly to form nanocrystalline architectures, as previously demonstrated for II−VI and IV−VI semiconductors, can be extended to the more highly ionic alkaline earth sulfides.

Aerogels↗

Efficient Synthesis of High-Performance Anion Exchange Membranes by Applying Clickable Tetrakis(dialkylamino)phosphonium Cations

Tetrakis(dialkylamino)phosphonium (TKDAAP) compounds exhibit extraordinary base resistance, a prerequisite feature for high-performance anion exchange membranes (AEMs). It is, however, challenging to synthesize a TKDAAP compound with reactive functionality that can be used to link the cation to a polymer backbone. In this study, two TKDAAP compounds with alkyne functionality were synthesized and incorporated into an azide-modified SBS triblock copolymer backbone via Cu(I)-catalyzed alkyne–azide cycloaddition (CuAAC) “click” chemistry. The properties of the resulting AEMs were characterized. It was found that (1) the triazole linker between the cation and the polymer backbone was stable under alkaline conditions; (2) varying the substituents of TKDAAP compounds could dramatically alter the stability; and (3) increasing the hydrophilicity of the AEM was an efficient way to enhance its ionic conductivity. Using clickable TKDAAP compounds makes it easy to combine various cations into polymer backbones with adjustable cation content, thus potentially leading to an efficient way to screen a wide variety of polyelectrolyte structures to identify the most promising candidates for high-performance AEMs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

From Molecules to Solids: A vdW-DF-C09 Case Study of the Mercury Dihalides

The mercury dihalides show a remarkable diversity in the structural preferences in their minimum energy structure types, spanning molecular to strongly bound ionic solids. A challenge in the development of density functional methods for extended systems is to arrive at strategies that serve equally well such a broad range of bonding modes or structural preferences. The chemical bonding and the stabilities of mercury dihalides and the general utility and reliability of the van der Waals density functional with C09 exchange (vdW-DF-C09) in predicting or describing the energetics and structural preferences in these metal dihalides is examined. Here, we show that, in contrast with the uncorrected generalized gradient approximation of the Perdew-Burke-Erzenhoff (PBE) exchange-correlation functional, qualitative and quantitative patterns in the bonding of the mercury dihalide solids are well reproduced with vdW-DF-C09 for the full series of HgX 2 systems for X = F, Cl, Br, and I. The possible existence of a low-temperature cotunnite polymorph for HgF 2 and PbF 2 is posited.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polarizability Plays a Decisive Role in Modulating Association between Molecular Cations and Anions

Electrostatic interactions involving proteins depend on not only the ionic charges involved but also their chemical identities. Here we examine the origins of incompletely understood differences in the strength of association of different pairs of monovalent molecular ions that are relevant to protein–protein and protein–ligand interactions. Cationic analogues of the basic amino acid side chains are simulated, along with oxyanionic analogues of cation-exchange ligands and acidic amino acids. Experimentally observed association trends with respect to the cations, but not anions, are captured by a nonpolarizable model. An effective continuum correction to account for electronic polarizability can capture both trends better but at the expense of fidelity to the underlying free energy landscape for ion-pair association. Finally, a polarizable model proves decisive in capturing experimentally suggested trends with respect to both cations and anions; critically, the free energy landscape for ion-pair association is itself altered, thus altering configurational sampling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗