Solvation Entropy Research Articles

A theoretical study of the dehydration of tertiary butanol in near-critical and supercritical water

Molecular dynamics simulations were performed to investigate the dehydration of tertiary butanol in water under ambient, near-critical and supercritical conditions. It was found that the equilibrium constant increased with temperature at a fixed pressure of 400 bar, favouring the dehydration reaction. This was mainly due to an increase in the entropy of reaction. The equilibrium was also favoured by low pressures. Studies of the solvation of isobutene gave an insight into how the hydrophobic effect varies with the state point of the water. It was seen that the solvation of isobutene becomes more favourable at higher temperatures due to the increasing entropy of solvation.

G_permute: Permutation-reduced phase space density compaction

Biomolecular processes are governed by free energy changes and thus depend on a fine-tuned interplay between entropy and enthalpy. To calculate accurate values for entropies from simulations is particularly challenging for the solvation shell of proteins, which contributes crucially to the total entropy of solvated proteins, due to the diffusive motion of the solvent molecules. Accordingly, for each frame of a Molecular dynamics (MD) trajectory, our software relabels the solvent molecules, such that the resulting configuration space volume is reduced by a factor of N! with N being the number of solvent molecules. The combinatorial explosion of a naive implementation is here overcome by transforming the task into a linear assignment problem, for which algorithms with complexity O ( N 3 ) exist. We have shown in previous research that the solvent entropy can be estimated from such a compacted trajectory by established entropy estimation methods. In this paper, we describe the software implementation which also allows applications beyond entropy estimation, such as the permutation of lipids in membrane bilayers. Program summary Program title: g_permute Catalogue identifier: AECJ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL No. of lines in distributed program, including test data, etc.: 45 173 No. of bytes in distributed program, including test data, etc.: 2 730 678 Distribution format: tar.gz Programming language: C Computer: PC-compatible running Linux Operating system: Linux RAM: Dependent on the number of solvent molecules, min 12 582 912 bytes Classification: 3, 4.8, 4.9 External routines: liblap (included); From GROMACS-3.3.1: libgmx (not included) Nature of problem: Estimating the entropy of solvent molecules from a molecular dynamics simulation trajectory cannot be performed on ordinary trajectories. Solution method: Compacting the configuration space of molecules by exploiting their permutation symmetry. Applies to trajectories either compatible to those obtained with the GROMACS simulation package [1] or multi-model pdb (Protein Data Bank) files. Restrictions: In rare cases the time to find a solution for the linear assignment problem can be very long. Running time: Dependent on trajectory length and number of molecules to be permuted.

Temperature dependence of the Kováts retention index: Convex or concave curves

The non-linearity in the temperature dependence of the Kováts index, I (the formation of convex or concave curves) was characterized by the second derivative, d 2 I/d T 2. The expression deduced on a purely mathematical–physicochemical basis is d 2 I/d T 2 = [2 TΔ S(CH 2)d I/d T − 100 δΔ C p]/ TΔ G(CH 2). The solute-dependent factor for d I/d T, d 2 I/d T 2, and the extreme temperature in the I vs. T relationship is δΔ C p, which is the molar solvation heat capacity difference between the solute and a hypothetical n-alkane which elutes at the same time as the given solute, while the solvent-dependent factors are the solvation entropy and free energy of the methylene unit, Δ S(CH 2) and Δ G(CH 2). Experimentally, convex I vs. T curves with a minimum are formed when δΔ C p ≫ 0, while concave ones with a maximum are observed when δΔ C p ≪ 0. In the event of a linear temperature dependence, the former equation can be simplified: d I/d T = 100 δΔ C p/2 TΔ S(CH 2) . The deviation from linearity (higher d 2 I/d T 2) increases with increasing δΔ C p values. The model equations were tested from the dataset published by the Kováts group on C78 (19,24-dioctadecyldotetracontane), POH (18,23-dioctadecyl-1-untetracontenol), PCN (1-cyano-18,23-dioctadecyluntetracontane) and TMO (1,38-dimethoxy-17,22-bis-(16-methoxyhexadecyl)-octatriacontane) and by present measurements on the Innowax phase.

Confinement free energy of flexible polyelectrolytes in spherical cavities

A weakly charged flexible polyelectrolyte chain in a neutral spherical cavity is analyzed by using self-consistent field theory within an explicit solvent model. Assuming the radial symmetry for the system, it is found that the confinement of the chain leads to creation of a charge density wave along with the development of a potential difference across the center of cavity and the surface. We show that the solvent entropy plays an important role in the free energy of the confined system. For a given radius of the spherical cavity and fixed charge density along the backbone of the chain, solvent and small ion entropies dominate over all other contributions when chain lengths are small. However, with the increase in chain length, chain conformational entropy and polymer-solvent interaction energy also become important. Our calculations reveal that energy due to electrostatic interactions plays a minor role in the free energy. Furthermore, we show that the total free energy under spherical confinement is not extensive in the number of monomers. Results for the osmotic pressure and mean activity coefficient for monovalent salt are presented. We demonstrate that fluctuations at one-loop level lower the free energy and corrections to the osmotic pressure and mean activity coefficient of the salt are discussed. Finite size corrections are shown to widen the range of validity of the fluctuation analysis.

One-dimensional model for water and aqueous solutions. III. Solvation of hard rods in aqueous mixtures

A simple one-dimensional model for aqueous solution is applied to study the solvation thermodynamics of a simple solute (here, a hard-rod particle) in mixtures of waterlike particles and a cosolvent. Two kinds of cosolvents are considered, one that stabilizes and one that destabilizes the "structure of water." The results obtained for the Gibbs energy, entropy, enthalpy, and heat capacity of solvation are in qualitative agreement with experimental data on the solvation of argon and methane in mixtures of water and ethanol and of water and p-dioxane.

Redox entropy of plastocyanin: Developing a microscopic view of mesoscopic polar solvation

We report applications of analytical formalisms and molecular dynamics (MD) simulations to the calculation of redox entropy of plastocyanin metalloprotein in aqueous solution. The goal of our analysis is to establish critical components of the theory required to describe polar solvation at the mesoscopic scale. The analytical techniques include a microscopic formalism based on structure factors of the solvent dipolar orientations and density and continuum dielectric theories. The microscopic theory employs the atomistic structure of the protein with force-field atomic charges and solvent structure factors obtained from separate MD simulations of the homogeneous solvent. The MD simulations provide linear response solvation free energies and reorganization energies of electron transfer in the temperature range of 280-310 K. We found that continuum models universally underestimate solvation entropies, and a more favorable agreement is reported between the microscopic calculations and MD simulations. The analysis of simulations also suggests that difficulties of extending standard formalisms to protein solvation are related to the inhomogeneous structure of the solvation shell at the protein-water interface combining islands of highly structured water around ionized residues along with partial dewetting of hydrophobic patches. Quantitative theories of electrostatic protein hydration need to incorporate realistic density profile of water at the protein-water interface.

Molecular origin of the hydrophobic effect: Analysis using the angle-dependent integral equation theory

The molecular origin of the hydrophobic effect is investigated using the angle-dependent integral equation theory combined with the multipolar water model. The thermodynamic quantities of solvation (excess quantities) of a nonpolar solute are decomposed into the translational and orientational contributions. The translational contributions are substantially larger with the result that the temperature dependence of the solute solubility, for example, can well be reproduced by a model simple fluid where the particles interact through strongly attractive potential such as water and the particle size is as small as that of water. The thermodynamic quantities of solvation for carbon tetrachloride, whose molecular size is approximately 1.9 times larger than that of water, are roughly an order of magnitude smaller than those for water and extremely insensitive to the strength of solvent-solvent attractive interaction and the temperature. The orientational contributions to the solvation energy and entropy are further decomposed into the solute-water pair correlation terms and the solute-water-water triplet and higher-order correlation terms. It is argued that the formation of highly ordered structure arising from the enhanced hydrogen bonding does not occur in the vicinity of the solute. Our proposition is that the hydrophobic effect is ascribed to the interplay of the exceptionally small molecular size and the strongly attractive interaction of water, and not necessarily to its hydrogen-bonding properties.

One-dimensional model for water and aqueous solutions. II. Solvation of inert solutes in water

The two one-dimensional models introduced in Part I are used to study the thermodynamics of solvation of inert solutes in water. It is shown that the anomalously large Gibbs energy of solvation of inert solutes in water, on one hand, and the large negative entropy of solvation, on the other hand, arise from different molecular sources. While the primitive model can give rise to a large positive solvation Gibbs energy, it fails to show large negative entropy and enthalpy of solvation. It is remarkable that the primitive cluster model can show both the large positive Gibbs energy and enthalpy of solvation.

Thermodynamics of Mixing and Solvation of Ibuprofen and Naproxen in Propylene Glycol + Water Cosolvent Mixtures

By using the van’t Hoff and Gibbs equations, solubility data of ibuprofen (IBP) and naproxen (NAP) determined at several temperatures in propylene glycol (PG) + water (W) cosolvent mixtures were used to evaluate the Gibbs energies, enthalpies, and entropies of solution, mixing and solvation. The solubilities are greater in pure PG and lower in W in both cases at all studied temperatures. These results clearly show that a cosolvent effect is present in these systems. The solvation of these drugs was greater in W compared to PG, and it was lower in the cosolvent mixtures compared with the pure solvents. By means of an enthalpy-entropy compensation analysis, non-linear ΔH soln o versus ΔG soln o compensation plots were obtained, with negative and positive slopes if all of the composition intervals are considered. Accordingly, it follows that at low PG solvent fractions the dominant factor for the solubility of IBP and NAP in this cosolvent system is the entropy, probably due to loosening of the water structure caused by the addition of the cosolvent.

Thermodynamic analysis of the solubility of naproxen in ethanol + water cosolvent mixtures

By using the van't Hoff and Gibbs equations the thermodynamic functions free energy, enthalpy, and entropy of solution, mixing, and solvation of naproxen (NAP) in ethanol (EtOH) + water (W) cosolvent mixtures, were evaluated from solubility data determined at several temperatures. The solubility was greater in pure ethanol and lower in water at all temperatures studied. This result shows the cosolvent effect present in this system. The solvation of this drug in the mixtures increases as the EtOH proportion is also increased in the mixtures. By means of enthalpy–entropy compensation analysis, nonlinear versus compensation with negative slope from pure water up to 30% EtOH and positive slope from 30% EtOH up to 70% EtOH was obtained. Over 70% EtOH the behavior was more complex. Accordingly to these results it follows that the dominant mechanism for solubility of NAP in water-rich mixtures is the entropy, probably due to water-structure loosing by EtOH; whereas, over 30% EtOH the dominant mechanism is the enthalpy probably due to NAP solvation increase by EtOH molecules.

Thermodynamic Analysis of Allosamidin Binding to a Family 18 Chitinase

Inhibition of family 18 chitinases is emerging as a target for pest and fungal control as well as asthma and inflammatory therapy. One of the best known inhibitors for these enzymes is allosamidin, a natural product. While interactions of this compound with family 18 chitinases have been studied in much detail by X-ray crystallography and standard enzymology, details of the driving forces behind its tight binding remain unknown. We have studied the thermodynamics of allosamidin binding to chitinase B (ChiB), a family 18 chitinase from Serratia marcescens, using isothermal titration calorimetry. At pH 6.0, Kd is 0.16 +/- 0.04 microM, and the binding reaction is entropically driven (DeltaSr = 44 cal/K mol) with an enthalpic penalty (DeltaHr = 3.8 +/- 0.2 kcal/mol). Dissection of the entropic term shows that a favorable conformational change in the allosamidin-ChiB complex (DeltaSconf = 37 cal/K mol) is the main contributor to the reaction. At pH 8.5, Kd decreases to 0.03 muM and the binding reaction is less entropically favorable (DeltaSr = 30 cal/K mol). While the solvation entropy change (DeltaSsolv) increases from 15 cal/K mol at pH 6.0 to 46 cal/K mol at pH 8.5, DeltaSconf becomes small and negative (-8 cal/K mol) because of an enthalpy-entropy compensation. Analyses of proton transfer showed that at pH 6.0 binding of allosamidin requires deprotonation of the Asp142-Glu144 catalytic diad. At pH 8.5, the 142-144 diad is ionized in the native enzyme, relieving the deprotonation penalty of binding and explaining why binding becomes enthalpically favorable (DeltaHr = -1.2 +/- 0.2 kcal/mol).

Ab Initio Aqueous Thermochemistry: Application to the Oxidation of Hydroxylamine in Nitric Acid Solution

Ab initio molecular orbital calculations were performed and thermochemical parameters estimated for 46 species involved in the oxidation of hydroxylamine in aqueous nitric acid solution. Solution-phase properties were estimated using the several levels of theory in Gaussian03 and using COSMOtherm. The use of computational chemistry calculations for the estimation of physical properties and constants in solution is addressed. The connection between the pseudochemical potential of Ben-Naim and the traditional standard state-based thermochemistry is shown, and the connection of these ideas to computational chemistry results is established. This theoretical framework provides a basis for the practical use of the solution-phase computational chemistry estimates for real systems, without the implicit assumptions that often hide the nuances of solution-phase thermochemistry. The effect of nonidealities and a method to account for them is also discussed. A method is presented for estimating the solvation enthalpy and entropy for dilute aqueous solutions based on the solvation free energy from the ab initio calculations. The accuracy of the estimated thermochemical parameters was determined through comparison with (i) enthalpies of formation in the gas phase and in solution, (ii) Henry's law data for aqueous solutions, and (iii) various reaction equilibria in aqueous solution. Typical mean absolute deviations (MAD) for the solvation free energy in room-temperature water appear to be ~1.5 kcal/mol for most methods investigated. The MAD for computed enthalpies of formation in solution was 1.5-3 kcal/mol, depending on the methodology employed and the type of species (ion, radical, closed-shell) being computed. This work provides a relatively simple and unambiguous approach that can be used to estimate the thermochemical parameters needed to build detailed ab initio kinetic models of systems in aqueous solution. Technical challenges that limit the accuracy of the estimates are highlighted.

Revisiting the Carboxylic Acid Dimers in Aqueous Solution: Interplay of Hydrogen Bonding, Hydrophobic Interactions, and Entropy

Carboxylic acid dimers are useful model systems for understanding the interplay of hydrogen bonding, hydrophobic effects, and entropy in self-association and assembly. Through extensive sampling with a classical force field and careful free energy analysis, it is demonstrated that both hydrogen bonding and hydrophobic interactions are indeed important for dimerization of carboxylic acids (except formic acid). The dimers are only weakly ordered, and the degree of ordering increases with stronger hydrophobic interactions between longer alkyl chains. Comparison of calculated and experimental dimerization constants reveals a systematic tendency for excessive self-aggregation in current classical force fields. Qualitative and quantitative information on the thermodynamics of hydrogen bonding and hydrophobic interactions derived from these simulations is in excellent agreement with existing results from experiment and theory. These results provide a verification from first principles of previous estimations based on two statistical mechanical hydrophobic theories. We also revisit and clarify the fundamental statistical thermodynamics formalism for calculating absolute binding constants, external entropy, and solvation entropy changes upon association from detailed free energy simulations. This analysis is believed to be useful for a wide range of applications including computational studies of protein-ligand and protein-protein binding.

Pressure Dependence of the Hildebrand Solubility Parameter and the Internal Pressure: Monte Carlo Simulations for External Pressures up to 300 MPa

Monte Carlo simulations were carried out to compute the Hildebrand solubility parameter and the internal pressure for n-hexane, benzene, and ethanol at a temperature of 303.15 K and for external pressures ranging from 0.1 to 300 MPa. In addition, the internal energy, molar volume, enthalpy of the liquid phase, and free energy, enthalpy, and entropy of solvation were calculated as a function of external pressure. For all three molecules, the solubility parameter is found to increase monotonically with increasing external pressure, while the internal pressure exhibits a maximum. The magnitude of the solvation free energy decreases monotonically as external pressure is increased and both enthalpic and entropic terms contribute to this decrease in solubility. Analysis of radial distribution functions indicates small structural changes in the liquid phase and differences between nonpolar and hydrogen-bonding fluids in response to external pressure changes.

Thermodynamic study of the solubility of ibuprofen and naproxen in some ethanol + propylene glycol mixtures

By using the Gibbs and van’t Hoff equations the thermodynamic functions Gibbs free energy, enthalpy, and entropy of solution, mixing and solvation of ibuprofen (IBP) and naproxen (NAP), in some ethanol (EtOH) + propylene glycol (PG) cosolvent mixtures, were evaluated from both drugs solubility values determined at several temperatures. The drugs solubility was greater in pure EtOH and lower in PG in almost all the cases studied. The solvation of these drugs was almost constant in all the cosolvent mixtures tested. By means of enthalpy–entropy compensation analysis, non-linear Δ H soln ° vs. Δ G soln ° compensation plots with positive and negative slopes were obtained for IBP and NAP, respectively. These behaviors are probably due to the increase in solvation of IBP by EtOH molecules; whereas in the NAP case, it is probably due to the solvent-structure loosing.

Sorption and diffusion of normal alkanes through poly(ethylene‐co‐vinyl acetate) membranes

AbstractThe transport behavior of uncrosslinked and crosslinked poly(ethylene‐co‐vinyl acetate) membranes has been investigated using normal alkanes as probe molecules, in the temperature range of 30–60 °C. Benzoyl peroxide was used for crosslinking the matrix. It has been observed that, a critical concentration of crosslinker is necessary for maximum solvent uptake, followed by a decrease at higher concentration. The effect of free volume on liquid transport was investigated by positron annihilation lifetime spectroscopy. The mechanism of transport has been found to deviate from the regular Fickian behavior. The dependence of the transport coefficients on crosslink density, nature of penetrants, and temperature was studied. The polymer–solvent interaction parameter, enthalpy, and entropy of sorption have also been estimated from the transport data. The affine and phantom models for chemical crosslinks were used to predict the nature of crosslinks. Finally, the experimental sorption data were compared with theoretical predictions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2470–2480, 2007

Solvation enthalpy and the thermodynamics of hydration of trans-cyclohexyl-1,4-diamine and cis-cyclohexyl-1,2-diamine

The enthalpy of solution of trans-cyclohexyl-1,4-diamine and cis-cyclohexyl-1,2-diamine in water was determined by calorimetry. The enthalpy of hydration was determined from this quantity and from the enthalpy of sublimation/vaporization presented in another paper by the authors. Considering the solvation process resulting from cavity creation in the solvent and variation of solute conformation transfer steps, the enthalpy corresponding to solute–solvent interaction was estimated. The entropies of solvation and interaction were calculated from the values given for the enthalpies in the present paper and those available for the Gibbs free energies.

Computation of entropy contribution to protein-ligand binding free energy

The entropy contribution DeltaS to protein-ligand binding free energy is studied for nine protein-lipid complexes. The entropy effect from the loss of the translational/rotational degrees of freedom (DeltaStr) is calculated using the ideal gas approach. The change in the vibrational entropy (DeltaSvib) is calculated using the effective quantum oscillator approach with frequencies derived from the coordinate covariance matrix, so the inharmonic effects are taken into account. The change in the entropy of solvation (DeltaSsolv) is considered using the binomial cell model (developed by the authors) for the hydrophobic effect. The entropy contribution from loss of conformations that are available for the free ligand (DeltaSconf) is also estimated. It is revealed that the negative in view of binding term DeltaStr is only partly compensated by increasing of DeltaSvib, so T(DeltaStr+DeltaSvib+DeltaSconf)<0 for all complexes under investigation, but taking into account DeltaSsolv leads to significantly increased DeltaS. For all complexes except biotin-streptavidin, the results are found to be in reasonable agreement with experimental data.

Solubility of carbon dioxide and ethane in three ionic liquids based on the bis{(trifluoromethyl)sulfonyl}imide anion

The objective of this work was to study the influence of changing the cation of the ionic liquid (IL) on gas solubility. For this purpose, the low-pressure solubility of carbon dioxide and of ethane in three ILs based on the bis{(trifluoromethyl)sulfonyl}imide anion ([NTf 2] −) was determined experimentally. Solubility data is reported for 1-ethyl-3-methylimidazolium ([C 1C 2Im] +), 1-butyl-1-methylpyrrolidinium ([C 1C 4pyrr] +) and propylcholinium ([N 1132-OH] +) bis{(trifluoromethyl)sulfonyl}imide ILs between 300 and 345 K. These data are precise to within ±1% and accurate to within ±5%. In these ILs, carbon dioxide (mole fraction solubility between 1 and 3 × 10 −2, molarity between 0.03 and 0.1 mol L −1) is one order of magnitude more soluble than ethane. The effect of changing the cation is small but significant. Changing the cation has a similar effect on both gases even if the differences are more pronounced in the case of ethane with the order of solubility [C 1C 4pyrr][NTf 2] > [C 1C 2Im][NTf 2] > [N 1132-OH][NTf 2]. For all the systems, the solubility decreases with temperature corresponding to exothermic processes of solvation and negative enthalpies and entropies of solvation were calculated. The properties of solvation of the two gases in [C 1C 4pyrr][NTf 2] do not vary significantly with temperature while important variations are depicted for both gases in [C 1C 2Im][NTf 2].

Hydrophobic association of α-helices, steric dewetting, and enthalpic barriers to protein folding

Efficient protein folding implies a microscopic funnel-like multidimensional free-energy landscape. Macroscopically, conformational entropy reduction can manifest itself as part of an empirical barrier in the traditional view of folding, but experiments show that such barriers can also entail significant unfavorable enthalpy changes. This observation raises the puzzling possibility, irrespective of conformational entropy, that individual microscopic folding trajectories may encounter large uphill moves and thus the multidimensional free-energy landscape may not be funnel-like. Here, we investigate how nanoscale hydrophobic interactions might underpin this salient enthalpic effect in biomolecular assembly by computer simulations of the association of two preformed polyalanine or polyleucine helices in water. We observe a high, positive enthalpic signature at room temperature when the helix separation is less than a single layer of water molecules. Remarkably, this unfavorable enthalpy change, with a parallel increase in void volume, is largely compensated for by a concomitant increase in solvent entropy, netting only a small or nonexistent microscopic free-energy barrier. Thus, our findings suggest that high enthalpic folding barriers can be consistent with a funnel picture of folding and are mainly a desolvation phenomenon indicative of a cooperative mechanism of simultaneous formation of multiple side-chain contacts at the rate-limiting step.