This work presents a comparison between a numerical solution of the Poisson-Boltzmann equation and the analytical solution of its linearized version through the Debye-Hückel equations considering both size-dissimilar and common ion diameters approaches. In order to verify the limits in which the linearized Poisson-Boltzmann equation is capable to satisfactorily reproduce the nonlinear version of Poisson-Boltzmann, we calculate mean ionic activity coefficients for different types of electrolytes as various temperatures. The divergence between the linearized and full Poisson-Boltzmann equations is higher for lower molalities, and both solutions tend to converge toward higher molalities. For electrolytes of lower valencies (1:1, 1:2, 2:1, and 1:3) and higher distances of closest approach, the full version of the Debye-Hückel equation is capable of representing the activity coefficients with a low divergence from the nonlinear Poisson-Boltzmann. The size-dissimilar full version of Debye-Hückel represents a clear improvement over the extended version that uses only common ion diameters when compared to the numerical solution of the Poisson-Boltzmann equation. We have derived a salt-specific index (Θ) to gradually classify electrolytes in order of increasing influence of nonlinear ion-ion interactions, which differentiate the Debye-Hückel equations from the nonlinear Poisson-Boltzmann equation.

Investigation of the Limits of the Linearized Poisson-Boltzmann Equation.

The thermophysical properties of aqueous electrolyte solutions are of interest for applications such as water electrolyzers and fuel cells. Molecular dynamics (MD) and continuous fractional component Monte Carlo (CFCMC) simulations are used to calculate densities, transport properties (i.e., self-diffusivities and dynamic viscosities), and solubilities of H2 and O2 in aqueous sodium and potassium hydroxide (NaOH and KOH) solutions for a wide electrolyte concentration range (0–8 mol/kg). Simulations are carried out for a temperature and pressure range of 298–353 K and 1–100 bar, respectively. The TIP4P/2005 water model is used in combination with a newly parametrized OH– force field for NaOH and KOH. The computed dynamic viscosities at 298 K for NaOH and KOH solutions are within 5% from the reported experimental data up to an electrolyte concentration of 6 mol/kg. For most of the thermodynamic conditions (especially at high concentrations, pressures, and temperatures) experimental data are largely lacking. We present an extensive collection of new data and engineering equations for H2 and O2 self-diffusivities and solubilities in NaOH and KOH solutions, which can be used for process design and optimization of efficient alkaline electrolyzers and fuel cells.

A New Force Field for OH– for Computing Thermodynamic and Transport Properties of H2 and O2 in Aqueous NaOH and KOH Solutions

Thermodynamics is the science of the interactions between energy and matter. It was formalized in the late 19th century and remains an essential piece in solving many technological challenges that society faces today. Yet, it is often considered complex and challenging, perhaps because it is often taught within a rigid mathematical framework, without highlighting the extensive range of applications and the tools that it offers for understanding and elaborating a sustainable future. The authors of this paper have performed an industrial survey (Kontogeorgis et al., Ind. Eng. Chem. Res., 2021, 60, 13, 4987-5013), which pointed out that thermodynamics is indeed a cornerstone of many processes in a large range of industries, but that as of today, many questions and needs remain unanswered. Some missing answers are caused by a lack of knowledge of the existing tools (educational issue), some by the unavailability of models, parameters or by the lack of transferability of the concepts from one system to another. In other cases, simply, no generally accepted approach exists, and fundamental research is required for understanding the phenomena. In all cases, data are needed, either to understand, develop, or validate the models. Specific recent examples of applied thermodynamics research relevant to industrial practice are discussed. This manuscript aims not only at promoting research but also at encouraging highly trained professionals to engage in education, laboratory work, fundamental developments, and/or model validation. Such professionals should find positions both in academia and in industry, as well as with software vendors. Collaboration between academia, industry, and software vendors is essential in order to foster new developments and serve the goals of sustainable development and circular economy. 

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A View on the Future of Applied Thermodynamics

The true Hückel equation for electrolyte solutions and its relation with the Born term

Multiple numerical studies have unambiguously shown the existence of a liquid–liquid critical point in supercooled states for different numerical models of water, and various structural indicators have been put forward to describe the transformation associated with this phase transition. Here we analyze numerical simulations of near-critical supercooled water to compare the behavior of several of such indicators with critical density fluctuations. We show that close to the critical point most indicators are strongly correlated to density, and some of them even display identical distributions of fluctuations. These indicators probe the exact same free energy landscape, therefore providing a thermodynamic description of critical supercooled water which is identical to that provided by the density order parameter. This implies that close to the critical point, there is a tight coupling between many, only apparently distinct, structural degrees of freedom.

Correlated Fluctuations of Structural Indicators Close to the Liquid–Liquid Transition in Supercooled Water

Electrolyte thermodynamics is a complex and broad subject of immense importance in very diverse applications. The models proposed for electrolyte solutions have some similarities to those for non-electrolytes but also significant differences. Not just due to additional contributions but also because of the way the models are developed for electrolytes vs. non-electrolytes. Moreover, there are still fundamental issues unresolved in electrolyte thermodynamics. It is still today the activity coefficient models, often extensions of local-composition models that are used in engineering practice for electrolytes e.g., the Pitzer, electrolyte NRTL and extended UNIQUAC. In this review, however, we investigate the area of equations of state (EoS) for electrolytes, a very rich field which essentially started with the Fürst and Renon model in 1993. Since then numerous electrolyte EoS (e-EoS) have been proposed; the literature is both rich and confusing. We have decided in this work to review mostly electrolyte versions of cubic and CPA (Cubic-Plus-Association) EoS, although some of the observations made may be applicable to e-EoS of the SAFT type as well, and some of them are also briefly discussed. Reviewing e-EoS is not an easy task due to especially the diversity of modeling and parameter estimation approaches which are followed as well as the way the models have been validated. Almost none of the e-EoS proposed in literature can be compared “on equal terms” with another e-EoS. Thus, a critical comparative analysis is proposed here, including some recent developments of the e-CPA approach. When possible, different modeling—parameter estimation—validation approaches are compared. It is hoped that this review can provide an insight on the current state-of-the-art of some e-EoS proposed in literature and point out areas where further research is needed. 

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A Review of Electrolyte Equations of State with Emphasis on Those Based on Cubic and Cubic-Plus-Association (CPA) Models

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Water is a fascinating substance with lots of properties not encountered in other compounds. It has been suggested that making use of water's “anomalous” properties can lead to exciting applications in various disciplines e.g. engineering, medicine and physiology. The origin of these anomalous properties is far from clear, with the strong hydrogen bonds of water being only part of the answer. Moreover, water's structure and dynamics are not entirely understood either and new theories have appeared and debated during the 21st century. This review, aiming at a broader/general audience, attempts to review briefly some research trends related to water's structure, properties and applications. New experimental results for the debated phenomena of water bridge and exclusion zone are also presented and discussed. Various explanatory mechanisms for the exclusion zone are reviewed and a new proposal is put forward. A –hopefully- unbiased discussion is presented for both “mainstream” and unconventional theories and trends and future directions are also outlined. 

Water Structure, Properties and Some Applications – A review

The existence of two structural forms in liquid water has been a point of discussion for a long time. A phase transition between these two forms of liquid water has been proposed based on evidence from molecular simulations, and experiments have also been very recently able to track the proposed transition of the low-density liquid form to the high-density liquid form. We propose to use the average angle an oxygen atom makes with its neighbors to describe the structural environment of a water molecule. The distribution of this order parameter is observed to have two peaks with one peak at ∼109.5^{∘}, corresponding to the internal angle of a regular tetrahedron, indicating tetrahedral arrangement. The other peak corresponds to an environment with a tighter arrangement of neighboring molecules. The distribution of O-O-O angles is decomposed into two skewed distributions to estimate the fractions of the two liquid forms in water. A good similarity is observed between the temperature and pressure trends of fractions of locally favored tetrahedral structure (LFTS) form estimated using the new order parameter and the reports in the literature, over a range of temperatures and pressures. We also compare the structural environments indicated by different order parameters and find that the order parameter proposed in this paper captures the structure of first solvation shell of the LFTS accurately.

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Xiaodong Liang

Papers

A Review of Electrolyte Equations of State with Emphasis on Those Based on Cubic and Cubic-Plus-Association (CPA) Models

A Review of Electrolyte Equations of State with Emphasis on Those Based on Cubic and Cubic-Plus-Association (CPA) Models

Water Structure, Properties and Some Applications – A review

Investigation of the Limits of the Linearized Poisson-Boltzmann Equation.

Structural characteristics of low-density environments in liquid water.