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Water anomalous thermodynamics, attraction, repulsion, and hydrophobic hydration

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Abstract

A model composed of van der Waals-like and hydrogen bonding contributions that simulates the low-temperature anomalous thermodynamics of pure water while exhibiting a second, liquid-liquid critical point [P. H. Poole et al., Phys. Rev. Lett. 73, 1632 (1994)] is extended to dilute solutions of nonionic species. Critical lines emanating from such second critical point are calculated. While one infers that the smallness of the water molecule may be a relevant factor for those critical lines to move towards experimentally accessible regions, attention is mainly focused on the picture our model draws for the hydration thermodynamics of purely hydrophobic and amphiphilic non-electrolyte solutes. We first focus on differentiating solvation at constant volume from the corresponding isobaric process. Both processes provide the same viewpoint for the low solubility of hydrophobic solutes: it originates from the combination of weak solute-solvent attractive interactions and the specific excluded-volume effects associated with the small molecular size of water. However, a sharp distinction is found when exploring the temperature dependence of hydration phenomena since, in contrast to the situation for the constant-V process, the properties of pure water play a crucial role at isobaric conditions. Specifically, the solubility minimum as well as enthalpy and entropy convergence phenomena, exclusively ascribed to isobaric solvation, are closely related to water's density maximum. Furthermore, the behavior of the partial molecular volume and the partial molecular isobaric heat capacity highlights the interplay between water anomalies, attraction, and repulsion. The overall picture presented here is supported by experimental observations, simulations, and previous theoretical results.

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... 1−5 One aspect of the problem that we are currently addressing concerns the role played by solvent water itself. 6,7 Specifically, we are trying to accurately establish to which extent is the thermodynamics of aqueous solvation of nonpolar solutes driven by the thermodynamics of liquid water. In the first part of this series, we approach this issue for small hard-sphere solutes interacting with solvent molecules via harsh repulsive forces. ...
... The presence of solvent's α p and κ T in the above equations illuminates a straightforward relationship between the thermodynamics of aqueous solvation and water's thermodynamics. While results on such a relationship have been reported previously, 14−19 only recently 6,7 has the joint consideration of isochoric and isobaric constraints been proved useful with a view to characterize it precisely. Figure 1 illustrates one relevant result in this connection: experimental data show that the temperature dependence of s ̅ p * and h̅ p * curves is dictated by that of the Tα p v ̅ p contribution in eq 8, with further analysis revealing 7 that the temperature dependence of Tα p v ̅ p is primarily dictated by that of water's unusual α p and hence by its unusual ρ(T) dependence. ...
... 22 Accordingly, there is a strong suggestion that the corresponding thermodynamics of solvophobic solvation should reflect Jagla-fluid unusual thermodynamics just as the thermodynamics of aqueous solvation reflects that of water. 6,7 While previous work on this indicates that "Jaglasolvation is aqueous-like", 23,24 it merits our attention to jointly approach isochoric and isobaric solvation for TIP4P/2005 and Jagla water-like solvents and thereby to expand the work on comparative studies of solvation in distinct solvents 13,25,26 as well as on the temperature and pressure dependence of solvation. 27−29 To this end, we report μ ̅ *(T,p), u ̅ V *(T,p), s ̅ V *(T,p), h̅ p *(T,p), s ̅ p *(T,p), v p (T,p), and v ̅ p (T,p) data as obtained from molecular simulation and analyze them with the aid of scaled-particle theory (SPT), 30 the Gaussian model of small-length-scale solvation, 14,31,32 and our current knowledge of water-like thermodynamics. ...
Article
We analyze the role of temperature, pressure, and solute's molecular size on the pattern of isochoric and isobaric solvation of small hard-sphere solutes in TIP4P/2005 water and in a water-like "Jagla" solvent exhibiting unusual thermodynamics. To this end, we employ molecular simulation to determine solvation free energies, isochoric solvation energies and entropies, isobaric solvation enthalpies and entropies, partial molecular volumes, and isothermal density derivatives of the solvation free energy along isobaric and isothermal paths covering solvent's stable liquid and supercritical states as well as supercooled and "stretched" liquid states. Results are found to be consistent with the most primitive scaled-particle theory and the Gaussian model of small-length-scale solvation. The temperature and pressure dependence of solvation quantities embraces solvent's water-like unusual thermodynamic behavior: its density is reflected in the solvation free energy; the isochoric solvation energy and entropy; and the isothermal density derivative of the solvation free energy, its isobaric thermal expansivity in the isobaric solvation enthalpy and entropy, and its isothermal compressibility in the partial molecular volume. The solute's size or length-scale dependence is found to combine with solvent's water-like behavior to produce the "convergence thermodynamics" picture characteristic of aqueous solutions of nonpolar solutes, which is unequivocally found here to be the mapping of the water-like density maximum into the isobaric solvation enthalpy and entropy versus temperature curves for a set of solutes of varying sizes.
... The behavior of the LLCP upon the addition of hydrophobic solutes was also studied on theoretical grounds. 188,315,316 In ref. 315 and 316 the canonical partition function for a family of binary solutions is considered and the corresponding phase behaviors are explored using numerical calculations. The theoretical models for the solutions are based on the van der Waals model and complemented by terms to account for the presence of hydrogen bonds. ...
... The behavior of the LLCP upon the addition of hydrophobic solutes was also studied on theoretical grounds. 188,315,316 In ref. 315 and 316 the canonical partition function for a family of binary solutions is considered and the corresponding phase behaviors are explored using numerical calculations. The theoretical models for the solutions are based on the van der Waals model and complemented by terms to account for the presence of hydrogen bonds. ...
... The authors suggest that such a behavior might be found in solutions containing moderately large amphiphilic molecules. 315 ...
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... HB HB cage cage LJ LJ (8) where ⟨u i ⟩'s and f i 's are the average energies and fractional populations of the states, respectively (calculated in the same Figure 1. Cage Water partition function for pure water. ...
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... Calculation of Thermodynamic Quantities in Solvation. Partition function of a water in the presence of a solute is calculated in the same way as in eq 7. (16) where n(σ s ) is the average number of water molecules in the solvation shell of the solute, calculated in the same way as in ref 31. Enthalpy and entropy are calculated from the following standard expressions. ...
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... Free-standing water droplets that are fully exposed to the air environment inside the chamber undergo gas-liquid vapor exchange due to the inter-diffusion of water vapor and gaseous molecules near the air-liquid interface. The dissolubility effect of gas molecules by diffusion from the air is an entropic effect and increases with decreasing temperature[Frank and Evans, 1945;Guillot and Guissani, 1993;Rettich et al., 2000;Koga, 2011;Abe et al., 2014;Cerdeirina and Debenedetti, 2016]. Dissolved gases in water ...
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... Another approach to the hydration of small hydrophobes highlights the role of water's unusual thermodynamics. This has been explored in the context of liquid state theory 18−20 as well as via simplified statistical mechanical models 21,22 and molecular simulation. 19,23 In this article we present broader evidence in support of this latter view, using arguments based on classical thermodynamics. ...
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We propose an extension of the van der Waals equation which is designed to incorporate, in an approximate fashion, the effects of the network of hydrogen bonds that exist in liquid water. The resulting model qualitatively predicts the unique thermodynamic properties of water, including those of the deeply supercooled states. It also reconciles two proposals for the phase behavior of supercooled and stretched water and provides a thermodynamic origin for the observed polymorphism of the amorphous solid form of water.
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The anomalous behavior of aqueous solutions of amphiphiles in the water-rich region is analyzed via a phenomenological approach that utilizes the isobaric heat capacity as an experimental probe. We report extensive data for solutions of 14 amphiphiles as a function of temperature at atmospheric pressure. Beyond that, data but also isobaric thermal expansivities and isothermal compressibilities for three solutions of tert-butanol as a function of both temperature and pressure are presented. Results rule out the possibility that the observed phenomenology is associated with the anomalous thermodynamics of pure water. Indeed, our data, quantitatively consistent with recent spectroscopic analyses, suggest that water-mediated interactions between the nonpolar parts of amphiphiles are at the origin of anomalies, with the effects of such “hydrophobic aggregation” being observed at mole fractions as small as 0.01. Physicochemical details like the size, the electronic charge distribution and the geometry of amphiphile molecules as well as third-order derivatives of the Gibbs energy and the associated Koga lines support the above claims while they further contribute to characterizing the role of hydrophobicity in these phenomena. Progress with a view to gain a deeper, more concrete understanding remains.
Article
With the temperature and composition dependence of the isobaric heat capacity as our experimental probe, previously reported anomalous behaviors for tert-butanol and 2-butoxyethanol in water are shown to belong to a general scheme for aqueous solutions of amphiphiles. As opposed to a pretransitional scenario, our results point towards aggregation of the hydrophobic moieties of solute molecules as the origin of the phenomenology. The locus in the mole fraction-temperature plane that maps anomalies for 1-pentylamine solutions extends to quite small concentrations and 330 K, thereby raising questions on the roles of hydration and aggregation in phenomena involving so-called 'molecular hydrophobic interfaces'.
Article
The thermodynamic response functions of water display anomalous behaviors. We study these anomalous behaviors in bulk and confined water. We use nuclear magnetic resonance (NMR) to examine the configurational specific heat and the transport parameters in both the thermal stable and the metastable supercooled phases. The data we obtain suggest that there is a behavior common to both phases: that the dynamics of water exhibit two singular temperatures belonging to the supercooled and the stable phase, respectively. One is the dynamic fragile-to-strong crossover temperature (TL ≃ 225 K). The second, T(*) ∼ 315 ± 5 K, is a special locus of the isothermal compressibility KT(T, P) and the thermal expansion coefficient αP(T, P) in the P-T plane. In the case of water confined inside a protein, we observe that these two temperatures mark, respectively, the onset of protein flexibility from its low temperature glass state (TL) and the onset of the unfolding process (T(*)).
Article
The experimental and theoretical studies of supercooled liquid water strongly suggest that the two liquid waters and their liquid-liquid critical point (LLCP) exist at low temperature. However, the decisive experimental evidence of the LLCP has not been obtained because of the rapid crystallization of liquid water in the "no-man's land." Here, we observed experimentally the pressure-induced polyamorphic transition in the dilute glycerol-water solution which relates to the water polyamorphism. We examined the effect of the glycerol concentration on the liquid-liquid transition, and found its LLCP around 0.12-0.15 mole fraction, 0.03-0.05 GPa, and ∼150 K. A 150 K was above, or around, the recently recognized glass transition temperatures of amorphous ices, and the crystallization did not occur, indicating that the direct observation of LLCP is feasible. The low-temperature LLCP has implication to the argument of the relation between the interaction potential of water molecule and the polyamorphic phase diagram.
Article
The structure of water in the hydration shells of small hydrophobic solutes was investigated through molecular dynamics. The results show that a subset of water molecules in the first hydration shell of a nonpolar solute have a significantly enhanced tetrahedrality and a slightly larger number of hydrogen bonds, relative to the molecules in water at room temperature, consistent with the experimentally observed negative excess entropy and increased heat capacity of hydrophobic solutions at room temperature. This ordering results from the rearrangement of a small number of water molecules near the nonpolar solutes that occupy one to two vertices of the enhanced water tetrahedra. Although this structuring is not nearly like that often associated with a literal interpretation of the term “iceberg” in the Frank and Evans iceberg model, it does support a moderate interpretation of this model. Thus, the tetrahedral orientational order of this ensemble of water molecules is comparable to that of liquid water at 10 °C, although not accompanied by the small contraction of the O–O distance observed in cold water. Further, we show that the structural changes of water in the vicinity of small nonpolar solutes cannot be inferred from the water radial distribution functions, explaining why this increased ordering is not observed through neutron diffraction experiments. The present results restore a molecular view where the slower translational and reorientational dynamics of water near hydrophobic groups has a structural equivalent resembling water at low temperatures.
Article
In a recent article, Galamba has investigated the structural organization of water around small nonpolar molecules, by performing molecular dynamics simulations in the polarizable AMOEBA water model. He claimed that there is an increase of tetrahedral order in the hydration shell of such solutes, lending support to the classical iceberg model of hydrophobic hydration. However, I would like to underscore that: (a) the results by Galamba, in line with experimental data and theoretical approaches, indicate that there is no structural order increase in the hydration shell of small nonpolar molecules; (b) the large entropy loss, characteristic of hydrophobic hydration at room temperature, is due to the solvent-excluded volume effect associated with the creation of a cavity suitable to host the solute molecule; (c) an almost complete enthalpy-entropy compensation holds for the water-water H-bond reorganization, and so the latter process cannot be the cause of the poor solubility of nonpolar species in water.
Article
The recommended liquid-liquid equilibrium (LLE) data for 32 binary n-alkane, isoalkane, and cycloalkane-water systems have been obtained after critical evaluation of all data (345 data sets) reported in the open literature up to the end of 2002. The evaluation of the alkane solubility data was based on a generalized equation, which allows prediction of the alkane solubility as a function of temperature. Using the predicted alkane solubilities the concentration of water in the alkane rich phase was calculated. The LLE calculations were performed with the equation of state appended with a chemical term (EoSC) proposed by Góral. The experimental solubilities of water in various alkanes were compared to each other and to the calculated values. The recommended data are presented in the form of individual pages containing tables, all the references, and optionally figures.
Article
A simple model of an associating fluid is proposed that accounts for the fact that hydrogen bonds are highly directional and favor the formation of locally open structures. The resulting analytical equation of state reproduces the distinguishing thermodynamic features of liquid water. In contrast to previous models in which the relationship between bonding and bulk density is assumed a priori, the extent of hydrogen bonding is derived in the present work from a simple microscopic model. Furthermore, by altering the parameters which control the geometric constraints on bonding, the model is able to exhibit the two thermodynamically consistent scenarios that can explain the observed behavior of supercooled liquid water, namely the two-critical-point and singularity-free scenarios. This suggests that the two scenarios are closely related through subtle features of the hydrogen-bond geometry.
Article
The anomalous properties of cold and supercooled water, such as the fact that at sufficiently low temperatures it becomes more compressible and less dense when cooled, and more fluid when compressed, have attracted the attention of physical scientists for a long time. The discovery in the 1970s that several thermodynamic and transport properties of supercooled water exhibit a pronounced temperature dependence and appear to diverge slightly below the homogeneous nucleation temperature inspired a large number of experimental and theoretical studies. Likewise, an important body of work on glassy water has been stimulated by experiments, starting in the mid-1980s and continuing to this date, which suggest that vitreous water can exist in at least two apparently distinct forms. A coherent theory of the thermodynamic and transport properties of supercooled and glassy water does not yet exist. Nevertheless, significant progress towards this goal has been made during the past 20 years. This article summarizes the known experimental facts and reviews critically theoretical and computational work aimed at interpreting the observations and providing a unified viewpoint on cold, non-crystalline, metastable states of water.
Article
The van der Waals equation of state is used to determine phase diagrams for a wide variety of binary fluid mixtures. The locus of the critical line in pressure-temperature-composition space is determined exactly by solving a set of equations with the aid of a computer. The van der Waals constants am and bm for the mixture depend quadratically and linearly upon the mole fractions xi: am = sumisumj xi xjaij and bm = sumixibii. Mixtures are characterized by three non-dimensional parameters: ξ = (b22-b11)/(b11+b22), zeta = (a22b22-2- a11b11- 2)/(a11b11- 2+a22b22-2) and Λ = (a11b11-2- 2a12/b11b22+a22b22-2)/(a11b11- 2+a22b22-2). The parameter Λ can be related to the low-temperature enthalpy of mixing and the parameter zeta to the difference between the gas-liquid critical pressures of the pure fluids. Most of the calculations are for molecules of equal size (ξ = 0), but calculations for a size ratio of two (ξ = 1/3) are also reported. Nine characteristic types of critical lines are distinguished and these correspond to nine separate regions on a Λ , zeta -diagram. Isobaric temperature-composition diagrams and pressure-temperature projections are given for one example from each region to illustrate the possible types of phase equilibrium. Special attention is given to the details of lower critical solution temperature behaviour (type IV) such as is found in the system methane + n-hexane, to tricritical points (symmetrical and unsymmetrical), to azeotropy, and to the possibility of double azeotropy. The phase diagrams calculated from the van der Waals equation seem to account, at least qualitatively, for all but one of the varieties of phase equilibria found in binary fluid mixtures: the low-temperature lower critical solution points in some highly structured aqueous solutions of alcohols and amines.
Article
The solubility in water of noble gases, at room temperature, increases with their size, whereas that of gaseous aliphatic hydrocarbons decreases on increasing their size. This puzzling experimental observation is a unique feature of water as solvent. No real explanation of the phenomenon exists, even though it has been suggested that it is evidence of clathrate-type structure formation around nonpolar molecules. In this paper, we show that the experimental data can be reproduced well by means of Lee's theory of hydrophobic hydration. A fundamental ingredient of this theory is the demonstration that the purely structural reorganization of H-bonds in the hydration shell of a nonpolar solute is a compensating process. The solubility is determined by the balance of two contrasting factors: the excluded volume entropy change due to cavity creation in the solvent, and the direct solute–solvent van der Waals interactions. The work of cavity creation is dominant, determining the poor solubility of nonpolar compounds in water. However, for noble gases, on increasing the hard-sphere diameter, the van der Waals interactions increase, in absolute value, more rapidly than the work of cavity creation, enhancing the solubility. On the contrary, for aliphatic hydrocarbons, on increasing the hard-sphere diameter the van der Waals interactions increase, in absolute value, less rapidly than the work of cavity creation, lowering the solubility. The experimental data of hydration Gibbs energies, therefore, can be accounted for without invoking an enhancement of water structure in the hydration shell of a nonpolar solute.
Article
The problem of hydrophobic bonding, i.e., the strong tendency of hydrocarbons in water to aggregate, can be related (at least if the aggregate contains a sufficiently high number of molecules) and is intuitively related to the original problem of the transfer of nonpolar solutes to a nonpolar solvent from water (e.g., transfer of CâHââ from liquid CâHââ to water or from cyclohexane to water). The scaled particle theory, which has been shown to successfully predict the solubility of nonpolar rare gases or hydrocarbons into water and organic solvents from the gaseous state, may be used either to compute the strength of aggregates of hydrocarbons in water (in a modified form), or the transfer of a hydrocarbon from water to its pure liquid phase. Calculations make it apparent that the solvent dimensions are an important parameter in determining the sign of the free energy of transfer for a nonpolar solute from one solvent to another. The structure of the solvent determines the sign of the entropy of transfer. (13 refs.)
Article
Dynamic light‐scattering measurements using photon correlation spectroscopy have been performed on four different concentrations of t‐butyl alcohol in water; 7.25, 13.2, 20.1, and 26.0 mol %. Temperatures ranged from as low as −16 °C in the supercooled regime to as high as 72 °C. Mutual diffusion constants of the concentration fluctuations were extracted from the light‐scattering data. Viscosity measurements were also performed on these solutions over these temperature ranges. The correlation length of the concentration fluctuations determined from these measurements increased with increasing temperature, leveled off near room temperature and then showed another increase at lower, especially supercooled temperatures. These behaviors suggested critical demixing or consolute points should exist at both temperatures above the equilibrium boiling and below the freezing points of the mixture. The high temperature critical point is probably due to t‐butyl alcohol and water association, whereas the low temperature critical point is most likely due to water–water self‐associating. The results are discussed in terms of the unusual critical‐phenomena‐like properties of supercooled pure water and the possibility that these unusual properties are due to water–water association in the form of clathrate‐type structure.
Article
A new equation of state for rigid spheres has been developed from an analysis of the reduced virial series. Comparisons with existing equations show that the new formula possesses superior ability to describe rigid‐sphere behavior.
Article
The ideas of the first and second papers in this series, which make it possible to interpret entropy data in terms of a physical picture, are applied to binary solutions, and equations are derived relating energy and volume changes when a solution is formed to the entropy change for the process. These equations are tested against data obtained by various authors on mixtures of normal liquids, and on solutions of non‐polar gases in normal solvents. Good general agreement is found, and it is concluded that in such solutions the physical picture of molecules moving in a ``normal'' manner in each others' force fields is adequate. As would be expected, permanent gases, when dissolved in normal liquids, loosen the forces on neighboring solvent molecules producing a solvent reaction which increases the partial molal entropy of the solute. Entropies of vaporization from aqueous solutions diverge strikingly from the normal behavior established for non‐aqueous solutions. The nature of the deviations found for non‐polar solutes in water, together with the large effect of temperature upon them, leads to the idea that the water forms frozen patches or microscopic icebergs around such solute molecules, the extent of the iceberg increasing with the size of the solute molecule. Such icebergs are apparently formed also about the non‐polar parts of the molecules of polar substances such as alcohols and amines dissolved in water, in agreement with Butler's observation that the increasing insolubility of large non‐polar molecules is an entropy effect. The entropies of hydration of ions are discussed from the same point of view, and the conclusion is reached that ions, to an extent which depends on their sizes and charges, may cause a breaking down of water structure as well as a freezing or saturation of the water nearest them. Various phenomena recorded in the literature are interpreted in these terms. The influence of temperature on certain salting‐out coefficients is interpreted in terms of entropy changes. It appears that the salting‐out phenomenon is at least partly a structural effect. It is suggested that structural influences modify the distribution of ions in an electrolyte solution, and reasons are given for postulating the existence of a super‐lattice structure in solutions of LaCl3 and of EuCl3. An example is given of a possible additional influence of structural factors upon reacting tendencies in aqueous solutions.
Article
We perform molecular dynamics computer simulations in order to study the equation of state and the structure of supercooled aqueous solutions of methanol at methanol mole fractions x(m) = 0.05 and x(m) = 0.10. We model the solvent using the TIP4P/2005 potential and the methanol using the OPLS-AA force field. We find that for x(m) = 0.05 the behavior of the equation of state, studied in the P - T and P - ρ planes, is consistent with the presence of a liquid-liquid phase transition, reminiscent of that previously found for x(m) = 0. We estimate the position of the liquid-liquid critical point to be at T = 193 K, P = 96 MPa, and ρ = 1.003 g/cm(3). When the methanol mole fraction is doubled to x(m) = 0.10 no liquid-liquid transition is observed, indicating its possible disappearance at this concentration. We also study the water-water and water-methanol structure in the two solutions. We find that down to low temperature methanol can be incorporated into the water structure for both x(m) = 0.05 and x(m) = 0.10.
Article
A single-component, nonionic fluid that exhibits a standard gas-liquid critical point is considered under the addition of a salt at concentration φ. The critical loci, Tc(φ), ρc(φ), and pc(φ) are studied perturbatively. Since the Debye screening length, ξD, diverges as φ-1/2 in the pure-fluid limit, singular behavior of the critical loci is to be expected when φ → 0. Using classical (i.e., van der Waals-type) theory for the solvent+ion mixture combined with Debye-Hückel theory for the ionic interactions, we find a φ3/2 dependence of the critical loci so that, e.g., (d2Tc/dφ 2) diverges when φ → 0. After extending the theory to allow for ion pairing, experimental data for Tc(φ) for solutions of sodium chloride in water are analyzed and found to support a φ3/2 anomaly of the predicted magnitude and sign. The latter turns out to be a consequence of the density dependence of the dielectric constant of pure water.
Article
The large heat capacity difference between gaseous and dissolved nonpolar molecules in water is commonly attributed to "iceberg" formation around the molecule. Recent experimental measurements show that the heat capacity difference is correlated with the number of water molecules in the first solvation shell. To a first approximation a two-state model in which each water molecule in the solvation shell behaves independently provides a satisfactory basis to quantitatively describe the heat capacity properties of the solvation shell. This noncooperative model explains the observed dependence of thermodynamic parameters upon molecular surface area, the magnitude of the heat capacity in water in terms of reasonable hydrogen-bond energies, and the temperature dependence of the excess heat capacity of apolar molecules in water.
Article
Hydrophobic hydration is studied with an information theory approximation, using the first two moments of the number of solvent centers in a cavity in liquid water, calculated from the density and the pair correlation function. The excess chemical potential, entropy, and heat capacity of solvation are determined for three cases: the two-dimensional MB model of water, in both the (i) NPT and (ii) NVT ensembles, and (iii) the central force CF1 model of water in the NPT ensemble. The results are compared with Monte Carlo simulations and experimental measurements from the literature. The information theory approximation, using only the first two moments, accurately determines the excess chemical potential and entropy of solvation but is unable to predict the excess heat capacity of solvation. Little difference is found between the results obtained using the uniform prior and the ideal gas prior. Molecular dynamics simulations are performed to calculate the excess chemical potential of solvation of soft-spheres as a function of solute size. These results are compared with the solvation of a hard sphere using the information theory approximation and previous molecular dynamics simulations of Lennard-Jones spheres in water. The information theory approximation is found to predict the free energy of solvation as a function of size accurately up to a cavity diameter of approximately 3.5 Å.
Article
The van der Waals approach for the excluded volume effect is used to calculate the thermodynamics of cavity creation in a liquid. By using the experimental density of c-hexane, benzene and water and a temperature independent hard sphere diameter for solvent molecules, the van der Waals approach leads to the following results: (a) the values of the work of cavity creation show a linear decrease in the two organic solvents, but a parabolic temperature dependence with a maximum around 170 C in water; (b) the cavity entropy changes are positive and practically independent of temperature in the two organic solvents; (c) the cavity entropy changes in water are large negative at room temperature and then increase showing the convergence phenomenon at 160 C. Therefore, the experimental density of solvents at each temperature and the hard sphere diameter of solvent molecules considered to be temperature independent are sufficient to distinguish water from c-hexane and benzene and to reproduce entropy convergence.
Article
According to the conventional definition, the hydrophobic effect is a result of thermodynamic changes occurring when a nonpolar group dissolves in water and attributable to the fact that water in contact with such a group has special structural and energetic properties. Disagreement now exists as to whether this effect promotes or hinders protein denaturation. Taking the heat capacity change of unfolding as a measure of the hydrophobicity of the protein interior, others have shown that protein stabilities are systematically affected by changes in hydrophobicity. It has been suggested that the observed trends show that hydrophobic hydration is intrinsically a destabilizing factor. Model calculations using known equations for the stability curves and certain simplifying assumptions now show that such regularities provide no evidence for or against this conclusion. All available data can be rationalized if hydrophobic terms are evaluated from models that require a positive hydrophobic contribution to the Gibbs energy of unfolding. The calculations also confirm the recent finding that any set of proteins with denaturation temperatures between about 330 and 380 K that exhibits entropy convergence at about 386 K is thermodynamically required to show enthalpy convergence at approximately the same temperature. © 1993 John Wiley & Sons, Inc.
Article
On the basis of a simple two-state association model (TSAM), a comprehensive study of thermodynamic response functions for nonaqueous associated solutions is presented. The excess isobaric heat capacities C(p)(E)(T) and excess thermal expansivities V(p)(E) ≡ (∂V(E)/∂T)(p) for a number of alcohol-alkane, amine-alkane, alcohol-ether, and alcohol-alcohol mixtures have been experimentally determined at atmospheric pressure within 278.15-338.15 K for C(p)(E) and 283.15-333.15 K for V(p)(E)(T). A rich variety (in some cases unreported) of temperature dependences for C(p)(E)(T) but also for V(p)(E)(T) curves has been observed. This thermodynamic information has been rationalized with the TSAM, which is found to qualitatively account for all observations. Specifically, the model provides a detailed dissection of the energetic and entropic effects of association that are reflected on C(p)(E)(T), and of the volumetric effects that are echoed on V(p)(E)(T). The latter, almost unexplored to date, are found to be opposite to what is currently being conjectured for "low-temperature water", and they stimulate further experimental studies on aqueous solutions of nonelectrolytes.
Article
The experimentally well-known convergence of solvation entropies and enthalpies of different small hydrophobic solutes at universal temperatures seems to indicate that hydrophobic solvation is dominated by universal water features and not so much by solute specifics. The reported convergence of the denaturing entropy of a group of different proteins at roughly the same temperature as hydrophobic solutes was consequently argued to indicate that the denaturing entropy of proteins is dominated by the hydrophobic effect and used to estimate the hydrophobic contribution to protein stability. However, this appealing picture was subsequently questioned since the initially claimed universal convergence of denaturing entropies holds only for a small subset of proteins; for a larger data collection no convergence is seen. We report extensive simulation results for the solvation of small spherical solutes in explicit water with varying solute-water potentials. We show that convergence of solvation properties for solutes of different radii exists but that the convergence temperatures depend sensitively on solute-water potential features such as stiffness of the repulsive part and attraction strength, not so much on the attraction range. Accordingly, convergence of solvation properties is only expected for solutes of a homologous series that differ in the number of one species of subunits (which attests to the additivity of solvation properties) or solutes that are characterized by similar solute-water interaction potentials. In contrast, for peptides that arguably consist of multiple groups with widely disperse interactions with water, it means that thermodynamic convergence at a universal temperature cannot be expected, in general, in agreement with experimental results.
Article
Most chemical processes on earth are intimately linked to the unique properties of water, relying on the versatility with which water interacts with molecules of varying sizes and polarities. These interactions determine everything from the structure and activity of proteins and living cells to the geological partitioning of water, oil, and minerals in the Earth’s crust. The role of hydrophobic hydration in the formation of biological membranes and in protein folding, as well as the importance of electrostatic interactions in the hydration of polar and ionic species, are all well known. However, the underlying molecular mechanisms of hydration are often not as well understood. This Account summarizes and extends emerging understandings of these mechanisms to reveal a newly unified view of hydration and explain previously mystifying observations. For example, rare gas atoms (e.g., Ar) and alkali-halide ions (e.g., K+ and Cl–) have nearly identical experimental hydration entropies, despite the significant charge-induced reorganization of water molecules. Here, we explain how such previously mysterious observations may be understood as arising from Gibbs inequalities, which impose rigorous energetic upper and lower bounds on both hydration free energies and entropies. These fundamental Gibbs bounds depend only on the average interaction energy of a solute with water, thus providing a deep link between solute-water interaction energies and entropies. One of the surprising consequences of the emerging picture is the understanding that the hydration of an ion produces two large but nearly perfectly canceling, entropic contributions: a negative ion–water interaction entropy and a positive water reorganization entropy.
Article
The chapter discusses the stability of proteins and presents the results obtained on small compact globular proteins, which represent one single cooperative system. Protein is a cooperative system and behaves in an all-or-none fashion. Sharp changes in the properties of a protein do not mean anything in themselves because sequential multistep transitions exhibit the same sharp sigmoidal changes in the observed parameters. The problem of stability of native proteins is closely connected with the problem of protein denaturation, as stability can be judged only by breaking the native structure—that is, denaturing protein by various treatments. The pH of the solution is one of the most important factors determining the state of a protein. Potentiometric titration of protein revealed that smooth changes are connected with the titration of groups with a pK not very different from that of free amino acids, while the gross conformational changes associated with pH denaturation are accompanied by the unmasking of buried groups. The chapter also discusses the temperature-induced changes in protein, denaturational and predenaturational changes in protein, thermodynamics of protein unfolding, and thermodynamic properties of protein.
Article
The experimental thermodynamic data for the dissolution of five simple hydrocarbon molecules in water were combined with the solute-solvent interaction energy from a computer simulation study to yield data on the enthalpy change of solvent reorganization. Similar data were generated for dissolving these same solute molecules in their respective neat solvents using the equilibrium vapor pressure and the heat of vaporization data for the pure liquid. The enthalpy and the free energy changes upon cavity formation were also estimated using the temperature dependence of the solute-solvent interaction energy. Both the enthalpy and T delta S for cavity formation rapidly increase with temperature in both solvent types, and the free energy of cavity formation can be reproduced accurately by the scaled particle theory over the entire temperature range in all cases. These results indicate that the characteristic structure formation around an inert solute molecule in water produces compensating changes in enthalpy and entropy, and that the hydrophobicity arises mainly from the difference in the excluded volume effect.
Article
Accurate calorimetric data for the thermodynamics of transfer of six liquid hydrocarbons to water have been combined with solubility data to provide a model for the temperature dependence of the hydrophobic interaction in protein folding. The model applies at temperatures for which the change in heat capacity (delta Cp) is constant. The extrapolated value of the temperature (Ts) at which the entropy of transfer (delta S degrees) reaches zero is strikingly similar (Ts = 112.8 degrees C +/- 2.2 degrees C) for the six hydrocarbons. This finding provides an interpretation for the empirical relation discovered by Sturtevant: the ratio delta S degrees/delta Cp measured at 25 degrees C is constant for the transfer of nonpolar substances from nonaqueous media to water. Constancy of this ratio is equivalent to Ts = constant. When applied to protein folding, the hydrocarbon model gives estimates of the contributions of the hydrophobic interaction to the entropy and enthalpy changes on unfolding and, by difference, estimates of the residual contributions from other sources. The major share of the large enthalpy change observed on unfolding at high temperatures comes from the hydrophobic interaction. The hydrophobic interaction changes from being entropy-driven at 22 degrees C to being enthalpy-driven at 113 degrees C. Finally, the hydrocarbon model predicts that plots of the specific entropy change on unfolding versus temperature should nearly intersect close to 113 degrees C, as observed by Privalov.
Article
Elementary but general statistical-mechanical relations are derived that relate the thermodynamic properties of the dissolution process to those of the pure solvent. A number of conclusions are drawn from qualitative arguments that these relations suggest. These include the following: (1) The low solubility of nonpolar solutes in water arises not from the fact that water molecules can form hydrogen bonds, but rather from the fact that they are small in size. (2) The large entropy decrease attending the transfer of an inert solute from a nonaqueous solvent to water is largely due to the decrease in entropy of the nonaqueous solvent as the solvent–solvent interaction is restored on removal of the solute from it. (3) It is improper to use values of thermodynamic quantities obtained from small-molecule transfer studies for those that involve macromolecular folding and interaction.
Article
Using Widom's potential distribution theory (J. Chem. Phys. 39 (1963) 2808; J. Phys. Chem. 86 (1982) 869), a general and a special theorems are derived, by means of which one can judge whether a particular sub-process of an overall process will produce compensating changes in enthalpy and entropy. The enthalpy-entropy compensation phenomena that are observed in the transfer process of a hydrophobic molecule from a non-aqueous phase to water are examined in the light of these theorems. It is concluded that most sub-processes involved in the hydrophobic transfer process are compensating except one, that of inserting a cavity corresponding to the solute molecule in the liquid. The reason that this process is non-compensating, and therefore most responsible for the hydrophobicity, is traced to the hard core overlap between solvent and the solute molecules.