**2. Effective pair potentials**

400 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

have confirmed that supposition. Despite apparent miscibility of both components, methanol and water clusters are observed over whole concentration range. At particular concentration, near 25-27 mol% of methanol, where transport and thermodynamic properties exhibit extrema, water and methanol form separate, percolating structures

Several experimental techniques were employed to investigate solvation of ions in methanol-water mixtures. Results are, however, inconsistent and lead to contradict conclusions. Therefore both a preferential hydration (Convington & Dunn, 1989; Hawlicka, 1995), as well as a lack of preferences (Holtz et al., 1977) have been postulated for alkali and halide ions in methanol-water mixtures. Though X-ray and neutron scattering measurements should provide a direct insight into the ion coordination shell, their results cannot be decisive for methanol-water mixture, because distances between these ions and the oxygens of either water (Neilson & Enderby, 1979; Licheri et al, 1975) or methanol (Megyes, 2004) are almost the same. Moreover a direct correlation between the alkali earth cations and the methyl group is lacking (Radnai et al., 1995). In such case the scattering techniques are not enough sensitive to investigate the preferential solvation in methanolwater mixture. Thus a molecular dynamics simulation seems to be a useful tool to provide

A quality of the simulation results depends on the methods used to describe all interactions in the solutions. *Ab initio* quantum mechanics would be the most accurate method, but its application to systems containing ions and a few hundred water molecules could not be expected for the near future. Therefore QM/MM MD simulation seems to be an elegant approach for investigating the aqueous solutions of electrolytes. The ion and its nearest water molecules are treated quantum mechanically. Such approach includes many-body interactions between particles within the solvation shell. QM/MM MD simulations were carried out for aqueous solutions of various ions (Tongraar & Rode, 2003, Rode et al., 2004, Öhrn & Karlström, 2004; Tongraar & Rode, 2005, Payaka et al., 2009; Tongraar et al., 2010). Their results evidenced a significant role of the many-body interactions on structural and dynamical properties of the hydrated ions. These simulations concerned, however, the systems, which contain only one ion, either cation or anion, and a few water molecules. Thus this technique is useless for studies more concentrated solutions, where an association of the ions occurs. The formation of the various types of the ionic pairs, solvent separated, solvent shared and contact pairs, is frequently observed in binary solvents. This phenomenon may affect significantly the

Classical MD simulations are usually carried out for NVE or NVT ensembles. The volume is fixed and it depends on a number of the particles, temperature, composition of the system. Particles are placed into a periodic cube. The size of the periodic box results from the experimental density of the simulated system. Initial coordinates of particles are frequently chosen from the crystal lattice (Heyes, 1998), however the random distribution of the

In classical simulations the interactions between molecules are represented by a sum of the pair potentials and many-body interactions are neglected. Usually the pair potential consists of Coulomb term, for which the Ewald summation is applied, and of short-range parts, for

particles in the cube is better, because it reduces a time of equilibration.

which shifted-force potential method (Allen & Tidesly, 1987) is used.

additional information concerning the structure of the ion shell.

(Dughan et al. 2004).

solvation of ions.

Several potentials have been proposed to describe the interaction of the water molecules, but this molecule still remains 'a challenge to model, because it is polar, polarizable, has light H atoms and is flexible' (Heyes, 1998). Only a few of the models consider the water molecule as a flexible body and permit internal vibrations. Most of them are a modification of the simple point charge potential of Berendsen *(*Berendsen et al., 1981) They use a potential of the spectroscopic type (Zhu & Wong, 1993; Ferguson, 1995) to describe an intramolecular interaction. Unfortunately SPC model neglects non-Coulomb interactions of hydrogen atoms, which seem to be important in hydrogen-bonded systems.

In simulations presented here the interactions of the water molecules has been described by the BJH potential (Bopp et al., 1983; Jancso & Bopp, 1983) which treats the intermolecular interactions of oxygens and hydrogens by mean of the central force model (CF) (Stillinger & Rahman, 1978) and uses a three body description of intermolecular interactions. This model has been frequently employed to simulate aqueous solutions of electrolytes, both in classical (Dietz et al., 1982; Jancso et al. 1985; Probst et al., 1985, Probst et al., 1991; Hawlicka & Swiatla-Wojcik, 1995, Lavenstein et al. 2000; Ibuki & Bopp, 2009) and in QM/MM MD (Tongraar & Rode, 2003, Rode et al., 2004, Öhrn & Karlström, 2004; Tongraar & Rode, 2005, Payaka et al., 2009; Tongraar et al., 2010) simulations. The BJH potential is appropriate to simulate the methanol-water mixtures, because it is fully consistent with the PHH flexible model (Palinkas et al. 1987) of the methanol molecule. The BJH and PHH, potentials reproduce properly the structure, energies and dynamic properties of the methanol-water mixtures (Palinkas et al., 1991a; Palinkas et al., 1991a, Hawlicka & Swiatla-Wojcik, 2000). An advantage of the flexible models is, that they permit a distortion of the solvent molecules from their equilibrium geometry. In consequence a molecular polarizability is incorporated.

The BJH and PHH potentials consist of two parts, which describe the inter- and intramolecular interactions respectively:

$$V(\rho\_i, r\_{a\beta}) = V^{\text{intra}}(\rho\_i) + V^{\text{inter}}(r\_{a\beta}) \tag{1}$$

The intermolecular parts are the sum of Coulombic and non-Coulombic terms. The Coulombic terms result from the partial charges of the interacting sites. In water molecule the partial charges are located on oxygen (-0.66 e) and hydrogen (+0.33 e) atoms. Methanol molecule consists of the charged oxygen (-0.6 e), hydroxyl hydrogen (+0.35 e) and the methyl group (+0.25 e), considered as the pseudo-atom. Non-Coulombic intermolecular O-O, O-H and H-H interactions of the water and methanol molecules are the same as in CF2 model for water (Stillinger & Rahman, 1978) The non-Coulomb interaction of the methyl group with the hydroxyl hydrogens has been neglected and that with oxygens and methyl groups has been represented by the Lennard-Jones potential (Jorgensen, 1981).

Intramolecular potentials for water and methanol are based on the formulation proposed by Carney et al. (Carney et al, 1976). They are expressed as power series of the internal coordinates, i, 'stretch' and 'bend' and the three-body interactions are included:

$$V(\rho\_i) = \sum L\_{ij}\rho\_i\rho\_j + \sum L\_{ijk}\rho\_i\rho\_j\rho\_k + \sum L\_{i\bar{j}k\bar{l}}\rho\_i\rho\_j\rho\_k\rho\_l \tag{2}$$

Usually in classical MD simulations the ion potentials are represented by the Coulomb and the Lennard-Jones terms. These potentials overestimate, however, the number of the solvent molecules in the ion shells (Hawlicka & Swiatla-Wojcik, 2002) and underestimate a stability of the ion shells (Hawlicka & Swiatla-Wojcik, 2002, Bujnicka & Hawlicka, 2006). Moreover such potentials are inconsistent with flexible models of the solvent molecules. Therefore the ion-water and ion-methanol potentials were evaluated from *ab initio* calculations and fitted to the BJH and PHH models.

The potential energy for the complexes of the ion and the solvent molecule was computed for several hundred configurations of the complexes. Then the potential surfaces were fitted to the analytical form:

$$\mathbf{V}\_{i\alpha}(\mathbf{r}) = \sum\_{\alpha=1}^{3} \left[ \frac{\mathbf{Q}\_{i\alpha}}{\mathbf{r}} + \frac{\mathbf{A}\_{i\alpha}}{\mathbf{r}^{n}} + \mathbf{B}\_{i\alpha} \cdot \exp(-\mathbf{C}\_{i\alpha} \cdot \mathbf{r}) \right] \tag{3}$$

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 403

Na Om -833.61 -172.23 2.5328× 105 4.1501 Na Hm 486.27 593.40 -8.3289× 102 0.9591 Na Me 347.34 -274.90 5.1674× 104 2.7930 Na Ow -916.28 -352.20 3.5555× 105 4.2988 Na Hw 458.14 151.60 5.1867× 104 5.3919 Ca Om -1667.30 -1372.63 2.5971× 105 3.4900 Ca Hm 972.58 933.29 8.3277× 102 0.9600 Ca Me 694.70 -474.95 5.1666× 104 2.7930 Ca Ow -1832.56 -1572.66 2.5972× 105 3.4900 Ca Hw 916.28 626.41 1.2022× 105 6.7900 Mg Om -1667.30 -721.86 4.0778× 105 4.3937 Mg Hm 972.58 -7.21 4.2904× 101 0.2749 Mg Me 694.70 -232.28 1.8277× 104 2.6485 Mg Ow -1832.56 -890.83 2.6954× 105 4.0800 Mg Hw 916.28 82.04 7.3844× 101 0.3490 Cl Om 833.61 127.02 1.4532× 105 3.1999 Cl Hm -486.27 -193.41 2.5091× 104 3.3082 Cl Me -347.34 6.77 5.9262× 105 3.2984 Cl Ow 916.28 9.34 1.1750× 105 2.6727 Cl Hw -458.14 -68.27 9.0210× 104 4.5420

Table 1. Parameters Qi, Ai, Bi and Ci in equation (3) for the interactions of ions with PHH

As seen the interactions of the ion with molecules of the solvent components are similar. The lowest binding energies for ion-water and ion-methanol complexes are observed at the same distances. This position of the energy minimum is shifted to larger distance as the ionic radius increases (Marcus & Hefter, 2004) As might be expected the energy minimum becomes deeper when the charge density increases. The binding energy of Na+ and Ca2+ ions with water is about 3% lower than that with methanol. An opposite features are found for of Mg2+ and Cl- ions, because their interactions with methanol are stronger than those

The pair potentials for interactions between ions were also derived from ab initio calculations. The potential energy surfaces were constructed from hundred configurations.

Then they were fitted to the equation (3). Parameters were summarized in Table 2.

with water. For Mg2+ ions the difference is about 10%, but for Cl-

Bi<sup>α</sup> [kJ mol-1]

ions is less than 2%.

Ci<sup>α</sup> [Ǻ-1]

Ai<sup>α</sup> [kJ Ǻ<sup>n</sup> mol-1]

i

methanol and BJH water.

Qi<sup>α</sup> [kJ Ǻ mol-1]

where Qi represents the Coulombic interactions, which are defined by the ion charge and partial charges of the water or methanol molecules. The energies of the Coulombic interactions were subtracted from the potential surfaces. Parameters Ai, Bi and Ci, were adjusted to the non-Coulomb part of the energy surface. They have no physical meaning. Parameters derived for ions, Na+(Marks et all, 1991; Hawlicka & Swiatla-Wojcik, 1995), Mg2+ (Dietz et al., 1982; Tamura et al., 1992), Ca2+( Probst et al., 185; Owczarek & Hawlicka, 2006), Cl- (Marks et all, 1991; Hawlicka & Swiatla-Wojcik, 1995) and the flexible molecules of BJH water and PHH methanol are summarized in Table 1.

The pair potentials for ions and solvent molecules are displayed in Figure 1 as a function of the ion-oxygen distance for the coplanar orientation shown in the insertion.

Fig. 1. Fitted pair potentials for the ion-water (solid) and ion-methanol (dashed) as function of the ion-oxygen distance for the orientation shown in the insertion.

molecules in the ion shells (Hawlicka & Swiatla-Wojcik, 2002) and underestimate a stability of the ion shells (Hawlicka & Swiatla-Wojcik, 2002, Bujnicka & Hawlicka, 2006). Moreover such potentials are inconsistent with flexible models of the solvent molecules. Therefore the ion-water and ion-methanol potentials were evaluated from *ab initio* calculations and fitted

The potential energy for the complexes of the ion and the solvent molecule was computed for several hundred configurations of the complexes. Then the potential surfaces were fitted

> i i i i

<sup>A</sup> V (r) B exp( C r) r r *i*

 

 

(3)

*n*

where Qi represents the Coulombic interactions, which are defined by the ion charge and partial charges of the water or methanol molecules. The energies of the Coulombic interactions were subtracted from the potential surfaces. Parameters Ai, Bi and Ci, were adjusted to the non-Coulomb part of the energy surface. They have no physical meaning. Parameters derived for ions, Na+(Marks et all, 1991; Hawlicka & Swiatla-Wojcik, 1995), Mg2+ (Dietz et al., 1982; Tamura et al., 1992), Ca2+( Probst et al., 185; Owczarek & Hawlicka, 2006), Cl- (Marks et all, 1991; Hawlicka & Swiatla-Wojcik, 1995) and the flexible molecules of BJH

The pair potentials for ions and solvent molecules are displayed in Figure 1 as a function of

Fig. 1. Fitted pair potentials for the ion-water (solid) and ion-methanol (dashed) as function

of the ion-oxygen distance for the orientation shown in the insertion.

3

water and PHH methanol are summarized in Table 1.

1

*Q*

the ion-oxygen distance for the coplanar orientation shown in the insertion.

to the BJH and PHH models.

to the analytical form:


Table 1. Parameters Qi, Ai, Bi and Ci in equation (3) for the interactions of ions with PHH methanol and BJH water.

As seen the interactions of the ion with molecules of the solvent components are similar. The lowest binding energies for ion-water and ion-methanol complexes are observed at the same distances. This position of the energy minimum is shifted to larger distance as the ionic radius increases (Marcus & Hefter, 2004) As might be expected the energy minimum becomes deeper when the charge density increases. The binding energy of Na+ and Ca2+ ions with water is about 3% lower than that with methanol. An opposite features are found for of Mg2+ and Cl- ions, because their interactions with methanol are stronger than those with water. For Mg2+ ions the difference is about 10%, but for Cl- ions is less than 2%.

The pair potentials for interactions between ions were also derived from ab initio calculations. The potential energy surfaces were constructed from hundred configurations. Then they were fitted to the equation (3). Parameters were summarized in Table 2.

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 405

xM ion Rmax1 g(Rmax1) rmin1 n1 Rmax2 g(Rmax2) rmin2 n2

Na 0.232 8.66 0.320 6.05 - - - - Ca 0.237 15.65 0.340 10 0.430 2.82 0.552 27 Mg 0.199 21.14 0.270 6.2 0.452 1.75 0.512 16 Cl 0.335 2.98 0.398 8 - - - -

Na 0.230 8.54 0.297 4.76 - - - - Ca 0.240 18.67 0.300 9.70 0.440 2.80 0.564 23 Mg 0.199 24.04 0.270 5.40 0.452 1.34 0.507 10 Cl 0.337 2.23 0.410 5.80 - - - -

Na 0.231 10.37 0.297 2.27 - - - - Ca 0.237 35.88 0.305 6.80 0.450 2.38 0.558 7 Mg 0.199 38.33 0.270 3 0.394 1.29 0.504 3 Cl 0.344 1.10 0.386 1.04 - - - -

Na 0.230 24.19 0.295 0.75 - - - - Ca 0.232 105.93 0.310 2.30 - - - - Mg 0.199 46.67 0.270 0.60 0.397 1.86 0.500 0.6 Cl - - - - - - - -

Na 0.300 3.41 0.375 13.3 - - - - Ca 0.307 5.93 0.380 20.0 0.500 1.41 0.620 59 Mg 0.274 6.42 0.337 12.5 0.492 1.05 0.575 40 Cl 0.242 2.50 0.310 7.38 - - - -

Na 0.295 3.27 0.367 9.96 - - - - Ca 0.312 7.57 0.382 19.4 0.512 2.28 0.620 51 Mg 0.274 7.03 0.337 10.8 0.497 1.10 0.575 22 Cl 0.242 1.86 0.310 4.96 - - - -

Na 0.301 4.08 0.374 4.6 - - - - Ca 0.312 30.69 0.382 13.6 0.518 3.50 0.623 15 Mg 0.274 11.11 0.337 6.2 0.496 0.90 0.567 7 Cl 0.251 0.87 0.306 1.06 - - - -

Na 0.300 9.38 0.392 1.52 - - - - Ca 0.310 42.35 0.370 4.5 - - - - Mg 0.274 15.48 0.339 1.2 0.472 1.22 0.557 1 Cl - - - - - - - -

Table 3. Characteristic parameters of the ion-water radial distribution functions: positions (in nm) of the first (Rmax1) and second (Rmax2) maxima, the first (rmin1) and second (rmin2) minima, heights of the first g(Rmax1) and second g(Rmax2) maxima and the first (n1) and

Mg2+Ow and Ca2+Ow functions. This may suggest that in mixed solvent the interactions of the cations with water molecules are favoured, despite similar binding energies of Ca2+ and Na+ ions with methanol and water. This preference for water is observed also for Mg2+ ion, despite its stronger interactions with methanol than with water (see Figure 1 b). Moreover the first peak of the gionOw(r) function increases, when the water content decreases. This is particularly remarkable for the Ca2+ ions and in the water deficit mixture, when the water

oxygen

hydrogen

0.0

0.1

0.5

0.9

0.0

0.1

0.5

0.9

second (n2) coordination numbers.


Table 2. Parameters Qi, Ai, Bi and Ci in equation (3) for the ion-ion interactions.

#### **3. Radial distribution functions for the ions**

Radial distribution function gion-(r) represents the probability of finding the ion and -site of the solvent molecule in a distance r, relative to the probability expected for a random distribution with the same density. These functions provide clear information about a structure of the ion surrounding. At room temperature the order is short-range thus the pair distribution function exhibits no more than two peaks. Positions of these peaks reflect average distances of neighbours in the first and second coordination shells.

Though the peak area is proportional to the number of the molecules in the shell, its height and width depend on a balance between the ion-solvent attraction and thermal motions of the solvent molecules. The first peak of the pair distribution functions increases with the increasing charge density, therefore it is generally higher and sharper for the cations than that for the anions and for the divalent ions than for the monovalent ions (Yu et al., 2010)

A surrounding of the ion in the methanol-water mixtures can be described by five radial distribution functions, two of them for the sites of water (Ow and Hw) and three for the sites of methanol (Om, Hm and Me). The characteristic parameters of these functions are listed in Tables 3 and 4. There are positions of the first (Rmax1) and second (Rmax2) maxima, the positions of the first (rmin1) and second (rmin2) minima and the numbers of the particles in the first (n1) and second (n2) coordination shells.

The radial distribution functions of cation-oxygen in water, methanol and equimolar methanol-water mixture are shown in Figure 2. In aqueous solutions of MgCl2 and CaCl2 the cation-oxygen functions exhibit a sharp first peak, followed by broad second maximum. Positions of the first and second peaks coincide with the average distances of the first and second neighbours deduced from diffraction experiments (Ohtaki & Radnai, 1993). The gNaOw(r) function shows only one peak. As might be expected the position of the first peak is shifted to larger distances as the radius of the cation increases. The peak height depends on the charge density and the Mg2+Ow radial distribution function shows the highest peak.

Addition of methanol does not affect the position of the first maximum of the gionOw(r) function. However the methanol addition increases the first peak, particularly that of the

Bi [kJ mol-1] Ci

[Ǻ-1] <sup>n</sup>

Ai [kJ Ǻn mol-1]

Table 2. Parameters Qi, Ai, Bi and Ci in equation (3) for the ion-ion interactions.

average distances of neighbours in the first and second coordination shells.

Radial distribution function gion-(r) represents the probability of finding the ion and -site of the solvent molecule in a distance r, relative to the probability expected for a random distribution with the same density. These functions provide clear information about a structure of the ion surrounding. At room temperature the order is short-range thus the pair distribution function exhibits no more than two peaks. Positions of these peaks reflect

Though the peak area is proportional to the number of the molecules in the shell, its height and width depend on a balance between the ion-solvent attraction and thermal motions of the solvent molecules. The first peak of the pair distribution functions increases with the increasing charge density, therefore it is generally higher and sharper for the cations than that for the anions and for the divalent ions than for the monovalent ions (Yu et al., 2010)

A surrounding of the ion in the methanol-water mixtures can be described by five radial distribution functions, two of them for the sites of water (Ow and Hw) and three for the sites of methanol (Om, Hm and Me). The characteristic parameters of these functions are listed in Tables 3 and 4. There are positions of the first (Rmax1) and second (Rmax2) maxima, the positions of the first (rmin1) and second (rmin2) minima and the numbers of the particles in the

The radial distribution functions of cation-oxygen in water, methanol and equimolar methanol-water mixture are shown in Figure 2. In aqueous solutions of MgCl2 and CaCl2 the cation-oxygen functions exhibit a sharp first peak, followed by broad second maximum. Positions of the first and second peaks coincide with the average distances of the first and second neighbours deduced from diffraction experiments (Ohtaki & Radnai, 1993). The gNaOw(r) function shows only one peak. As might be expected the position of the first peak is shifted to larger distances as the radius of the cation increases. The peak height depends on the charge density and the Mg2+Ow radial distribution function shows the highest peak. Addition of methanol does not affect the position of the first maximum of the gionOw(r) function. However the methanol addition increases the first peak, particularly that of the

Na Na 1389.4 -9.9154× 102 1.0180× 106 5.5909 6 Na Cl -1389.4 -7.9000× 101 1.7172× 105 3.1940 2 Ca Ca 5557.6 -1.5198× 104 2.6010× 106 4.4870 6 Ca Cl -2778.8 -3.5301× 102 3.6608× 105 3.0100 2 Mg Mg 5557.6 -1.4799× 103 1.8226× 106 6.3600 6 Mg Cl -2778.8 -2.0069× 103 1.1854× 105 2.6500 2 Cl Cl 1389.4 -2.8672× 104 9.1704× 105 3.3863 6

i

Qi [kJ Ǻ mol-1]

**3. Radial distribution functions for the ions** 

first (n1) and second (n2) coordination shells.


Table 3. Characteristic parameters of the ion-water radial distribution functions: positions (in nm) of the first (Rmax1) and second (Rmax2) maxima, the first (rmin1) and second (rmin2) minima, heights of the first g(Rmax1) and second g(Rmax2) maxima and the first (n1) and second (n2) coordination numbers.

Mg2+Ow and Ca2+Ow functions. This may suggest that in mixed solvent the interactions of the cations with water molecules are favoured, despite similar binding energies of Ca2+ and Na+ ions with methanol and water. This preference for water is observed also for Mg2+ ion, despite its stronger interactions with methanol than with water (see Figure 1 b). Moreover the first peak of the gionOw(r) function increases, when the water content decreases. This is particularly remarkable for the Ca2+ ions and in the water deficit mixture, when the water


406 Molecular Dynamics – Theoretical Developments and Applications in Nanotechnology and Energy

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 407

Fig. 2. Cation-oxygen radial distribution functions in solutions of NaCl (solid), MgCl2 (dashed) and CaCl2 (dotted) in water (a), methanol (c) and equimolar water-methanol

A comparison of the radial distribution functions for the cations in aqueous and methanolic solutions shows that the average distance to the methanol's oxygen is almost the same as to the water's oxygen. Such feature is in good agreement with the experimental results (Megyes et al., 2004; Neilsen & Enderby, 1979). The first peaks of all ion-oxygen functions in methanolic solutions are higher that those in aqueous solutions. This suggests that positions of the methanol molecules in the cation shells are more restricted than those of water molecules. As seen from Table 4 the height of the gionOm(r) peak decreases when the methanol content decreases. A striking behaviour has been notice for calcium ions. In water rich mixture, for the methanol content 10 mol%, the first and second maxima of the gCaOm(r) function, expected at 0.25 and 0.49 nm, are absent. This suggests that the methanol molecules do not enter the first and even the second coordination shell of Ca2+ ions, despite

Radial distribution functions of the cations and the hydroxyl hydrogens of water and

The cation-hydroxyl hydrogen functions coincide with the cation-oxygen pair distribution functions. Therefore is not surprising that the positions of the sharp first peak of gionH(r) do not depend on the methanol content. As seen from Tables 3 and 4 the cation-hydroxyl hydrogen distance is longer, by about 0.07 nm, than that of the water's and methanol 's oxygen. This suggests an antidipole orientation of the solvent molecules in the first coordination shells of the cations. The radial distribution functions for the cations and the methyl group are not shown, because a direct correlation between these sites is lacking.

Radial distribution functions computed for chloride ions in the solutions of NaCl, MgCl2 and CaCl2 are very similar, therefore the pair distribution functions, computed for CaCl2

mixture: oxygen of water (b) and methanol (d).

very similar energy of interactions (see Figure 1c).

methanol are shown in Figure 3.

Table 4. Characteristic parameters of the ion-methanol radial distribution functions: positions (in nm) of the first (Rmax1) and second (Rmax2) maxima, the first (rmin1) and second (rmin2) minima, heights of the first g(Rmax1) and second g(Rmax2) maxima and the first (n1) and second (n2) coordination numbers.

content does not exceed 10 mol%, the first peaks of the Ca2+Ow function is about 7 times higher than that in aqueous solution (see Table 3). This suggests that in methanol rich solvents the Ca2+ shell contains several water molecules. The second maximum of the gCaOw(r) function shows also a distinct behaviour. In aqueous solution it is split into two peaks of similar heights, at 0.43 and 0.49 nm, respectively. When the methanol is added this splitting becomes less visible and vanishes in equimolar mixture.

xM ion Rmax1 g(Rmax1) rmin1 n1 Rmax2 g(Rmax2) rmin2 n2

Na 0.237 15.46 0.317 1.25 - - - - Ca - - - - 0.652 1.90 0.760 ~5 Mg 0.202 26.66 0.270 0.7 0.397 7.33 0.519 5 Cl 0.325 14.09 0.410 2.25 - - - -

Na 0.234 14.24 0.316 3.56 - - - - Ca 0.252 5.75 0.332 1.7 0.478 3.05 0.555 8 Mg 0.202 34.57 0.270 2.92 0.392 3.55 0.495 8 Cl 0.324 9.84 0.414 6.10 - - - -

Na 0.235 13.72 0.312 5.61 - - - - Ca 0.250 15.60 0.347 5.7 0.480 3.47 0.565 ~10 Mg 0.202 46.67 0.270 5.4 0.399 3.17 0.472 7 Cl 0.325 6.84 0.418 7.1 - - - -

Na 0.238 15.90 0.340 5.8 - - - - Ca 0.247 22.03 0.362 7.6 0.488 3.05 0.565 9 Mg 0.202 50.22 0.270 6 0.397 3.35 0.472 7 Cl 0.328 7.00 0.430 7.2 - - - hydroxyl hydrogen

Na 0.282 7.29 0.380 1.25 - - - - Ca - - - - 0.732 1.58 0.825 ~5 Mg 0.259 9.81 0.259 0.7 0.444 4.74 0.580 5 Cl 0.227 27.12 0.312 2.20 - - - -

Na 0.300 4.07 0.380 4.60 - - - - Ca 0.337 2.96 0.419 1.7 0.545 2.38 0.623 ~6.5 Mg 0.262 11.91 0.262 2.92 0.492 2.28 0.574 9 Cl 0.231 18.26 0.326 5.32 - - - -

Na 0.290 5.86 0.385 5.59 - - - - Ca 0.335 8.46 0.440 5.7 0.550 2.41 0.635 ~12 Mg 0.262 16.73 0.262 5.4 0.510 2.16 0.530 8 Cl 0.235 13.56 0.335 6.70 - - - -

Na 0.295 6.90 0.380 5.90 - - - - Ca 0.332 11.90 0.400 7.6 0.562 2.19 0.635 ~11 Mg 0.262 17.98 0.262 6 0.505 2.19 0.522 8 Cl 0.235 12.70 0.340 7.00 - - - -

content does not exceed 10 mol%, the first peaks of the Ca2+Ow function is about 7 times higher than that in aqueous solution (see Table 3). This suggests that in methanol rich solvents the Ca2+ shell contains several water molecules. The second maximum of the gCaOw(r) function shows also a distinct behaviour. In aqueous solution it is split into two peaks of similar heights, at 0.43 and 0.49 nm, respectively. When the methanol is added this

Table 4. Characteristic parameters of the ion-methanol radial distribution functions: positions (in nm) of the first (Rmax1) and second (Rmax2) maxima, the first (rmin1) and second (rmin2) minima, heights of the first g(Rmax1) and second g(Rmax2) maxima and the first (n1) and

splitting becomes less visible and vanishes in equimolar mixture.

oxygen

0.1

0.5

0.9

1.0

0.1

0.5

0.9

1.0

second (n2) coordination numbers.

Fig. 2. Cation-oxygen radial distribution functions in solutions of NaCl (solid), MgCl2 (dashed) and CaCl2 (dotted) in water (a), methanol (c) and equimolar water-methanol mixture: oxygen of water (b) and methanol (d).

A comparison of the radial distribution functions for the cations in aqueous and methanolic solutions shows that the average distance to the methanol's oxygen is almost the same as to the water's oxygen. Such feature is in good agreement with the experimental results (Megyes et al., 2004; Neilsen & Enderby, 1979). The first peaks of all ion-oxygen functions in methanolic solutions are higher that those in aqueous solutions. This suggests that positions of the methanol molecules in the cation shells are more restricted than those of water molecules. As seen from Table 4 the height of the gionOm(r) peak decreases when the methanol content decreases. A striking behaviour has been notice for calcium ions. In water rich mixture, for the methanol content 10 mol%, the first and second maxima of the gCaOm(r) function, expected at 0.25 and 0.49 nm, are absent. This suggests that the methanol molecules do not enter the first and even the second coordination shell of Ca2+ ions, despite very similar energy of interactions (see Figure 1c).

Radial distribution functions of the cations and the hydroxyl hydrogens of water and methanol are shown in Figure 3.

The cation-hydroxyl hydrogen functions coincide with the cation-oxygen pair distribution functions. Therefore is not surprising that the positions of the sharp first peak of gionH(r) do not depend on the methanol content. As seen from Tables 3 and 4 the cation-hydroxyl hydrogen distance is longer, by about 0.07 nm, than that of the water's and methanol 's oxygen. This suggests an antidipole orientation of the solvent molecules in the first coordination shells of the cations. The radial distribution functions for the cations and the methyl group are not shown, because a direct correlation between these sites is lacking.

Radial distribution functions computed for chloride ions in the solutions of NaCl, MgCl2 and CaCl2 are very similar, therefore the pair distribution functions, computed for CaCl2

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 409

hydroxyl hydrogen (dotted). Solutions of CaCl2 in water (a), methanol (c) and equimolar

The numbers of the -sites in the coordination shells are equal to the running integration numbers, which have been computed by the integration of the gion(r) function within the

2

1 <sup>2</sup> 4 () *r*

where denotes the number density of the -sites. The boundaries of the shells correspond to the minima of the g(r) functions. Well-separated peaks of the radial distribution functions for the cations permit to compute unambiguously the number of the molecules in the first and even in the second shell. The number of the solvent molecules in the Cl- shell is not

Diffraction experiments have shown that sodium and magnesium ions are six-coordinated both in aqueous (Ohtaki&Radnai,1993) and methanolic (Megyes et al., 2004) solutions. The hydration number of Ca2+ is greater, it strongly depends on the salt concentration and covers a wide interval, from 10.7 to 5.5 (Yamagouchi et al., 1989). The salt concentration influences also the number of the methanol molecules coordinated by Ca2+, but this

Coordination numbers of Na+ and Mg2+, obtained from MD simulations, agree with the experimental results. Despite higher charge density of Mg2+ both cations, Na+ and Mg2+, are

 

*ion r n g r r dr*

and water and methanol sites: oxygen (solid) and

(4)

Fig. 4. Radial distribution functions for Cl-

**4. Coordination numbers of the ions** 

boundaries of the shell, r1 and r2, respectively.

certain, because the peaks are badly pronounced.

dependence is weaker (Megyes et al., 2004).

water-methanol mixture: water's (b) and methanol's (d) sites.

solutions are displayed in Figure 4 as the example of the Cl- -oxygen and Cl- -hydroxyl hydrogen pair distribution functions.

Fig. 3. Cation-hydroxyl hydrogen radial distribution functions in solutions of NaCl (solid), MgCl2 (dashed) and CaCl2 (dotted) in water (a), methanol (c) and equimolar water-methanol mixture: oxygen of water (b) and methanol (d).

In aqueous and methanolic solutions of NaCl, MgCl2 and CaCl2 the first peak of the Cl- Ow and Cl- Om functions is centred at 0.33 nm. This agrees with the average distance, deduced from X-ray diffraction, from the Cl ion to oxygens in aqueous (Yu et al., 2010) and methanolic (Megyes et al., 2004; Neilsen & Enderby, 1979) solutions. Position of the gClHw(r) and gClHm(r) functions, at 0.242 nm, coincides with the anion-oxygen distance. This shorter, by about 0.09 nm, distance suggests almost linear hydrogen bond between the anion and the solvent molecules. In aqueous solutions the first peaks of the gClOw(r) and gClHw(r) functions are not distinctly separated from the bulk. This evidences a high flexibility of the hydrated anion and suggests an easy exchange of the water molecules between the coordination shell and the bulk solvent. In methanolic solutions the peaks of the gClOm(r) and gClHm(r) functions are higher and better pronounced. This may indicate that the coordination shell of the anion in methanolic solutions is more stable.

The composition of the mixed solvent does not affect the peak positions, but it influences remarkably the peak height. The changes of the peak height follows the changes of the solvent components, therefore the gClOm(r) and gClHm(r) peaks increase and the gClOw(r) and gClHw(r) peaks should decrease with the increasing methanol content. However the influence of the solvent composition on the Cl- -water radial distribution function is more dramatic. In equimolar mixture the first peaks of the gClOw(r) gClHw(r) functions, expected at 0.33 and 0.242 nm, respectively, are absent. This means that the coordination shells of the anions do not contain the water molecules. This is observed despite the very similar energy interactions of the Cl- ion with water and methanol molecules (see Figure 1d).

solutions are displayed in Figure 4 as the example of the Cl- -oxygen and Cl- -hydroxyl

Fig. 3. Cation-hydroxyl hydrogen radial distribution functions in solutions of NaCl (solid), MgCl2 (dashed) and CaCl2 (dotted) in water (a), methanol (c) and equimolar water-methanol

In aqueous and methanolic solutions of NaCl, MgCl2 and CaCl2 the first peak of the Cl- Ow and Cl- Om functions is centred at 0.33 nm. This agrees with the average distance, deduced from X-ray diffraction, from the Cl- ion to oxygens in aqueous (Yu et al., 2010) and methanolic (Megyes et al., 2004; Neilsen & Enderby, 1979) solutions. Position of the gClHw(r) and gClHm(r) functions, at 0.242 nm, coincides with the anion-oxygen distance. This shorter, by about 0.09 nm, distance suggests almost linear hydrogen bond between the anion and the solvent molecules. In aqueous solutions the first peaks of the gClOw(r) and gClHw(r) functions are not distinctly separated from the bulk. This evidences a high flexibility of the hydrated anion and suggests an easy exchange of the water molecules between the coordination shell and the bulk solvent. In methanolic solutions the peaks of the gClOm(r) and gClHm(r) functions are higher and better pronounced. This may indicate that the coordination shell of the anion

The composition of the mixed solvent does not affect the peak positions, but it influences remarkably the peak height. The changes of the peak height follows the changes of the solvent components, therefore the gClOm(r) and gClHm(r) peaks increase and the gClOw(r) and gClHw(r) peaks should decrease with the increasing methanol content. However the influence

equimolar mixture the first peaks of the gClOw(r) gClHw(r) functions, expected at 0.33 and 0.242 nm, respectively, are absent. This means that the coordination shells of the anions do not contain the water molecules. This is observed despite the very similar energy

interactions of the Cl- ion with water and methanol molecules (see Figure 1d).


hydrogen pair distribution functions.

mixture: oxygen of water (b) and methanol (d).

in methanolic solutions is more stable.

of the solvent composition on the Cl-

Fig. 4. Radial distribution functions for Cl and water and methanol sites: oxygen (solid) and hydroxyl hydrogen (dotted). Solutions of CaCl2 in water (a), methanol (c) and equimolar water-methanol mixture: water's (b) and methanol's (d) sites.

#### **4. Coordination numbers of the ions**

The numbers of the -sites in the coordination shells are equal to the running integration numbers, which have been computed by the integration of the gion(r) function within the boundaries of the shell, r1 and r2, respectively.

$$m\_{\alpha} = 4\pi \rho\_{\alpha} \int\_{r\_1}^{r\_2} g\_{ion\alpha}(r) r^2 dr \tag{4}$$

where denotes the number density of the -sites. The boundaries of the shells correspond to the minima of the g(r) functions. Well-separated peaks of the radial distribution functions for the cations permit to compute unambiguously the number of the molecules in the first and even in the second shell. The number of the solvent molecules in the Cl- shell is not certain, because the peaks are badly pronounced.

Diffraction experiments have shown that sodium and magnesium ions are six-coordinated both in aqueous (Ohtaki&Radnai,1993) and methanolic (Megyes et al., 2004) solutions. The hydration number of Ca2+ is greater, it strongly depends on the salt concentration and covers a wide interval, from 10.7 to 5.5 (Yamagouchi et al., 1989). The salt concentration influences also the number of the methanol molecules coordinated by Ca2+, but this dependence is weaker (Megyes et al., 2004).

Coordination numbers of Na+ and Mg2+, obtained from MD simulations, agree with the experimental results. Despite higher charge density of Mg2+ both cations, Na+ and Mg2+, are six-coordinated in aqueous and methanolic solutions. Thus the coordination number should be independent of the solvent composition. Though the charge density of Ca2+ is smaller than that of Mg2+ , the first shell of Ca2+ is larger. In aqueous solution the Ca2+ shell consists of 10 water molecules. In methanolic solution the Ca2+ shell contains less molecules. The coordination number is 7.6. This means that the Ca2+ shells contain either seven or eight methanol molecules. Thus one may expect that the methanol addition will slightly reduce the coordination number of Ca2+.

In aqueous solutions of NaCl, MgCl2 and CaCl2 the chloride ion coordinates about eight water molecules. Smaller hydration number, about 6, was deduced from the X-ray experiments (Yu et al., 2010) Such discrepancy can be understood, because the hydration shell of the anion is badly pronounced. In methanolic solution the Cl- ion coordinates less molecules, about 7. Different coordination numbers of Cl-, six (Megyes et al., 2004) and more than seven (Yamagouchi et al., 1989) have been deduced from X-ray scattering in methanol solutions of CaCl2 and MgCl2. The discrepancy might be due to the higher concentration of the experimentally examined solution.

Interactions of the ions with water and methanol are very similar (see Figure 1) therefore a selective solvation of the ions has been not expected. The inspection of the results listed in Tables 3 and 4 shows, however, that the influence of the methanol addition on the composition of the ion shells can be dramatic. To describe this effect the real composition of the ion shells has been compared with the expected composition.

 The 'real' methanol mole fraction in the first and second coordination shells of the ions has been computed as follows:

$$\mathbf{n}(\mathbf{x}\_{\rm m})\_{\rm obs} = \frac{(\mathbf{n}\_{\rm m})\_{\rm k}}{(\mathbf{n}\_{\rm m})\_{\rm k} + (\mathbf{n}\_{\rm w})\_{\rm k}} \tag{5}$$

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 411

The non-linear changes of the mixed solvent density should give a slight excess of methanol in the primary coordination shells of the ions. The results of MD simulation show, however, significant deviations of the real composition of the ion shells. This suggests a selective solvation of the ions. To demonstrate the preferences of the ions the observed methanol mole fraction, (xm)obs, is shown as the function of the expected methanol mole fraction (xm)exp

The content of methanol in the first coordination shells of Ca2+ and Mg2+ ions is remarkably smaller than expected. Thus the Ca2+ and Mg2+ ions favour water molecules in their shells. As seen from Figure 5 the preferential hydration of these cations is observed over whole range of the mixture composition. The Na+ ion also favours the water molecules in its primary shell, but this inclination is weaker, therefore the preferential hydration occurs only in the water deficit mixtures. This agrees with experiments, which have shown the equality of the self-diffusion coefficients of water and Na+ ions in water deficit mixtures (Hawlicka, 1986). The self-diffusion experiments have also shown that the addition of CaCl2 to the methanol water-mixture does not influence the methanol self-diffusion coefficient, but it reduces strongly the water self-diffusion coefficient (Palka & Hawlicka, 2004) . This means that translations of the cation and water molecules are correlated, because these species

Fig. 5. The dependence of the observed methanol mole fraction in the primary shell of Na+

Though all cations favour water molecules in the nearest surrounding, some difference should be noticed. The Mg2+ shells contain about 10% more water than expected, the significant excess is observed only in equimolar mixture. The Ca2+ ions exhibit the stronger preference for water, because in the water deficit region the calcium ion coordinates most of the water molecules. Moreover the Ca2+ ion favours the water molecules also in its second shell. In water rich mixture both shell of the Ca2+ ions consist only of the water molecules. Preferences of the Mg2+ and Na+ ions in their second shells are opposite and an excess of the

(), Mg2+ (), Ca2+ () and Cl- () ions on the expected methanol mole fraction.

in Figure 5.

form an aggregate.

methanol content is observed.

where (nw)k and (nm)k are the running integration numbers of the methanol and water molecules, respectively, computed for the first or second coordination shells.

The number density of the methanol and water molecules in the mixture depends nonlinearly on the methanol mole fraction. Therefore even when the preferential solvation of ions does not occur, the methanol concentrations in the coordination shell and the bulk solvent are not the same. Assuming a lack of the selective solvation, the expected mole fraction of methanol in the ion shell can be calculated as follows (Hawlicka & Switla-Wojcik, 2000):

$$(\mathbf{x}\_{\rm m})\_{\rm exp} = \frac{(\mathbf{n}\_{\rm m})\_{\rm o} \frac{\rho\_{\rm m}(\mathbf{x}\_{\rm m})}{(\rho\_{\rm m})\_{\rm o}}}{(\mathbf{n}\_{\rm m})\_{\rm o} \frac{\rho\_{\rm m}(\mathbf{x}\_{\rm m})}{(\rho\_{\rm m})\_{\rm o}} + (\mathbf{n}\_{\rm w})\_{\rm o} \frac{\rho\_{\rm w}(\mathbf{x}\_{\rm m})}{(\rho\_{\rm w})\_{\rm o}}} \tag{6}$$

(nw)o and (nm)o are the numbers of the coordinated solvent molecules in pure water and methanol, (w)o and (m)o denote the number densities of the solvent components in the aqueous and methanolic solutions of the salts, while w(xm) and m(xm) are the number densities of water and methanol, respectively, in ternary systems: salt-methanolwater.

six-coordinated in aqueous and methanolic solutions. Thus the coordination number should be independent of the solvent composition. Though the charge density of Ca2+ is smaller than that of Mg2+ , the first shell of Ca2+ is larger. In aqueous solution the Ca2+ shell consists of 10 water molecules. In methanolic solution the Ca2+ shell contains less molecules. The coordination number is 7.6. This means that the Ca2+ shells contain either seven or eight methanol molecules. Thus one may expect that the methanol addition will slightly reduce

In aqueous solutions of NaCl, MgCl2 and CaCl2 the chloride ion coordinates about eight water molecules. Smaller hydration number, about 6, was deduced from the X-ray experiments (Yu et al., 2010) Such discrepancy can be understood, because the hydration shell of the anion is badly pronounced. In methanolic solution the Cl- ion coordinates less

than seven (Yamagouchi et al., 1989) have been deduced from X-ray scattering in methanol solutions of CaCl2 and MgCl2. The discrepancy might be due to the higher concentration of

Interactions of the ions with water and methanol are very similar (see Figure 1) therefore a selective solvation of the ions has been not expected. The inspection of the results listed in Tables 3 and 4 shows, however, that the influence of the methanol addition on the composition of the ion shells can be dramatic. To describe this effect the real composition of

The 'real' methanol mole fraction in the first and second coordination shells of the ions has

<sup>m</sup> <sup>k</sup> <sup>m</sup> obs )n()n(

where (nw)k and (nm)k are the running integration numbers of the methanol and water

The number density of the methanol and water molecules in the mixture depends nonlinearly on the methanol mole fraction. Therefore even when the preferential solvation of ions does not occur, the methanol concentrations in the coordination shell and the bulk solvent are not the same. Assuming a lack of the selective solvation, the expected mole fraction of methanol in the ion shell can be calculated as follows (Hawlicka & Switla-

> om mm om

(nw)o and (nm)o are the numbers of the coordinated solvent molecules in pure water and methanol, (w)o and (m)o denote the number densities of the solvent components in the aqueous and methanolic solutions of the salts, while w(xm) and m(xm) are the number densities of water and methanol, respectively, in ternary systems: salt-methanol-

<sup>ρ</sup> )x( )n(

om mm om

(ρ ) <sup>ρ</sup> )x( )n(

<sup>ρ</sup> )x( )n( (<sup>ρ</sup> )

molecules, respectively, computed for the first or second coordination shells.

m k w k

)n( )x( (5)

ow mw ow

(6)

(ρ )

, six (Megyes et al., 2004) and more

the coordination number of Ca2+.

the experimentally examined solution.

been computed as follows:

Wojcik, 2000):

water.

molecules, about 7. Different coordination numbers of Cl-

the ion shells has been compared with the expected composition.

expm

)x(

The non-linear changes of the mixed solvent density should give a slight excess of methanol in the primary coordination shells of the ions. The results of MD simulation show, however, significant deviations of the real composition of the ion shells. This suggests a selective solvation of the ions. To demonstrate the preferences of the ions the observed methanol mole fraction, (xm)obs, is shown as the function of the expected methanol mole fraction (xm)exp in Figure 5.

The content of methanol in the first coordination shells of Ca2+ and Mg2+ ions is remarkably smaller than expected. Thus the Ca2+ and Mg2+ ions favour water molecules in their shells. As seen from Figure 5 the preferential hydration of these cations is observed over whole range of the mixture composition. The Na+ ion also favours the water molecules in its primary shell, but this inclination is weaker, therefore the preferential hydration occurs only in the water deficit mixtures. This agrees with experiments, which have shown the equality of the self-diffusion coefficients of water and Na+ ions in water deficit mixtures (Hawlicka, 1986). The self-diffusion experiments have also shown that the addition of CaCl2 to the methanol water-mixture does not influence the methanol self-diffusion coefficient, but it reduces strongly the water self-diffusion coefficient (Palka & Hawlicka, 2004) . This means that translations of the cation and water molecules are correlated, because these species form an aggregate.

Fig. 5. The dependence of the observed methanol mole fraction in the primary shell of Na+ (), Mg2+ (), Ca2+ () and Cl- () ions on the expected methanol mole fraction.

Though all cations favour water molecules in the nearest surrounding, some difference should be noticed. The Mg2+ shells contain about 10% more water than expected, the significant excess is observed only in equimolar mixture. The Ca2+ ions exhibit the stronger preference for water, because in the water deficit region the calcium ion coordinates most of the water molecules. Moreover the Ca2+ ion favours the water molecules also in its second shell. In water rich mixture both shell of the Ca2+ ions consist only of the water molecules. Preferences of the Mg2+ and Na+ ions in their second shells are opposite and an excess of the methanol content is observed.

MD Simulation of the Ion Solvation in Methanol-Water Mixtures 413

antidipole orientation of the water molecules in the cation shells dominates. The distribution of the angle for Mg2+ is narrower than those for Na+ and Ca2+. This is not surprising that the water molecules are better oriented in the field of Mg2+, which is stronger than the fields of Na+ and Ca2+. The primary shell of Ca2+ contains more water molecules than the shells of the six-coordinated Na+ and Mg2+ions, therefore the angular distribution for Ca2+ shows a shoulder for cos -0.7. This means that the dipole moments of a few water molecules in the Ca2+ shell are tilted, by about 45o, from the antidipole orientation. This 'improper' orientation vanishes in equimolar mixture when the coordination number decreases from 10

The antidipole orientation of the methanol molecules is also observed in the Na+ and Mg2+ shells. A different orientation has been noticed for the methanol molecules in the Ca2+ shell. The distribution of the O-Ca2+O angles, shows the dominant peak at cos =-0.9. Thus the

As might be expected the orientation of the solvent molecules in the vicinity of chloride ions is different. The distance from the anion to oxygen is longer than that to hydrogen. This suggests a hydrogen bond between the anion and the nearest solvent molecules. In aqueous and methanolic solutions the dominant peaks of the angular distributions are centred at cos=0.68. This confirms that H-bond between the anion and solvent molecules is almost linear. As might be expected the orientation of the solvent molecules in the anion shell for all

To describe a geometrical arrangement of the solvent molecules in the solvation shells two angles can be defined. The angle is the angle between two vectors pointing from the ion to the nearest oxygens. The angle, which is the angle between the three oxygens, permits to deduce a difference between the order of the water molecules in the coordination shells and the tetrahedral structure of water. The distributions of the angles have been computed without any distinction between oxygens belonging to water and methanol molecules. The

Fig. 7. Distribution of angles, for the water (a) and methanol (b) molecules in the primary

The distribution of angles computed for the coordination shells of the Na+ and Mg2+ ions is independent of the solvent composition. Two peaks, centred at 90o and 180o, indicate that the water and methanol molecules form an octahedron around the cation. The distribution

(dotted).

dipole moments of the methanol molecules in the Ca2+vicinity are tilted by about 25o.

to 7. This suggests that the coordination shell of Ca2+ is compact.

studied solutions is independent of the solvent composition.

results are displayed in Figure 7.

shells of Na+ (solid), Mg2+(dashed), Ca2+() and Cl-

Interactions of the chloride ions with methanol and water are weaker than those of cations. The coordination shell of Cl is flexible, but its composition differs significantly from that of the bulk solvent. The chloride ions favour methanol molecules in their coordination shells. This preference is observed in solutions of NaCl, CaCl2 and MgCl2, over the whole range of the composition of the mixed solvent. The preferential solvation of Cl- by methanol has been postulated from self-diffusion coefficients. The diffusion experiments have shown that in methanol rich solvents translations of the chloride ions and methanol molecules are strongly correlated (Hawlicka, 1986). The Cl ion favours the methanol molecules in its primary shell despite very similar binding energies of the anion with the solvent components.
