Compensation Between the Entropic and Enthalpic Changes Arising from Changes in Solvent–Solvent Interactions in Mixed Solvents

A theorem presented by Professor Ben-Naim (J Phys Chem 82:874–885, 1978) states that the standard state enthalpy and entropy changes arising from changes in the solvent structure that are induced by solvation of a solute cancel exactly in the standard state Gibbs energy. In this paper this is explored by consideration of the thermodynamics of transfer of electrolytes in mixed solvents, using previously developed models of the solvation process. Two cases are considered. One is random solvation, where curvatures in plots of the transfer enthalpies and entropies, which arise from changes in solvent–solvent interactions, exactly compensate in the transfer Gibbs (free) energies, which are sensibly linear with solvent composition. The second type of system are those with strong preferential solvation where it is found that the transfer Gibbs energies can be accounted for quantitatively in terms of changes in the solute–solvent interactions, with no contribution from changes in solvent–solvent interactions. The results are entirely consistent with the Ben-Naim theorem.     

Changes in thermodynamic quantities upon contact of two solutes in solvent under isochoric and isobaric conditions

The changes in excess thermodynamic quantities upon the contact of two solutes immersed in a solvent are analyzed using the radial-symmetric and three-dimensional versions of the integral equation theory. A simple model mimicking a solute in water is employed. The solute-solute interaction energy is not included in the calculations. Under the isochoric condition, the solute contact always leads to a positive entropy change irrespective of the solute solvophobicity or solvophilicity. The energy change is negative for solvophobic solutes while it is positive for solvophilic ones. Under the isobaric condition, the contact of solvophobic solutes results in system-volume compression but that of solvophilic ones gives rise to expansion. Effects of the compression and expansion on the changes in enthalpy and entropy are enlarged with rising temperature. When the solute solvophobicity is sufficiently high, the entropy change (multiplied by the absolute temperature) can become negative due to the compression, except at low temperatures with the result of an even larger, negative enthalpy change. The expansion in the case of solvophilic solutes leads to a large, positive entropy change accompanied by an even larger, positive enthalpy change. The changes in enthalpy and entropy are strongly dependent on the temperature. However, the changes in enthalpy and entropy are largely cancelled out and the temperature dependency of the free-energy change is much weaker. The authors also discuss possible relevance to the enthalpy-entropy compensation experimentally known for a variety of physicochemical processes in aqueous solution such as protein folding.     

Role of entropy and autosolvation in dimerization and complexation of C60 by Zn7 metallocavitands

The supramolecular chemistry of bowl-shaped heptazinc metallocavitands templated by Schiff base macrocycles has been investigated. Dimerization thermodynamics were probed by (1)H NMR spectroscopy in benzene-d(6), toluene-d(8), and p-xylene-d(10) and revealed the process to be entropy-driven and enthalpy-opposed in each solvent. Trends in the experimentally determined enthalpy and entropy values are related to the thermodynamics of solvent autosolvation, solvent molecules being released from the monomeric metallocavitand cavity into the bulk solvent upon dimerization. The relationship established between experimentally measured dimerization thermodynamics and autosolvation data successfully predicts the absence of dimerization in CH(2)Cl(2) and CHCl(3) and was used to estimate the number of solvent molecules interacting with the monomeric metallocavitand in solution. Host-guest interactions between heptazinc metallocavitands and fullerene C(60) have also been investigated. Interestingly, metallocavitand-C(60) interactions are only observed in solvents that facilitate entropy-driven dimerization suggesting entropy and solvent autosolvation may be important in explaining concave-convex interactions.     

Micellar solubilization thermodynamics of acetophenone in surfactant mixtures: Case of benzyldimethyltetradecylammonium chloride and trimethyltetradecylammonium chloride

The thermodynamics of micellar solubilization of acetophenone in mixtures of two cationic surfactants [benzyldimethyltetradecylammonium chloride +trimethyltetradecylammonium chloride] has been derived from calorimetric measurements at controlled solute activity. The partition coefficient between micelles and water as well as the standard enthalpy and entropy of transfer between micelles and water were calculated. The results were compared to the case of benzylalcohol in the same cationic mixtures. For acetophenone, the variation of all thermodynamic transfer functions with micellar composition may be described by the regular solution formalism. The same conclusion has been achieved for most polar solutes in various surfactant mixtures: favorable interaction between unlike surfactants induces an unfavorable micellar solubilization. Exceptions should be found with the cases where solute solubilization induces profound micellar changes. It seems to be the case with some alcohols in the cationic surfactant mixtures studied.     

Enthalpy-entropy contributions to salt and osmolyte effects on molecular-scale hydrophobic hydration and interactions

Salts and additives can significantly affect the strength of water-mediated interactions in solution. We present results from molecular dynamics simulations focused on the thermodynamics of hydrophobic hydration, association, and the folding-unfolding of a hydrophobic polymer in water and in aqueous solutions of NaCl and of an osmolyte trimethylamine oxide (TMAO). It is known that addition of NaCl makes the hydration of hydrophobic solutes unfavorable and, correspondingly, strengthens their association at the pair as well as the many-body level (Ghosh, T.; Kalra, A.; Garde, S. J. Phys. Chem. B 2005, 109, 642), whereas the osmolyte TMAO has an almost negligible effect on the hydrophobic hydration and association (Athawale, M. V.; Dordick, J. S.; Garde, S. Biophys. J. 2005, 89, 858). Whether these effects are enthalpic or entropic in origin is not fully known. Here we perform temperature-dependent simulations to resolve the free energy into entropy and enthalpy contributions. We find that in TMAO solutions, there is an almost precise entropy-enthalpy compensation leading to the negligible effect of TMAO on hydrophobic phenomena. In contrast, in NaCl solutions, changes in enthalpy dominate, making the salt-induced strengthening of hydrophobic interactions enthalpic in origin. The resolution of total enthalpy into solute-solvent and solvent-solvent terms further shows that enthalpy changes originate primarily from solvent-solvent energy terms. Our results are consistent with experimental data on the hydration of small hydrophobic solutes by Ben-Naim and Yaacobi (Ben-Naim, A.; Yaacobi, M. J. Phys. Chem. 1974, 78, 170). In combination with recent work by Zangi, Hagen, and Berne (Zangi, R.; Hagen, M.; Berne, B. J. J. Am. Chem. Soc. 2007, 129, 4678) and the experimental data on surface tensions of salt solutions by Matubayasi et al. (Matubayasi, N.; Matsuo, H.; Yamamoto, K.; Yamaguchi, S.; Matuzawa, A. J. Colloid Interface Sci. 1999, 209, 398), our results highlight interesting length scale dependences of salt effects on hydrophobic phenomena. Although NaCl strengthens hydrophobic interactions at both small and large length scales, that effect is enthalpy-dominated at small length scales and entropy-dominated for large solutes and interfaces. Our results have implications for understanding of additive effects on water-mediated interactions, as well as on biocompatibility of osmolyte molecules in aqueous solutions.     

硝基甲苯异构体的液晶溶液热力学性质的色谱法研究

本文用气液色谱方法研究了o-, m-, p-硝基甲苯三种异构体在双(对己氧基苯甲酸)对苯二酚酯(PBH~xB)和双(对庚氧基苯甲酸)对苯二酚酯(PBH~pB)两种向列液晶固定液中无限稀薄条件下的活度系数, 进而求得了超额焓, 超额自由能和超额熵, 同时得到溶解焓和溶解熵, 并对结果进行了分析和讨论。     

A molecular dynamics study of chirality transfer: The impact of a chiral solute on an achiral solvent

A solvation shell may adapt to the presence of a chiral solute by becoming chiral. The extent of this chirality transfer and its dependence on the solute and solvent characteristics are explored in this article. Molecular dynamics simulations of solvated chiral analytes form the basis of the analysis. The chirality induced in the solvent is assessed based on a series of related chirality indexes originally proposed by Osipov [M. A. Osipov et al., Mol. Phys. 84, 1193 (1995)]. Two solvents are considered: Ethanol and benzyl alcohol. Ethanol provides insight into chirality transfer when the solvent interacts with the solute primarily by a hydrogen bond. Several ethanol models have been considered starting with a nonpolarizable model, progressing to a fluctuating charge model, and finally, to a fully polarizable model. This progression provides some insights into the importance of solvent polarizability in the transfer of chirality. Benzyl alcohol, by virtue of the aromatic ring, increases the number of potential solvent-solute interactions. Thus, with these two solvents, the issue of compatibility between the solvent and solute is also considered. The solvation of three chiral solutes is examined: Styrene oxide, acenaphthenol, and n-(1-(4-bromophenyl)ethyl)pivalamide (PAMD). All three solutes have the possibility of hydrogen bonding with the solvent, the last two may also form ring-ring interactions, and the last also has multiple hydrogen bonding sites. For PAMD, the impact of conformational averaging is examined by comparing the chirality transfer about rigid and flexible solutes.     

Thermodynamic Study of the Solubility of Some Sulfonamides in Octanol, Water, and the Mutually Saturated Solvents

The free energy, enthalpy and entropy of solution, were evaluated from solubility data for a group of sulfonamides from 25 to 40°C in octanol, water, and the mutually saturated solvents. In aqueous media, the solubility was determined at the isoelectric point and ionic strength 0.15 mol-L^–1. The excess free energy and the activity coefficients of the solutes also were determined. The results are discussed in terms of solute–solvent interactions.     

Effects of solvent density on retention in gas-liquid chromatography. II. Polar solutes in poly(ethylene glycol) stationary phases

Effects of solvent density on the solubility of polar probes which undergo specific interactions with poly(oxyethylene) are studied. The analysis of retention data on capillary columns coated with oligomeric poly(oxyethylene) stationary phases shows that, within the experimental error, the enthalpic contribution to the solubility is practically independent of variations in the solvent density. Average values of enthalpies of solute transfer are reported for different probes and temperatures. The observed systematic decrease of solubility with the increasing density is due to a change of entropy. Some thermodynamic consequences inferred from these general results are discussed. One relevant observation is that the influence of solvent's final groups must be negligible. This is even the case for oligomers with number-average degrees of polymerization as low as 13, hosting solutes capable of strong interactions with the end hydroxyl groups of linear poly(ethylene glycols). Possible explanations for this behavior are explored through molecular dynamics simulations of the liquid solvent.     

Effect of phase ratio on van't Hoff analysis in reversed-phase liquid chromatography,and phase-ratio-independent estimation of transfer enthalpy

In analysis of the thermodynamics of the transfer of a solute from the mobile phase to the stationary phase in reversed-phase liquid chromatography, it is nearly always assumed that the phase ratio is constant. This type of analysis is typically performed by applying a form of the van't Hoff equation, which relates the retention factor to temperature via the enthalpy and entropy of transfer. When non-linear van't Hoff plots are observed, it is often assumed that the enthalpy and entropy of transfer change with temperature. However, when the possibility of a change in the phase ratio is considered, it becomes apparent that non-linear van't Hoff behavior may or may not be due to changes in enthalpy or entropy. In this work, we present mathematical evidence that phase ratio changes, if they occur, can cause deviations from linearity in a van't Hoff plot. We also show that the phase ratio influence can be eliminated by considering the molecular difference between two solutes instead of the solutes themselves. The resulting selectivity van't Hoff plots may be linear, even when the van't Hoff plots of the two solutes are non-linear. In such cases, temperature-dependent phase ratio changes, and not necessarily changes in the transfer enthalpy, may be responsible for the curved van't Hoff plots of the individual solutes. In addition, we present chromatographic evidence that different solutes may "see" different thermodynamic phase ratios. It is clear that the concept of a phase ratio in reversed-phase chromatography is not nearly as well defined as a phase ratio in a bulk system like a liquid-liquid extraction.     

Solution Models for Binary Components of Significantly Different Molecular Sizes

As a solution theory, Raoult’s law is commonly used to estimate the activities of solutes and solvents of comparable molecular sizes while the Flory–Huggins (F–H) model is used for the activities of small liquids in high polymers. For a great many systems where the solute and solvent differ only moderately in molecular size (e.g., by 4–10 times), there has been no confirmed choice of a preferred model; examples of such systems are those of ordinary organic compounds in liquid triolein (MW = 885.4 g·mol^?1) and poly(propylene glycol) (PPG) (MW = ~1,000 g·mol^?1). The observed nearly athermal solubilities of many nonpolar organic solids in these solvents provide unique experimental data to examine the merit of a solution model. As found, Raoult’s law underestimates widely, and the F–H model underestimates slightly, the solid solubilities in triolein and PPG because these models underestimate the solution entropy for these solute–solvent pairs. To rectify this problem, the molecular segments of a large sized liquid solvent (e.g., triolein) are assumed to act as independent mixing units to increase the solute–solvent mixing entropy. This adjustment leads to a modified F–H model in which the “ideal” or “athermal” solubility of a solid in volume fraction, at a particular temperature, is equal to the solid’s activity at that temperature. Results from other studies give further support for the modified F–H model to interpret the partition data of compounds with organic solvents.     

Solvent effects on chemical exchange in a push-pull ethylene as studied by NMR and electronic structure calculations

NMR measurements of chemical exchange in a push-pull ethylene, dissolved in a number of different solvents, are presented. These are complemented by high-level electronic structure calculations, using both gas-phase conditions and those which simulate solvents. The results show that it is essential to include entropy effects in order to understand the observed trends. For instance, the equilibrium state in this case represents the state with lowest Gibbs free energy, as it must, but not the lowest enthalpy. The particular molecule is methyl 3-dimethylamino-2-cyanocrotonate (MDACC). The geometry at the carbon-carbon double bond can be either E or Z with roughly equal populations at ambient temperature. We have measured the equilibrium constant and the rates for the exchange between these states in a number of solvents: methanol, chloroform, acetonitrile, toluene, dichloromethane, acetone, and tetrahydrofuran. Furthermore, the N,N-dimethylamino group attached to the double bond also shows restricted rotation, and this has been measured in both the E and Z conformations. The equilibrium constant and the three rotational barriers provide excellent probes of the solvent effects. Electronic structure calculations with a number of basis sets up to the 6-311++G(2df,2p) level, using both Hartree-Fock and density functional (B3LYP) methods were used to predict the E and Z ground states, and the three transition states. The calculations were done for an isolated molecule and also for solvent models representing toluene, acetone, and ethanol. The E conformation is more stable in solution, is the structure in the crystal, and is also the prediction for the gas phase from the calculations. However, the dependence of the equilibrium constant on temperature shows that the Z conformation actually has lower enthalpy. The stability of the E conformation in solution must be due to entropic effects. Similarly, the solvent effect on the E-Z barrier is primarily due to entropy. The measured enthalpy of activation is similar in all the solvents, but the entropy of activation increases with the solvent polarity. The barrier to rotation of the N,N-dimethylamino group shows a combination of entropy and enthalpy effects. This combination of experiments and theory gives an extraordinarily detailed picture of solvent-solute interactions.     

Solutes probe hydration in specific association of cyclodextrin and adamantane

Using microcalorimetry, we follow changes in the association free energy of beta-cyclodextrin (CD) with the hydrophobic part of adamantane carboxylate (AD) due to added salt or polar (net-neutral) solutes that are excluded from the molecular interacting surfaces. Changes in binding constants with solution osmotic pressure (water activity) translate into changes in the preferential hydration upon complex formation. We find that these changes correspond to a release of 15-25 solute-excluding waters upon CD/AD association. Reflecting the preferential interaction of solute with reactants versus products, we find that changes in hydration depend on the type of solute used. All solutes used here result in a large change in the enthalpy of the CD-AD binding reaction. In one class of solutes, the corresponding entropy change is much smaller, while in the other class, the entropy change almost fully compensates the solute-specific enthalpy. For many of the solutes, the number of waters released correlates well with their effect on air-water surface tensions. We corroborate these results using vapor pressure osmometry to probe individually the hydration of reactants and products of association, and we discuss the possible interactions and forces between cosolute and hydrophobic surfaces responsible for different kinds of solute exclusion.     

Self-assembly does not account for the hydrophobic effect

Marmur has claimed that large values of activity coefficients for nonelectrolytes, particularly in the context of hydrophobic interactions between solutes in aqueous solution at ambient temperature and pressure, cannot be accounted for by thermodynamics, and has suggested that association (self-assembly) of solute molecules in solution solves this dilemma. We show that the analysis of Marmur is incorrect, specifically because the equilibrium in solution between monomeric solute molecules and associated solute molecules is entirely ignored. We show further that activity coefficients such as that for nitromethane solute in hexane solvent, 39.7, and that for solute hexane in solvent water, 4.48 x 10(5), can be calculated as 31.9 and 4.71 x 10(5), respectively, by methods based on well-known molecule-molecule interactions. No assumption of self-assembly is required.     

Solute-solvent interactions between a range of solutes and trifluoropropyl siloxane stationary phases in terms of gas-liquid chromatography activity coefficients

Summary Several poly(3,3,3-methyltrifluoropropyl siloxane) stationary phases with a low percentage of trifluoropropyl have been recharacterised by means of activity coefficients at temperatures in the range 60–140°C. The temperature effect of activity coefficients was studied. Thermodynamic magnitudes: excess Gibbs energy, excess enthalpy and excess entropy for 44 solutes on these polymers were calculated, and their relationships with solutes’ molecular connectivity indexes were tested. Solute-polymer interactions were calculated at 120°C according to the solvation parameter model, and several correlations for selected solutes and polymers were investigated, mainly the effect of solutes’ structure on the non-polar interactions and the effect of the solute dipole moment on the polar interactions. In addition, the influence of polymer polarity on the different polar and non-polar interactions was investigated.     

Individual solvent/solute interactions through social isomerism

Reversible coencapsulation of a solute molecule and a single solvent molecule takes place in solution at ambient temperature. Two isomeric complexes are formed (social isomers), and their relative energies are assessed by NMR methods. Intermolecular interactions between 3 aromatic solutes and 15 common solvents are evaluated.     

Enthalpy-entropy compensation in micellization of sodium dodecyl sulphate in water/methanol,water/ethylene glycol and water/glycerol binary mixtures

The enthalpy-entropy compensation in micellization of sodium dodecyl sulphate (SDS) in binary mixtures of water/methanol (MeOH), water/ethylene glycol (EG) and water/glycerol (GL) over a temperature range of 10–60°C was examined. When the cosolvent concentration was low, the critical micelle concentration (CMC) depended only on the total amount of the hydroxyl group added. When the cosolvent concentration was high, the increase in CMC followed the sequence: MeOH>EG>GL. Enthalpy and entropy changes were evaluated from which the compensation temperature was determined. Both enthalpy and entropy changes decreased on the addition of the cosolvents, indicating a lowering of solution hydrophobicity. The compensation temperature was found as a constant over the cosolvent concentration range, as a result, was not a good index for characterizing the solute/solvent interactions. The two reference temperatures at which the enthalpy-entropy change respectively became zero were strongly influenced by the cosolvent addition, therefore could serve as a proper index for solution hydrophobicity.     

Solubility of KF in four organic solvents and thermodynamic dissolution functions

The solubilities of potassium fluoride (KF) in protic and aprotic polar solvents (N,N-dimethylethanolamine, diethanolamine, pyridine, and sulfolane) were measured at temperatures ranging from 308.73 to 367.37 K, and the data were correlated using the modified Apelblat equation. The dissolution enthalpy and dissolution entropy were calculated from the solubility data. The interactions between solute and solvent were discussed. The data obtained can be helpful in the search of optimal ways of preparation of 2,3,4,5-tetrafluorobenzoic acid.     

Use of Masson's and Jones–Dole equations to study different types of interactions of three pharmacologically important drugs in ethanol

The volumetric and viscometric study of three allopathic drugs (sodium valporate, benzalkonium chloride, and losartan potassium) in ethanol solvent is reported here. This study was carried out at four different temperatures that is, from 288.15 to 318.15 K. The accurately measured density values were used to calculate partial molar volume at infinite dilution, solute–solute interaction parameter, Hepler's constant, partial molar expansivity constant, and isobaric thermal expansion coefficient. The viscosity measurements were carried out for the calculation of constants of Jones–Dole equation and to calculate different thermodynamic parameters of viscous flow which include standard free energy change, standard enthalpy change, and standard entropy change of viscous flow. All these viscometric and volumetric parameters are useful for understanding the different types of interactions of drugs in solution and to study the drug action in body. The results of both volumetric and viscometric studies showed that all drugs had structure promoting effect on solvent, existing of strong solute–solvent interaction, and very weak solute–solute interaction. For all these drugs, solvophobic interaction was found to be dominant over electrostriction. Viscometric studies also showed the existing of stronger solute–solvent interaction in ground state as compared to that in transition state.     

Confusing cause and effect: energy-entropy compensation in the preferential solvation of a nonpolar solute in dimethyl sulfoxide/water mixtures

We performed molecular simulations to analyze the thermodynamics of methane solvation in dimethyl sulfoxide (DMSO)/water mixtures (298 K, 1 atm). Two contributions to the interaction thermodynamics are studied separately: (i) the introduction of solute-solvent interactions (primary contribution) and (ii) the solute-induced disruption of cohesive solvent-solvent interactions (secondary contribution). The energy and entropy changes of the secondary contribution always exactly cancel in the free energy (energy-entropy compensation), hence only the primary contribution is important for understanding changes of the free energy. We analyze the physical significance of the solute-solvent energy and solute-solvent entropy associated with the primary contribution and discuss how to obtain these quantities from experiments combining solvation thermodynamic and solvent equation of state data. We show that the secondary contribution dominates changes in the methane solvation entropy and enthalpy: below 30 mol % DMSO in the mixture, methane, because of more favorable dispersion interactions with DMSO molecules, preferentially attracts DMSO molecules, which, in response, release water molecules into the bulk, causing an increase in the entropy. This large energy-entropy compensating process easily causes a confusion in the cause for and the effect of preferred methane-DMSO interactions. Methane-DMSO dispersion interactions are the cause, and the entropy change is the effect. Procedures that infer thermodynamic driving forces from analyses of the solvation entropies and enthalpies should therefore be used with caution.