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Structures, intermolecular interactions, and chemical hardness of binary water–organic solvents: a molecular dynamics study

  • Sonia M. Aguilera-Segura
  • Francesco Di Renzo
  • Tzonka MinevaEmail author
Original Paper
  • 180 Downloads
Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday

Abstract

The evolution of structural properties, thermodynamics and averaged (dynamic) total hardness values as a function of the composition of binary water–organic solvents, was rationalized in view of the intermolecular interactions. The organic solvents considered were ethanol, acetonitrile, and isopropanol at 0.25, 0.5, 0.75, and 1 mass fractions, and the results were obtained using molecular dynamics simulations. The site-to-site radial distribution functions reveal a well-defined peak for the first coordination shell in all solvents. A characteristic peak of the second coordination shell exists in aqueous mixtures of acetonitrile, whereas in the water–alcohol solvents, a second peak develops with the increase in alcohol content. From the computed coordination numbers, averaged hydrogen bonds and their lifetimes, we found that water mixed with acetonitrile largely preserves its structural features and promotes the acetonitrile structuring. Both the water and alcohol structures in their mixtures are disturbed and form hydrogen bonds between molecules of different kinds. The dynamic hardness values are obtained as the average over the total hardness values of 1200 snapshots per solvent type, extracted from the equilibrium dynamics. The dynamic hardness profile has a non-linear evolution with the liquid compositions, similarly to the thermodynamic properties of these non-ideal solvents.

Graphical abstract

Computed dynamic total hardness, as a function of the cosolvent mass fraction for water–ethanol (EtOH), water–isopropanol (2PrOH) and water–acetonitrile (AN)

Keywords

Binary water-organic solvent Molecular dynamics simulations Radial distribution function Hydrogen bond Dynamic chemical hardness 

Introduction

The intermolecular interactions between water and organic solvents drive the microstructuring in aqueous mixtures of simple organic solvents, which determines their thermodynamic properties [1]. In recent years, studies of the structural organization and mixing behavior at the molecular level in binary water–simple organic solvents has attracted renewed interest because of their use in biomass fractionation processes [2, 3, 4, 5, 6], and in the formation of membranes for CO2/flue gases (N2) separation [7], in addition to the plethora of well-established applications in electrochemistry, organic synthesis, chromatography, and solvent extraction. Moreover, the individual properties of the organic components confer distinctive features when mixed with water at various contents, temperatures and pressure conditions.

In this work, we will focus on aqueous mixtures of ethanol (EtOH), isopropanol (2PrOH), and acetonitrile (AN). A variety of physical [8, 9, 10, 11, 12], thermodynamic [13, 14, 15, 16], transport [9, 17, 18, 19], electronic [12, 20, 21, 22, 23], and structure [24, 25, 26, 27, 28] properties are available from experimental and computational studies. Simple alcohols, such as EtOH and 2PrOH, are miscible in water, form strong hydrogen bonds with water molecules, and are thought to be inhibitors of clathrate hydrate formation. The thermodynamics of short (methanol and ethanol) alcohol–water mixtures have been shown to depend on solvent composition in a very complex way [29, 30, 31, 32, 33, 34, 35, 36, 37, 38]. Study of 1H NMR measurements [33] at −10 °C found that a decrease of the alcohol mole fraction to ~0.2 strengthens the H-bonds between water and hydroxyl OH groups in ethanol, while enhancing the water structure through H-bonding. Pozar et al. [34] used NMR techniques to understand the microheterogeneity of EtOH–water mixtures [34], and suggested that ethanol is entirely structured by hydrogen bonding, whereas this is not true for water. The calculated structure factors pointed to the conclusion that water is less hydrogen bonded when the EtOH concentration increases, even if the change in intensities is smooth. Petong et al. [35] observed non-linear changes in the ethanol dipole moment with changes in the mixture concentration. From molecular dynamics (MD) simulations of pure liquid ethanol, the role of H-bonding on the structural and dynamical properties was evidenced by Saiz et al. [1, 36]. A hydrogen bonding study in water–alcohol mixtures by X-ray absorption spectroscopy by Lam et al. [37] suggested that the additional hydrogen bonding interactions generated from the water–alcohol interaction would result in superior ordering in the liquid structures, leading to a reduction in entropy and a negative enthalpy of mixing. This would be true for EtOH. However, the spectra of the 2PrOH–water mixtures exhibit an increase in the number of broken alcohol hydrogen bonds for mixtures containing a water mole fraction of up to 0.5. Therefore, this explanation does not account for the negative excess entropy of the 2PrOH–water mixtures, and still needs to be addressed. Finneran et al. [38] succeeded in registering the rotational spectrum of an isolated EtOH-dimer using Fourier transform microwave spectroscopy, and identified the presence of only the gauche EtOH conformer, stabilized by H-bonding with water. These measurements confirm that ethanol is a better hydrogen-bond acceptor than donor. Ab initio calculations [38] identified water and EtOH as donor and acceptor, respectively.

AN, on the other hand, although miscible with water, is not a hydrogen bond donor, and the water–AN mixture is known to present a microheterogeneity [39]. The term microheterogeneity has been introduced to define the structural organizations of multi-component liquids, where the molecules of each component are surrounded by molecules of the same kind. The various patterns hitherto proposed [16, 26, 40, 41, 42, 43, 44, 45, 46, 47] for microstructural organization in water–AN mixtures revealed that the structuring of this binary solvent is a complex function of the liquid compositions, similarly to the short alcohols–water mixtures. Starting with an earlier thermodynamics study by Robertson and Sugamori [41] on the temperature dependence of the enthalpy (ΔH) and of the specific heat capacity at constant pressure (Cp), the water structure was found to be broken, or partially molten, due to the presence of the AN component in the liquid. Moreau and Douheret [42] established the existence of three interaction regions with different structural patterns in water–AN mixtures. In the water-rich region, below 0.2 mol fraction of AN, the voids of the aqueous structure are progressively filled by AN, without enhancement of the water cluster. The geometry of the AN molecules could not easily fit into the void, which led to the disruption of the H-bond network. By increasing the AN concentration, an intermediate region between ~0.2 to ~0.8 mol fraction was characterized by progressive breaking of the H-bonds, which resulted in a reduction of the water aggregates and giving rise to a region of microheterogeneity. In this region, water molecules were mostly surrounded by water, and AN molecules were surrounded by AN. At AN concentrations, above ~0.8 mol, the domains of predominantly AN molecules were progressively disrupted by the addition of water molecules. Thus, although aqueous mixtures of AN are characterized by microheterogeneity, the formation of water clusters has been excluded from the analysis of IR spectra for mixtures above 0.15 mol concentration [45]. Moreover, above the equimolar mixture, water preferably solvated AN over other water molecules, which suggested that water molecules form short water chains and rings [45]. In mixtures with high AN content, water molecules can gain motional freedom, whereas at lower AN concentration water dimers and trimers are observed [44]. Formation of true H-bonds between water and AN molecules at low AN concentration have been concluded from X-ray diffraction and IR spectroscopy [46] and radial distribution functions [26]. From MD simulations, H-bond life time was found to increase with the decrease in water content [47]. The dipole–dipole dimers between water and AN were suggested to coexist with the first-shell H-bonds in the mixtures with AN content of between 0.2 and 0.6 mol [46]. This correlates with the ab initio results [43], which established two types of water–AN dimers, one favoring the hydrogen bonding with water, and another favoring the dipole–dipole interaction. However, the dipole–dipole interactions in pure AN clusters were reduced in the presence of water, because hydrogen bonded AN dimers appear [48].

Тhis work aims to provide a systematic comparative study of the structural, dynamic and thermodynamics properties of aqueous mixtures of three organic solvents (called cosolvent throughout this paper), namely EtOH, 2PrOH and AN at 0.25, 0.50, and 0.75 mass fraction concentrations (XCosol), using MD simulations. The results for the four pure liquids obtained at the same theoretical level are also included. In addition, for the first time, it is proposed to evaluate the chemical hardness at equilibrium dynamics and to analyze its behavior as a function of cosolvent mass concentration.

Methods and computational details

MD simulations

All-atom MD simulations were carried out using the GROMACS [49, 50, 51, 52, 53] package version 2016.3, along with the CHARMM36 additive force field [54, 55] and the TIP4P model for liquid water [56, 57, 58], which better reproduces the electrostatic distribution around water molecules in comparison with other three-site models. Solvent structures for EtOH, 2PrOH, and AN are available in the GROMACS molecule and liquid database [59]. The compositions of the cubic boxes of 4 nm, used in our simulations, are presented in Table 1 together with the calculated number of molecules to reproduce the experimental densities at each concentration.
Table 1

Compositions of the simulated systems in 4 nm cubic boxes for the modeled solvent mixtures, studied in this work. EtOH Ethanol, 2PrOH isopropanol, AN acetonitrile

Solvent system

X Cosol

χCosol

NCosol

Nwater

Pure water

0

0

0

2133a

Pure EtOH

1

1

657b

0

Pure 2PrOH

1

1

501c

0

Pure AN

1

1

730d

0

EtOH-water mixture

0.25

0.115

201

1539

0.50

0.281

381

973

0.75

0.540

534

455

2PrOH-water mixture

0.25

0.910

153

1531

0.50

0.231

288

960

0.75

0.473

448

851

AN-water mixture

0.25

0.128

224

1534

0.50

0.305

417

950

0.75

0.568

582

442

The cosolvent mass fraction (XCosol) and the cosolvent molar fraction (χCosol), the number of cosolvent molecules (NCosol) and the number of water molecules (Nwater) are reported

a6399 atoms +2133 virtual sites

b5913 atoms

c6012 atoms

d4380 atoms

For each simulation box, energy minimization was performed using the steepest descent algorithm until convergence to a tolerance of 100 kJ mol−1 nm−1. After minimization, unconstrained simulations to stabilize and distribute the solvent molecules were performed for 200 ps at 298.15 K and 1 bar with a 0.5-fs time step, and a frame-saving rate (for analysis) of 1 ps. Temperature and pressure coupling were handled using the leap-frog stochastic dynamics integrator and the Parrinello-Rahman method [60, 61], respectively. Initial velocities were generated from a Maxwell distribution at 298.15 K and 15-ns MD simulations were performed. The isothermal-isobaric (NPT) ensemble was considered for data collection. Neighbor searching and short-range non-bonded interactions were handled with the Verlet cut-off scheme.

Electrostatics were treated with the fast smooth particle-mesh Ewald (SPME) method, with a Coulomb cut-off of 1.2 nm, a fourth-order interpolation and Fourier spacing of 0.12 nm. Van der Waals (vdW) interactions were treated using the Lennard-Jones (LJ) potential with a cut-off distance of 1.2 nm. The potential was decreased over the whole range, whereas the forces were decayed smoothly to zero between 1.0 nm to the cut-off distance. A LINCS algorithm was used to constrain the bonds, when constraints applied, 12 being the highest order in the expansion of the constraint coupling matrix.

The structure and dynamics of the water-cosolvent mixtures, using the GROMACS analysis tools, were characterized by site-to-site radial distribution functions (RDFs), coordination numbers (CN), average number of hydrogen bonds (HBs), HB lifetimes, and intermolecular energies. Each of these descriptors was calculated for all the water-cosolvent concentrations considered in this study, using the last 5-ns trajectory for analysis. Site-to-site RDFs were computed for the water–water, cosolvent–cosolvent, and cosolvent–water pairs using the water oxygen, EtOH oxygen, 2PrOH oxygen, and AN nitrogen. The number of neighbor molecules was obtained by integration of the RDFs up to a 2-nm correlation distance, from where the CN can be extracted at the first minimum of RDF. HBs were calculated using a geometrical criterion with a maximum donor–acceptor distance of 0.35 nm and a hydrogen–donor–acceptor angle of 30°. The forward HB lifetimes were computed from the autocorrelation function of each HB type, using the theory of Luzar and Chandler [62, 63], as described by van der Spoel et al. [64].

Dynamic total hardness

The concepts of chemical hardness and softness, introduced by Pearson [65], have proven useful to classify acids and bases as hard or soft in many chemical reactions with the aim of predicting product stability prior to laboratory work. Hard (soft) chemical species are characterized as hardly (easily) polarizable. Since the formulation of the hard-soft-acid-base principle of Pearson [65], the chemical hardness and softness concepts have been widely explored in the fields of organic chemistry and homogeneous catalysis [66]. The theoretical formulation of the chemical hardness and softness was derived in the frame of density functional theory (DFT) by Parr et al. [67], followed by developments and implementations of various algorithms for their numerical calculations [68, 69, 70, 71, 72]. Various reactivity indices within DFT were derived from the chemical hardness/softness, giving rise to the entire research field called conceptual DFT (see for example the exhaustive recent review in [73]).

Among these algorithms, the reactivity indices, computed with the orbitally resolved hardness tensor approach (ORHT) [74] were successfully applied in isomerization [75, 76] and protonation [77] reactions, as selectivity descriptors [78], and in the framework of Pearson’s hard-soft-acid-base principle [77, 78]. A simplification of the ORHT method was also proposed, where the diagonal orbital hardness elements are the atomic hardnesses, either computed at the DFT level from the energies of orbitals with fractional electron occupations [69, 74, 75, 76, 77, 78, 79, 80], or, obtained from the experiments as the sum of the measured ionization potential (I) and the electronic affinity (A) [66]. This approach, which is called the atomically resolved hardness tensor (ARHT), provides an efficient scheme for easy and relatively fast calculations of reactivity indices in large scale systems. Here, for the first time, we apply the ARHT approach to large scale dynamic systems, as in the 4 nm boxes used in the present MD simulations, in order to compute the averaged total hardness. In the present ARHT calculations, the hardness value (ηA) of each constituent atom A is the experimental atomic hardness, taken from [66]. In a molecular system at equilibrium, the electronegativity equalization principle (EEP) holds, which allows us to estimate interactions between every AB atom pair from their interatomic distances in a molecule. Keeping in mind that EEP holds for the molecular structures (snapshots), extracted from the equilibrium dynamics simulations, the interatomic hardness (ηAB) can be obtained from the atomic hardness values, ηA and ηB, and the interatomic distances RAB.RAB distances are provided by MD simulations and ηAB are computed from the empirical relation proposed by Ohno [81]:

$$ {\displaystyle \begin{array}{l}{\eta}_{AB}=\frac{1}{\sqrt{b_{AB}^2+{R}_{AB}^2}}\\ {}{b}_{AB}=\frac{2}{\eta_A+{\eta}_B}\end{array}} $$
(1)
The elements of the inverse hardness tensor are the atomic softness elements sAB, [69, 74, 75, 76, 77, 78, 79, 80], their sum gives the total softness (S), from which the total hardness can be computed as follows:
$$ {\displaystyle \begin{array}{l}S=\sum \limits_{AB}{S}_{AB}\\ {}\eta =\frac{1}{S}=\frac{1}{\sum \limits_{AB}{S}_{AB}}\end{array}} $$
(2)

The dynamic hardness can therefore be derived within the ARHT scheme as the average over the total hardnesses ηI, I = 1,...N, computed for every snapshot, extracted from the equilibrium dynamics trajectories. Each snapshot, thus, provides the RAB distances, used in Eq. (1). For N trajectories, the dynamic total hardness is \( \left\langle \eta \right\rangle =\left({\sum}_{I=1}^N{\eta}_I\right)/N \). The total hardness for each solvent model and content was calculated for a set of 1200 snapshots extracted from the last 300 ps of the simulation trajectories, recorded at every 0.25 ps. The number of molecules in each box, used for the ARHT computations, is provided in Table 1. The experimental atomic hardness values, ηA in eV, are 6.43 for H, 5.00 for C, 7.23 for N, and 6.08 for O [66].

Results and discussion

Thermodynamic properties: validation of the MD simulations

The models used in the MD simulations were first validated for the pure water, EtOH, 2PrOH and AN solvents from a comparison between the computed and experimental density (ρ), diffusivity (D), enthalpy of vaporization (ΔHvap), and the average number of HBs. These thermodynamic properties were obtained over 5 ns of the equilibrium MD trajectories. The theoretical results, collected in Table S1 in the Supporting Information (SI) section, reproduce closely the reference experimental data. This demonstrates the very good performance of the TIP4P water model and CHARMM36 additive force field [82]. The thermodynamic properties, calculated for the three aqueous mixtures of EtOH, 2PrOH, and AN are collected in Table S2 (SI materials). All the simulated solvent mixtures reproduced closely the reference experimental conditions, that are T = 298.15 K and p = 1, similar to the pure solvents (see Table S1).

The density profile as a function of the binary mixture composition, plotted in Fig. 1, demonstrates the non-ideality of the water–cosolvent mixtures. Again, a good reproduction (with errors below 3% for all mixed solvents) of the experimental density profile in Fig. 1 was obtained. Similar conclusions were obtained from the mixing enthalpy (Fig. 2), calculated as
Fig. 1

Computed densities for solvents and their aqueous mixtures. Experimental curves are included for comparison, and were taken from[8, 9], [10], and [11, 12] for ethanol (EtOH), isopropanol (2PrOH), and acetonitrile (AN), respectively

Fig. 2a–c

Computed enthalpy of mixing, ΔHvap, for the water. a EtOH, b 2PrOH, and c AN solvent mixtures at different cosolvent mass fractions, Xcosol

$$ \varDelta {H}_{mix}={H}_{liq, mix}-{H}_{liq,1}\ast {y}_1+{H}_{liq2}\ast {y}_2={\left(U+ PV\right)}_{liq, mix}-{\left(U+ PV\right)}_{liq,1}\ast {y}_1+{\left(U+ PV\right)}_{liq2}\ast {y}_2, $$

The internal energy, U, of the liquid mixture was obtained directly from the potential energy (see Tables S1 and S2) during the simulation, and yi is the molar fraction of component i. The ΔHmix profiles, reported in Fig. 2, display correctly the expected non-ideal behavior for all the solvent mixtures, in agreement with experimental data [14, 15, 16]. The curves show that the mixing of EtOH and water is exothermic at all concentrations, whereas 2PrOH-water mixing becomes endothermic with increasing cosolvent content. Mixing of AN with water is endothermic, since the penetration of AN molecules into the water HB network requires additional energy to break the water–water HBs. In conclusion, we note that this excellent comparison between the calculated and known experimental thermodynamic features demonstrates the very good performance of the chosen force-fields and numerical details.

Structures of the aqueous binary solvents

In order to analyze the structural properties, we computed RDFs of the cosolvent–cosolvent, water–water, and cosolvent–water pairs at each solvent composition. The RDFs of the cosolvent–cosolvent pairs are displayed in Fig. 3. Figure 3a compares well with previously studied RDFs in pure and mixed solvents [27, 36, 83, 84, 85]. The EtOH O–O radial distribution curve (in Fig. 3a, left panel) attains a maximum of 4.7 at a distance of 0.284 nm, thus agreeing with the results of Saiz et al. [36]. The 2PrOH O–O RDF (in Fig. 3a, middle panel) displays the peak of 5.9 at a distance of 0.286 nm, and compares well with the results of Anisimov et al. [83]. In the acetonitrile N–N RDF profile in Fig. 3a, right panel, the first peak has a height of 1.36 and appears at 0.398 nm, followed by a second peak of height 1.2 at 0.58 nm, similarly to the N–N RDF obtained from 3- and 6-sites model potentials [27, 84]. In Fig. 3b, the RDF of the distances between oxygen atoms in H2O molecules (Owater) displays a sharp first peak with an intensity of 3.00 at 0.276 nm, which reproduces well the experimental 3.09 peak probability [85]. Moreover, the second and third peaks, experimentally observed around 0.452 nm and 0.677 nm, can be appreciated near the same values. The Owater–Ocosolv RDFs are presented in Fig. 3c.
Fig. 3

Radial distribution functions [RDFs; g(r)] of the a cosolvent–cosolvent, b water–water, and c cosolvent–water pairs. The water oxygen, EtOH oxygen, 2PrOH oxygen, and AN nitrogen are the reference sites

From all the RDFs in Fig. 3, we conclude that the solvent content does not affect the positions of the maximum peaks of the mixed solvents, but only their heights and depths. On the contrary, the secondary peaks in the RDFs are significantly affected by the presence of water. It is evident that the ordering in the solvents disappears beyond the first coordination shell with the increase in water content. In Fig. 3a, left panel, the second shell structure of EtOH is gradually recovered as the content of EtOH increases. Similarly, the second shell structure in 2PrOH (Fig. 1 a, middle) rises with the 2PrOH concentration. Moreover, the 2PrOH shell is found to be more extended in comparison to EtOH, which indicates that the 2PrOH aggregates formed in the mixture have a more complex organization than in EtOH. Following NAN–NAN RDFs, we note that the second coordination sphere is preserved with the increase in water content. Moreover, a visual inspection of the trajectories (see Fig. S1) showed predominantly an anti-parallel mutual displacement between the CH3CN molecules in the first shell. Perpendicular mutual orientations are also observed in the first coordination shell. Parallel orientations between the AN molecules dominate in the second shell. The RDF profiles in the alcohol–water mixtures display significantly sharper peaks than the RDF profile in the water–AN solvents.

With the increase in alcohol contents, the first-coordination peak develops and has a well distinguishable high intensity in the pure alcohol solvents. The opposite behavior of RDF peaks is established for the acetonitrile cosolvent. In addition, the RDFs profiles in the AN-water mixtures are not characterized by sharp peaks (Fig. 3a,c), and the intensity ratio between the first and second peak decreases with the amount of AN up to the pure solvent. It seems that the presence of water promotes the structural ordering in acetonitrile at variance to the alcohols. The large overlapping area between the first and second peaks in the acetonitrile RDF indicates high numbers of AN and water molecules between the first and second coordination shells, increasing with AN content .

The cumulative number of molecules as a function of distance was calculated from the integration of RDFs and plotted in the range of r = 0.5 nm for the cosolvents and r = 0.35 nm for OW–OW pairs (Fig. 4). At the first coordination sphere distances, cumulative number corresponds to the coordination number within the first coordination sphere (Table 2).
Fig. 4

Cumulative numbers, n(r), in the short range distance (r < 0.5 nm) of the a cosolvent–cosolvent, b water–water, and c cosolvent–water pairs. The water oxygen, EtOH oxygen, 2PrOH oxygen, and AN nitrogen are the reference sites

Table 2

Cutoff distance of the first coordination peak (rmin) and coordination numbers (CN) of each interaction pair, calculated from the cumulative numbers, n(r), at rmin

 

Cosolvent–cosolvent

Water–water

Cosolvent–water

rmin (nm)

CN

rmin (nm)

CN

rmin (nm)

CN

X EtOH

 0

0.338

4.6

 0.25

0.352

0.3

0.338

3.9

0.344

2.6

 0.50

0.346

0.6

0.346

3.3

0.348

2.1

 0.75

0.358

1.1

0.35

2.2

0.35

1.3

 1

0.364

2.0

X 2PrOH

 0

0.338

4.6

 0.25

0.348

0.2

0.338

4.0

0.354

2.7

 0.50

0.356

0.5

0.344

3.5

0.346

2.1

 0.75

0.364

1.0

0.35

2.6

0.354

1.4

 1

0.378

2.0

X AN

 0

0.338

4.6

 0.25

0.53

2.7

0.34

4.1

0.338

1.6

 0.50

0.524

4.1

0.344

3.8

0.342

0.9

 0.75

0.516

4.6

0.352

3.0

0.35

0.6

 1

0.51

5.2

The cumulative numbers of AN–AN neighbors increase with their concentration, whereas the number of water–water neighbors decreases. For AN, this finding is in a very good agreement with acoustic and positron annihilation measurements of aqueous solutions of AN reporting a destabilization of AN–clathrates with the increase in AN concentration in water [86]. It also points to microheterogeneity, hitherto largely accepted in the literature (see Introduction). Moreover, the number of water–water neighbor molecules is higher in the AN mixture than in the alcohol mixtures. We attribute this behavior to the chemical nature of the intermolecular interactions of the solvents that define the local homogeneity of the mixture. In the AN liquid the dipole–dipole interactions dominate, whereas in EtOH and 2PrOH a network of HBs is formed. Since AN is less polar than the other solvents, does not make HBs with itself, and can interact with water only as HB acceptor, the individual molecules will repel each other as the mixture becomes more concentrated, leading therefore to a local phase separation, as exemplified in Fig. S2. As observed by mass spectrometry [16], several aprotic solvents exhibited ‘additional mixing’, in which AN molecules cannot substitute water molecules inside their clusters, thus they interact with the water cluster as an external agent.

The number of water-to-water neighbors (Fig. 4b) decreases as the cosolvent concentration increases. This means that water structures experience rupture due the presence of cosolvents. Alcohols, known to be strong structure breakers, particularly EtOH, interact with water molecules by substitution, contrary to the AN–water interactions. At all the concentrations, AN molecules display the lowest structure breaker power. Also, from the values of the coordination numbers, it can be inferred that water is a strong structure breaker for alcohol structures, but promotes partially the ordering of the AN liquid component. On the other hand, the number of cosolvent molecules surrounding water molecules increases with the cosolvent concentration. At short distances, < 0.35 nm, the coordination of cosolvent to water neighbors is controlled by HBs. At this distance, the number of alcohol neighbors to the water molecules increases if the alcohol content >0.5 mass concentration (see Fig. 4c), which shows that the alcohols are H-bonded with water. The number of AN neighboring the water molecules is significantly smaller at r < 0.35 nm ,and increases faster than the alcohol–water neighbors at larger distances, r ≥ 0.7 nm, as follows from the cumulative numbers in the range of 2 nm, presented in Fig. S3. This indicates that the water–AN interactions are not dominated by H-bonding. The much faster increase of NAN–NAN cumulative number in comparison to NEtOH–NEtOH and N2PrOH–N2PrOH in the interval of 0.35–0.5 nm, suggests an enhanced microheterogeneity of the water–AN mixture in this region.

Analysis of the intermolecular interaction types

The variations in Coulomb and LJ energies, and in HBs with the type and content of the cosolvent, were used to infer the effect of the mixture compositions on the intermolecular interactions. Figure 5 plots the water–water, cosolvent–cosolvent, and cosolvent–water Coulomb and LJ energies for the considered mixed and pure liquids. The cosolvent–cosolvent energies (Fig. 5a) decrease rapidly (meaning the electrostatic interactions increase) with the content of organic solvents, which is expected. In EtOH, the water–EtOH coulombic interactions (Fig. 5b) attain their maximum at X = 0.75 mass fraction content. In 2PrOH, the maximum of the electrostatic and LJ interactions (minimum in Fig. 5a) is observed near 0.5 XCosol. This suggests a decrease in the 2PrOH–water interactions occurring already at concentrations of about 0.5 XCosol, most probably because of predominant 2PrOH–2PrOH interactions. This leads us to conclude that 2PrOH aggregations start to occur between 0.5 and 0.75 Xcosol. The water-AN interactions find a minimum of LJ interactions at the same concentration; however, Coulomb interactions increase up to 0.75 XCosol. This points to the conclusion that the electrostatic interactions between the water and the organic component do not follow a linear behavior with the liquid composition, and that they are cosolvent specific. The electrostatic and LJ energies (Fig. 5c) computed for the water–water component of the solvents do not experience any significant variation in the presence of cosolvents.
Fig. 5

Coulomb and Lennard-Jones (LJ) interaction energies of a cosolvent–cosolvent, b cosolvent–water, and c water–water types

HB evolution with liquid composition can be analyzed from the computed averaged number of HBs reported in Table 3. Our simulations reproduce well the average HBs per molecule obtained by previous MD simulations for the same water potential [64, 87, 88]. For example, Noskov et al. [89] obtained an average number of HBs per water molecule of 3.03 but using the SWM4-DP polarizable water model. Likewise, our results for the calculated HB numbers in EtOH agreed closely with the results of Noskov et al. [89], reporting HB = 1.65 using a polarizable potential, and of Saiz et al. [36], who found a value of 1.9 using the united atom OPLS force field. We did not find reference values for HB in 2PrOH; however, this value should be similar to EtOH since the two compounds have the same number of OH groups, even though 2PrOH is less polar. AN does not make any HBs with itself since no hydrogen is bonded to any N atom.
Table 3

Calculated average numbers of hydrogen bonds (HB) per molecule from molecular dynamics (MD) simulations of cosolvent–water mixtures at 0.25, 0.50, 0.75, and 1 cosolvent mass fraction (Xcoso)

 

EtOH

X cosol

0.25

0.50

0.75

1

HBsys

3.35

3.06

2.60

1.84

HBW-W

2.83

1.93

0.85

HBEtOH-EtOH

0.03

0.14

0.50

1.84

HBEtOH-W

0.50

0.98

1.25

 

2POH

X cosol

0.25

0.50

0.75

1

HBsys

3.38

3.12

2.67

1.83

HBW-W

2.97

2.20

1.12

HB2PrOH-2PrOH

0.02

0.10

0.39

1.83

HB2PrOH-W

0.39

0.82

1.16

 

AN

X cosol

0.25

0.50

0.75

1

HBsys

3.08

2.44

1.50

HBW-W

2.83

2.07

1.05

HBAN-AN

HBAN-W

0.24

0.37

0.45

The HBs between water molecules dominate in the three binary solvents up to 0.50 Xcosol. The averaged number of alcohol-water HBs becomes greater than HBw–w only when alcohols attain a concentration of 0.75 Xcosol. Interestingly, the presence of water, even at its minimal concentration, disturbs the HB network in the alcohols. This follows from the significantly smaller values of HBEtOH-EtOH and HB2PrOH-2PrOH in the mixed solvents compared with the pure alcohol liquids. Both alcohols interact in a similar manner with water; that is, they preferably form HBs with H2O than between themselves for cosolvent concentrations ≤0.75. This leads us to conclude that a molecular aggregation of the short alcohols in water is not evidenced from the present MD simulations. We believe that, in mixtures above 0.50 Xcosol, the water molecules optimize the number of H-bonding sites available in order to reduce non-favorable interactions with the alcohol solvents. This is also an indication for the hydrophobic character of EtOH and 2PrOH alcohols.

As stated above, AN does not form HBs with itself. Note that the AN–AN HBs were not taken in consideration. The AN–water HB grows with increasing AN content, which confirms experimental studies, reporting on the existence of HBs between water and AN molecules [46]. The H-bonded water-alcohol molecules are, however, significantly fewer in number in comparison to H-bonded water–alcohol molecules, thus confirming the microheterogeneity of this mixture and the predominant dipole–dipole interactions.

Furthermore, we calculated the HB autocorrelation functions and HB lifetimes, as described in Methods and computational details. The HBs autocorrelation functions (see Fig. S4) display a fast decay of the HBs studied here, and the velocity of this decay is influenced by the cosolvent concentration. The lifetimes of the HBs are summarized in Table 4.
Table 4

HB lifetimes for the water–water (w–w), water–cosolvent (w–cosol), and cosolvent–cosolvent (cosol–cosol) interaction types, obtained from the HB autocorrelation functions of each HB type

 

HB lifetimes (ps)

Solvent mixture

Water-EtOH

Water-2PrOH

Water-AN

X cosol

W-W

Cosol- W

Cosol-Cosol

W-W

Cosol- W

Cosol-Cosol

W-W

Cosol- W

0

4.3

4.3

4.3

0.25

7.1

8.3

8.5

7.5

11.3

16.7

6.0

2.3

0.50

12.4

13.1

13.2

11.1

14.5

26.3

7.3

3.1

0.75

21.7

21.3

20.4

21.4

28.6

44.3

10.2

3.9

1

40.3

119.1

In all cases, we noted an increase in the HB lifetime with the cosolvent content in line with the results in the literature [4, 47]. This tendency is well pronounced for the water and alcohols liquids and their mixtures, in contrast to water–AN solvents. Our computed HB lifetimes display durations in line with those obtained by other authors [4, 90]. Very recent 2D infrared spectroscopy studies of diluted alcohols solutions (≤ 0.09 mol fraction) [90] revealed a vibrational lifetime of ~ 3 ps of the OH stretching mode, comparable with the expected values of our alcohol–alcohol HB lifetimes, if extrapolated for diluted alcohol concentrations. Furthermore, we obtained water–AN and water–water HB lifetimes comparable to those obtained for water–tetrahydrofuran (THF) mixtures—another aprotic solvent [4]—reporting HB lifetimes in the range of between ~2 and ~4.5 ps. As inferred from the water diffusivities in THF mixtures [4], the increase in water–water HB lifetimes obeys a reduction in the free motion of water molecules in solvent mixtures.

The significantly longer HB lifetimes in pure EtOH (40.3 ps) and 2PrOH (119.1 ps) solvents, in comparison to those in their water mixtures, suggests a strong perturbation of the alcohols structures when mixed with water. Again, the relatively short lifetime of water–AN HBs corroborates the microheterogeneity. Moreover, HB lifetimes vary only little with the increase in AN content. This is in agreement with the observations of X-ray diffraction and IR spectroscopy [46]. This authors established that water and acetonitrile HB interactions play an important role in the formation of a large interface between water agglomeration domains and AN agglomeration domains. In summary, the water structure mixed with AN appears to be only slightly perturbed, whereas this structure perturbation is stronger in alcohol mixtures. Furthermore, the alcohol structure experiences a significant change in its HB networks.

Averaged hardness from MD simulations

The characterization of mixed liquids as hard or soft is of interest in providing qualitative prediction of reactivity and product stability of numerous chemical reactions that take place in solvents. The main problem faced when using gas-phase reactivity indices (including the chemical hardness) for reactivity predictions of reactions in solvents, is associated with modulation of gas-phase reactivity due to hydration energies [66]. This effect causes failure of the hard-soft-acid-base principle [65], which states that hard (soft) acids (bases) preferably react with hard (soft) bases (acids). Examples are described in [66] together with the difficulties associated with the experimental estimations of the chemical hardness (or, equally, chemical softness). It is therefore of interest to establish a methodology for theoretical computations of the total chemical hardness, or, total chemical softness, of solvents by explicitly considering their atomic structures along equilibrium dynamics.

Figure 6 and Table S3 present the computed dynamic total hardness values, <η>, as a function of the liquid composition. As follows, the variations of <η > in the three binary mixtures are nonlinear with the increase of the cosolvent content, similar to the nonlinear behavior of the enthalpy of mixing seen in Fig. 2. Therefore, dynamic hardness can also be considered as a measure for the non-ideal behavior of binary solvents, analogous to the thermodynamic properties (vide supra).
Fig. 6

Computed dynamic total hardnesses, <η>, as a function of the cosolvent composition, Xcosol

Note that the dynamic hardnesses of the pure solvents remains close to the available experimental values [66], which were obtained from the measured ionization potential and electron affinity of the molecules of water (9.4 eV), 2PrOH (8.0 eV) and AN (7.5 eV). In comparison to the pure water solvents, the addition of the organic component causes a decrease of <η >  of up to 0.50 Xcosol of the three cosolvents, but the water-EtOH mixture becomes softer also at 0.75 XEtOH. The behavior of the other two cosolvents is the opposite; the addition of X = 0.75 2PrOH and AN into water increases the hardnesses of these mixtures. The mixed solvents have systematically smaller <η > values compared with <η > = 8.38 eV of pure water, with the exception of the dynamic hardness of water-2PrOH at 0.75 Xcosol. In the latter case, <η > increases notably (<η > 2PrOh solvent = 8.94 eV).

With an attempt to better understand this behavior, we computed, using a DFT approach, the total hardness for the two simplest molecular patterns that appear in the mixed solvents, namely the water–cosolvent and cosolvent–cosolvent dimers. Their total hardness values, reported in Table 5, were obtained from the HOMO–LUMO energy differences and labeled as ηH-L. For the DFT calculations, we used the PBE exchange-correlation functional with DZVP and TZVP basis sets. For these simple dimers, exactly the same trend of ηH-L was found with both bases.
Table 5

Density functional theory (DFT) total hardness (ηH-L) in eV computed as HOMO–LUMO energy difference using DFT–PBE and TZVP basis for the water-water (w–w), water–cosolvent, and cosolvent–cosolvent dimers

Dimer

w-w

w-EtOH

EtOH-Et-OH

w-2PrOH

2PrOH-2PrOH

w-AN

AN-AN

η H-L

6.38

5.28

5.63

6.21

5.71

5.18

6.94

The water–EtOH dimer is found to be softer than the EtOH–EtOH dimer. The observed softening of the w–EtOH solvent mixture with the increase in EtOH concentration (see Fig. 6) can thus be explained with a continuous increase of water–EtOH interactions when increasing the EtOH concentration. In the pure EtOH solvent, the hardness increases because of the harder EtOH–EtOH pair interactions. Contrary to the ethanol cosolvent, ηH-L reveals that the water–2PrOH dimer is harder than the dimer of 2PrOH–2PrOH. This correlates with the strong increase of <η > = 8.94 eV at X2PrOH = 0.75, which suggests that mixed water–2PrOH interactions are predominant at this concentration, and the 2PrOH solvent structure is significantly disrupted by H2O molecules. At the smaller X2PrOH = 0.25 and 0.5 concentrations, the 2PrOH–2PrOH interactions dominate, because these mixtures are softer and their <η > values are close to the hardness of the pure 2PrOH solvent. In the case of AN, the relation ηH-L (w-AN) < ηH-L (AN-AN) generally correlates with the decrease of the dynamic hardness profile in Fig. 6, but does not explain the softer pure AN-solvent. For the AN solvent with dipole–dipole interactions (not H-bonding as in the case of alcohol-containing solvents) the total hardness seems to be dependent on the size of the cluster. We computed ηH-L for a cluster of 20 AN molecules, extracted from MD simulations and optimized at DFT level, and found ηH-L = 6. 24 eV, i.e., smaller than ηH-L of the dimer. Therefore, a decrease in the total hardness as a function of the AN solvent structure and size of the box seems plausible.

Furthermore, comparing <η > between the pure solvents, the following trend holds: water ≥2PrOH > EtOH > AN. Therefore, it appears that mixtures with predominant HB interactions between the constituent molecules are harder than those with predominant dipole–dipole interactions. The <η > tendency in the pure solvents respects the molecular hardness trend [66], which is in line with the fact that the individual molecular properties in the studied liquids are well preserved. However, mixing with water alters this <η > tendency non-negligibly; moreover, in a non-linear manner. Therefore, the variation in the averaged dynamic hardness appears to be a complex function of mixed solvent compositions, analogous to the structural and thermodynamical features. The latter conclusion justifies the need for tools for relatively easy, but robust, estimations of hardness (respectively softness) in complex solvents, which will enable rational reactivity predictions of various chemical processes in liquids within the HSAB principle, providing the chemical hardness (or softness) of the solute systems are also computed.

Conclusions

This work covered a systematic comparative study of the structural and thermodynamic properties of selected pure solvents (water, EtOH, AN, and 2PrOH) and their aqueous mixtures at different concentrations, using the tools of the MD simulations. In addition, a simple method for the averaged, dynamic, total hardness computations is suggested. The obtained thermodynamic properties are in good agreement with experimental and previous theoretical studies, demonstrating the excellent potential of the TIP4P (water) and CHARMM36 (organic solvents) model performances for these types of binary mixtures.

The site-to-site RDFs reveal that the concentrations of the mixed solvents do not affect the positions in the peaks and valleys, but only their heights and depths. The latter effect is particularly pronounced for the peaks, which are characteristic for second coordination shells. Analysis of the average numbers of HBs with the liquid composition, shows that the maximum interaction between water and the organic solvents occurs at mass fractions of 0.75. At this concentration, alcohol molecules tend to substitute water molecules, allowing compensating for the loss of HBs in the water solvent domains. The alcohol structures experience a significant changes at all concentrations. AN is not a HB donor, and it is inferred that the presence of water and the formation of HBs helps it to reduce strong dipole–dipole interactions, while preserving the microheterogeneity of the mixture.

The averaged hardness, similar to the other dynamic and thermodynamic properties, has a nonlinear profile with the solvent compositions. As a general trend, softening of the water solvent by introducing organic cosolvents was successful, the only exception being the isopropanol-water mixture at X = 0.75. The proposed method could be applied within HSAB principles to rationalize the behavior of complex solute systems in mixed solvents, providing dynamic hardness values of the solutes are also assessed.

Notes

Acknowledgments

This work was granted access to the HPC resources of [CCRT/CINES/IDRIS] under the allocation 2017 [×2017087369] made by GENCI (Grand Equipement National de Calcul Intensif] and was partially funded through the ENSCM SINCHEM EMJD PhD grant. SINCHEM is a Joint Doctorate programme selected under the Erasmus Mundus Action 1 Programme (FPA 2013-0037).

Supplementary material

894_2018_3817_MOESM1_ESM.pdf (965 kb)
ESM 1 (PDF 964 kb)

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Matériaux Avancés pour la Catalyse et la Santé, UMR 5253 CNRS/UM/ENSCMInstitut Charles Gerhardt de Montpellier (ICGM)Montpellier cedex 5France

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