Unraveling thermodynamic anomalies of water: A molecular simulation approach to probe the two-state theory with atomistic and coarse-grained water models

Thermodynamic and dynamic anomalies of water play a crucial role in supporting life on our planet. The two-state theory attributes these anomalies to a dynamic equilibrium between locally favored tetrahedral structures (LFTSs) and disordered normal liquid structures. This theory provides a straightforward, phenomenological explanation for water's unique thermodynamic and dynamic characteristics. To validate this two-state feature, it is critical to unequivocally identify these structural motifs in a dynamically fluctuating disordered liquid. In this study, we employ a recently introduced structural parameter (θavg) that characterizes the local angular order within the first coordination shell to identify these LFTSs through molecular dynamics simulations. We employ both realistic water models with a liquid-liquid critical point (LLCP) and a coarse-grained water model without an LLCP to study water's anomalies in low-pressure regions below 2 kbar. The two-state theory consistently describes water's thermodynamic anomalies in these models, both with and without an LLCP. This suggests that the anomalies predominantly result from the two-state features rather than criticality, particularly within experimentally accessible temperature-pressure regions.

Theoretical and practical investigation of ion-ion association in electrolyte solutions

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

Prediction of water anomalous properties by introducing the two-state theory in SAFT

Water is one of the most abundant substances on earth, but it is still not entirely understood. It shows unusual behavior, and its properties present characteristic extrema unlike any other fluid. This unusual behavior has been linked to the two-state theory of water, which proposes that water forms different clusters, one with a high density and one with a low density, which may even form two distinct phases at low temperatures. Models incorporating the two-state theory manage to capture the unusual extrema of water, unlike traditional equations of state, which fail. In this work, we have derived the framework to incorporate the two-state theory of water into the Statistical-Associating-Fluid-Theory (SAFT). More specifically, we have assumed that water is an ideal solution of high density water molecules and low density water molecules that are in chemical equilibrium. Using this assumption, we have generalized the association term SAFT to allow for the simultaneous existence of the two water types, which have the same physical parameters but different association properties. We have incorporated the newly derived association term in the context of the Perturbed Chain-SAFT (PC-SAFT). The new model is referred to as PC-SAFT-Two-State (PC-SAFT-TS). Using PC-SAFT-TS, we have succeeded in predicting the characteristic extrema of water, such as its density and speed of sound maximum, etc., without loss of accuracy compared to the original PC-SAFT. This new framework is readily extended to mixtures, and PC-SAFT-TS manages to capture the solubility minimum of hydrocarbons in water in a straightforward manner.

Novel Model for Predicting the Electrical Conductivity of Multisalt Electrolyte Solutions

This study presents a novel model to predict the electrical conductivity of multisalt electrolyte solutions by incorporating corrections to the ideal behavior due to relaxation and electrophoretic effects. The performance of the model is evaluated by comparing its predictions with the experimental data of 24 multisalt aqueous solutions. The comparison reveals good agreement for solutions with an ionic strength below 1 mol/L without adjusting any parameter to fit to the experimental data. However, the model tends to overestimate the molar conductivity at higher ionic strengths. The discrepancy is attributed to the neglect of the solvent structure and the formation of ion pairs. It has been speculated how the accuracy of the developed model could be improved in relation to these limitations. Furthermore, the performance of the model is rigorously tested in systems with ion complex formation. It has been demonstrated that when the distribution of ion complexes is calculated from a thermodynamic model and then used to predict the electrical conductivity with the developed model, a satisfactory level of accuracy is attained for these systems.

New Electrical Conductivity Model for Electrolyte Solutions Based on the Debye-Hückel-Onsager Theory

A new electrical conductivity model is developed for unassociated electrolyte solutions based on the Debye-Hückel-Onsager theory. In this model, we assume that a single cation and a single anion with their crystallographic ionic radii are in a continuum medium of the solvent(s). We compare the predictions of the developed model with the experimental measurements of binary 1:1, 2:1, 1:2, 2:2, 1:3, 3:1, 2:3, 3:2, 3:3, 1:4, and 2:4 aqueous solutions in the temperature range 273.15-373.15 K. Our results are in good agreement with the experimental data. An extension of the model was formulated to incorporate ion pairing, and its effectiveness was evaluated across three essential systems: 2:2 aqueous sulfate solutions, ionic liquid-co-solvent systems, and NaCl-water-1,4-dioxane solutions. This adaptation demonstrated a strong correlation with experimental data, highlighting the broad applicability.

Binding Debye-Hückel theory for associative electrolyte solutions

This study presents a new equation of state (EOS) for charged hard sphere fluids that incorporates ion-ion association. The EOS is developed using the Debye-Hückel (DH) theory, reference cavity approximation, and Wertheim's theory. Predictive accuracy is evaluated by comparing the model's predictions with Monte Carlo simulations for various charged hard-sphere fluids. The assessment focuses on mean ionic activity coefficient, individual ionic activity coefficient, and osmotic coefficients. The results demonstrate good agreement between the model and simulations, indicating its success for different electrolyte systems. Incorporating ion-ion association improves accuracy compared to the DH theory. The importance of the cavity function and ion-dipole interactions is emphasized in accurately representing structural properties. Overall, the developed EOS shows promising predictive capabilities for charged hard sphere fluids, providing validation and highlighting the significance of ion-ion association in thermodynamic predictions of electrolyte solutions.

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.

Multiple insights call for revision of modern thermodynamic models to account for structural fluctuations in water

Modern thermodynamic models incorporate the concept of association (hydrogen bonding) and they can describe very satisfactorily many properties of water containing mixtures. They have not been successful in representing water's anomalous properties and this work provides a possible explanation. We have analyzed and interpreted recent experimental data, molecular simulation results, and two-state theory approaches and compared against the predictions from thermodynamic models. We show that the dominance of the tetrahedral structure implemented in modern thermodynamic models may be the reason for their failure for describing water systems. While this study does not prove the two-state theories for water, it indicates that a high level of tetrahedral structure of water is not in agreement with water's anomalous properties when used in thermodynamic models.

Investigation of the Limits of the Linearized Poisson-Boltzmann Equation

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.

Structural characteristics of low-density environments in liquid water

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.

Distinguishing Weak and Strong Hydrogen Bonds in Liquid Water-A Potential of Mean Force-Based Approach

The ability to form hydrogen bonds is one of the most important factors behind water's many anomalous properties. However, there is still no consensus on the hydrogen bond structure of liquid water, including the average number of hydrogen bonds in liquid water. We use molecular dynamics simulations of the polarizable iAMOEBA water model for investigating the hydrogen bond characteristics of liquid water over a wide range of temperatures and pressures. Geometric definitions of a hydrogen bond often use a rectangular region on the plane of hydrogen bond distances and angles. In this work, we find that an elliptical region is more appropriate for the identification of hydrogen bonds, based on statistically favorable molecular configurations. The two-dimensional potential of mean force (PMF) landscape along the hydrogen bond distance (O-H) and angle (O-H-O) is calculated for identifying the statistically favored molecular configurations, which is then used for defining hydrogen bond formation as well as the strength of a hydrogen bond. We further propose a new approach to characterize the hydrogen bonds as strong when the PMF is lower than -2 kT. Using this definition, a consistent explanation for the different average numbers of hydrogen bonds in water is obtained in agreement with the literature. Simulations are also performed with the rigid and nonpolarizable TIP4P/2005 water model. Both water models are qualitatively consistent in predicting the distribution of double-, single-, and non-donor configurations, in line with experimental data, while the iAMOEBA water model yields more quantitatively precise results, including a 10-15% double-donor fraction at 90 °C and 1 atm. The method is also demonstrated to be applicable to the recent, and more general, three-dimensional PMF-based definition of hydrogen bonds.

Ionic liquid-based in situ product removal design exemplified for an acetone-butanol-ethanol fermentation

Selecting an appropriate separation technique is essential for the application of in situ product removal (ISPR) technology in biological processes. In this work, a three-stage systematic design method is proposed as a guide to integrate ionic liquid (IL)-based separation techniques into ISPR. This design method combines the selection of a suitable ISPR processing scheme, the optimal design of an IL-based liquid-liquid extraction (LLE) system followed by process simulation and evaluation. As a proof of concept, results for a conventional acetone-butanol-ethanol fermentation are presented (40,000 ton/year butanol production). In this application, ILs tetradecyl(trihexyl)phosphonium tetracyanoborate ([TDPh][TCB]) and tetraoctylammonium 2-methyl-1-naphthoate ([TOA] [MNaph]) are identified as the optimal solvents from computer-aided IL design (CAILD) method and reported experimental data, respectively. The dynamic simulation results for the fermentation process show that, the productivity of IL-based in situ (fed-batch) process and in situ (batch) process is around 2.7 and 1.8fold that of base case. Additionally, the IL-based in situ (fed-batch) process and in situ (batch) process also have significant energy savings (79.6% and 77.6%) when compared to the base case.

Industrial Requirements for Thermodynamic and Transport Properties: 2020

This paper reports the results of an investigation of industrial requirements for thermodynamic and transport properties carried out during the years 2019-2020. It is a follow-up of a similar investigation performed and published 10 years ago by the Working Party (WP) of Thermodynamics and Transport Properties of European Federation of Chemical Engineering (EFCE).1 The main goal was to investigate the advances in this area over the past 10 years, to identify the limitations that still exist, and to propose future R&D directions that will address the industrial needs. An updated questionnaire, with two new categories, namely, digitalization and comparison to previous survey/changes over the past 10 years, was sent to a broad number of experts in companies with a diverse activity spectrum, in oil and gas, chemicals, pharmaceuticals/biotechnology, food, chemical/mechanical engineering, consultancy, and power generation, among others, and in software suppliers and contract research laboratories. Very comprehensive answers were received by 37 companies, mostly from Europe (operating globally), but answers were also provided by companies in the USA and Japan. The response rate was about 60%, compared to 47% in the year 2010. The paper is written in such a way that both the majority and minority points of view are presented, and although the discussion is focused on needs and challenges, the benefits of thermodynamics and success stories are also reported. The results of the survey are thematically structured and cover changes, challenges, and further needs for a number of areas of interest such as data, models, systems, properties, and computational aspects (molecular simulation, algorithms and standards, and digitalization). Education and collaboration are discussed and recommendations on the future research activities are also outlined. In addition, a few initiatives, books, and reviews published in the past decade are briefly discussed. It is a long paper and, to provide the reader with a more complete understanding of the survey, many (anonymous) quotations (indicated with "..." and italics) from the industrial colleagues who have participated in the survey are provided. To help disseminate the specific information of interest only to particular industrial sectors, the paper has been written in such a way that the individual sections can also be read independently of each other.