Quantifying non-specific interactions via liquid chromatography

Determinations of solute-cosolute interactions from chromatography have often resulted in problems, such as the “antibinding” (or a negative binding constant) between the solute and micelle in micellar liquid chromatography (MLC) or indeterminacy of salt-ligand binding strength in high-performance affinity chromatography (HPAC). This shows that the stoichiometric binding models adopted in many chromatographic analyses cannot capture the non-specific nature of solvation interactions. In contrast, an approach using statistical thermodynamics handles these complexities without such problems and directly links chromatographic data to, for example, solubility data via a universal framework based on Kirkwood-Buff integrals (KBI) of the radial distribution functions. The chromatographic measurements can now be interpreted within this universal theoretical framework that has been used to rationalize small solute solubility, biomolecular stability, binding, aggregation and gelation. In particular, KBI analysis identifies key solute-cosolute interactions, including excluded volume effects. We present (i) how KBI can be obtained directly from the cosolute concentration dependence of the distribution coefficient, (ii) how the classical binding model, when used solely as a fitting model, can yield the KBIs directly from the literature data, and (iii) how chromatography and solubility measurements can be compared in the unified theoretical framework provided via KBIs without any arbitrary assumptions about the stationary phase. To perform our own analyses on multiple datasets we have used an “app”. To aid readers’ understanding and to allow analyses of their own datasets, the app is provided with many datasets and is freely available on-line as an open-source resource

Thermodynamic stability condition can judge whether a nanoparticle dispersion can be considered a solution in a single phase

Establishing that a nanoparticle dispersion can, in fact, be treated as a solution has an important practical ramification, namely the application of solubility theories for solvent selection. However, what distinguishes a solution and dispersion has remained ambiguously understood. Based on the recent progress in statistical thermodynamics on multiple-component solutions, here we establish the condition upon which a nanoparticle dispersion can be considered a single-phased solution. We shall provide experimental evidence already found in the literature showing the solution nature of nanoparticle dispersions

Cooperative sorption on porous materials

Sorption isotherms are determined by underlying molecular interactions. However, doubts have been raised whether the sorption mechanism can be understood in principle from analyzing sorption curves via a range of competing models. We have shown recently that it is possible to translate a sorption isotherm to the underlying molecular interactions via rigorous statistical thermodynamics. The aim of this paper is to fill the gap between the statistical thermodynamic theory and analyzing experimental sorption isotherms, especially of microporous and mesoporous materials. Based on a statistical thermodynamic approach to interfaces, we have derived a cooperative isotherm, as a generalization of the Hill isotherm and our cooperative solubilization model, without the need for assumptions on adsorption sites, layers, and pore geometry. Instead, the statistical characterization of sorbates, such as the sorbate-interface distribution function and the sorbate number distribution, as well as the existence of statistically independent units of the interface, underlies the cooperative sorption isotherm. Our isotherm can be applied directly to literature data to reveal a few key system attributes that control the isotherm: the cooperative number of sorbates and the free energy of transferring sorbates from the saturated vapour to the interface. The sorbate-sorbate interaction is quantified also via the Kirkwood-Buff integral and the excess numbers

Fluctuation adsorption theory: quantifying adsorbate-adsorbate interaction and interfacial phase transition from an isotherm

How adsorbate-adsorbate interaction determines the functional shape of an adsorption isotherm is an important and challenging question. Many models for adsorption isotherm have been proposed to answer this question. However, a successful fitting of an isotherm on its own is insufficient for the correctness of the model assumptions. Instead, starting from the principles of statistical thermodynamics, we propose how adsorbate-adsorbate interactions can be quantified from an isotherm. This was made possible by extending the key tools of solution statistical thermodynamics to adsorbates in interface, namely, the Kirkwood-Buff and Macmillan-Mayer theories, as well as their relationship to the thermodynamic phase stability condition. When capillary condensation and interfacial phase transition are absent, adsorbate-adsorbate interactions can be quantified from an isotherm using the Kirkwood-Buff integrals, and virial coefficients can yield multiple-body interaction between adsorbates. Such quantities can be obtained directly from the fitting parameters for the well-known isotherm models (e.g., Langmuir, BET). The size of adsorbate cluster involved in capillary condensation and interfacial phase transition can also be evaluated from the isotherm, which was demonstrated by the adsorption isotherm of water on activated carbons of varying pore sizes from the literature. Signatures of the isotherm classifications by IUPAC have been characterized in terms of multiple-body interactions between adsorbates

A unified perspective on preferential solvation and adsorption based on inhomogeneous solvation theory

How cosolvents affects solvation has been revealed through the independent determination of solute-solvent and solute-cosolvent interactions guaranteed by the phase rule. Based on the first principles of inhomogeneous solvation theory, we present here a general matrix theory encompassing both preferential solvation and surface adsorption. The central role of the stability conditions that determine how many excess numbers (surface excesses) are independently determinable, have been clarified from the first principles. The advantage of the inhomogeneous approach has been demonstrated to be in its ease in treating solvation and adsorption in a unified manner, while its disadvantage, for example in membrane dialysis experiments, can be overcome by the inhomogeneous-homogeneous conversion

Statistical thermodynamics of regular solutions and solubility parameters

Solubility parameters, developed originally for regular solutions, have been applied to solutions beyond the presumed weak non-ideality, implying that the true foundation of the solubility parameters may be more general than the regular solution theory. To assess the root of regularity on rigorous statistical thermodynamics, here we re-examine the classical iodine dissolution experiments by Shinoda and Hildebrand, who concluded that the entropy of mixing is ideal regardless of solute-solvent size ratio.We show that iodine solubility is concerned with the limit of infinite dilution,while the regular solution theory is a scheme to describe the dependence on the solute concentration. This means that the solubility of iodine cannot be a foundation of the regular solution; it is further shown that the differences in the solvation free energy among organic solvents are dominated by enthalpy with negligible role of the entropic component. In addition, the validity of the regular solution concept, i.e., the enthalpic nature of the solution non-ideality, can now be examined quantitatively by expressing the Margules model in terms of the Kirkwood-Buff integrals, which incorporate the excluded volume effects and the potential of mean force nature of interactions that were beyond the reach of the classical thermodynamic models. Such insights into the physical basis of solubility parameters may be useful for improving solubility prediction

Cooperativity in micellar solubilization

Sudden onset of solubilization is observed widely around or below the critical micelle concentration (CMC) of surfactants. It has also been reported that micellization is induced by the solutes even below CMC and the solubilized solute increases the aggregation number of the surfactant. These observations suggest enhanced cooperativity in micellization upon solubilization. Recently, we have developed a rigorous statistical thermodynamic theory of cooperative solubilization. Its application to hydrotropy revealed the mechanism of cooperative hydrotropy: hydrotrope self-association enhanced by solutes. Here we generalize our previous cooperative solubilization theory to surfactants. We have shown that the well-known experimental observations, such as the reduction of CMC in the presence of the solutes and the increase of aggregation number, are the manifestations of cooperative solubilization. Thus, the surfactant self-association enhanced by a solute is the driving force of cooperativity and a part of a universal cooperative solubilization mechanism common to hydrotropes and surfactants at low concentrations

Molecular interpretation of preferential interactions in protein solvation : a solvent-shell perspective by means of minimum-distance distribution functions

Preferential solvation is a fundamental parameter for the interpretation of solubility and solute structural stability. The molecular basis for solute-solvent interactions can be obtained through distribution functions, and the thermodynamic connection to experimental data depends on the computation of distribution integrals, specically Kirkwood-Bu integrals for the determination of preferential interaction or exclusion. Standard radial distribution function functions, however, are not convenient for the study of the solvation of complex, non-spherical solutes, as proteins structures. Here we show that minimum-distance distribution functions can be used to compute KB integrals while at the same time providing a rich view of solute-solvent interactions at the molecular level. We compute preferential solvation parameters for Ribonuclease T1 in aqueous solutions of urea and trimethylamine N-oxide (TMAO), and show that, while macroscopic solvation shows that urea is preferentially bound to the protein surface and TMAO is preferentially excluded, both display specic density augmentations at the protein surface. Therefore, direct protein-osmolyte interactions can play a role in the stability and activity of the protein even for preferentially hydrated systems. The generality of the distribution function and its natural connection to thermodynamic data suggests that it will be useful in general for the study of solvation in mixtures of structurally complex solutes and solvents