Overview

- Single-Ion Solvation: Experimental and Theoretical Approaches to Elusive Thermodynamic Quantities
- By Philippe Hünenberger & Maria Reif
- RSC Computational Chemistry Series
- Series Editors: Jonathan Hirst (Nottingham, UK), Ken Jordan (Pittsburgh, USA),
  Carmay Lim (Taipei, Taiwan) and Walter Thiel (Mülheim, Germany)
- Hardcover Edition
- ISBN: 978-1-84755-187-0
- external pageRSC eBookcall_made DOI: 10.1039.9781849732222 (RSC eBook external pagelinkcall_made)
- Copyright: 2011
- Format: Hardback
- Extent: 690 pages
- Initial Sale Price: £144.99 (~ $235 / €165 / CHF210) at external pagepublishercall_made
- Current Sale Price: see e.g. RSC and amazon links provided here

- 42 Tables
- 42 Figures
- 2406 Literature references

This book provides an up-to-date and consistent account of a research field that has over hundred years of history and remains nowadays largely unsettled: single-ion solvation thermodynamics. Ions are ubiquitous in chemical, technological, ecological and biological processes. Characterizing their role in these processes requires in the first place the evaluation of the thermodynamic parameters associated with the solvation of a given ion. Yet, due to the constraint of electroneutrality, the involvement of surface effects and the ambiguous connection between microscopic and macroscopic descriptions, the determination of single-ion solvation properties via both experimental and theoretical approaches has turned out to be a very difficult and highly controversial problem. By reviewing the various approaches employed to date, establishing the relevant connections between single-ion thermodynamics and electrochemistry, resolving conceptual ambiguities, and reporting an exhaustive data compilation (in the context of alkali and halide hydration, along with relevant values for the proton), this book provides a consistent synthesis of a large and sometimes very confusing research field. It represents an essential text for in-depth understanding and further research.

• Discusses both experimental and theoretical approaches, and establishes connections between them.
• Provides both an account of the past research, covering over hundred years, and a discussion of current directions, in particular on the theoretical side.
• Involves a comprehensive reference list of over 2400 citations
• Employs a very consistent notation, including table of symbols and unambiguous definitions of all introduced quantities.
• Provides a discussion and clarification of ambiguous concepts, i.e. concepts that have not been defined clearly, or have been defined differently by different authors, leading to confusion in the past literature (e.g. thermodynamic standard states, real vs. intrinsic vs. conventional quantities, variants of the Volta, surface and Galvani potentials, variants of absolute electrode potentials...).
• Encompasses an exhaustive data compilation (in the restricted context of alkali and halide hydration, along with relevant values for the proton), along with recommended values based on the critical analysis of 221 raw sources.
• Is illustrated by a number of synoptic (color) figures, that should help the reader grasp the connections between different concepts.
• Provides a compact account of the research field.
• Provides a clarification of the research field.
• Provides up-to-date information on current research, in particular on the theoretical side.
• Provides in-depth understanding.
• Introduces new concepts, nomenclature and symbols whenever needed.

The book is primarily aimed at researchers (professors, postgraduates, graduates, industrial researchers) concerned with processes involving ionic solvation properties (these are ubiquitous, e.g. in physical/organic/analytical chemistry, electrochemistry, biochemistry, pharmacology, geology, ecology, …). Because of the concept definitions and data compilations it contains, it is also a useful reference book to have in a (university) library. Finally, it may be of general interest to anyone wanting to learn more about ions and solvation. However, due to the advanced treatment of the topic, it is not really meant for school education or as a basic textbook in undergraduate studies.

Ions are ubiquitous in nature and play a fundamental role in many essential ecological, biochemical, physiological and technological processes. Under the conditions of pressure and temperature prevailing on earth, ions would probably not play such an important role if their presence was not associated with that of large amounts of water. In the absence of water, at room temperature and ambient pressure, the extremely strong Coulombic interactions existing between oppositely-charged ions promote their aggregation into solid salts, exceptionally ionic liquids. The magnitude of these interactions is such that gas-phase ions are essentially non-existing species at equilibrium. Yet, in polar solvents, prominently water, dielectric screening of these direct Coulombic interactions by the dipolar solvent molecules represents an almost equally strong opposing force that permits, in synergy with entropic effects, the existence of solvated ions as dissociated entities. The properties of ions in solution crucially depend on the nature and magnitude of these solvation forces. Their characterization is thus an essential step towards the understanding of the properties of ions in solution. The key quantity accounting for the magnitude of ion-solvent interactions, in the simplest context of an individual ion at infinite dilution in a given solvent, is the corresponding single-ion solvation free energy, knowledge of the pressure and temperature dependence of which also gives access to all other derivative thermodynamic solvation parameters, e.g. the single-ion solvation enthalpy, entropy, volume, heat capacity, compressibility or expansivity, as well as to the corresponding partial molar variables in solution. The determination of single-ion solvation free energies and of their derivatives via experimental measurements or theoretical calculations is an issue that has preoccupied the physical chemistry community for more than one century. It is a very fundamental problem, which could well be viewed as the “hydrogen-atom problem” of ion thermodynamics and electrochemistry. Yet, this apparently simple issue hides an unexpected amount of complexity and truly represents a challenge, which cannot be claimed to have found a satisfactory solution even nowadays. The goal of Chapter 1 is to introduce the topic in the broad context of physics and chemistry, and to provide an overview of the aim, scope and content of the book.

The experimental determination of single-ion solvation free energies, as well as of corresponding derivative thermodynamic solvation parameters, is complicated by two fundamental problems: (i) the local electroneutrality of macroscopic matter at equilibrium and its corollary, the absence of free gas-phase ions in equilibrium situations; (ii) the presence of a surface polarization at air-liquid interfaces. Chapter 2 discusses these two problems in sequence, and provides a summary of their practical implications. The local electroneutrality constraint implies that single-ion solvation parameters are only directly accessible, via calorimetry and gas-phase spectroscopy-based statistical mechanics, in the form of sums over neutral ion combinations or, equivalently, as conventional (relative) values, i.e. with the proton parameters set to zero by definition. Absolute single-ion solvation parameters can also be obtained via Voltaic cell experiments and workfunction measurements. However, the presence of surface polarization effects at air-liquid interfaces implies that these determinations lead to real values, i.e. including the reversible work of interface crossing. The absolute single-ion solvation parameters that are of greatest theoretical relevance are intrinsic, i.e. solely characterizing the interaction of the ion with its polarized solvent environment, without contamination from surface effects. They cannot be accessed on the sole basis of experimental data and require the introduction of some apparently reasonable but formally unprovable postulate or model, called in this context an extra-thermodynamic assumption. The introduction of a specific assumption permits to anchor the conventional scale by providing estimates for either of three equivalent experimentally-elusive solvent-dependent quantities, namely the intrinsic solvation free energy G_H,svt of the proton, the intrinsic absolute potential V_H,svt of the reference hydrogen electrode, or the air-liquid interfacial potential χ_svt, along with their pressure or/and temperature derivatives. Unfortunately, considering the case of water, the use of different experimental approaches along with distinct extra-thermodynamic assumptions leads to a very large uncertainty range on the order of 0.5−1.0 V (potentials) or 50−100 kJ/mol (free energy) in the estimated values for the three above quantities.

The theoretical evalutation of single-ion solvation free energies, as well as of corresponding derivative thermodynamic solvation parameters, relies on models involving three different levels of resolution: (i) continuum-electrostatics calculations; (ii) classical atomistic simulations; (iii) quantum-mechanical computations. Chapter 3 introduces these three types of modeling approaches, and provides a summary of their strengths and shortcomings. On the low-resolution end, continuum-electrostatics calculations, inspired from the Born model, typically describe the ion as a rigid non-polarizable sphere and the solvent as a continuous medium of infinite extent, linear dielectric response, and homogeneous permittivity. These approaches have a long history and the merit of providing a simple and qualitatively correct framework for intuitive reasoning. However, they neglect the microscopic structure of the solvent molecules and the specific details of ion-solvent interactions, and rely on the ill-defined concept of an ionic radius. In the middle-resolution range, classical atomistic simulations describe the ion in solution as a system of classical point particles (atoms) interacting according to an empirically designed and calibrated potential energy function, called a force field. These methods should in principle be more accurate than continuum-electrostatics approaches, by accounting for the microscopic structure of the solvent molecules. However, in contrast to the latter methods, the averaging over solvent configurations must be carried out explicitly and the considered system is now of finite extent, e.g. liquid droplet or periodic computational box. The latter difference introduces serious methodological issues regarding the choice of boundary conditions, the approximate treatment of electrostatic interactions, and the evaluation of electric potentials based on the sampled configurations. The third issue appears in particular in the form of puzzling inconsistencies affecting the results of calculations involving slightly different potential-evaluation schemes. The origin of these inconsistencies is analyzed in more detail in Chapters 4, 6 and 7. The results of atomistic simulations also depend on the choice of ion-solvent van der Waals interaction parameters, which can be viewed as representing the atomistic analog of the ionic radius of continuum-electrostatics calculations, and suffer from a similar kind of ambiguity. Finally, on the high-resolution end, quantum-mechanical computations describe the ion in solution as a many-particle system characterized by a wavefunction obeying the Schrödinger equation, given a Hamiltonian encompassing Coulombic interactions between all the elementary particles involved. As first-principles approaches, these methods have a bright future and promise to enable the calculation of experimentally-elusive quantities G_H,svt, V_H,svt and χ_svt based on the most accurate physical model available nowadays, without relying on the specification of ambiguous quantities such as ionic radii or ion-solvent van der Waals interaction parameters. Unfortunately, they have the major shortcoming of being computationally expensive, which results in practice nowadays in severe restrictions concerning the system size, configurational sampling, basis-set size, and treatment of electron correlation.

The problem of the experimental and theoretical determination of single-ion solvation free energies, as well as of corresponding derivative thermodynamic solvation properties, is relatively complex. However, it is often further complicated by imprecisions, alternatives or ambiguities in the definitions of a number of fundamental concepts. Chapter 4 aims at clarifying these concepts and definitions within thermodynamics and electrochemistry, in the context of: (i) thermodynamics (variables, basic relationships, ideal behaviors, standard states, processes and cycles relevant to ionic solvation); (ii) electrostatics (interfacial effects, electric potentials, chemical potentials, workfunctions, electrode potentials); (iii) electrochemistry (types of measurements, relationship to thermodynamic quantities and electric potentials); (iv) single-ion properties (conventional, real, and intrinsic scales). Great attention is paid here to the critical examination of the physics underlying key concepts, as well as to the clarity and consistency of the employed terminology and mathematical notation, new terms or symbols being introduced whenever necessary. Care is also taken here to precisely define and consistently apply a unique thermodynamic standard-state convention, referred to as the bbme_T convention (1 bar reference pressure for solids and liquids, 1 bar reference pressure for gases, 1 molal reference concentration for solutes, warm-electron convention with Fermi-Dirac statistics). Due to incomplete or ambiguous specification in many literature sources, alternative conventions represent an important source of complication and mistakes in the field, and can be encountered at no less than six different levels: (i) choice of a reference pressure and of a reference solution concentration; (ii) choice of a standard or density-corrected solute standard-state variant; (iii) choice of a warm- or cold-electron convention for the standard-state ideal electron gas; (iv) choice of Boltzmann or Fermi-Dirac statistics for calculating the properties of the standard-state electron and proton; (v) choice of a reference electric potential for the ideal electron gas in the definition of absolute electrode potentials; (vi) choice of a specific anchoring point for the conventional scale of single-ion solvation parameters. These include the presence of an ambiguity in the standard-state definition for solute species, namely the existence of standard and density-corrected variants. The natural variant in which a standard quantity is determined and reported depends on the type of measurement performed. However, to our knowledge, this issue is probably raised for the first time in this book, although the ambiguity affects all standard thermodynamic quantities reported in the literature concerning processes involving solute species. Note, finally, that the physics of the solvation process is most directly characterized by what is referred to as semi-standard point-to-point solvation parameters, which characterize the transfer of the ion from a fixed point in the gas phase to a fixed point in solution and are exempt of standard-state bias, besides the specification of a reference pressure and temperature for the solvent properties.

In Chapter 5, the approaches employed for the experimental determination of thermodynamic parameters related to ionic solvation are reviewed, and the results of investigations employing these methods are discussed in the restricted context of alkali and halide hydration in the infinitely-dilute regime. Closely related properties formally pertaining to the pure solvent (water), namely the absolute solvation parameters of the proton, the absolute potential of the reference hydrogen electrode and the air-liquid interfacial potential, are also considered in view of their central role in single-ion solvation thermodynamics, in both their real and intrinsic forms. The discussion proceeds roughly incrementally, from the most directly accessible quantities to the more elusive ones, namely: (i) molar thermodynamic parameters of the elements; (ii) structural and molar thermodynamic parameters of the salts (ionic crystals); (iii) gas-phase equilibrium ion-pair distances; (iv) effective ionic radii; (v) relative electrode (redox) potentials (anchored based on the reference hydrogen electrode); (vi) thermodynamic parameters of salt formation; (vii) thermodynamic parameters of dissolved salt formation; (viii) thermodynamic parameters of salt dissolution; (ix) thermodynamic parameters of atomization; (x) thermodynamic parameters of ionization; (xi) thermodynamic parameters of reticulation; (xii) thermodynamic parameters of salt solvation; (xiii) metal workfunctions; (xiv) real absolute potential of the reference hydrogen electrode; (xv) real single-ion solvation parameters; (xvi) conventional single-ion solvation parameters; (xvii) air-liquid interfacial potential of the pure solvent; (xviii) intrinsic proton solvation parameters. Three additional sections provide: (i) a summary of recommended data concerning alkali and halide hydration, along with relevant pure-solvent properties; (ii) a discussion of suggested intrinsic single-ion solvation parameters for the alkali and halide ions, in connection with the Hofmeister series; (iii) a brief discussion of the properties of the solvated electron. The recommended data is based on the careful investigation of experimental results from 221 literature sources over the past nearly hundred years. This data is presented in the form of a minimal (non-redundant) set of parameters concerning the gas-phase, salt and solution properties the alkali and halide ions, as well as of the proton, with reference to water as a solvent, converted to a unique standard-state convention (bbme_T convention).

In Chapter 6, the approaches employed for the theoretical determination of thermodynamic parameters related to ionic solvation are reviewed, and illustrative results of these investigations are discussed, mainly in the restricted context of alkali and halide hydration. The relevant features of the basic physical models employed are presented in Chapter 3, and Chapter 6 is principally concerned with practical issues, improvements and corrections concerning these basic models. The most severe shortcomings of continuum-electrostatic calculations are to neglect the microscopic structure of the solvent molecules and the specific details of ion-solvent interactions, and to rely on the ill-defined concept of an ionic radius. Although numerous types of correction terms have been proposed in the past for various neglected effects, including semi-atomistic approaches, none of these arguably improved models can be considered to be at the same time quantitative and predictive. The most severe shortcomings of classical atomistic simulations are caused by finite-size effects, approximate electrostatics and ambiguity of the electric potential calculation. These issues have, up to recently, prevented the obtension of consistent results for single-ion thermodynamic solvation parameters and air-liquid interfacial potentials. Fortunately, the situation has changed in the past few years with the realization that the corresponding errors could be corrected ex post, so as to achieve methodological independence in the simulation results. Still, the outcome of these calculations remains, even after correction, affected by three major sources of error: the mean-field treatment of electronic polarizability (in most calculations), the approximate representation of van der Waals interactions (functional form and combination rules), and the dependence of the results on the choice of ion-solvent van der Waals interaction parameters, which suffer from a similar kind of ambiguity as the ionic radius of continuum-electrostatics calculations. It is nevertheless possible that the results of simulations concerning a large spectrum of ionic properties, including but extending beyond single-ion solvation free energies, provides in the near future a reliable approach for the accurate evaluation of the experimentally-elusive quantities G_H,svt, V_H,svt and χ_svt. The corresponding extra-thermodynamic assumption is termed in this book the atomistic-consistency assumption. Finally, quantum-mechanical computations, including quasi-chemical theory, hybrid quantum-classical approaches and Car-Parrinello molecular dynamics simulations, have the major shortcoming of being computationally expensive, which results in practice nowadays in severe restrictions concerning the system size, configuration sampling, basis-set size and treatment of electron correlation. As a result, the computation of single-ion solvation free energies with a sufficient accuracy represents a considerable challenge. However, the steady increase in computing power along with recent methodology developments in the area suggest that the calculation of ionic solvation parameters may become feasible with a sufficient accuracy in the coming decades.