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The structure of water in solutions containing di- and trivalent cations by empirical potential

structure refinement

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2013 J. Phys.: Condens. Matter 25 454213

(http://iopscience.iop.org/0953-8984/25/45/454213)

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J. Phys.: Condens. Matter 25 (2013) 454213 (5pp) doi:10.1088/0953-8984/25/45/454213

The structure of water in solutionscontaining di- and trivalent cations byempirical potential structure refinement

Daniel T Bowron1 and Sofia Dıaz Moreno2

1 ISIS Neutron and Muon Source, Science and Technology Facilities Council, Rutherford AppletonLaboratory, Harwell - Oxford, Didcot, OX11 0QX, UK2 Diamond Light Source Ltd, Diamond House, Harwell Science and Innovation Campus, Didcot,Oxfordshire, OX11 0DE, UK

E-mail: daniel.bowron@stfc.ac.uk

Received 28 January 2013, in final form 16 April 2013Published 18 October 2013Online at stacks.iop.org/JPhysCM/25/454213

AbstractEmpirical potential structure refinement (EPSR) has been used to build experimentallyconsistent models of a range of electrolyte solutions containing di- and trivalent cations:Cu(ClO4)2 at concentrations of 0.5 and 2.0 m, and Cr(NO3)3, YCl3 and LaCl3 at aconcentration of 1.0 m. The resulting models are used to investigate the perturbation of theseelectrolytes on the pair distribution and triplet angle correlations between solvent watermolecules, compared with those found in the pure solvent. The results elucidate thedifferences that derive from the reflected range of highly structured local cation environmentsand provide a complementary viewpoint on the hydration shell geometries.

(Some figures may appear in colour only in the online journal)

1. Introduction

Developments in the technique of empirical potentialstructure refinement (EPSR) of diffraction data [1], nowfacilitate the construction of atomistic models of multi-component systems that are also consistent with chemicallyspecific extended x-ray absorption fine structure (EXAFS)spectroscopy data [2]. This methodology has subsequentlybeen utilized to comprehensively investigate the structureof aqueous solutions of a number of di- and trivalentcations at moderate solution concentrations in the 0.5–2.0 mrange [2–5] and generate models that are consistent withbulk (neutron/x-ray diffraction) and local (EXAFS) structuralinformation. The results confirmed the distinctly differentlocal geometries for the hydration shells of Y3+ (squareantiprism) [2], Cr3+ (octahedral) [3] and La3+ (tricappedtrigonal prism) [4] cations, and the range of hydration shellgeometries for the Cu2+ (tetrahedral, trigonal bipyramidaland octahedral) [5–9] cation where there is an emphasison tetrahedral configurations [5, 6]. Although these earlierstudies were primarily focused on the hydration structure of

the cations and the extent of ion pairing within the solutions,the generated EPSR models contain a wealth of additionalinformation that has not yet been discussed. For example,taken as a coherent body of work the studies present a valuableopportunity to systematically investigate the effect of thedifferent cation environments on the structure of the solventmedium itself. Here we will present a selection of these resultsas an illustration of the value of experimentally consistent(reverse Monte Carlo type [10]) atomistic models.

2. EPSR models and structural baseline: liquidwater

Since its creation, EPSR has been used extensively toinvestigate the structure of liquid water [11–14], witheach study further refining the accuracy or improving theunderstanding of the resulting model of the real material.As there is the potential for a small degree of variation inthe final models based on the underlying reference potentialsand molecular descriptions that are used in the structurerefinement, it is worth outlining the reference model that has

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J. Phys.: Condens. Matter 25 (2013) 454213 D T Bowron and S D Moreno

Figure 1. The EPSR model fits (red solid line) and fit residuals(blue dotted line) to the isotopic samples of D2O, HDO, and H2Omeasured by neutron scattering, where F(Q) is the interferencedifferential scattering cross section and Q the magnitude of themomentum transfer vector. The experimental data are shown asblack circles. For clarity the model fits and experimental data arevertically offset by 0.0, 0.75, and 1.5 units, respectively, for theD2O, HDO, and H2O solutions, while the corresponding fitresiduals are vertically offset by −0.25, 0.5, 1.25 units.

been consistently used in the modelling of the ionic solutionsthat will be discussed in this paper. The pure system will alsobe used to illustrate the typical quality of the resulting modelswhich was comparable for each of the investigated solutions.

All of the investigated systems that will be discussedwere studied at room temperature ≈298 K, and atmosphericpressure. Within the EPSR models the dominant experimentalinformation on the structure of the solvent was obtainedfrom neutron diffraction measurements performed on H2O,D2O and HDO isotopic analogues of the solutions, usingthe small angle neutron diffractometer for amorphous andliquid samples (SANDALS) at the ISIS pulsed neutronfacility, Rutherford Appleton Laboratory, UK. Each samplewas contained in a null scattering Ti0.676Zr0.324 alloy cell ofinternal dimensions 40 mm height × 35 mm width × 1 mmthickness and an alloy wall thickness of 1 mm. All scatteringdata were processed in the same way using the Gudrun [15]data reduction package and the experimental data, EPSRmodel and model fit residuals for the pure water referencesample are shown in figure 1.

Within the EPSR models of the solutions, the solventmedium was refined from a reference structure for the watermolecules based upon a mean molecular geometry definedby an intra-molecular OW–HW bond length of 0.976 Aand a HW–HW distance of 1.540 A. Where the interactionsof the atomic sites on the molecule were specified by aseries of Lennard-Jones and Coulomb charge parameters [16]combined using the well known Lorentz–Berthelot mixingrules: εOW = 0.650 kJ mol−1, σOW = 3.166 A, qOW =

−0.8476e, εHW = 0.000 kJ mol−1, σHW = 0.000 A, qHW =

+0.4238e. The pure water reference model consists of 1800water molecules in a cubic box of side length 37.8 A,

Figure 2. The water oxygen to water oxygen partial pairdistribution function, gOWOW(r), derived from the EPSR model ofthe pure solvent shown in figure 1. The vertical lines show thedistance criteria used in the calculation of the OW–OW–OW triplet,including angle distribution functions.

corresponding to an atomic density of the sample of0.1 atoms A

−3.

The resulting model of the pure solvent system isreflected in the gOWOW(r) partial pair distribution functionthat is shown in figure 2. This shows the well known firstneighbour distance of 2.76 A between the oxygen atomsof neighbouring water molecules, and the second neighbourdistance of ≈4.25 A. These features are separated by thecharacteristic minimum at 3.4 A and the function integratesto show an average first shell coordination of 4.6 ± 1.0neighbours around each water molecule to this point, or acoordination of 3.0 ± 1.0 if one only integrates to rmax =

3.0 A.Aside from gOWOW(r), the EPSR model allows us to

investigate the OW–OW–OW included angle distributionfunction which reflects the triplet distribution of theneighbouring water molecules in the solvent network [17].If the solvent was formed from a perfectly tetrahedrallyconnected network of molecules, this function would beexpected to sharply peak at an angle of 109.47◦. Thedistribution is calculated based on a distance criterion inwhich atoms are considered to be a component of a tripletconfiguration if they fall within a specified range of molecularseparations. Figure 3 shows the results for this function basedon two criteria. The first only includes molecules that clearlyfall within the nearest first neighbour feature of gOWOW(r) :2.5 A ≤ r ≤ 3.0 A. The second evaluation includes slightlymore distant neighbours in the calculation by utilizing a rangeof molecular separations of 2.5 A ≤ r ≤ 3.4 A.

The comparison of these functions tells us that the nearestneighbour correlations between water molecules favour atriplet distribution with included angles peaking close to≈100◦, whilst if molecules slightly outside the immediatefirst shell of neighbours are included in the evaluation,the angular distribution function becomes flatter and thepresence of triplet correlations with much tighter included

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J. Phys.: Condens. Matter 25 (2013) 454213 D T Bowron and S D Moreno

Figure 3. The OW–OW–OW included angle triplet distributionfunction derived from the EPSR model of the pure solvent shown infigure 1. The solid black line shows the function in which wateroxygen atoms are considered to be part of a triplet if they areseparated by a distance in the range 2.5 A ≤ r ≤ 3.0 A, and thebroken red line the function using a more relaxed criterion of2.5 A ≤ r ≤ 3.4 A for deciding whether a pair of neighbouringwater molecules are associated.

angle correlations centred around 54◦ become evident witha concomitant shift in the mode of the distribution functionto ≈95◦. Taken together with the coordination numberinformation from gOWOW(r), these functions tell us that inthe liquid state the nearest neighbour interactions reflect asolvent connectivity that loosely approximates to a tetrahedralnetwork where the included angle would be ∼109◦, but thatthe disorder and configurational flexibility in the underlyingnetwork rapidly increases as one moves away from the closestmolecular contacts.

3. Solvent structure in the ionic solutions

Having established the baseline structure of the pure solvent,we can now turn our attention to the solvent structurecorrelations in the ionic solutions. In the following sectionthe discussion is centred on the effect of solute cations on thestructure of the water network. This is because the cations aredirectly solvated by the water oxygen atoms and thus have thestrongest perturbation on the pair and triplet angle correlationsunder discussion (gOWOW(r) and OW–OW–OW). Anions aresolvated by the hydrogen atoms on the water molecules andconsequently do not have the marked ability of the cations tomaintain distinct geometric hydration shell structures, as thehydrogen linkage allows for a marked degree of orientationalflexibility in the ion–water correlations. Each ionic solutionstructure refinement was performed using a cubic simulationbox with periodic boundary conditions, using a box sidelength of ≈32 A, and containing ≈1000 water molecules.See [2–5] for precise details. Figure 4 compares the gOWOW(r)pair distribution functions from the five solutions investigatedwith the baseline pure water.

The EPSR models for all systems except for the 1 mLaCl3 solution, result in the first peak in gOWOW(r) at

Figure 4. The water oxygen to water oxygen partial pairdistribution function, gOWOW(r), derived from the EPSR models ofpure water and the ionic solutions of Cu(ClO4)2,Cr(NO3)3, YCl3and LaCl3. Each subsequent distribution function is vertically offsetby 1.0 units.

a position of 2.76 A ± 0.02 A which is the estimatedaccuracy that can be expected for distance determination.In the LaCl3, this peak is slightly shifted to a value of2.82 A, and the peak itself is generally broader in extent. Thenext noticeable feature is the reduction in the depth of thecharacteristic minimum between the first and second shells ofwater molecules and the associated change in definition of thesecond neighbour peak itself. In the trivalent cation solutionsthere is also a clear feature that moves to longer distances overthe series Cr3+ (3.94 A) to Y3+ (4.43 A) to La3+ (4.66 A),and which corresponds to well defined correlations betweenwater molecules across the highly structured first hydrationshells of these cations, reflecting the cation’s increasing ionicradii ∼0.7 A,∼0.9 A and ∼1.1 A respectively. Althoughnot seen in the Cu2+ system, due to the complex range ofhydration shell structures [5–9], such features are not justthe preserve of the trivalent cations as they have also beenobserved in Mg2+ and Ca2+ systems [18]. These divalentspecies also have highly structured first hydration shells ofoctahedral and square antiprism forms respectively [18], anda comparison allows us to note the effect of the cation chargeon the relative positions of these features given the similarityof the ionic radii of the divalent species, ∼0.7 A (Mg2+) and∼1.0 A (Ca2+), to the size of the Cr3+ and La3+ cations. Thiscomparison shows that the reduced charge has resulted in thelonger distance feature moving to slightly greater distances by∼0.2 A and∼0.05 A respectively, compared to the features ofthe similarly sized but more highly charged trivalent species.This is consistent with the reduced electrostatic attractionbetween the divalent cations and the negatively polarizedwater oxygen atoms, although it is important to remember thatchanges in the ion hydration shell geometry will also play arole e.g. square antiprism for Ca2+ versus tricapped trigonalprism for La3+.

Table 1 shows the first shell coordination numbers thatcan be compared with the previously quoted values for purewater (3.0 ± 1.0 and 4.6 ± 1.0). This shows that in the 0.5 m

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J. Phys.: Condens. Matter 25 (2013) 454213 D T Bowron and S D Moreno

Table 1. First shell coordination numbers for gOWOW(r) for aqueous solutions of Cu(ClO4)2,Cr(NO3)3, YCl3 and LaCl3 evaluated forrmax = 3.0 and 3.4 A. The quoted error is indicative of the range of coordination sites found in a discrete analysis of sites in the EPSRmodel structures as opposed to the statistical error on the quoted mean value.

Solution C.N. rmax = 3.0 A atoms C.N. rmax = 3.4 A atoms

0.5 m Cu(ClO4)2 3.0 ± 1.0 4.7 ± 1.02.0 m Cu(ClO4)2 3.2 ± 1.0 5.1 ± 1.01.0 m Cr(NO3)3 3.0 ± 1.0 4.6 ± 1.01.0 m YCl3 3.2 ± 1.0 4.8 ± 1.01.0 m LaCl3 3.2 ± 1.0 5.1 ± 1.0

Figure 5. The OW–OW–OW included angle triplet distributionfunctions derived from the EPSR models of pure water and the ionicsolutions of Cu(ClO4)2,Cr(NO3)3, YCl3 and LaCl3. The functionshave been calculated for the distance criterion in which wateroxygen atoms are considered to be part of a triplet if they areseparated by a distance in the range 2.5 A ≤ r ≤ 3.0 A. Eachfunction has been vertically offset by 0.01 units for clarity.

Cu(ClO4)2, 1.0 m Cr(NO3)3 and 1.0 m YCl3 solutions thewater structure appears to very similar to the pure solvent,but in the 2.0 m Cu(ClO4)2 and 1.0 m LaCl3 solutions thereis an apparent increase in local density, packing a few moremolecules into the distance range 3.0 A < r ≤ 3.4 A.

Figure 5 shows how the triplet correlations between watermolecules are affected by the presence of the electrolytesin the nearest neighbour region, whilst figure 6 shows thefunctions if the slightly more distant triplet correlations areincluded. An immediate observation, most obviously visiblein the nearest neighbour triplet analysis, is that the presenceof the investigated electrolytes appears to increase the numberof tighter angular correlations evident in the near-neighboursolvent water environment with a peak appearing at ≈60◦ inthe distribution functions. A comparison with figure 6 showsthat these features are not due to the slightly more distantwater correlations that produce the ≈54◦ feature shown infigure 3, but instead were found to correspond to correlationsbetween water molecules in the ion’s first hydration shells.This explanation also accounts for the marked higher anglefeatures in the triplet angle distributions for the trivalent cationsystems, Cr3+ (≈90◦), Y3+ (≈103◦) and La3+ (≈108◦).

It is interesting to note that the higher angle feature alsoprovides an alternative fingerprint for the preferred geometry

Figure 6. The OW–OW–OW included angle triplet distributionfunctions derived from the EPSR models of pure water and the ionicsolutions of Cu(ClO4)2,Cr(NO3)3, YCl3 and LaCl3. The functionshave been calculated for the distance criterion in which wateroxygen atoms are considered to be part of a triplet if they areseparated by a distance in the range 2.5 A ≤ r ≤ 3.4 A. Eachfunction has been vertically offset by 0.01 units for clarity.

of the cation hydration shell to the OW-cation-OW angledistribution functions [2–4] as the observed angles correspondto preferred included angles in shells of octahedral, squareantiprismatic and tricapped trigonal prismatic character forthe Cr3+, Y3+ and La3+ systems respectively, albeit with thewidths of these features allowing for a degree of disorder inthe shell and which is a particularly marked effect for the La3+

system.The Cu2+ system has a somewhat different effect on

the triplet correlations in the solvent. At the more diluteconcentration of 0.5 m, there is small increase in tighterangular correlations at ≈60◦, but the main effect of theelectrolyte is to move the mode of the distribution functionfrom ≈100◦ in the pure liquid to a value of ≈105◦. Thistells us that the ions in the solution are enhancing the nearneighbour tetrahedral distribution of the water molecules.As the concentration of the ions is increased to 2.0 m, thisbehaviour is reversed and modal value of the distributiondrops to ≈95◦.

The findings of the detailed study of the Cu(ClO4)2system established the importance of tetrahedral correlationsin the system [5], both for the cation, but also for theClO−4 anion, and this inherently compatible geometry with

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J. Phys.: Condens. Matter 25 (2013) 454213 D T Bowron and S D Moreno

the solvent matrix probably explains why the triplet angledistribution functions are more similar to those found for thepure liquid.

4. Conclusions

Clearly the EPSR models of the investigated solutions showthat di- and trivalent ions have a very marked effect upon thesolvent water network, both in terms of the OW–OW pairdistribution function, but also in the OW–OW–OW tripletangle correlations. In the nearest neighbour environment thesolvent molecules manage to maintain a close to tetrahedralorder in their correlations, as shown by the first peak ingOWOW(r) and the corresponding coordination numbers, butbeyond this, the ions induce many marked changes to thelonger range order.

The loss of the clear minimum in gOWOW(r) at ≈3.4 Atells us that the ions change the organization of the watermolecule correlations in the distance range that would fallbetween the first and second shells in the pure liquid.

The investigated series of 1.0 m trivalent cationsolutions show that the well defined geometry of theirimmediate hydration shells could be ‘fingerprinted’ viathe OW–OW–OW triplet, included angle distributions. Thissuggests an alternative means to elucidating characteristicsof this kind to the traditional geometry probes of thelocal ion environments such as x-ray absorption near edgestructure (XANES) spectroscopy [19]. This is provided thatthe analysis is weighted towards the nearest neighbourwater oxygen correlations, as the underlying configurationalnetwork flexibility of the solvent rapidly begins to dominate ifcorrelations at distances beyond the immediate first neighbourenvironment are included in the triplet analysis.

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