Buff Theory Research Articles

Extension of Kirkwood–Buff Theory: Partial Enthalpies, Fluctuations of Energy Density, Temperature, and Pressure, and Solute-Induced Effects in a Mixture Solvent

Extension of Kirkwood–Buff Theory: Partial Enthalpies, Fluctuations of Energy Density, Temperature, and Pressure, and Solute-Induced Effects in a Mixture Solvent

Characterization of the inner edge of the neutron star crust

The poorly known crustal equation of state plays a critical role in many observational phenomena associated with a neutron star. Using semi-classical Monte Carlo simulations, we explore the possible configurations of the inner edge of the neutron-star crust for a variety of baryon densities and proton fractions. Applying the Kirkwood--Buff theory to these two-component systems, we observe how the isothermal compressibility reaches a maximum when isolated non-symmetric clusters are formed in an extremely dilute neutron gas. To determine the neutron fraction, we suggest a geometrical model based on the behavior of the proton-neutron pair correlation function. Accordingly, the equation of state of the inner crust is calculated, illustrating that the nuclear energy in beta-equilibrium follows a power-law behavior with baryon density. As a possible astrophysical outcome of this study, our results could help refine the mass-radius relation. Finally, our results pave the way towards further investigations of the impact of the proton-neutron pair correlation function on transport properties within the neutron-star crust.

Mixing Thermodynamics and Flory–Huggins Interaction Parameter of Polyethylene Oxide/Polyethylene Oligomeric Blends from Kirkwood–Buff Theory and Molecular Simulations

Mixing Thermodynamics and Flory–Huggins Interaction Parameter of Polyethylene Oxide/Polyethylene Oligomeric Blends from Kirkwood–Buff Theory and Molecular Simulations

How sensitive are physical properties of choline chloride-urea mixtures to composition changes: Molecular dynamics simulations and Kirkwood-Buff theory.

Deep eutectic solvents (DESs) have emerged as a cheaper and greener alternative to conventional organic solvents. Choline chloride (ChCl) mixed with urea at a molar ratio of 1:2 is one of the most common DESs for a wide range of applications such as electrochemistry, material science, and biochemistry. In this study, molecular dynamics simulations are performed to study the effect of urea content on the thermodynamic and transport properties of ChCl and urea mixtures. With increased mole fraction of urea, the number of hydrogen bonds (HBs) between cation-anion and ion-urea decreases, while the number of HBs between urea-urea increases. Radial distribution functions (RDFs) for ChCl-urea and ChCl-ChCl pairs shows a significant decrease as the mole fraction of urea increases. Using the computed RDFs, Kirkwood-Buff Integrals (KBIs) are computed. KBIs show that interactions of urea-urea become stronger, while interactions of urea-ChCl and ChCl-ChCl pairs become slightly weaker with increasing mole fraction of urea. All thermodynamic factors are found larger than one, indicating a non-ideal mixture. Our results also show that self- and collective diffusivities increase, while viscosities decrease with increasing urea content. This is mainly due to the weaker interactions between ions and urea, resulting in enhanced mobilities. Ionic conductivities exhibit a non-monotonic behavior. Up to a mole fraction of 0.5, the ionic conductivities increase with increasing urea content and then reach a plateau.

Extension of Kirkwood-Buff theory to solids and its application to the compressibility of fcc argon.

In fluids, the compressibility and related thermodynamic properties can be obtained from Kirkwood-Buff integrals (KBIs), i.e., infinite volume integrals over the radial distribution function (RDF). KBI theory has never been applied to crystals because the KBIs diverge when computed in the standard way as running integrals. Here, we show that KBI theory can be applied to solids without divergence, provided that the recently developed finite volume KBI method is used. In order to accelerate the integral convergence as a function of system size, we introduce a physically motivated convolution of the RDF. When using the convoluted RDF and an extrapolation of the finite-volume KBI, the zero-temperature KBI converges very fast to the exact value. We apply the theory to solid argon at finite temperatures. The RDF is computed with a Lennard-Jones potential using Monte Carlo and molecular dynamics simulations, and the isothermal compressibility κT is obtained from the KBI. The variation of κT with temperature agrees very well with experiment. The absolute value of κT is, however, underestimated by 40%-50%, which is attributed to finite size effects of the RDF obtained from molecular simulation. The error can be corrected by a single scaling factor that can be easily calculated at zero temperature. By extending Kirkwood-Buff solution theory to solids, this work lays a new framework for the thermodynamic modeling of complex structures, alloys, and solid solutions.

Unfolding of DNA by co-solutes: insights from Kirkwood–Buff integrals and transfer free energies

Many organic co-solutes are known to stabilize or to destabilize native structures of proteins or DNA. Most of these effects can be explained by co-solute binding or exclusion mechanisms. A beneficial approach to study the underlying principles relies on the computation of Kirkwood–Buff integrals, which can be also used to derive detailed expressions for transfer free energies and changes of the chemical equilibrium between the unfolded and the native states. In this article, we use the framework of Kirkwood–Buff theory in order to study the influence of ectoine on the stability of short DNA hairpins. Our results highlight a strong binding of ectoine, which reveals a pronounced destabilization of DNA in good agreement with experimental findings.

Basic Kirkwood – Buff Theory of Solution Structure and Appropriate Application of Wyman Linkage Equation to Biochemical Phenomena

Background: Researchers who have shown interest in the consequence of introducing dry biomolecules or a solution of it into cosolvents generally known as osmolyte, have applied many models for the elucidation of the scientific basis of the results obtained. The Kirkwood and Buff theory (KBT) or its reverse form has been the basis for the interpretation of the effect of the osmolyte. There seems to be no generally acceptable definition of terms in the basic KBT mathematical formalism. There is also error in stated equations describing solution structure and misapplication of Wyman linkage relation. Therefore, the objectives of this research are 1) to show how the equation of preferential interaction parameter is derived based on KBT, 2) to show the appropriate way in which Wyman linkage relation can be applied, 3) to apply biochemical approach (using generated data) to the equation of preferential interaction parameter (preferential interaction parameter is symbolised as ) for its calculation and calculation of parameters linked to KBT derived equations.
 Methods: The research is mainly theoretical and partly experimental. The experiment entails Bernfeld method of enzyme assay for the generation of data.
 Results and Discussion: The change in solvation preference upon the ethanol partial denaturation of the enzyme and the corresponding change in preferential interaction parameter were respectively positive and negative in sign. Unexpectedly ethanol was preferentially excluded from the enzyme.
 Conclusion: The equations of preferential interaction parameters were derived. The appropriate way is either by calculation or measurement of preferential interaction parameter. Therefore, or for the change, cannot be a constant (or slope) and an instrumentation–based measurable parameter at the same time. Based on Wyman linkage relation, purely biochemical thermodynamic parameter is linked to preferential interaction parameters which are therefore, thermodynamic parameters.

Study of molecular interactions and preferential solvation in binary mixtures of cyclohexane and (C5–C10) 1-alkanol by Kirkwood-Buff integrals

Mixtures formed by cyclohexane + 1-alkanol have been investigated in the framework of the Kirkwood–Buff theory of solution. The alcohols considered are 1-pentanol up to 1-decanol. Data for the Kirkwood–Buff integrals, Gij excess or deficit number of molecules around the central ones, Δnij and coefficients of linear solvation, δij are reported. For solutions with a given cyclohexane, the increase in the CH2 groups of alcohols chain causes a decrease in G12 by the following sequences: 1-decanol > 1-nonanol > 1-octanol > 1-heptanol > 1-hexanol > 1-pentanol. The comparison of G12 and other calculated parameters for cyclohexane + 1-alkanol mixtures reveals that the interactions between similar molecules are more outstanding and the decrease in the alkyl chain of alcohols leads to the weakening of interactions related to the self–association of 1-alkanol, differences in the free volumes, hydrophobic interactions, and structural changes. These trends are consistent with experimental data on the excess molar volumes.

Calculation of Kirkwood-Buff integrals for binary mixtures of 1-butyl-3-methylimidazolium nitrate ionic liquid and alcohols at 298.15 K

Mixtures formed by 1-butyl-3-methylimidazolium + 2-Alkanol have been investigated in the framework of the Kirkwood–Buff theory of solution. The alcohols considered are 2-propanol, 2-butanol, and 2-pentanol. Data for the Kirkwood–Buff integrals, Gij excess or deficit number of molecules around the central ones, Δnij and coefficients of linear solvation, δij are reported. For solutions with a given ionic liquid (IL), the increase in the –CH2 groups of alcohols chain causes a decrease in G12 by the following sequences: 2-propanol > 2-butanol > 2-pentanol. The comparison of G12 and other calculated parameters for IL + 2-alkanol mixtures reveals that the interactions between dissimilar molecules are more outstanding and the rise of alkyl chain in alcohols leads to the weakening of interactions related to the self–association of 2-alkanol and structural effects. These trends are consistent with experimental data on excess molar volumes.

Revisiting electrolyte thermodynamic models: Insights from molecular simulations

Pitzer and electrolyte nonrandom two‐liquid (eNRTL) models are the two most widely used electrolyte thermodynamic models. For aqueous sodium chloride (NaCl) solution, both models correlate the experimental mean ionic activity coefficient (γ±) data satisfactorily up to salt saturation concentration, that is, ionic strength around 6 m. However, beyond 6 m, the model extrapolations deviate significantly and diverge from each other. We examine this divergence by calculating the mean ionic activity coefficient over a wide range of concentration based on molecular simulations and Kirkwood–Buff theory. The asymptotic behavior of the activity coefficient predicted by the eNRTL model is consistent with the molecular simulation results and supersaturation experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3728–3734, 2018

Influence of Cosolutes on Chemical Equilibrium: a Kirkwood–Buff Theory for Ion Pair Association–Dissociation Processes in Ternary Electrolyte Solutions

We present an application of the Kirkwood–Buff theory, which is introduced to describe the influence of cosolutes on the chemical equilibrium between dissociated and associated ion pairs in ternary electrolyte solutions. Our approach makes use of Kirkwood–Buff integrals and the introduction of a local/bulk partition model. The cosolute species can be either charged or uncharged, and our approach is applicable for ideal and weak nonideal solutions in combination with low ion concentrations. As the main result, the theory reveals that differences in the local cosolute accumulation behavior around the ions induce a shift of the chemical equilibrium either to the associated or the dissociated state. The findings of our analysis are useful for a deeper understanding of electrolyte solutions in modern electrochemical storage devices. All results are verified by atomistic molecular dynamics simulations in terms of sodium chloride pairs in dimethylacetamide–water mixtures.

Kirkwood–Buff integrals of finite systems: shape effects

ABSTRACTThe Kirkwood–Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.

Finite-size effects of Kirkwood–Buff integrals from molecular simulations

The modelling of thermodynamic properties of liquids from local density fluctuations is relevant to many chemical and biological processes. The Kirkwood–Buff (KB) theory connects the microscopic structure of isotropic liquids with macroscopic properties such as partial derivatives of activity coefficients, partial molar volumes and compressibilities. Originally, KB integrals were formulated for open and infinite systems which are difficult to access with standard Molecular Dynamics (MD) simulations. Recently, KB integrals for finite and open systems were formulated (J Phys Chem Lett. 2013;4:235). From the scaling of KB integrals for finite subvolumes, embedded in larger reservoirs, with the inverse of the size of these subvolumes, estimates for KB integrals in the thermodynamic limit are obtained. Two system size effects are observed in MD simulations: (1) effects due to the size of the simulation box and the size of the finite subvolume embedded in the simulation box, and (2) effects due to computing radial distribution functions (RDF) from a closed and finite system. In this study, we investigate the two effects in detail by computing KB integrals using the following methods: (1) Monte Carlo simulations of finite subvolumes of a liquid with an analytic RDF and (2) MD simulations of a WCA mixture for various simulation box sizes, but at the same thermodynamic state. We investigate the effect of the size of the simulation box and quantify the differences compared to KB integrals computed in the thermodynamic limit. We demonstrate that calculations of KB integrals should not be extended beyond half the size of the simulation box. For finite-size effects related to the RDF, we find that the Van der Vegt correction (J Chem Theory Comput. 2013;9:1347) yields the most accurate results.

Protein Partial Molar Volumes in Multicomponent Solutions from the Perspective of Inverse Kirkwood-Buff Theory.

Inverse Kirkwood-Buff (KB) solution theory can be used to relate macroscopic quantities with molecular scale interactions and correlation functions, in the form of KB integrals. Protein partial specific volumes ([Formula: see text]) from high-precision density measurements can be used to quantify solvent-solute and solute-solute KB integrals. Currently, general expressions for [Formula: see text] as a function of cosolute concentration (c3) have been provided for only binary and ternary solutions. We derive a general multicomponent expression for [Formula: see text] in terms of the relevant KB integrals for the case of low (infinite dilution) protein concentration but arbitrary cosolute concentrations. To test the utility of treating a quaternary system with a pseudoternary approximation, α-Chymotrypsinogen (aCgn) solutions with a series of solutes (NaCl, sucrose, and trehalose) were compared as a function of solute concentration with and without buffer present. Comparison between those ternary and quaternary solutions shows equivalent results within experimental uncertainty and suggests the pseudoternary approximation may be reasonable. In the case of aCgn, doing so also revealed that the preferential interactions can depend on pH. Analysis of steric contributions also provides an example that illustrates how KB integrals allow one to interpret [Formula: see text] in terms of contributions from molecular volume, excluded volume, and hydration/solvation effects.

From solutions to molecular emulsions

Abstract Concentration fluctuations play an important role in the statistical description of the stability of liquids, particularly in the neighborhood of phase transitions. Classical thermodynamics is blind to fluctuations, and statistical thermodynamics is required to fully understand quantities such as the isothermal compressibility or heat capacity, by linking them to fluctuations of appropriate statistical microscopic quantities and showing that they are response functions. This is illustrated by the seminal Kirkwood–Buff theory of solutions. However, the existence of micro-heterogeneous structures, particularly in aqueous mixtures, which leads to large Kirkwood–Buff integrals, suggest that micro-heterogeneity is a form of concentration fluctuation. This interpretation becomes difficult to accept when extrapolated to larger micro-heterogeneous structures such as micellar aggregates in micro-emulsions. By analyzing how different methods, experimental, computer experiments and theoretical approaches deal with the underlying duality behind these two physical manifestations, we put in evidence the need to reconsider the description of liquids by incorporating the description of emergent “objects”, such as the micro-heterogeneous structures from a molecular point of view. On this path, the concept of “molecular emulsion” allows to describe in a unified way all type of disordered liquids, from solutions to the organized liquids of soft matter.

Gelation of carrageenan: Effects of sugars and polyols

The gelation of κ-carrageenan, a common polysaccharide for food gelling and thickening, is enhanced by the addition of sugars and polyols. Three different hypotheses have been proposed to explain this phenomenon: (i) the enhancement of the water structure around polysaccharides, and the concurrent change in polysaccharide hydration, induced by the cosolvent; (ii) exclusion of cosolvents from polysaccharide surfaces; (iii) binding between sugars/polyols and polysaccharides in the gel phase. To examine the above hypotheses, as well as to reveal the true driving forces responsible for gelation enhancement, we applied our recent statistical thermodynamic theory of gelation, derived from the rigorous Kirkwood–Buff theory. The hydration change is shown to be negligibly small relative to cosolvent exclusion and cosolvent-biopolymer binding, which can be rationalized by considering a sol–gel equilibrium in which (1) the exclusion of sugars/polyols from κ-carrageenan's surface in the sol phase, and (2) the binding of sugars and polyols in the gel phase, shift the sol–gel equilibrium of κ-carrageenan to the gel state. This novel picture is consistent with a wealth of experimental evidence and provides a mechanistic insight into how polyol and sugar cosolvents influence the gelation of κ-carrageenan on a molecular level.

Choice of the center of water molecules in calculations of partial molar volume of single ions immersed in water: A molecular simulation study

In the Kirkwood–Buff theory, the center of each solvent molecule can be arbitrarily chosen. However, this arbitrariness is not obvious in the calculation of the Kirkwood–Buff integral for a single ion. Actually, the Kirkwood–Buff integral depends on the choice of the center of a solvent molecule, if each solvent molecule has a dipole moment and the solute has a net charge. A few examples based on molecular dynamics simulations are shown. A surrogate definition for the center of a water molecule is also shown. A good agreement between the calculated and experimental values of partial molar volumes for single ions is observed.

Molecular simulation study on Hofmeister cations and the aqueous solubility of benzene.

We study the ion-specific salting-out process of benzene in aqueous alkali chloride solutions using Kirkwood-Buff (KB) theory of solutions and molecular dynamics simulations with different empirical force field models for the ions and benzene. Despite inaccuracies in the force fields, the simulations indicate that the decrease of the Setchenow salting-out coefficient for the series NaCl > KCl > RbCl > CsCl is determined by direct benzene-cation correlations, with the larger cations showing weak interactions with benzene. Although ion-specific aqueous solubilities of benzene may be affected by indirect ion-ion, ion-water, and water-water correlations, too, these correlations are found to be unimportant, with little to no effect on the Setchenow salting-out coefficients of the various salts. We further considered LiCl, which is experimentally known to be a weaker salting-out agent than NaCl and KCl and, therefore, ranks at an unusual position within the Hofmeister cation series. The simulations indicate that hydrated Li(+) ions can take part of the benzene hydration shell while the other cations are repelled by it. This causes weaker Li(+) exclusion around the solute and a resulting, weaker salting-out propensity of LiCl compared to that of the other salts. Removing benzene-water and benzene-salt electrostatic interactions in the simulations does not affect this mechanism, which may therefore also explain the smaller effect of LiCl, as compared to that of NaCl or KCl, on aqueous solvation and hydrophobic interaction of nonpolar molecules.

Influence of methane and carbon monoxide in the volumetric behaviour of the anthropogenic CO2: Experimental data and modelling in the critical region

Density measurements of the systems CO2+CH4 at T=304.21K and CO2+CO at T=304.21 and 308.15K were carried out at pressures and compositions of interest in the process of transport and storage of CO2 (CCS technology): P=0.1 to 20MPa, and xCO2≥0.97. From the experimental P–ρ–T–xCO2 data, we have studied the dependence of the isothermal compressibility, the excess molar volume, and the partial molar volume of the solute with composition, pressure and temperature within the critical region. We have modelled the volumetric behaviour of these systems with Peng–Robinson, PC-SAFT and GERG Equations of State, thus validating these equations under the conditions considered. Furthermore, we have confirmed the weakly attractive behaviour of these systems by performing a study of the interactions between solvent molecules, CO2, and those of the solute, CO or CH4, using the Krichevskii Function concept and the Kirkwood–Buff Theory. Finally, we have quantified the influence of small amounts of CH4 and CO in the transport of anthropogenic CO2 through several normalized parameters, related to the design and operation of the fluid transport process.

How to apply the Kirkwood–Buff theory to individual species in salt solutions

It is generally assumed that the Kirkwood–Buff (KB) theory cannot be applied to anions and cations individually in a solution, as one cannot simulate this system in an open ensemble due to the electroneutrality constraint. By applying our recently derived KB theory for closed systems, we show that one does have access to single-ion properties in Molecular Dynamics. Our findings are supported by simulations for a model of a salt solution in which particles interact with WCA potentials, as well as for the NaCl/water system using the Particle Mesh Ewald technique for electrostatics.