Diffraction and Molecular Dynamics Simulation Study - American

4054

J. Phys. Chem. B 2009, 113, 4054–4064

Solution Structure of NaNO3 in Water: Diffraction and Molecular Dynamics Simulation Study† Tu¨nde Megyes,*,‡ Szabolcs Ba´lint,*,‡ Emanuel Peter,§ Tama´s Gro´sz,‡ Imre Bako´,‡ Hartmut Krienke,§ and Marie-Claire Bellissent-Funel| Institute of Structural Chemistry, Chemical Research Center of the Hungarian Academy of Sciences, Pusztaszeri u. 59-67, H-1025 Budapest, Hungary, Institute of Physical and Theoretical Chemistry, UniVersity of Regensburg, D-93040 Regensburg, Germany, and Laboratoire Leon Brillouin (CEA-CNRS), CEN-Saclay, 91191 Gif-sur-YVette Cedex, France ReceiVed: July 21, 2008; ReVised Manuscript ReceiVed: NoVember 3, 2008

The structure of a series of aqueous sodium nitrate solutions (1.9-7.6 M) was studied using a combination of experimental and theoretical methods. The results obtained from diffraction (X-ray, neutron) and molecular dynamics simulation have been compared and the capabilities and limitations of the methods in describing solution structure are discussed. For the solutions studied, diffraction methods were found to perform very well in description of hydration spheres of the sodium ion but do not yield detailed structural information on the anion’s hydration structure. Molecular dynamics simulations proved to be a suitable tool in the detailed interpretation of the hydration sphere of ions, ion pair formation, and bulk structure of solutions. 1. Introduction Alkali ion solutions have important role in solution chemistry, biochemistry, and pharmacology and therefore are especially interesting in the study of aqueous electrolyte solutions. Knowledge of their solution structure is central to understanding the transport properties of ions,1 the ionic permeability of organic structures such as biological membranes,2 and the efficacy of ions in precipitating, or salting-out, proteins from aqueous solutions.3 A comprehensive report4 summarizes the experimental studies, X-ray and neutron diffraction, EXAFS, and NMR, as well as traditional computer simulation results on the structure and dynamics of hydrated ions until 1993. These results account for an uncertainty as far as hydration number of Na+ is concerned, placing it between 4 and 85-9 and the general concept of sodium being a “loosely hydrated” ion is described. The first neighbor distance rNa-H2O is estimated to be between 2.4 and 2.5 Å from experiments, but computer simulations suggest shorter values, varying from 2.24 to 2.37 Å.10,11 Second hydration shell around the sodium ion in aqueous solution is also described but with even greater ambiguity. Until a few years, ago neutron diffraction6,9 and X-ray scattering5,7,8,12 experiments were performed to study sodium ion hydration in various sodium salt solutions. Recently a joint X-ray diffraction and simulation study performed on sodium hydroxide solutions in a wide concentration range (2.5-19.2 mol · dm-3) resulted in rNa-H2O ≈ 2.43, and the water coordination number decreases with increase in concentration from 5.4 to 4.3.13 The nature of NO3--H2O interactions in aqueous solutions and at interfaces is of prime importance in many fields including areas as diverse as atmospheric chemistry and nuclear waste.14 Nitrate ion is one of the most abundant ionic species in the atmosphere as well as in acidic wastes.15 Being present in †

Part of the special section “Aqueous Solutions and Their Interfaces”. * To whom correspondence should be addressed. E-mail: (T.M.) [email protected]; (S.B.) [email protected]. ‡ Chemical Research Center of the Hungarian Academy of Sciences. § University of Regensburg. | Laboratoire Leon Brillouin (CEA-CNRS).

atmospheric aerosols both in the polluted and remote troposphere, nitrate ions are involved in a variety of atmospheric chemical processes.16 For a long time, the hydration structure of the nitrate ion was an attractive subject in the solution chemistry. The nitrate ion has been classified as the “orderdestroying” anion in hydrogen-bonded liquid water, owing to its large ionic size and relatively small charge.17 The hydration number of nitrate in an aqueous NaNO3 solution has been reported to be 0.5 from NMR measurements18 indicating a very weak direct coordination of water molecules to nitrate in the solution. A double-difference infrared spectroscopic study on Ni(NO3)2 solution shows a wide distribution of nitrate-water distances,19 and the hydration number of nitrate has been estimated to be 3.7. Recent spectroscopic studies20 have found that distinctly different shifts of IR bands are observed in the hydrated clusters of nitrate for different kinds of bonding environments of O-H and NdO stretching modes compared to isolated water and nitrate anion. Further on, the nitrate ion becomes less planar and the N-O bond lengths are no longer equivalent.21 The hydration structure of NO3- has been investigated by X-ray diffraction for concentrated NH4NO3 and NaNO3 aqueous solutions.8,22 However, it is rather difficult to deduce the hydration structure of NO3- from the X-ray diffraction data alone, because several interatomic correlations overlap in the range of the radial distance, where the nitratewater correlation should appear. Despite the difficulties, very reliable estimation was obtained for nitrate-water correlation parameters on the basis of X-ray diffraction measurements. Enderby et al. in their neutron diffraction study of NaNO3 solution applying the 14N/15N isotopic substitution technique revealed the presence of strong hydrogen bond between N and D atoms in the NaNO3 aqueous solution.23 However, a later neutron diffraction study on concentrated ND4NO3 and LiNO3 solution gives no indication of the pronounced first peak, as a proof of the strong hydrogen bond, concluding that there still remain some unclear structure features in the hydration structure of NO3- in an aqueous solution.24 Recently neutron diffraction experiments with isotopic substitution (NDIS) and molecular

10.1021/jp806411c CCC: $40.75  2009 American Chemical Society Published on Web 02/20/2009

Solution Structure of NaNO3 in Water

J. Phys. Chem. B, Vol. 113, No. 13, 2009 4055

TABLE 1: Physical Properties of NaNO3 Solutions Studied: Salt Concentration c, Mass Density G, Linear X-ray Absorption Coefficient µ, and Atomic Number Density G0 sample name

c (mol · dm-3)

F (g · cm-3)

µ (cm-1)

F0 (10-24 cm-3)

NaNO3/H2O

A B C D

1.875 2.500 5.630 7.504

1.099 1.210 1.303 1.377

1.248 1.296 1.623 1.787

0.0999 0.0985 0.0993 0.0967

1:27.84 1:20.15 1:8.09 1:5.44

dynamics simulations have been used to study the structuring of cesium carbonate and cesium nitrate in aqueous solution.25 It has been found that stronger hydrogen bonds are formed between the water molecules and the carbonate ions than those formed to the nitrate ions, causing differences in the clustering properties of the two solutions. The structure of aqueous clusters of sodium26-28 and nitrate20,29,30 ions has been the target of computational studies by quantum mechanical (QM) methods. The calculations showed that stable, probably highly symmetric Na-water clusters are formed with up to eight water molecules. The given number of water molecules around a sodium ion can be arranged in different, closely isoenergetic configurations, depending on the positions of the water molecules in the first or second shell of the sodium ion. These configurations are results of competing sodium-water and water-water interactions. The main conclusion from quantum mechanical calculations on nitrate hydration are the following: three different types of arrangements, namely, symmetrical double hydrogen bonding, single hydrogen bonding, and interwater hydrogen bonding are obtained in these hydrated clusters. A structure having interwater hydrogen bonding is more stable compared to other arrangements. Up to five water molecules can stay around the nitrate anion in structures having an interwater hydrogen-bonded cyclic network. Solvation of sodium and nitrate ions has been studied by classical molecular dynamics,5,10-12,51,31 QM/MM,32,33 Monte Carlo,34,52 and ab initio molecular dynamics simulation methods.35,36 These studies were performed mostly in very diluted solutions. The main conclusions of these studies are that the anion forms a distinct but very loosely bound first hydration shell, based on weak nitrate oxygen-water hydrogen bonds. The instability of this shell results in frequent exchanges of water molecules and causes a typical structure-breaking behavior of this ion in aqueous solution. Rather, the neighboring water molecules than hydrogen bonding to the anion define the orientation of the hydration shell around the anion. Studies in higher concentrated solutions were focusing on the description of the phenomena at air/water interfaces. With decreasing solution concentration, the ionic hydration number varies from 3.5 to 4.7 for anion. In order to gain a better insight into these problems, a new and systematic structural study performed by traditional solution chemistry methods of X-ray and neutron diffraction combined with molecular dynamics simulation over a series of moderately and highly concentrated solutions of sodium nitrate are reported in the present paper. Our aim was to monitor the structural changes in the solution and thus to reveal more detail on hydration, contact ion pairing, and solvent-separated ion pairing in sodium nitrate solutions as a function of concentration. 2. Details of the Experimental Study 2.1. X-ray Diffraction Measurement and Method of Structural Analysis. Concentrated NaNO3 stock solutions (ca. 7.6 M) were prepared from Millipore MilliQ water and a.r. grade NaNO3 (Aldrich, 99% purity). Solution series for the X-ray diffraction measurements were prepared by accurate gravimetric

TABLE 2: Box length, L, and Number of Sodium and Nitrate Ions and Water Molecules Used in the Molecular Dynamics Simulations sample

L (Å)

Na+/NO3-

H2O

A B C D

31.606 30.883 28.668 27.467

36 45 92 94

984 898 601 500

TABLE 3: Intermolecular Potential Parameters for Water, Sodium, and Nitrate Anion Ow Hw Na N ON

ε (kJ/mol)

σ (Å)

q (e.u.)

0.650 0.000 0.360 0.837 0.649

3.165 0.000 2.730 3.900 3.154

-0.848 0.424 1.000 0.860 -0.620

dilution of the sodium-nitrate stock solution. The concentrations and densities of the solutions studied together with their acronyms, which will be used hereafter in the text, are shown in Table 1. The X-ray scattering measurements were performed at room temperature (24 ( 1 °C) with a Philips X’Pert goniometer in a vertical Bragg-Brentano geometry with a pyrographite monochromator in the scattered beam and proportional detector using Mo KR radiation (λ ) 0.7107 Å). Quartz capillaries (1.5 mm diameter, 0.01 mm wall thickness) were used as the liquid sample holder. The scattering angle range of measurement spanned over 1.28 e 2Θ e 130.2° corresponding to a range of 0.2Å-1 e k e 16.06 Å-1 of the scattering variable k ) (4π/ λ)sin Θ. Over 100 000 counts were collected at each angle in ∆k ≈ 0.05 Å-1 steps. Background and absorption corrections were applied based on an algorithm reported by Paalman and Pings37 for cylindrical sample holders. This algorithm assumes that significant coupling does not occur between the sample and cell,38 therefore the experimentally observed intensities are considered as linear combination of an independent component from the confined sample and a component from the sample cell. The correction procedure was applied using in house software written in a Fortran language. The polarization and Compton scattering corrections were applied using standard methods given in earlier works.39 The experimental structure function, h(k), is defined as

h(k) ) [I(k) -

∑ xRf2R(k)]/M(k)

(1)

R

where I(k) is the corrected coherent intensity of the scattered beam normalized to electron units;40 fR(k) and xR are the scattering amplitude and mole fraction for an R-notated particle, respectively; M(k) is the modification function, [ΣxRfR(k)]2. The coherent scattering amplitudes were calculated as previously described.39 The sodium nitrate molecules were treated in atomic

4056 J. Phys. Chem. B, Vol. 113, No. 13, 2009

Megyes et al.

Figure 1. Comparison of structure functions h(k) multiplied by k (a) and radial distribution functions (b) for sodium nitrate solutions obtained from X-ray diffraction (open circles) and molecular dynamics simulations (solid line).

representation, and the necessary parameters were taken from the International Tables for X-ray Crystallography.41 The experimental radial distribution function (RDF) was computed from the structure function h(k) by Fourier transformation according to eq 2

g(r) ) 1 +

1 2π2rF0

∫kk

max

min

kh(k)sin(kr)dk

(2)

where r is the interatomic distance, kmin and kmax are the lower and upper limits of the experimental data, and F0 is the atomic number density. After repeated Fourier transformations, the nonphysical peaks present in the g(r) at small r values were removed, and the structure function was corrected for residual systematic errors.42 In order to characterize the structure of the solution, as a first step a visual evaluation and a preliminary semiquantitative analysis of the observed structure functions kh(k) and RDF g(r) were performed. Further on, the observed data were analyzed by geometrical model constructions and fitting the model structure functions to the corresponding experimental ones by

the nonlinear least-squares method. The fitting strategy was previously described in ref 39. 2.2. Neutron Diffraction Measurement and Method of Structural Analysis. Neutron scattering patterns were obtained from 7C2 diffractometer of the Laboratoire Leo´n Brillouin CEASACLAY in a range of 0.3 e k e 15.3Å-1. The solutions were prepared by direct dissolution of the salts in heavy-water. The concentrations of the solutions were the same as those studied by X-ray diffraction (Table 1). The samples were kept in a cylindrical vanadium container with 6 mm diameter and 0.1 mm wall thickness. The incident neutron wavelength was 0.70 Å. For standard corrections and normalization procedures, additional runs (vanadium bar, cadmium bar, empty container and background) were also performed. The raw diffraction data were corrected for background, inelastic effects, container- and sample absorption, multiple scattering, and then the intensities were normalized, by using scattering data on a vanadium sample. The detailed description of the above-mentioned correction procedure can be found in the literature.43 All measurements were converted to absolute cross-section scale using a standard vanadium rod of 6.4 mm diameter after the usual corrections



for cell scattering, self-attenuation, multiple scattering, and Placzek effects.43b The conversion of the observed total cross section dσ/dω to an r-space representation was performed with the MCGR method44 (“Monte Carlo treatment of the experimental radial distribution function”). In this method, the radial distribution functions, either total or partial, are generated numerically and modified by a stepwise random Monte Carlo process until its inverse Fourier transform agrees with the experimentally scattering cross section within the limits of experimental error. 3. Computational Details 3.1. Molecular Dynamics Simulation. A classical molecular dynamics (MD) simulation has been performed in the NVT canonical ensemble at 300 K temperature. The simulation parameters are listed in Table 2. Cross terms were calculated using Lorentz-Berthelot combining rules. The rigid SPC/E potential model was applied to water.45 The ion-ion and ion-water short-range interactions were represented by Lennard-Jones potentials shown in Table 3.46 During the 600 000 time steps of equilibration, the Nose´-Hoover thermostat was used to control the temperature. The simulation was performed by the DLPOLY 2.15 software47 for 2 000 000 time steps leading to the total simulation time of 2 ns. 3.2. Comparison of Simulations and Diffraction Experiments. The RDFs obtained from the diffraction experiments are compared with those obtained from simulation. The part of total structure function, which is relevant to the liquid structure (without intramolecular contribution) has been calculated from the partial RDFs according to the equation

H(k) )

∑∑

Rgβ

(2 - δRβ)xRxβfRfβhRβ(k) M(k)

(3)

where fR is the scattering length of the R-type atom (the equivalent quantity denoted by bR in the case of neutron diffraction is independent of momentum transfer k unlike the scattering length of X-ray diffraction), and xR is the mole fraction of the R atom. hRβ(k) is defined according to the following equation:

hRβ(k) ) 4πF

∫0r

max

r2(gRβ(r) - 1)

sin(kr) dr kr

(4)

The total RDF is defined as the Fourier transform of the structure function. 4. Results and Discussion 4.1. X-ray and Neutron Diffraction Results. The experimental structure functions obtained from X-ray diffraction (XD) (Figure 1a) exhibit systematic variations across the solution series measured. The appearance of the first double peak in the range of 1.1-3.8 Å-1 is a typical structural feature in water and aqueous solutions, and it is associated with the extended hydrogen-bonded network in the liquids. It is well known that the shape of the second peak (∼5 Å-1) is particularly sensitive to the degree of disruption of the hydrogen bonding. Other factors such as differences in cationic radii may have similar effects because the structure function is a sum of interfering waves, each originating from different contributions of the component species. However, we are looking for changes, which can be clearly assigned to specific structural or composition

TABLE 4: Structural Parameters from the X-Ray Diffraction Refinement with Estimated Errors in the Last Digitsa bond type Na · · · Ow

Na · · · N O w · · · Ow

A B C D C D A B C D

r

σ

n

2.44(2) 2.44(1) 2.45(1) 2.45(2) 3.50(2) 3.49(1) 2.85(2) 2.80(2) 2.82(2) 2.85(3)

0.15(1) 0.15(1) 0.15(1) 0.15(2) 0.13(2) 0.09(2) 0.20(1) 0.20(1) 0.20(2) 0.20(2)

5.65(10) 5.35(10) 4.45(10) 4.10(9) 1.35(10) 2.10(10) 3.83(10) 3.45(9) 3.20(9) 2.50(10)

a n is the coordination number. Distances (r) and their mean-square deviations (σ) are given in Å. Superscript w refers to water.

dependent factors in the present solution series. Thus, the increasing concentration of sodium ions in the solutions causes a broadening and shift of the second peak and at the same time, the emergence and broadening of the fourth and fifth peaks. This means, in other words, that the sodium containing structural units in the system gradually and strongly distort the original water structure. At first a semiquantitative structural analysis was performed at the level of the RDFs (Figure 1b). As a second step, the leastsquares fitting method was used to determine both the intraand the intermolecular structural parameters. After examination of the weights of the contributions to the structure function one contribution for each type of interatomic distances listed in Table 4 was introduced in the fitting procedure. Some changes in the interesting structure features are displayed more plausible on the RDFs shown in Figure 1b than on the corresponding structure functions of Figure 1a. For information here we give the notations as used in the remaining part of the article. Thus, subscript w means the oxygen or hydrogen originating from water molecules, N is for the same elements in the nitrate group, and unmarked elements are either from water or NO3- ions. The peak centered around 2.85 Å obviously corresponds to the hydrogen-bonded first neighbor distances.48 A broadening of this peak with substantial decrease in height and a significant shift in the peak position up to 3.05 Å can be observed. The reason of this shift is the emergence of the Na · · · N (∼3.5 Å) and N · · · Ow (∼3.7 Å) contributions with increase of the salt concentration, which appears like a shoulder at 3.6 Å at high concentrations. Further on, a shoulder appears at 2.4 Å on the left side of the first peak. The most likely reason for this change is that a contribution of Na · · · O interaction appears around 2.4 Å.4,8,13 Thus the main peak includes contributions of the shorter Na · · · O distances and the longer Ow · · · Ow, and the effect of Na · · · N and N · · · Ow interactions also appear. Accordingly, with an increase in concentration the Na · · · O contribution becomes more and more significant and the Ow · · · Ow contribution gradually disappears, leading to the separation of the two peaks. A gradual structural rearrangement can also be observed in the range of longer distances, between 3.7-5.3 Å. It is not possible to assign these changes to one or two pair contributions only. This longer-range structure replaces the broad minimum of pure water between 3.2 and 4.2 Å followed by a maximum around 4.2-5 Å. This is obviously due to a structural rearrangement, most probably the breakup of the longer-range


Megyes et al.

Figure 2. Radial distribution functions for sodium nitrate solutions obtained from neutron diffraction experiment (total, intermolecular, and intramolecular part of the total radial distribution function) (a) and comparison with molecular dynamics simulation (b).

structure of bulk water and a development of a more compact, shorter-range local order in the more concentrated electrolyte solutions. This phenomenon has been analyzed quantitatively. The structural parameters obtained from the least-squares fit of the structure functions kh(k) shown in Figure 1a are given in Table 4. The fitting procedure resulted in values of 2.44-2.45 Å for the intermolecular Na · · · Ow distances. The sodium ions are coordinated by 4.10-5.65 water molecules, which is in agreement with earlier findings.4,13 The decrease of the coordination number with increasing concentration is not so drastic as one could expect on the basis of stoichiometric arguments. Considering that the NaNO3/H2O ratio decreases from ca. 1:28 to ca. 1:5, it is obvious that these “high” coordination numbers can be achieved only if some water molecules are shared between the hydration spheres of the sodium ions. Description of Na · · · N distances was possible only for the highly concentrated solutions, because of their low contribution to the total scattering picture. In the most concentrated solutions, the Na · · · N distance was found to be 3.50 Å. In the most concentrated solution, the coordination number is around 2, meaning that contact ion pairs appear only in highly concentrated solutions. The Ow · · · Ow distance was found to be between 2.80-2.85 Å. A decrease of water-water coordination number can be observed with increase in concentration, showing that the hydrogen-bonded structure of the bulk water is gradually destroyed as the salt concentration grows. Owing to their small contribution to the total scattering picture in low concentrated solutions, N · · · Ow intermolecular interactions were not possible to be determined. There are many contributions convoluted at the same distance. Consequently, those with lower weights are not possible to be resolved. Unfortunately, it is not possible to describe quantitatively these interactions on the basis of X-ray diffraction measurements because the corresponding peak is rather broad and blurred. Figure 2a shows the radial distribution functions obtained from neutron diffraction (ND) experiments. The first peak is centered around 1 Å corresponding to the Ow-H and N-ON intramolecular distances. The next peak at 1.55 Å appears due to H · · · H intermolecular contribution and Ow · · · H intermolecular

contributions. From the fitting of structure functions it has been obtained that the Ow · · · H (0.98 ( 0.02) and H · · · H (1.55 ( 0.03) intramolecular distances do not change with increase in salt concentration. On the contrary, the N-ON distance was found to be shifted up from 1.21 ( 0.02 to 1.24 ( 0.02, because of the ion-ion ordering signatures with increase in the salt concentration. Other intermolecular contributions were not possible to be determined from the neutron diffraction experiments due to their small contribution to the total scattering picture. Furthermore there are a lot of interactions contributing to the same distance. The total structural modeling of the NaNO3 solutions can only be performed with simultaneous evaluation of diffraction and molecular dynamics simulation data. For this reason, we have compared the structure functions (Figure 1a) and radial distribution functions (Figure 1b, 2b) obtained from diffraction experiments and calculated from molecular dynamics simulations. 4.2. Results from Molecular Dynamics Simulation. Figures 1b and 2b show the total radial distribution functions RDFs for each concentration obtained from simulation and diffraction experiments. Comparing the XD and MD RDFs, it can be observed that the position and height of the main peak at lower concentration (samples A and B) agree very well and the changes in the range between 3.0-5.7 Å are well reproduced. For the samples at higher concentrations, a significant difference can be observed in the range of 3.0-5.7 Å, which arises from correlations between the anion oxygen atoms and those in water as well as from cation-anion correlations. The source of this discrepancy is unclear but it may arise from errors in the MD representation of the nitrate-water interaction using a nonpolarizable point charge model. However, these inaccuracies do not prevent the MD simulations from investigating of tendency of ion pair formation and tracking of water-water correlation with increase in salt concentration. From Figure 2b, it can be concluded that the agreement of MD and ND RDFs is fairly good. However, it should be taken into consideration that the contributions of anion-water and anion-cation correlation to the total neutron scattering picture are very low, hence it is difficult to describe the discrepancies



Figure 3. Partial radial distribution functions obtained from molecular dynamics simulation for sodium nitrate solutions. Subscripts w and N refer to water and nitrate, respectively. The notations of both figures are the same.

possibly caused. In the lowest concentrated solution the contribution of the water-water correlations to the total scattering picture is 88%, and even in the most concentrated solution it amounts 60%. The structures of the solutions were analyzed in terms of RDFs, denoted as gRβ(r), for the various atom-atom pairs. The corresponding running integration numbers nRβ(r) are defined by

nRβ(r) ) 4πFβ

∫0r gRβ(r)r2dr

(5)

The value of this integral up to the first minimum (rm1) in g(r) is equal to the number of coordinating atoms of type β around atoms of type R and Fβ is the number density of the atoms of type β. The molecular dynamics simulation yields individual pair distribution functions for each of these interactions and thus can be employed to get an insight into the arrangement of the molecules in the solution. The RDFs of the solutions obtained from MD simulations are presented in Figure 3a,b, and the characteristic values of RDFs obtained are given in Table 5.

Examining the Na · · · Ow RDFs, a slight decrease of the first peak can be observed with increasing concentration, due to the decrease in the coordination number from 5.7 to 4.0. This is in agreement with XD results. The broad peak around 4-5 Å corresponds to the second hydration sphere of the sodium ion. From MD simulations a slight decrease in the Na · · · Ow coordination number from 13.3 to 9.9 can be observed in the second hydration shell. Figure 4, upper panel, shows the coordination number distribution of water molecules around sodium ion, and it reveals that the sodium ion is coordinated preferably by 5 or 6 oxygen atoms in lower concentrated solutions. Three- and fourcoordinated sodium ion appears mostly in the more concentrated solutions; coordination numbers higher than 6 are more frequently present in the less concentrated ones. It is interesting to analyze the concentration dependence of the total coordination number of the sodium ion. Figure 5 shows the total coordination number nNa-O in the solvation shell of sodium ions with oxygen atoms as well as the specific ones with oxygen atoms belonging either to water or nitrate. It is worth noting that the Na · · · Otot total coordination number including oxygen atoms both from water molecules and


Megyes et al.

TABLE 5: Characteristic Values for the Radial Distribution Functions grβ(r)a bond type

sample

rmax

gRβ(rmax)

rmin

nRβ(rmin)

Na · · · Ow

A B C D A B C D A B C D A B C D A B C D A B C D

2.43

7.66 7.57 7.30 6.84 3.73 5.25 5.15 5.75 2.26 2.30 2.45 2.49 4.32 4.78 5.08 5.35 2.66 2.58 2.30 2.20 1.61 1.54 1.53 1.43

3.50

5.68 5.45 4.65 4.05 0.50 0.75 1.77 2.56 11.20 11.30 10.88 10.20 0.39 0.60 1.42 2.02 3.79 3.71 3.24 2.62 2.98 2.98 2.87 2.67

Na · · · ON

N · · · Ow

Na · · · N

Ow · · · Ow

ON · · · Ow

2.43

3.73

3.48

2.78

2.83

3.50

4.50

4.10

3.50

3.28

a nRβ is the running integration number. Atom-atom distances are given in Å. Subscripts w and N refer to water and nitrate, respectively.

Figure 4. Coordination number distribution (P(n)) of water molecules around sodium (upper panel), nitrate around sodium ion (middle panel), and water around nitrate ion (lower panel) obtained from molecular dynamics simulation.

from nitrate ions slightly increases from 6.18 to 6.61. While the coordination number usually decreases with solute concentration,49 this behavior already observed in the case of sodium

Figure 5. Oxygen coordination numbers around sodium in the studied sodium nitrate solutions obtained from molecular dynamics simulation.

hydroxide solutions13 is rather uncommon. Figure 5 reveals that with an increase in concentration the Na-Ow coordination number slightly decreases but the Na-ON coordination increases considerably from 0.5 to 2.56. The total Na · · · Otot coordination number increases with increasing concentration most probably due to the formation of contact ion pairs in solution. Ion pairing can be observed in Figure 3a on both RDFs of Na · · · ON and Na · · · N. With increase in concentration, the peak height (Na · · · ON RDF) positioned at 2.43 Å increases due to the formation of contact ion pairs in the solutions. In solution A the coordination number of contact ion pairs was found to be 0.5 and increases with concentration to 2.65 as presented in Figure 4, middle panel. For the second broad peak (at 4.5 Å), partly the longer Na · · · ON distances in the contact ion pairs (oxygen atoms not directly bounded to the sodium ions) and partly the solvent separated ion pairs are responsible. On Na · · · N RDF, the first peak appears at 3.48 Å and corresponds to the sodium-nitrate contact ion pairs. The second peak at 5.43 Å can be assigned to the solvent-separated ion pairs formed in solution. The coordination number of solvent separated ion pairs increases with increase in concentration from 1.2 to 3.2. The first peak of N · · · Ow RDFs is centered around 3.7 Å and the increase in concentration leads to a slight decrease of coordination numbers around the nitrate ion from 11.2 to 10.2. Figure 4 lower panel presents the coordination number distribution of water molecules around the nitrate ions, showing the variation of coordination numbers described above. The first peak of Ow · · · Ow RDFs at 2.78 Å in Figure 3b decreases with increasing concentration and, simultaneously, a shoulder appears at 3.3 Å, caused by the Ow · · · Ow contribution from the first hydration sphere of the ions. In pure water, on the oxygen-oxygen RDF a characteristic second peak at 4.4 Å appears,50 which cannot be observed even in the case of the lowest concentrated A solution. This effect clearly indicates the loss of the tetrahedral coordination of water in the second hydration sphere of the water in all solutions. Also the Ow · · · Hw and ON · · · Hw RDFs are shown in Figure 3b. The position of first peaks (∼1.75 Å) is not changing, which clearly demonstrates that the intermolecular Ow · · · Hw distance does not change from solution A to D. A slight decrease in the height of the first peaks can be observed, indicating that the water structure is breaking up with increasing concentration. Figure 6 shows spatial distribution of the water neighbor molecules as well as sodium and nitrate ions in the first shell around the central water molecule in the origin of the reference


Figure 6. The spatial distribution of the water (gray), sodium (yellow), and nitrate (blue) ions around a central water molecule, when Ow · · · Ow < 3.5 Å, Ow · · · Na < 3.5 Å, Ow · · · N < 4.5 Å in the first hydration shell for solutions A (a) and D (b). (Contour levels for water, sodium, and nitrate ions are 2.50, 2.50, and 2.00, respectively.)

frame obtained from simulation of solutions A and D (Ow · · · Ow < 3.5 Å, Ow · · · Na < 3.5 Å, Ow · · · N < 4.5 Å). The tetrahedral coordination of liquid water is maintained as the concentration increases. The sodium ions (marked with orange color) appear in the direction of bisector of the angle between both lone pair directions of the water molecule at ∼2.4 Å distance. With the increase in concentration significantly higher, the probability of occurrence of sodium ions can be found. The blue isosurface of probability shows the regions where nitrate ions belonging to the first shell are likely to be found. Owing to contact ion pair formation, nitrate ions at high concentration appear with certain probability also in the H-O-H plane of the central water molecule in the opposite side with respect to the nitrate ions hydrogen bonded to the central water, owing to contact ion pair formation.


Figure 7. The spatial distribution of the water (gray) and sodium ions (yellow) around a central water molecule, in the first (Ow · · · Ow < 3.5 Å, Ow · · · Na < 3.5 Å) and second hydration shells (3.5 Å < Ow · · · Ow < 5.5 Å, 3.5 Å < Ow · · · Na < 5.5 Å) for solutions A (a) and D (b). (Contour levels of the first shell are defined in the caption of Figure 6 and for the second hydration shells of water and sodium ion are 1.50 and 1.50, respectively.)

The modifications in the second shell around the central water molecule are depicted in Figure 7 and 8. Figure 7 presents the spatial distribution of the water neighbor molecules and sodium ions in the first and second shell. The probability isosurfaces were obtained from simulation of solutions A and D, with limits of ranges Ow · · · Ow < 3.5 Å, Ow · · · Na < 3.5 Å, for the first shell and 3.5 Å < Ow · · · Ow < 5.5 Å, 3.5 Å < Ow · · · Na < 5.5 Å for the second shell. The water isosurface is gray, the sodium first and second spheres are marked with orange and yellow, respectively. It can be observed from both Figures 7 and 8 that with increase in concentration the slight tetrahedral orientation


Megyes et al.

Figure 9. The spatial distribution of the water (gray) and sodium ions (yellow) around a central nitrate ion, in the first hydration shell, when N · · · Ow < 4.5 Å and N · · · Na < 4.5 Å for solutions A (a) and D (b). (Contour levels for water and sodium ion are 2.50 and 2.10, respectively.) Figure 8. The spatial distribution of the water (gray) around a central water molecule, in the first (Ow · · · Ow < 3.5 Å) and second hydration shells (3.5 Å < Ow · · · Ow < 5.5 Å) for solutions A (a) and D (b). (Contour levels are defined in the captions of Figures 6 and 7.)

of water in the second shell completely disappears. Also the sodium second shell is rearranged, namely at high concentration sodium ions are likely found in the direction of the hydrogen atoms. Figure 9 presents the spatial distribution of water molecules and sodium ions around a central nitrate ion (limits of ranges: N · · · Ow < 4.5 Å and N · · · Na < 4.5 Å). The orange isosurface of probability identifies the regions where the sodium ions are likely found in the first sphere of nitrate ion, forming contact ion pairs. It can be clearly observed that at high concentration the isosurface of probability is denser supporting that the contact ion pair formation in highly concentrated solution is more

extended. Simultaneously the gray marked probability isosurface of water becomes narrower indicating that with the increase in concentration less water molecules are found in the hydration sphere of the nitrate ion. In spite of the known methodological limitation, that is, that both the experimental and modeling data contain systematic errors arising however from different sources, the comparison of data resulting from diffraction experiment and MD simulation proved to be sensitive and successful tool of collecting detailed information about ion-ion ordering in solution. Regarding the experimental methods, the X-ray and neutron diffraction applied simultaneously provide valuable complementary information about the investigated ionic solution for the X-ray and neutron scattering cross sections, that is, the weight of subsequent contributions of atom-atom correlations to the scattering function are different and therefore they are sensitive for

Solution Structure of NaNO3 in Water different components of complex total scattering function. Moreover, simulation and experimental results mutually corroborate each other because not only does the modeling support the conclusions that resulted from experimental data but also the quality of potentials used in MD simulation can be tested in this way. 5. Conclusions This is the first time when such a systematic work has been performed for NaNO3 solutions in a wide concentration range using a joint diffraction and molecular dynamics study. Besides the evaluation of the solution structure, the limitations of the methods applied are discussed. The agreement between the RDFs obtained by diffraction and the theoretical RDF is fairly good, meaning that the average picture of the structure of sodium nitrate solutions obtained by simulation is confirmed by X-ray and neutron diffraction. In the case of high concentrated solutions, significant difference can be observed in the range of 3.0-5.7 Å. The reason for this discrepancy is unclear, but it may arise from the description of correlations between the anion oxygen atoms and those in water as well as from cation-anion correlations using a nonpolarizable point charge model in the molecular dynamics simulation. The more detailed analysis of the partial RDFs casts a comprehensive and convincing picture about both sodium and nitrate ion solvation. The concentration effect of decreasing coordination numbers around sodium ions by increasing concentration is proven and even more, a building up of sodiumnitrate ion pairs is demonstrated, which probably would not be possible to find out without simulation. Beyond the description of solvation structure of ions, a detailed analysis of disruption of “bulk” water structure could also be given - an oftenneglected area of studies. Qualitative conclusions seem to be evident; hydrogen bonds of Ow · · · Ow types are breaking up and of Ow · · · ON types are building up. Acknowledgment. The research was supported by project NAP VENEUS08 OMFB-00650/2005 as well as HungarianGerman (HAS/DFG-185 and DFG 436UNG113/184/0-1) and Hungarian-French HAS/CNRS 21418 collaboration projects. The Hungarian Scientific Research Funds (OTKA) is also acknowledged (project number K 68140). References and Notes (1) Gurney, R. W. Ionic Processes in Solution; Dover: New York, 1953. (2) Cantor, C. R.; Schimmel, P. R. Biophysical Chemistry; W. H. Freeman and Company: New York, 1980. (3) Collins, K. D.; Washabaugh, M. W. Q. ReV. Biophys. 1985, 18, 323. (4) Ohtaki, H.; Radnai, T. Chem. ReV. 1993, 93 (3), 1157. (5) Pa´linka´s, G.; Radnai, T.; Hajdu, F. Z. Naturforsch. 1980, 35a, 107. (6) (a) Ohtomo, N.; Arakawa, K. Bull. Chem. Soc. Jpn. 1980, 53, 1789. (b) Maeda, M.; Ohtaki, H. Bull. Chem. Soc. Jpn. 1975, 48, 3755. (c) Caminiti, R.; Licheri, G.; Paschina, G.; Piccalugga, G.; Pinna, G. J. Chem. Phys. 1998, 72, 4522. (7) Radnai, T.; May, P. M.; Hefter, G. T.; Sipos, P. J. Phys. Chem. A 1998, 102, 7841. (8) (a) Neilson, G. W.; Adya, A. K.; Ansell, S. Annu. Rep. Prog. Chem., Sect. C 2002, 98, 273. (b) Botti, A.; Bruni, F.; Imberti, S.; Ricci, M. A.; Soper, A. K. J. Chem. Phys. 2004, 120, 10154. (c) Mancinelli, R.; Botti, A.; Bruni, F.; Ricci, M. A.; Soper, A. K. Phys. Chem. Chem. Phys. 2007, 9, 2959. (9) Kameda, Y.; Sugawara, K.; Usuki, T.; Uemura, O. Bull. Chem. Soc. Jpn. 1998, 71, 2769. (10) Jancso´, G.; Heinzinger, K.; Bopp, P. Z. Naturforsch. 1985, A40, 1235. (11) Schwendinger, M. G.; Rode, B. M. Chem. Phys. Lett. 1989, 155, 527. (12) Bouzazi, S.; Nasr, S.; Jaidane, N.; Bellisent-Funel, M. C. J. Phys. Chem. B 2006, 110, 23515.

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Diffraction and Molecular Dynamics Simulation Study - American

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