Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed SaltsEwa Hawlicka and Agnieszka Kuba

Institute of Applied Radiation Chemistry, Department of Chemistry, Technical University,Zeromskiego 116, 90-924 Lodz, Poland

Reprint requests to E. H.; E-mail: hawlicka@p.lodz.pl

Z. Naturforsch. 68a, 139 – 144 (2013) / DOI: 10.5560/ZNA.2012-0097Received September 28, 2012 / published online February 15, 2013

Dedicated to Professor Alfred Klemm in honour of his 100th birthday

Molecular dynamic simulations of aqueous solutions containing Me4NCl and an inorganic salt,NaCl, MgCl2 or CaCl2, have been performed at room temperature. Flexible models have been em-ployed for the Me4N+-ions and the water molecules. The hydration of the ions has been discussed onthe basis of the radial and angular distribution functions. The geometrical arrangement of the watermolecules in the coordination shell has been deduced form the distributions of the angles betweentwo vectors connecting the ion and an oxygen and of the angles between three oxygens. The additionof Me4N+ does not influence noticeably the size and structure of the cationic hydration shells, butit affects remarkably their persistence, causing a fast exchange of the water molecules between theshell and the bulk solvent.

Key words: Hydration of Ions; Aqueous Solutions of Hydrophobes; MD Simulation.

1. Introduction

Hydrophobic hydration and hydrophobic associa-tion play a key role in chemistry and biology. De-spite a lot of experiments and computer simulations,the nature of these effects is not yet fully under-stood. There are, however, no doubts that the waterH-bonded network and a tendency to maintain theseH-bonds are crucial [1]. Intuitive models of hydropho-bic hydration, based on thermodynamic findings [2],see water molecules forming a clathrate around apo-lar solutes and assume an enhancement of the waterstructure in the vicinity of hydrophobes. It is knownthat the mobility of water molecules in solutions ofhydrophobes is reduced. This has often been taken asevidence for the enhancement of the water structure.Computer simulations [3] have shown a tangential ori-entation of the water molecules around apolar solutes,which is consistent with the clathrate-like structuresdeduced from thermodynamic finding. Recent nuclearmagnetic resonance (NMR), dielectric relaxation, andfemto-second infrared (IR) experiments have also con-firmed that hydrophobes affect the dynamics of thewater molecules [4 – 6], but neither computer simula-tions nor diffraction experiments [7, 8] have demon-strated an enhancement of the water structure.

Alkali and alkali earth ions play an important rolein many biological processes, which occur in systemscontaining hydrophobic groups. There are several cluesthat the biological activity of the metal ions depends ontheir hydration [9]. Thus, the question appears whetherthe presence of apolar groups affects the hydration ofmetal ions. Though the interactions of apolar soluteswith water are weaker than those of metal ions, self-diffusion experiments [10 – 12] have shown that in so-lutions of inorganic salts and apolar compounds the hy-drodynamic radii of Na+ and Ca2+ ions are reduced,whereas that of (CH3)4N+ remains unaffected. Thissuggests a partial dehydration of the metal ions.

Aqueous solutions of tetraalkylammonium salts arefrequently employed as model systems to investigatehydrophobic phenomena. Though their ‘hydrophobic’behaviour increases with the increasing length of thealkyl chain, the aqueous solution of (CH3)4NCl canalso serve as the model system since (CH3)4N+ is‘more apolar’ then ‘ionic’ [13].

In order to investigate a possible interrelation be-tween the hydration of the biologically important(Na+, Mg2+, Ca2+) ions and the ‘apolar’ (CH3)4N+

ion, we have carried out molecular dynamics (MD)simulations of NaCl, MgCl2, and CaCl2 dissolved inaqueous solutions of (CH3)4NCl.

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140 E. Hawlicka and A. Kuba · Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed Salts

2. Details of the Simulation

The MD simulations were carried out at an averagetemperature of 299 K in the microcanonical (NVE) en-semble. The concentrations of both salts were 0.55 M.This means that in all simulations the periodic cubecontained 400 water molecules, four molecules of(CH3)4NCl, and four molecules of the inorganic salt.The lengths of the boxes were calculated from the ex-perimental densities of the aqueous solutions of themixed salts at 298 K.

The water molecule was treated as a flexible three-site body with partial charges located on the oxygen(qO = −0.66 eo) and the hydrogens (qH = 0.33 eo).The interactions between the water molecules were de-scribed by the potential derived by Bopp, Jancso, andHeinzinger, called BJH potential [14]. This effectivepotential is the sum of two parts representing the intra-and intermolecular interactions; it permits internal vi-brations of the molecule.

The effective potentials for the inorganic ions werederived from ab initio calculations by fitting the poten-tial energies between the ions and water molecule, as-suming the BJH model. Details of the potential param-eters have been presented previously [15 – 17]. Thesepotentials describe the structures of the coordinationshells of the inorganic ions in aqueous solutions cor-rectly.

The (CH3)4N+ ion was considered as a flexiblefive-site body with partial charges located on ni-trogen (qN = −0.56 eo) and on the methyl groups,treated as pseudo-atoms (qMe = +0.39 eo) [18].A spectroscopic-type potential was employed to keepthe charged sites together. This potential was expressedin terms of two internal coordinates: the stretch of theN–Me bond and the bending of the Me–N–Me angle.The intermolecular part of the potential was the sumof Coulomb and Lennard–Jones terms. The Lennard–Jones parameters were presented previously [18]. Allinteractions of the inorganic ions with Me4N+ werealso expressed as sums of Coulomb and Lennard–Jones terms and the potential parameters were calcu-lated according to the standard combining rules. TheLennard–Jones parameters for the inorganic ions weretaken from Koneshan et al. [19].

In all simulations, the initial configurations wereobtained by a random placement of the particles inthe cubic box. Ewald summation was applied for theCoulomb interactions and the shifted force potential

method was used for all non-Coulomb ones [20]. Thesimulation time step was 0.25 fs. After about 10 psof equilibration, the simulations were extended up to100 ps. Coordinates and velocities of all sites were col-lected in 1 fs intervals. In all simulations the stabilityof the potential energy was better than 0.1%. For allsimulated solutions the temperature, averaged over thewhole simulation runs, was 299 ± 4 K.

3. Results and Discussion

In all simulated solutions, an ion association doesnot occur and the hydration shells of Cl− are indepen-dent of the cations. Also in the presence of Me4NCl,ionic association does not occur. Therefore the radialdistribution functions between Cl− and the water sitesare identical in all simulated solutions. The gClO andgClH functions exhibit peaks at 0.330 and 0.242 nm.The position of the gClO peak agrees with the aver-age distance between the anion and the oxygen atomsdeduced from X-ray diffraction, 0.326 nm [21]. Thesefirst peaks are not clearly separated from the bulk. Thisis evident for the high flexibility of the anionic hy-dration shell and for an easy exchange of the watermolecules between this shell and the bulk. The shortdistance between the anion and the hydrogens suggestsalmost linear hydrogen bonds between the anion andthe water molecules. Indeed, the most probable valuefor the angle between the vector connecting Cl−withthe water-oxygen and the intramolecular OH bond isabout 10◦. Integration of the first peaks of the gClO andgClH functions indicates that the coordination shell ofCl− consists of about 8 water molecules. The same co-ordination number has been reported for aqueous solu-tions of NaCl, MgCl2, and CaCl2 [22].

3.1. Structure of the Hydration Shells of the MetalIons

The radial distribution functions for the metalcations and water-oxygen in solutions of Me4NCl arepresented in Figure 1 and compared with the analogousfunctions in aqueous solutions. The influence of theMe4NCl on the distribution of the oxygens around thesodium and magnesium cations is seen to be almostnegligible. The first peaks of the radial distributionfunctions between the Na+ and Mg2+ ions and oxygenappear at 0.23 and 0.202 nm, respectively. The samedistances, which agree very well with the experimental

E. Hawlicka and A. Kuba · Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed Salts 141

Fig. 1. Cation-oxygen radial distribution functions in aque-ous (dashed) and Me4NCl solutions of NaCl (a), MgCl2 (b),and CaCl2 (c).

data (0.24 [23] and 0.20 nm [24], respectively), havebeen obtained in simulations of aqueous solutions ofNaCl [17] and MgCl2 [25]. One should, however, no-tice that these first peaks are slightly lower than those inaqueous solutions. Integration of the first peaks of theion–oxygen radial distribution function up to its firstminimum yields the number of the water molecules inthe first coordination shell. In aqueous solutions, theNa+ and Mg2+ ions are six-coordinated [17, 22]. Theaddition of Me4NCl does not affect the size of the Na+

shell and this cation remains six-coordinated, but thefirst coordination shell of Mg2+ is slightly larger andconsists of 7 water molecules.

As seen from Figure 1, the presence of Me4NCldoes not influence the second shell of Mg2+ and thegMgO function, similar to the one in aqueous solution ofMgCl2, exhibits a second broad and asymmetric peak,centred around 0.45 nm. Its position coincides with thedistance 0.41 nm extracted from X-ray scattering [26].The first and second maxima of gMgO are well sepa-rated, thus the number of water molecules in the sec-ond shell can be determined unambiguously. In aque-ous solution, the second coordination shell of Mg2+

contains 16 water molecules, in solution with the apo-lar Me4N+ ions this second shell is slightly bigger andcontains 18 water molecules.

Addition of Me4NCl affects the position and shapeof the first peak of the gCaO function. In aque-ous solution, the average distance from Ca2+ tothe nearest oxygens, computed from MD simulation,

0.237 nm [27] coincides with the experimental result,about 0.24 nm [28]. In the solution with Me4NCl, thefirst peak is lower and is upshifted to 0.25 nm. ThegCaO function also exhibits a second peak, centred at0.46 nm. It is worthwhile noticing that in aqueous so-lutions this second maximum is split into two peaksof similar heights, centred around at 0.43 and 0.49 nm.As seen from Figure 1c, in the solution of Me4NCl thissplitting vanishes. An addition of methanol producesa similar effect [27].

When Me4NCl is added, both shells of Ca2+ in-crease in population. The first shell consists of 11molecules whereas the second one contains more than30. In aqueous solution, these shells consist of 10 and27 water molecules [15, 27]. The slight increase ofthe larger coordination number seems to be in contrastwith a decrease of the hydrodynamic radius of Ca2+,and in consequence a decrease of the ‘dynamic’ hy-dration number of this cation [12]. This ‘dynamic’ hy-dration number, however, concerns only the moleculesthe motions of which are correlated with the ion. Theirresidence time in the ionic shell must be longer thana characteristic time for the ion translations. We shallcome back to this point below.

The internal structure of a coordination shell can becharacterized by the following angels:

(i) the angle ϕ , i. e. the angle between the dipole mo-ment and the vector pointing from the ion centreto the oxygen;

(ii) the angle θ , i. e. the angle between two vectorspointing from the ion centre to the nearest oxy-gens and

(iii) the angle ψ , i. e. the angle between three oxygenatoms of molecules in the hydration shells.

The distributions of ϕ (not shown here) with a per-sistent dominant peak at cos(ϕ) = −1 show that theaddition of Me4NCl does not affect the orientationof the water molecules in the first shells of the inor-ganic cations, and the antidipole orientation is alwaysfavoured. However, the dipole moments of a few watermolecules in the Ca2+ shell are tilted by about 50◦

from the antidipole orientation, as it can be deducedfrom a shoulder at cos(ϕ) =−0.65. Similar distortionof the antidipole orientation has been observed previ-ously [15, 27] in aqueous solution.

The distributions of the angle between pairs of vec-tors pointing from the cation to the neighbouring oxy-gen atoms, presented in Figure 2, describe the symme-

142 E. Hawlicka and A. Kuba · Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed Salts

Fig. 2. Distribution of the angle θ between two vectors con-necting the cation with the nearest oxygen atoms in the shellsof Na+ (dashed), Mg2+ (dotted), and Ca2+ (solid).

try of the first coordination shell. Two peaks centred at90◦ and 180◦ prove that the addition of Me4NCl doesnot affect the structure of the shells of Na+ and Mg2+

and that the water molecules form octahedra aroundthese cations. The distribution of the angles betweentriplets of oxygen atoms, with two peaks centred at 60◦

and 90◦, shown in Figure 3, confirms the lack of influ-ence of the Me4N+ on the octahedral symmetry of theNa+ and Mg2+ shells.

The addition of the apolar Me4N+ ion improvesthe symmetry of the Ca2+ shell. In aqueous solu-tion, the angular distribution exhibits two peaks, cen-tred at 65◦ and around 135◦, and only the formerpeak might be expected for tetrahedral or hexahedral

Fig. 3. Distribution of the angle ψ between three oxygens inthe shells of Na+ (dashed), Mg2+ (dotted), and Ca2+ (solid).

symmetries [15, 27]. In Me4NCl solutions, as seenfrom Figure 2, the most probable angles are smaller,about 60◦ and 120◦. These most probable angles areclose to values, which might be expected for tetrahe-dral or hexahedral symmetry. Even though the struc-ture of the Ca2+ shell seems to be closer to tetrahe-dral or hexahedral symmetry, the shoulder observed atabout 135◦ suggests that some of the water moleculesdo not fit into a polyhedron around Ca2+. The improve-ment of the symmetry of the Ca2+ shell is also con-firmed by the O–O–O angles (see Fig. 3). This angu-lar distribution exhibits two broad peaks around 64◦

and 120◦, which fit better the tetrahedral or hexahedralsymmetry than the angles about 55◦ and 107◦ found inaqueous solution [25].

3.2. Structure of the Me4N+ Shell

Despite strong interactions between water and metalcation, the addition of the inorganic salts does not af-fect the hydration shell of the Me4N+ ion at the con-centration studied. In solutions of metal chlorides thegNO and gMeO functions are almost identical to the onesin aqueous solution. As an example the gNO and gMeOfunctions, determined in the CaCl2 solutions, are pre-sented in Figure 3 and compared with those in pureMe4NCl solution. Broad peaks of the gNO and gMeOfunctions are observed around 0.45 and 0.36 nm, re-spectively. Their positions coincide with the distancesof 0.47 and 0.37 nm extracted from neutron diffractionexperiments [29]. It is worthwhile noticing that the re-sult 0.36 nm from the methyl group to oxygen is typi-cal for the distance between the carbon atom of an ap-olar group and water [30].

Integration of the gNO functions up to their first min-ima indicates that the addition of NaCl and MgCl2 af-fects neither the size nor the structure of the Me4N+

shell, which consist, like in aqueous solution, of27 – 28 tangentially oriented water molecules. Thoughthe presence of CaCl2 does not influence the tangen-tial orientation of the water molecules in the Me4N+

shell, it reduces the hydration number to about 20molecules.

3.3. Residence Time of the Water Molecules in the IonShells

An important feature of ions in solutions is the per-sistence of the water molecules in the hydration shells.

E. Hawlicka and A. Kuba · Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed Salts 143

Fig. 4. Residence correlation functions for the watermolecules in the shells of Na+ (dashed), Cl− (dotted), andMe4N+ (solid).

A residence time of the water molecules in the ionicshells was calculated from the time correlation func-tion R(t), proposed previously by Impey et al. [31].This time correlation function is defined as follows:

R(t) =∑

Nα

i=1 ∑Nβ

j=1 κi j (t +∆ t)

Nα Nβ

. (1)

Nα is the number of ions, and Nβ denotes the numberof water molecules in the sphere of the radius definedby the first minimum of gionO. κi j(t) is the step func-tion: κi j(t) = 1 if the j molecule is in the ion shell andκi j(t) = 0 otherwise. R(t) has been computed for atleast 500 consecutive configurations with a time inter-val ∆ t = 0.2 ps [27].

Examples of R(t) obtained for the ions in theNaCl+Me4NCl solution are displayed in Figure 4. Itis seen that R(t) decrease monotonously. They can befitted by a double exponential decay:

R(t) = A1 exp

(− t

τ1

)+A2 exp

(− t

τ2

). (2)

Assuming that τ1 is the shorter of the two times, thesecond term describes the persistence of the moleculesin the ion shells, whereas the first one concerns the es-cape of a molecule located close to the border of theionic shell. A1 and A2 are the fractions of the moleculesinvolved into both processes.

The influence of the Me4N+ ions on the lifetime ofthe hydration shells of the inorganic ions is dramatic.In aqueous solutions, the first coordination shells of the

Na+, and particularly those of Ca2+ and Mg2+ ions,are very stable. About 90% of the water moleculesstay in the Na+ shells for about 170 ps [32]. The per-sistence times of the first coordination shells of thealkali earth cations are much longer, and more than95% of the water molecules do not leave the shellsof Ca2+ and Mg2+ during the whole simulation timeof 150 ps [22, 27]. Such feature agrees with the verylong lifetime of the first coordination shells of Ca2+

(about 700 ps) and Mg2+ (about 420 ps) reported byKoneshan et al. [19]. The addition of Me4NCl desta-bilizes the first shells of the metal cations. Less than90% of the water molecules stay in the Na+ shellduring about 20 ps. The persistence of the Ca2+ andMg2+ shells is much longer, but remarkably shorterthan in aqueous solutions. Only about 80% of the watermolecules stay in the Ca2+ shell during 80 ps. Themost stable one is the first shell of Mg2+ since wefind about 90% of the molecules to reside there formore than 120 ps. The shorter persistence of the co-ordination shells agrees with a decrease of the hydro-dynamic radii of Na+ and Ca2+, postulated from theself-diffusion experiments [12].

Even though the Cl− shell is not very stable in aque-ous solution, the addition of Me4NCl destabilizes alsothis shell. In aqueous solution about 76% of the watermolecules stay in the Cl− shell for at least 20 ps [32].When Me4NCl is added, the Cl− shell becomes veryflexible, only about 60% of the water molecules residelonger than 6 ps. The exchange of the water moleculesbetween the Me4N+ shell and the bulk water is ratherfast. In aqueous solution the persistence of this shelldoes not exceed 5 ps, yet the addition of metal chlo-rides does not affect the residence time.

4. Conclusions

The results presented here indicate that the influ-ence of the ‘apolar’ Me4N+ ion on the hydration ofthe metal ions is stronger than the influence of thestrongly hydrated metal cations on the Me4N+ shells.The addition of Me4NCl affects only very little the co-ordination numbers and the structures of the hydra-tion shells of Na+, Mg2+, and Ca2+ ions. The pres-ence of the ‘apolar’ cation affects, however, remark-ably the exchange of water molecules between thecation shells and the bulk solvent. This may be a phe-nomenon, which influences the biological activity ofthe metal ions.

144 E. Hawlicka and A. Kuba · Hydration of Metal and (CH3)4N+ Ions in Solutions of Mixed Salts

Despite strong interactions of the metal ions withwater, the addition of NaCl, MgCl2, and CaCl2 doesnot affect noticeably the hydration shells of theMe4N+ ions. Only in CaCl2 solution, the numberof water molecules in the Me4N+ shell is slightlyreduced.

Acknowledgements

The financial support of the Interdisciplinary Centrefor Mathematical and Computational Modeling (ICM)of Warsaw University, Project Number G27-17, isgratefully acknowledged.

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