Gibbs Energy Of Solvation Research Articles

Calculating the Gibbs Energies of Solvation of 2,2'-Dipyridyl in Nonaqueous Solvents

The Gibbs energies of solvation of 2,2'-dipyridyl (2,2'-Dipy) in methanol (MeOH), acetonitrile (AN), dimethylsulfoxide (DMSO), and N,N-dimethylformamide (DMF) are calculated via quantum chemical modeling. Estimates are made for the contributions from universal and specific types of interaction between the molecules of 2,2'-Dipy and the solvent to the change in the Gibbs energies of solvation of the amine when MeOH is replaced with AN, DMSO, and DMF.

The activity coefficient within the solvation thermodynamics formalism: Fundamentals and applications to neutral solutes

The solvation thermodynamics is a molecular based statistical mechanics description of the solvation process, which provides a proper distinction from other processes that uniquely and unambiguously defines the solvation of any species in any environment. Because the activity coefficient involves the behavior of a given species in different environments, it is then related to the solvation process, which should be described within the solvation thermodynamics formalism. Indeed, the activity coefficient of a species i within an α phase, γi,αo,ρ, is expressed in terms of the binding energy of i to the α phase, Bi, α, and to the dilute-ideal phase, Bi, o. In addition to this molecular description, the activity coefficient can also be related to the Gibbs solvation energies of these two phases within the solvation thermodynamics formalism, which can provide, for instance, unique values of the activity coefficients from the experimental Gibbs solvation energies. The relevance and advantages of using the binding energy (or the coupling work of the solute with its surroundings) as the main molecular quantity for evaluating the activity coefficient is explored in detail. For instance, several cancellations occur when evaluating the binding energies, especially those related to the non-additive corrections (many-body effects), which can more promptly justify the use of the pairwise approximation. In addition, by partitioning the potential energy into two or more contributions, the activity coefficient can also be partitioned into these contributions, yielding exact expressions that are suitable for approximations and interpretations. In fact, a direct connection with perturbation theories can be established and new partitions can be proposed to explore recent approaches based on embedded quantum calculations of the potential energy in condensed phases. It has been shown that the approximation 〈e−βBi, α〉 ≅ e−β〈Bi, α〉, with β−1 = kBT, can be valid even when the condition 〈Bi, α〉 ≪ kBT is not satisfied, as long as the fluctuations, 〈(Bi, α − 〈Bi, α〉)2〉, and the higher order deviations of the binding energy, 〈(Bi, α − 〈Bi, α〉)n〉, (n ≥ 3), are negligible. This small fluctuations approximation (SFA) can rationalize and justify the good results obtained for systems with large binding energies. The SFA can also provide a new interpretation and insights for the activity coefficient. The partition of the potential energy into hard sphere (cavity) and attractive (non-cavity) contributions and the SFA were employed to obtain approximate expressions that allowed to explore the general behavior of the activity coefficient of neutral systems. For instance, the activity coefficient of strongly interacting large molecules (hard-spheres interacting by Lennard-Jones potential in an implicit solvent) tends to decrease with the increasing of the concentration of the solute, which is accentuated by the increase of the dielectric constant of the medium. In addition, the cavity contribution (modeled by hard-sphere mixtures of different sizes) to the activity coefficient is influenced by the relative sizes of the molecules and by the pure liquid densities. This contribution dominates the behavior of the activity coefficient with the concentration.

Can we safely predict solvation Gibbs energies of pure and mixed solutes with a cubic equation of state?

Abstract Solvation Gibbs energies are basically defined as a chemical potential change when transferring a fixed molecule from a perfect gas to a real liquid mixture. This quantity is of special interest for many practical applications as it quantifies the degree of affinity of a solute for its solvent. Few methods are currently available in the literature for the prediction of solvation Gibbs energies. In this article, a new approach is proposed: the use of a predictive cubic equation of state (EoS). The UMR-PRU (Universal Mixing Rule Peng-Robinson UNIFAC) EoS has been selected for its known capacity to semi-predict behaviors of complex systems including polar and associating compounds (by semi-prediction, it is meant that the EoS predicts binary interaction parameters but requires pure-component properties as input parameters). UMR-PRU predictions have been compared to experimental data extracted from the extensive CompSol database (containing around 22 000 pure component data and 70 000 binary data). Accurate predictions were obtained (a mean absolute deviation of 0.36 kcal/mol was obtained for all the binary data). Finally, when using a fully-predictive approach (i.e. pure-component EoS parameters are predicted from group-contribution methods), the prediction accuracy is roughly preserved.

Solubility of gases in ionic liquids using PHTC equation of state

In our previous work, a perturbed hard trimer chain (PHTC) equation of state (EOS) was used to compute the volumetric properties of several ionic liquids (IL) (M. M. Alavianmehr et al., Ionics (2016) 2447–2459). In the present study, the proposed EOS is employed to model the solubilities of CO2, H2S and R143a gases in some ionic liquids for temperatures ranging from 282 K to 353.15 K and at pressures (gas mole fractions) up to 5 MPa (0.8). The proposed EOS is applied to estimate Henry's constant and Gibbs energy of solvation of CO2 in [C8mim][PF6] ionic liquid. The outcomes of the results for the Henry constant on the mole fraction scale are compared with the experimental data. Parameters appeared in the EOS for pure ILs and considered gases are obtained using densities given in literature over a broad range of temperature. Using three parameters together with one binary interaction parameter one can predict solubility parameters with acceptable accuracies.

On the Assumption-Free Determination of Single-Ion Gibbs Energies of Transfer

Since about 100 years, the quest on the determination of Gibbs energies of transfer of single-ions exists. While some consider that the chemical potential of single-ions is physically senseless, other determined Gibbs solvation energies or Gibbs transfer energies of single-ions with the help of extra-thermodynamic assumptions (e.g. TATB-assumption, ferrocene-assumption and others), thereby introducing an error of the respective quantity of insufficiently assessable magnitude.[1] We suggest a procedure for the thermodynamically rigorous, experimental determination of the Gibbs energy of transfer of single-ions Δtr G°(i, S1--> S2). The method is based on potential difference measurements between two electrochemical half-cells with different solvents (solvation cells) connected by an ideal ionic liquid salt bridge (ILSB).[2] We point out the specific requirements for the IL with regard to the procedure, thus ensuring that those parts of liquid junction potentials (LJP) at both ends of the ILSB cancel which depend on the redox system used. The remaining parts of the LJPs can be determined by separate electromotive force measurements, the knowledge of the ionic transference numbers and Gibbs energies of transfer of the used salts is mandatory. No extra-thermodynamic assumptions are necessary for this procedure. The accuracy of the target quantity is an inherent part of the measurements and depends, amongst others, on the ideality of the IL used. We present results concerning the crucial steps a) and b) of the methodology exemplarily for Ag+ and Cl− with S1 being water and S2 being acetonitrile as an important intermediate goal to evaluate our concept for the assumption-free determination of single-ion Gibbs transfer energies Δtr G°(i, S1--> S2).[3] The used IL, [N2225]+[NTf2]−, shows nearly ideal behavior, that is, nearly identical diffusion of anion and cation, in the pure IL, but also in water and acetonitrile solution. Electromotive force measurements of solvation cells between S1 and S2 demonstrate Nernstian behavior for Ag+ concentration cells and constant like cell potentials for solutions with five tested Ag+ counterions. The Gibbs transfer energies can be utilized to collect data for the unified scales of acidity pHabs and reducity and peabs and for their two dimensional plot, the Protoeletric Potential Map (PPM), enabling the possibility to easily compare acidities and redox potentials between different media.[4] Literature:[1] P. Hünenberger, M. Reif, Single-Ion Solvation. Experimental and Theoretical Approaches to Elusive Thermodynamic Quantities, The Royal Society of Chemistry, Cambridge, 2011.[2] V. Radtke, A. Ermantraut, D. Himmel, T. Koslowski, I. Leito, I. Krossing, Angew. Chem. Int. Ed. 2018, 57, 2344.[3] A. Ermantraut, V. Radtke, N. Gebel, D. Himmel, T. Koslowski, I. Leito, I. Krossing, Angew. Chem. Int. Ed. 2018, 57, 2348.[4] D. Himmel, V. Radtke, B. Butschke, I. Krossing, Angew. Chem. Int. Ed., 2018, doi:10.1002/anie.201709057.

Guaiacol and its mixtures: New data and predictive models. Part 2: Gibbs energy of solvation

Guaiacol is a model molecule for lignocellulosic biomass processing, and thus understanding its interactions with solvents is an important step when developing units for processing lignocellulosic biomass. In this work, activity coefficient measurements of different solvents (acetonitrile, ethanol, tetrahydrofuran) in guaiacol have been performed at different concentrations and temperatures. These measurements have been used to estimate the infinite dilution activity coefficients and the Gibbs energy of solvation of guaiacol in the different solvents, and of each solvent in guaiacol. These estimated values were compared to those obtained with different predictive models: UNIFAC DMD, Monte Carlo Molecular Simulation, COSMO-SAC and GC-PPC-SAFT. The predictions are in very good agreement with the Gibbs energies of solvation derived from experimental data. Some conclusions are also drawn regarding the inter- and intramolecular hydrogen bonding in guaiacol and about its affinity with different solvents on the basis of the inter- and intramolecular interactions taking place.

Carbon dioxide solubility in 1-butyl-3-methylimidazolium tetrafluoroborate and 1-butyl-3-methylimidazolium tetrachloroferrate over an extended range of temperature and pressure

Solubility data of carbon dioxide (CO2) in the two ionic liquids 1-butyl-3-methylimidazolium tetrafluoroborate [BMIM][BF4] and 1-butyl-3-methylimidazolium tetrachloroferrate [BMIM][FeCl4] at T = (273.15–413.15) K and pressures up to p = 4.5 MPa are presented. In addition to the experiments, a literature review was done to compare the new results with published solubility data. The measurements were carried out using an isochoric method which operates in decrements of ΔT = 20 K within the investigated temperature range and at selected four different pressure steps ranging from a pressure p of around 4.5 MPa to around 0.5 MPa. The solubility of CO2 decreases in both ionic liquids with increasing temperatures. Within the p,T-range investigated, CO2 displayed a solubility in [BMIM][BF4] from a mole fraction x = 0.0117 and a corresponding molality m = 0.0526 mol·kg−1 at T = 413.15 K and p = 0.417 MPa up to x = 0.4876 and m = 4.2094 mol kg−1 at T = 293.15 K and p = 4.349 MPa. The corresponding values for the solubility in [BMIM][FeCl4] start at a mole fraction x = 0.0268 and a corresponding molality m = 0.0818 mol·kg−1 at T = 413.15 K and p = 0.443 MPa and end at x = 0.5126 and m = 3.1216 mol·kg−1 at T = 293.15 K and p = 4.478 MPa. At a constant temperature, CO2 is better soluble in [BMIM][FeCl4] than in [BMIM][BF4] and the mean value of the solubility difference related to mole fraction x over the pressure range investigated amounts to about 4% at T = 273.15 K and monotonously increases to about 92% at T = 413.15 K. Henry's law constant as well as derived thermodynamic properties, such as the Gibbs energy of solvation, the enthalpy of solvation, the entropy of solvation, and the heat capacity of solvation, were calculated and discussed regarding the solute–solvent molecular interactions.

A thermodynamic model for strong aqueous electrolytes based on the eSAFT-VR Mie equation of state

The latest formulation of the SAFT-VR Mie equation of state (EoS) is extended to solutions of salts which are assumed to be strongly dissociating in water – through the addition of a Born term for accurate representation of the Gibbs energy of solvation, and a Debye-Hückel term for long-range, electrostatic interactions. Two adjustable parameters are assigned to each ionic species, the ion-solvent (here water) cross dispersion energy parameter and the ion segment diameter, which are optimized against experimental data for electrolyte solution densities and mean ionic activity coefficients. Model correlations for the activity coefficients and liquid densities, as well as predictions for vapor pressure and osmotic coefficients, show that the developed model performs accurately and, in many cases, is more accurate than other recent formulations for electrolyte solutions. Finally, a methodology for equation of state parameterization is presented to capture the non-monotonic temperature dependence of activity coefficient isotherms at low temperatures.

Computational Analysis of Solute–Solvent Coupling Magnitude in the Z/E Isomerization Reaction of Nitroazobenzene and Benzylideneanilines

The dynamic solvent effect often arises in solution reactions, where coupling between chemical reaction and solvent fluctuation plays a decisive role in the reaction kinetics. In this study, the Z/E isomerization reaction of nitoroazobenzene and benzylideneanilines in the ground state was computationally studied by molecular dynamics simulations. The non-equilibrium solvation effect was analyzed using two approaches: (1) metadynamics Gibbs energy surface exploration and (2) solvation Gibbs energy evaluation using a frozen solvation droplet model. The solute–solvent coupling parameter (Ccoupled) was estimated by the ratio of the solvent fluctuation Gibbs energy over the corresponding isomerization activation Gibbs energy. The results were discussed in comparison with the ones estimated by means of the analytical models based on a reaction–diffusion equation with a sink term. The second approach using a frozen solvation droplet reached qualitative agreement with the analytical models, while the first metadynamics approach failed. This is because the second approach explicitly considers the non-equilibrium solvation in the droplet, which consists of a solute at the reactant geometry immersed in the pre-organized solvents fitted with the solute at the transition state geometry.

Thermodynamic study of mixtures containing dibromomethane

Isothermal vapor–liquid equilibria at 298.15 K for dibromomethane + an organic compound (C5–C8 n-alkanes, cyclohexane, tetrachloromethane, diethyl ether, dipropyl ether, dibutyl ether, tetrahydrofuran, and 3-pentanone) were determined by head-space gas chromatographic analysis of the vapor phase. Excess molar Gibbs energies, GE, and activity coefficients for the investigated systems were obtained by a least-square treatment of equilibrium data. All systems except mixtures with tetrahydrofuran and 3-pentanone revealed positive deviations from ideality. The Gibbs energies of solvation, ΔsolvG°, for the examined substances in dibromomethane were evaluated and compared with those in dichlorometane. The effect of polar groups, chain lengthening, and cyclization upon ΔsolvG° was discussed.

Estimation of Solvation Quantities from Experimental Thermodynamic Data: Development of the Comprehensive CompSol Databank for Pure and Mixed Solutes

The Gibbs energy of solvation measures the affinity of a solute for its solvent and is thus a key property for the selection of an appropriate solvent for a chemical synthesis or a separation process. More fundamentally, Gibbs energies of solvation are choice data for developing and benchmarking molecular models predicting solvation effects. The Comprehensive Solvation—CompSol—database was developed with the ambition to propose very large sets of new experimental solvation chemical-potential, solvation entropy, and solvation enthalpy data of pure and mixed components, covering extended temperature ranges. For mixed compounds, the solvation quantities were generated in infinite-dilution conditions by combining experimental values of pure-component and binary-mixture thermodynamic properties. Three types of binary-mixture properties were considered: partition coefficients, activity coefficients at infinite dilution, and Henry’s-law constants. A rigorous methodology was implemented with the aim to select data at appropriate conditions of temperature, pressure, and concentration for the estimation of solvation data. Finally, our comprehensive CompSol database contains 21 671 data associated with 1969 pure species and 70 062 data associated with 14 102 binary mixtures (including 760 solvation data related to the ionic-liquid class of solvents). On the basis of the very large amount of experimental data contained in the CompSol database, it is finally discussed how solvation energies are influenced by hydrogen-bonding association effects.

Algebraic conditions, in terms of the solvent partition constants, for the separation of chemical classes by gas–liquid chromatography

ABSTRACTThe interdependence between the solvation Gibbs energy of several functional groups and the solvent partition coefficients was studied, starting from gas chromatographic data. Single-parameter relationships were derived for the –OH, -CHO, -CO, -O-,-COO (acetate), -COO (methyl ester)-, and -CN group increments. The obtained equations were found to be temperature independent, and could be successfully used for the evaluation of 19 stationary phases with respect to certain separation questions. The selectivity problem was converted into an inequality system. The graphical solution of such a system provides an image of the separation abilities of a sorbent material with respect to a given pair of solutes, and allows an efficient comparison of a great number of stationary phases. The graphs are also illustrative for the temperature effect on the selectivity features.

Correction to Force Field Benchmark of Organic Liquids. 2. Gibbs Energy of Solvation.

Correction to Force Field Benchmark of Organic Liquids. 2. Gibbs Energy of Solvation.

Determination of Gibbs energies of formation in aqueous solution using chemical engineering tools

Standard Gibbs energies of formation are of primary importance in the field of biothermodynamics. In the absence of any directly measured values, thermodynamic calculations are required to determine the missing data. For several biochemical species, this study shows that the knowledge of the standard Gibbs energy of formation of the pure compounds (in the gaseous, solid or liquid states) enables to determine the corresponding standard Gibbs energies of formation in aqueous solutions. To do so, using chemical engineering tools (thermodynamic tables and a model enabling to predict activity coefficients, solvation Gibbs energies and pKa data), it becomes possible to determine the partial chemical potential of neutral and charged components in real metabolic conditions, even in concentrated mixtures.

Thermodynamic study of tetrachloromethane or heptane + cycloalkane mixtures

Vapor–liquid equilibria at 298.15 K have been determined for binary mixtures of tetrachloromethane or heptane plus a cyclic hydrocarbon (cyclopentane, cyclohexane, cycloheptane, cyclooctane, cyclodecane, cis-decalin, norbornane, octahydro-4,7-methano-1H-indene, adamantane), using a head-space gas chromatographic technique. Excess molar Gibbs energies and activity coefficients for the systems investigated have been obtained by a least-squares treatment of the equilibrium results. All mixtures exhibit positive deviations from ideality, increasing with the cycloalkane size. The Gibbs energies of solvation, Δsolv G°, for cyclic hydrocarbons in the two solvents have been evaluated and compared with those of linear and branched alkanes. The effect of cyclization upon Δsolv G° has been discussed.

Solvation enthalpies and Gibbs energies of the proton and electron: Influence of solvation models

A comprehensive examination of the solvation enthalpies and Gibbs energies of the proton and electron in twenty solvents of different polarities was carried. Eleven quantum mechanical methods were applied in conjunction with the 6-311++G(d,p) basis set and C-PCM solvation model. It was found that different methods produce consistent values for the solvation enthalpy and Gibbs energy of the proton in all solvents, while the corresponding values for the electron are mutually notably different. The fact that the Minnesota functionals often produced inconsistent solvation enthalpy and Gibbs energy values of the electron indicates their unreliable performance without the corresponding SMD solvation model, whereas other studied methods only slightly depend on solvation models. A comparison of the results of the present investigation to those obtained by employing SMD reveals that C-PCM produces slightly more negative (less positive) solvation enthalpies and Gibbs energies of the electron, and less negative values for the proton. These results are also in accord with the literature data where the IEF-PCM solvation model was used.

A Hybrid Capacitor Based on Fe3O4-Graphene Nanocomposite/Few-Layer Graphene in Different Aqueous Electrolytes

Graphene nanoplatelets have been used for synthesis of Fe3O4-graphene nanocomposite negative electrode. A high-resolution transmission electron microscopy measurements of the graphene areas surrounded by Fe3O4 nanoparticles show that the graphene has folded on itself and the edges have some amounts of waviness which could indicate existence of amorphous carbon. A high energy density hybrid capacitors (HC) have been completed based on 1 M Li2SO4, Na2SO4, Rb2SO4, Cs2SO4 and MgSO4 aqueous electrolytes and Fe3O4-graphene nanocomposite/few-layer graphene electrode materials. The optimal working potential region of each electrode has been regulated by optimized mass balance of the electrodes. After optimization the cell voltage increased up to 1.4 V and an energy density (maximal) up to 9.4 Wh kg−1 in 1 M Cs2SO4 electrolyte. The maximal power density 41.1 kW kg−1 has been calculated for 1 M Rb2SO4 aqueous electrolyte based HC. The energy and power density of completed HC cells decreased with solvation Gibbs energy of the cations. The cycling efficiency values have been calculated being highest for 1 M Rb2SO4 and 1 M Cs2SO4 electrolyte based systems, 98.4% and 99.9%, respectively. Thus, promising HC cells based on Fe3O4-graphene nanocomposite/few-layer graphene electrodes in different aqueous electrolytes have been developed and characterized.

Impact of structural modification of 1,2,4-thiadiazole derivatives on thermodynamics of solubility and solvation processes in 1-octanol and n-hexane

Influence of a structural modification on thermodynamic aspects of solubility and solvation processes of the 1,2,4-thiadiazole drug-like compounds in pharmaceutically relevant solvents n-hexane and 1-octanol was investigated. The solubility of the compounds in 1-octanol does not substantially depend on the nature and position of the substituent in the phenyl moiety. In n-hexane, however, the introduction of any substituent in the phenyl ring of the 1,2,4-thiadiazole molecule reduces the solubility in the solvent. In order to rationalize the relationships between the structure of 1,2,4-thiadiazoles and their solubility, the latter was considered in terms of two fundamental processes: sublimation and solvation. It was found that for the most of the compounds the solubility change in both solvents is a consequence of competition between the sublimation and solvation contributions, i.e. the introduction of substituents leads to growth of the sublimation Gibbs energy and increase in the solvation Gibbs energy. Thermodynamic parameters of the transfer process of the compounds from n-hexane to 1-octanol, which is a model of the blood–brain barrier (BBB), were also analyzed.

Generalized Born and Explicit Solvent Models for Free Energy Calculations in Organic Solvents: Cyclodextrin Dimerization.

Evaluation of solvation (binding) free energies with implicit solvent models in different dielectric environments for biological simulations as well as high throughput ligand screening remain challenging endeavors. In order to address how well implicit solvent models approximate explicit ones we examined four generalized Born models (GB(Still), GB(HCT), GB(OBC)I, and GB(OBC)II) for determining the dimerization free energy (ΔG(0)) of β-cyclodextrin monomers in 17 implicit solvents with dielectric constants (D) ranging from 5 to 80 and compared the results to previous free energy calculations with explicit solvents ( Zhang et al. J. Phys. Chem. B 2012 , 116 , 12684 - 12693 ). The comparison indicates that neglecting the environmental dependence of Born radii appears acceptable for such calculations involving cyclodextrin and that the GB(Still) and GB(OBC)I models yield a reasonable estimation of ΔG(0), although the details of binding are quite different from explicit solvents. Large discrepancies between implicit and explicit solvent models occur in high-dielectric media with strong hydrogen bond (HB) interruption properties. ΔG(0) with the GB models is shown to correlate strongly to 2(D-1)/(2D+1) (R(2) ∼ 0.90) in line with the Onsager reaction field ( Onsager J. Am. Chem. Soc. 1936 , 58 , 1486 - 1493 ) but to be very sensitive to D (D < 10) as well. Both high-dielectric environments where hydrogen bonds are of interest and low-dielectric media such as protein binding pockets and membrane interiors therefore need to be considered with caution in GB-based calculations. Finally, a literature analysis of Gibbs energy of solvation of small molecules in organic liquids shows that the Onsager relation does not hold for real molecules since the correlation between ΔG(0) and 2(D-1)/(2D+1) is low for most solutes. Interestingly, explicit solvent calculations of the solvation free energy ( Zhang et al. J. Chem. Inf. Model . 2015 , 55 , 1192 - 1201 ) reproduce the weak experimental correlations with 2(D-1)/(2D+1) very well.

Computer Simulation Study of the Interactions Between Gold Clusters and Glutamate in Aqueous Solution

The objective of this study is to discuss the quantitative simulation results of Au n clusters (n = 3, 4) and glutamate–Au n complexes in water. To attain this goal, each species was first modeled by quantum mechanical calculations, and subsequently their properties in aqueous solution were studied by applying Monte Carlo simulations. The results of gas phase calculations showed that the glutamate–Au4 complex has a relatively higher interaction energy than do the other complexes. Solvation of glutamate–Au n complexes was investigated in terms of solvation Gibbs energy and, in continuation, compared with that of pure Au n clusters. The computations showed that complex formation enhances the solubility in water. Of the two glutamate–Au n complexes, glutamate–Au4 has the larger solubility in water. The resulting complexation Gibbs energies were also used to study the stability of related structures, indicating glutamate–Au3 is the most stable complex in aqueous solution.