Aspects of Ion Hydration. Adiabatic Compressibility Compared to the

Article pubs.acs.org/JPCB

Aspects of Ion Hydration. Adiabatic Compressibility Compared to the Dielectric Properties of Aqueous Electrolyte Solutions Udo Kaatze* Drittes Physikalisches Institut, Georg-August-Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany ABSTRACT: Adiabatic compressibility data and principal dielectric relaxation times for aqueous solutions of 1:1 and 2:1 valent electrolytes are evaluated to yield their relative molal shifts Bκ and Bd, respectively, at low solute concentration. Cationic (Bx+) and anionic (Bx−) contributions to these quantities are calculated and compared to one another. For some ions also the correspondent relative molal shifts (B±m) in the intramolecular proton magnetic relaxation rates are considered. Clear correlations between B±κ and Bd± values are found for most series of ions. Within the series of halide ions, for example, B−κ increases, whereas B−d decreases with anion radius. For large hydrophobic cations the opposite is true; that is, B+κ increases and B+d decreases with molar volume of ion. In general, the magnitudes |B±k | in the changes of the compressibility coefficient are smaller than in the shifts of the dielectric relaxation time. The situation is more complicated with dielectrically saturated small ions. Since the apparently irrotationally bound water molecules around such ions do not contribute to the dielectric spectra by reorientation, comparison of compressibility changes with changes in the proton magnetic relaxation rate rather than in the dielectric relaxation time is more appropriate. Some composite ions, such as BF4−, show special features which can, however, be explained by a nonspherical charge distribution at the ion surface.

1. INTRODUCTION The properties of electrolyte aqueous solutions are relevant in basic research as well as in a wide range of applications, including chemical engineering and biological processes. Because of their outstanding importance the hydration properties of ions have been the focus of considerable scientific interest in the past decades. Nevertheless, our understanding of ion hydration is still imperfect in many respects. Hence the behavior of aqueous electrolyte continues to be the subject of a lively scientific debate.1 Besides computer simulation studies,2,3 sophisticated experimental methods are used to investigate the puzzling properties of ion hydration. Among those methods are broadband dielectric techniques,4−7 including terahertz spectroscopy,7 femtosecond infrared pump−probe spectroscopy,7,8 and two-dimensional infrared vibrational echo experiments,9,10 as well as large angle X-ray scattering and double difference infrared spectroscopy.11 The unique features of water, as liquid and solvent, are closely related to the ability of this small molecule to form up to four hydrogen bonds, generating extended, nearly tetrahedrally structured hydrogen-bond networks thereby. The Gibbs free hydrogen-bond energy (23 kJ/mol12) exceeds thermal energy (2.5 kJ/mol) at room temperature much less than the covalent bond energy 492 kJ/mol. As a consequence, the hydrogen network fluctuates rapidly. Hydrogen bonds weaken and strengthen continually, with correlation times on the order of 100 fs,13 so that the water structure can reform almost instantaneously by a correlated hydrogen-bond rearrangement. The high degree of plasticity of the hydrogen network and the resultant ability of water to widely correspond to solute © 2013 American Chemical Society

properties are doubtless essential factors in the unique position of water among liquids. But still today our knowledge of the rapid hydrogen network fluctuations is incomplete. The tetrahedral symmetry of the water hydrogen network is imperfect. Deviations from symmetry originate structure defects, exerting a noticeable influence on the molecular mobility in liquid water.13−16 It is the hope of liquid state physicists to infer features of the water structure and dynamics from solute-induced changes in the hydrogen-bond network. Over and above this aspect it is necessary to precisely know such changes for a proper assessment of solute effects in complex materials. An example is the ion contributions to the intriguing control system of living cells. The focus of this paper is the subnanometer hydration layers of predominantly monovalent ions. Evidence from adiabatic compressibility data and dielectric spectra of electrolyte solutions is summarized in order to combine effects in solution properties which reflect different factors of the water structure. Comparison will be particularly made between the limiting relative molal shifts Bκ = κS,w −1 lim (∂κS/∂m) m→0

(1)

and Bd = τw −1 lim (∂τs/∂m) m→0

(2)

Received: July 31, 2013 Revised: September 9, 2013 Published: September 16, 2013 12252

dx.doi.org/10.1021/jp407633c | J. Phys. Chem. B 2013, 117, 12252−12260

The Journal of Physical Chemistry B

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of the adiabatic compressibility κS and the principal dielectric relaxation time τs of electrolyte solutions. Here subscript “w” refers to the pure water values, respectively, and m denotes the molal concentration of solute. Bκ reflects in an obvious manner variations in the voluminous hydrogen network structure, whereas Bd is sensitive to changes in the network fluctuations. Hydration studies normally aim at two key physical quantities, the number Zh of hydration water molecules and the degree to which the parameters of these molecules, viz. the compressibility κS,h and relaxation time τh, respectively, are influenced by the solute. Such an approach implies already a simple hydration model, assuming only one kind of affected water. Even so, of course, two quantities, namely Zh and κS,h, of that water cannot derive from one measurand. In the evaluation of compressibility data κS,h = 0 is thus often presumed. Additionally neglecting small contributions from heat exchange and solute particle thermal motions to the adiabatic compressibility,17 the prominent Pasynski formula18−22 Z hκ = (c w /c)[1 − (κS/κS,w )]

φκ0,S = lim φκ ,S m→0

⎡ κS,w κs − κS,w ⎤ = lim ⎢ + κSφV ⎥ ⎥⎦ m → 0⎢ ⎣ ρw κS,wm ⎛ B0 ⎞ = κS,w ⎜⎜ κ ⎟⎟ + φV0 ⎝ ρw ⎠

of various electrolyte solutions relative molal shifts Bκ0 = φκ0,S/κS,w − φV0

(5) 25−36

are used to calculate the (6)

in addition to the data derived from solutions at higher solute content. In the above equations, ϕκ,S and ϕV are the apparent molar adiabatic compressibility and apparent molar volume, respectively, and ϕ0V is the limiting apparent molar volume. Since ϕ0κ,S and ϕ0V are additive in cation and anion contributions, relative molal shifts Bκ0 ± = φκ0,S±/κS,w − φV0 ±

(3)

(7)

have been assigned to the compressibility variations of − −8 individual ions. In doing so, ϕ0− κ,S (Cl , 25 °C) = 1.7 × 10 3 −1 −1 cm mol Pa has been assumed, as proposed by Mathieson + and Conway,28 and ϕ0V ± data39,40 based on ϕ0+ V (H , 25 °C) = 3 −1 −5.4 cm mol have been used. The approximate additivity of the individual ϕ0V ± values is demonstrated in Figure 1 by

is frequently applied to determine the number Zhκ of hydration water molecules from the compressibility κS. Here c and cw are the molar concentrations of the solute and solvent, respectively. The assumption of incompressible hydration shells may be questioned, not just with the water surrounding flexible molecules,23 but also with water neighboring medium sized and large ions. The attempt is therefore made to characterize effects in the compressibility by the linear coefficient in its variation with the molal concentration of solute (eq 1) and to compare the coefficient to the corresponding parameter of the dielectric relaxation time (eq 2). Ions in water are often referred to as “structure makers” and “structure breakers”1 or, somewhat more specifically, are considered to induce effects of “positive”, “negative”, and “hydrophobic” hydration.24 The main question to be tackled here is, whether or not these categories, which clearly show up in the dielectric spectra of aqueous electrolyte solutions, also appear in their compressibilities.

2. EXPERIMENTAL DATA

(4)

Figure 1. Limiting apparent molar compressibility data for aqueous solutions of alkali halides28−30,33,37 as a function of Pauling cationic radii38 r+. Points (●) indicate the mean considering the experimental uncertainties of the individual data (○). Lines are drawn to show the trend in the data.

the adiabatic compressibility κS = −V−1(∂V/∂p)S, with V denoting the molar volume and p denoting the hydrostatic pressure, is normally directly derived from the density ρ and sound velocity cs of the sample. Both ρ and cs can be measured with high precision so that small deviations from the water values ρw and csw are accessible to measurement. Compressibility data at solute concentrations down to millimoles per liter are thus available and extrapolation of such data to zero solute content (eq 1) can be compared to results from data at higher solute concentration. The availability of compressibility data at low solute concentrations is most beneficial for the exclusion of effects from any overlap of hydration regions which may occur at higher concentrations. In this paper, literature data for the limiting apparent molar compressibility

limiting molar compressibilities for aqueous solutions of alkali halides. For two series of electrolyte solutions the relative deviations of experimental compressibility data κS from the water value κSw are displayed as a function of solute molality m in Figure 2. At large m, due to overlaps of hydration regions, there exist indeed significant deviations from linear behavior. However, at m smaller than about 0.2 mol/kg, the experimental data nicely approach Bκm, with Bκ obtained from independent ϕ0κ,s determinations. 2.2. Dielectric Relaxation Time. In the microwave region hydrogen-bonded water molecules cannot instantaneously follow changes of an external electrical field. In harmonically alternating electrical fields the polarization of aqueous solutions thus becomes frequency dependent, and a phase shift between

2.1. Adiabatic Compressibility. Using the Newton− Laplace relation κS = ρ−1cs−2

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ε( ν ) = ε(∞ ) +

ε(0) − ε(∞) 1 + iωτw

(9)

with discrete relaxation time τw and with low-frequency (“static”) and extrapolated high-frequency permittivities ε(0) and ε(∞), respectively. As a common feature of aqueous solutions, the dielectric part εd(ν) = ε(ν) + iσ/(ε0ω) in the spectrum of the salt solution reveals an underlying relaxation time distribution. The related broadening of the spectrum is usually satisfied by an empirical relaxation spectral function, such as the Havriliak−Negami function49 εd(ν) = ε(∞) + Figure 2. Relative deviation of the adiabatic compressibility κS from the water value κS,w versus salt molality m for aqueous solutions of tetrabutylammonium bromide41 (○) and sodium chloride (closed symbols) at 25 °C. Dashed lines indicate the limiting behavior at small 0− m, as predicted from the relative molal shifts B0κ = B0+ κ + Bκ of compressibility data at low salt concentrations. Closed figure symbols discriminate between data from different sources: (▼) ref 30; (●) ref 42; (▲) ref 43; (■) ref 44.

ε(0) − ε(∞) [1 + (iωτs)(1 − h)](1 − b)

(10)

in which τs is a principal relaxation time and h as well as b (0 ≤ h, b < 1) are parameters controlling the width and shape of the relaxation time distribution function. The relaxation time τw of water at different temperatures45 had been obtained from fitting the Debye spectral function to experimental spectra. The relaxation times τs of aqueous solutions followed from a regression analysis of the corresponding spectra in terms of eq 10, in which often one of the distribution parameters can be omitted (h ≡ 0 or b ≡ 0). Principal dielectric relaxation times τs for a series of lithium chloride solutions are shown as a function of molal concentration m in Figure 4. Toward large concentrations the

the polarization and the field strength occurs. Both effects are considered by assuming the relative permittivity ε, providing the relation between the polarization and the field strength, to be frequency dependent and complex. In electrolyte solutions, in addition to the dielectric loss εd″(v), the dc conductivity σ adds another contribution to the loss, so that the total complex permittivity is given by ε(ν) = ε′(ν) − iε″(ν) = ε′(ν) − i[εd″(ν) + σ /(ε0ω)] (8)

Here ν is the frequency, ω = 2πν, i2 = −1, and ε0 denotes the electrical field constant. As examples the complex dielectric (permittivity) spectra of water and of an aqueous solution of sodium chloride are displayed in Figure 3. For the latter the negative imaginary part is shown in both formats, as total loss ε″d (v) and as dielectric contribution ε″d . Within the microwave region the dielectric spectrum of water can be well represented by a Debye-type relaxation function48

Figure 4. Relaxation time ratio τs/τw versus solute molality m for aqueous solutions of LiCl50,51 (●) at 25 °C. The dashed line shows the linear relation at small m, where overlaps of hydration regions may be neglected.

τs data exhibit a slight curvature. At m ≤ 1 mol/kg, however, a linear relationship exists so that the experimental data can be simply represented by τs/τw = Bdm. Ionic molal shifts B+d and B−d of the principal dielectric relaxation time have been calculated according to the additivity relation

m+ + m− − Bd + Bd (11) m m −1 Cl− assuming Bd = 0.01 (mol/kg) . This assumption has been derived51 from relative molal shifts of intramolecular proton magnetic relaxation rates of electrolyte solutions for which the anionic and cationic contributions are known separately.52 Bd =

3. RESULTS AND DISCUSSION 3.1. Hydrophobic Cations. In a recent study23 it has been shown that the Bκ and Bd data of aqueous solutions of hydrophobic solutes are correlated. With increasing hydrophobic character of solute the adiabatic compressibility decreases (Bκ < 0) and the dielectric relaxation time increases (Bd > 0). Hence there appears to be a denser structure of the

Figure 3. Real parts and negative imaginary parts (eq 8) of the complex permittivity spectra for water45,46 (●) and a 0.5 mol/L solution of NaCl in water (open symbols47) at 25 °C. For the electrolyte solution the total loss ε″(◊) and the dielectric part ε″d (□) in ε″ is shown. 12254



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is, with increasing number nC of methyl groups per ion, the B+κ values decrease and the B+d values increase. The relative increments |ΔB+x /ΔnC|, however, are much larger with the dielectric parameter (x = d) than with the compressibility coefficient (x = κ). For tetraalkylammonium ions the relative dielectric increment is ΔB+d /ΔnC = (0.056 ± 0.03)(mol/kg)−1, in nice agreement with the results for derivatives of the heterocyclic aromatic solutes pyrazine (ΔB+d /ΔnC = (0.06 ± 0.02)(mol/kg)−1) and quinoxaline (ΔBd+/ΔnC = (0.05 ± 0.02)(mol/kg)−1) as well as for derivatives of urea (ΔB+d /ΔnC = (0.045 ± 0.15)(mol/kg)−1).23 For the series of azoniaspiroalkane ions (ΔB+d /ΔnC = (0.06 ± 0.03)(mol/kg)−1) and nalkylammonium ions (ΔB+d /ΔnC = (0.04 ± 0.03)(mol/kg)−1), also shown in Figure 5, increments on the same order result. Small deviations between the B+d versus nC (or B+d versus ϕ+v , ϕ+v = molar volume of cation) relations of the three series of organic cations (Figure 5) report on the fact that, in addition to the number of hydrocarbon groups, specific properties of the ions may also act an influence on hydration water. Such properties include the shape and structure of solute and also its flexibility which, in turn, controls the ability of solute to correspond to the water structure. The changes in the magnitude of the relative molal shifts of the compressibility are again smaller. For the larger (nC = 16, ..., 20) tetraalkylammonium ions |ΔB k+/Δn C| = (0.016 ± 0.001)(mol/kg)−1 is found, corresponding with |ΔB+k /ΔnC| = 0.35·B+d /ΔnC. For the smaller ions of that series the change in the compressibility coefficient is even less (ΔB+k /ΔnC = −0.008 (mol/kg)−1 when going from the ammonium ion to the tetramethylammonium ion, ΔB+k /ΔnC = −0.012 (mol/kg)−1 for the change of the latter to the tetraethylammonium ion). The compressibilities of the series of solutions containing nalkyltrimethylammonium ions reveal analogically small changes when the number of methyl groups is varied (ΔB+k /ΔnC = −(0.016 ± 0.002)(mol/kg)−1). Many dielectric relaxation properties of dipolar liquids can be well described in terms of a wait-and-switch model,57 based on X-ray experiments and computer simulation studies of water.13−16 Because of these simulations, as briefly mentioned in the Introduction, the hydrogen-bond strength of the hydrogen network of water varies rapidly, with correlation times as small as 0.1 to 1 ps.13 Despite these fluctuations, reorientations through a significant angle, however, occur only on a much longer time scale, with correlation times of about 10 ps, corresponding with the principal dielectric relaxation time. Since the reorientation itself of the dipolar water molecules into a new direction occurs within the short period of only 0.1 ps13 and thus resembles a switching, the dominating part in the dielectric relaxation time of water is the period for which a water molecule has to wait until favorable conditions for reorientation exists. Such conditions are provided by defects in the predominantly tetrahedral hydrogen-bond network of water.14−16 Defects catalyze water reorientation especially effective when, at the same time, an appropriate new hydrogen-bond partner is offered. Favorable defects are therefore fifth neighbors in the coordination shell of a tetrahedrally hydrogen-bound water molecule.14−16 The fifth neighbor induces a bifurcated hydrogen bond and lowers the potential energy barrier for reorientation of the temporarily 5fold hydrogen-bonded water molecule. At the same time it offers a suitable site for the formation of a new hydrogen bond. Within the framework of the wait-and-switch model the dielectric relaxation time of water is largely controlled by the

liquid and a reduced orientational mobility. The magnitude of effects, however, is distinctly smaller with the compressibility than with the dielectric relaxation time, indicating that hydrophobic solutes affect the mechanical stiffness of their surrounding water to a lesser extent than the hydrogen-bond network dynamics. An illustrative example of this feature is shown in the inset of Figure 5, where relative shifts in the

Figure 5. Relative molal shifts in the adiabatic compressibility (full symbols) and the principal dielectric relaxation time (open symbols) for the hydration water of some series of organic cations: (●,○) tetraalkylammonium [CH3(CH2)n−1]4N+, n = 1, ..., 5; (▲) nalkyltrimethylammonium CH3(CH2)n−1(CH2)3N+, n = 3, ..., 6, 8, 10; (■) ethyl-, diethyl-, and triethylammonium [CH3CH2]nH4−nN+, n = 1, ..., 3; (Δ) n-alkylammonium CH3(CH2)n‑1H3N+, n = 4, 6, ..., 8; (▽) azoniaspiroalkane ions (CH2)nN+(CH2)n, n = 4, ..., 6. B0+ κ data have been derived from literature data for ϕ0κ,S26,28,29,32 and cs.41,53,54 B+d data result from literature data for τs.55,56 The inset presents relative deviations of the adiabatic compressibility (⧫) and of the principal dielectric relaxation time (◊) of aqueous solutions of nondipolar triethylenediamine (TED, N(C2H5)3N) from the water values, respectively, as a function of molal concentration of solute.23 All data refer to 25 °C. Also shown is the structure of the TED molecule.

compressibility and dielectric relaxation time of aqueous solutions of triethylene diamine (TED) are shown as a function of molal concentration of organic solute. Bicyclic TED, the structure of which is also given in Figure 5, offers favorable properties for the investigation of hydration water characteristics. It is nondipolar, almost spherically shaped, and conformationally stable. Therefore, compressibility data as well as dielectric spectra can be also consistently evaluated in terms of hydration models, in order to yield the numbers Zhκ and Zhd of hydration water molecules per molecule of solute. Using the Pasynski formula (eq 3) which, as mentioned before, proceeds from the assumption of completely incompressible hydration water Zhκ = 5.3 results, corresponding with Zhκ ≈ 0.23·Zhd, where Zhd = 23.24 Even though Pasynski’s formula may indeed be questioned because the hydration water may be slightly compressible, this result is nevertheless taken to indicate a comparatively small extent of water with modified compressibility around hydrophobic solutes. Such general trends emerge also in the B+κ and B+d values which are shown for some series of organic cations in Figure 5. With increasing cation volume, that 12255



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probability density for the occurrence of a fifth neighbor or another appropriate network defect, thus by the concentration cHB of appropriate hydrogen-bonding sites. At increasing cHB, other than may be anticipated intuitively, the dielectric relaxation time decreases. Illustrative examples are normal alcohols. The principal dielectric relaxation time decreases by a factor of 50 from τs = 2.43 to 0.049 ns (25 °C58) when going from n-dodecanol to methanol, whereas cHB increases from 4.45 to 24.7 mol/L. The large concentration of hydrogen-bonding sites is doubtless the essential factor provoking the exceptionally small dielectric relaxation time of water (8.27 ps, 25 °C45). It is an obvious approach to turn this argument the other way around when discussing the enhanced relaxation times of aqueous solutions of hydrophobic solutes. The reduced availability of hydrogen-bonding sites resulting from the presence of nonbonding hydrophobic material (a sketch is given in Figure 6) increases the waiting period for the

orientations of the water molecules around those ions are largely fixed in the strong Coulombic fields, the B+d values do not just reflect molecular reorientations but also the exchange of water molecules between the hydration region and the bulk phase.51 A sketch of the preferentially radial dipole moment orientation of such “dielectrically saturated” water24,51 is given in the figure. To account for this effect B+m values as resulting from the relative molal shifts Bm = Bm+ + Bm− = (1/T1)−1 lim [∂(1/T1)/∂m] m→0

(12)

of intramolecular proton magnetic relaxation rates52 1/T1 are additionally presented for the Li+ and Na+ ions. For the small alkali ions the B+m values are positive, revealing a slowdown in the proton-around-proton motions of the hydration water molecule due to electrostriction in the strong ionic fields. To distinguish these slowdown effects from hydrophobic hydration it is usually named “positive hydration”. Judging from the orientational mobility of the water molecules, the positive hydration of monovalent cations decreases rapidly with ion radius and is below the limit of detection at a radius corresponding with the dimensions of the water molecule. The B+κ,S values for Li+ and Na+ are again slightly negative and highlight the reduction of the water compressibility in the strong ionic fields. Surprisingly this reduction appears to be larger with Na+ than with Li+. The small lithium ion apparently induces strong electrostriction effects within the layer of coordination water molecules but leaves further water layers almost unaltered, whereas the sodium ion causes indeed a smaller electrostriction effect but disturbs the water structure also outside the first coordination shell. Extrapolated static permittivities of relevant salt solutions yield Z = 3.9 apparently irrotationally bound water molecules around the Li+ ion and Z = 2.6 around the Na+ ion.24 Around larger monovalent cations no such water is found (Z = 0). The latter finding supports the idea that the compressibility of Na+ hydration water is predominantly subject to more extensive structure changes than to short-range saturation effects: potassium, rubidium, and cesium ions induce the same relative change in the compressibility as the sodium ion. In contrast the B+d values for K+, Rb+, and Cs+ differ significantly from the B+m value of Na+ (Figure 6). The relative molal shifts in the dielectric relaxation time are even negative, showing an increased orientational mobility of the hydration water. This feature of medium-sized ions, with radii roughly between 0.14 and 0.23 nm, is called “negative hydration” and is well understood in terms of the wait-and-switch model of dielectric relaxation. Medium-sized cations do not affect the water structure by dielectric structure saturation but offer a large positively charged surface with which the lone-pair electrons of a water molecule can interact. Such interaction resembles a hydrogen bond so that the concentration of hydrogen-bonding sites is virtually increased and the waiting period for the formation of a new bond is decreased by the presence of ions. Whereas the B+d value of the ammonium ion only marginally differs from that of the equally sized rubidium ion the B+κ values of both cations are noticeably different. The H4N+ ion hardly affects the mechanical stiffness of the surrounding water structure (B+κ = 0.016 ± 0.005) (mol/kg)−1, the Rb+ ion does. This result shows that factors other than the size, and thus the strength of the electric field at the ion surface, are important in influencing the hydrogen structure of hydration water. It also indicates that the adiabatic compressibility and the

Figure 6. Cation parts B+κ and B+d in the relative molal shifts of the adiabatic compressibility κS26,28−30,33 and the dielectric relaxation time τs,24 respectively, at 25 °C displayed versus radius r+ of some monovalent ions. The data have been derived from aqueous salt solutions with halides as anions. Open symbols mark data from intramolecular proton magnetic relaxation rates52 (eq 12). Sketches illustrate the arrangement of water molecules around cations. When r+ exceeds a value somewhat larger than 0.2 ns, the water dipole moments tend to be more tangentially than radially oriented to the ion surface. The shaded area shows the range of radii, in which negative hydration occurs.

occurrence of a network defect as well as of a suitable new hydrogen-bond partner and thereby reduces the orientational mobility of the water molecules. Evidently, small changes in the network structure produce noticeable variations in the water dynamics. The restructuring of water, that happens in order to minimize the interactions of water dipole fields with hydrophobic (inert) materials, appears to have only a much smaller influence on the compressibility of the solvent. This is a surprising result since water, with its open voluminous hydrogen-bond structure, is supposed to exhibit a quite different compressibility when this structure partially breaks down. 3.2. Small Monovalent Cations. In Figure 6 relative molal shifts of the adiabatic compressibility and the dielectric relaxation time are shown for some small monovalent cations. Dielectric relaxation times of water around lithium and sodium ions need special attention. Since the dipole moment 12256



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the B−d value be positive. The electronic structure of the composite [BF4]− ion, however, is different from the spherically symmetric electron shell of the halides. Since fluorine, the most electronegative of all elements (xF = 4.0,59 x = electronegativity value) attracts an electron from the boron atom (xB = 2.059) the (fluorine) vertices of the tetrahedrally structured tetrafluoroboronate ion hold an excess negative charge, whereas the boron in the center of the tetrahedron is positively charged. The limiting form of the anion made of completely ionic bonds is sketched in Figure 7. Hence [BF4]− neither provides an inert surface that promotes a clathrate-like hydration shell with reduced compressibility, equivalent to the hydrophobic cations (Figure 6), nor reduces the concentration of potential hydrogen-bonding sites. Rather the electrically charged fluorine vertices of the [BF4]− tetrahedron allocate sites for the formation of new hydrogen bonds and thus increase dielectric relaxation of the surrounding water. 3.4. Bivalent cations. It is well established that 2:2 valent salts do not completely dissociate when dissolved in water but form ion complex structures, such as inner-sphere complexes (contact ion pairs), outer-sphere complexes, in which the ions are separated by one water layer, and outer−outer sphere complexes with two water layers between the anion and the cation.60−64 Sometimes, however, ion complexes are also formed in solutions of 2:1 valent electrolytes, such as chlorides or bromides. Often the concentration of those dipolar complexes is too small or their lifetime is too short to contribute a relaxation term to the dielectric spectra. But complex formation can be inferred from the small number Z of apparently saturated water molecules per cation. For the transition metal ions Zn2+ and Cd2+, for example, Z is 4.3 and 1.3 only, whereas similar-sized alkaline earth metal ions exhibit values between 5.4 (Ba2+) and 7.0 (Mg2+, Sr2+).24,65 The smaller Z values are assumed to reflect the reduced electric field of ion complex structures. Ion complex formation appears to be characteristic for transition metal ions rather than ions from main group metals.65 Even though isolated Zn2+ and Cd2+ with s2p6d10 electronic structure, like the alkaline earth metal ions with s2 structure, have a spherically symmetric charge distribution, their directed d orbitals obviously cause noticeable interactions when anions approach. Mediated by the different molar volumes of differently associated ions, the kinetics of ion complex formation and disintegration leads to relaxation terms in the ultrasonic excess attenuation spectra of the relevant solutions. Three examples of such spectra are displayed in Figure 8. Ultrasonic excess attenuation

dielectric relaxation time may respond to such factors in a different way. 3.3. Monovalent Anions. The B−κ and B−d values for some monovalent anions are displayed versus ion radius r− in Figure 7. The relative molal shifts of the adiabatic compressibility

Figure 7. Anion contributions B−κ and B−d to the Bx values (x = κ26,28−30,33 and d24) for aqueous solutions of 1:1 valent salts at 25 °C shown as a function of ion radius r−. Open symbols are for dielectric and close symbols for compressibility data. The shaded area indicates again the range of ion radii characteristic of negative hydration. A limiting form of the charge distribution of the [BF4]− ion is also presented.

related to the halide ions are negative and increase with anion radius, corresponding with a decreasing shift in the dielectric relaxation time. Owing to its size fluoride just belongs to the group of positively hydrated ions. It induces a small effect of dielectric saturation, equivalent to Z = 1.2 apparently having irrotationally bound water molecules in its hydration shell. Because of electrostriction, the reorientational mobility of the hydration water is reduced, and also reduced is the compressibility. Both effects become smaller with increasing radius of the halide ions. The chloride ions shows already a small reduction of the hydration water relaxation time with respect to pure water (B−d = −0.01 (mol/kg)−1)24 and thus belongs to the class of negatively hydrated ions. A sketch in Figure 7 illustrates negative hydration of anions in the light of the wait-and-switch model. Large monovalent anions with their soft electron shell, over a significant angular range, provide a site for hydrogen-bond-like interactions with slightly positively charged hydrogen atoms of water molecules. Therefore the concentration of potential hydrogen-bond partners is large around such large anions and the waiting period of water molecules for the formation of a new hydrogen bond is comparatively small. The reduced waiting period leads to faster dielectric relaxation, as outlined above. The effect is especially strong with the iodide ion, the hydration water relaxation time of which is only half that of undisturbed water at the same temperature.24 Also with reduced Coulombic field the decrement in the compressibility becomes smaller: with iodide the amount of the relative shift is as small as 0.04 (mol/kg)−1. At first glance the B−κ and B−d values for the tetrafluoroboronate ion do not fit into the schemes discussed before. Being larger than the iodide ion this anion may be expected to display an even smaller effect in the compressibility. Alternatively, as due to its size [BF4]− belongs to the group of hydrophobic ions (Figure 6), it may be anticipated that the B−κ value be only slightly more negative than that of I− and that

(αλ)exc = αλ − Bv

(13)

is the part in the total attenuation coefficient α per wavelength λ (= cs/ν) that exceeds the asymptotic high-frequency part Bν. The (αλ)exc spectra for the solutions of transition metal chlorides (ZnCl2, 0.2 mol/L;66,67 CuCl2, 0.5 mol/L66) exhibit significant contributions with relaxation characteristics. The former reveals a relaxation time distribution, probably a superposition of two Debye-type relaxation terms. It reflects some steps in the complicated reaction scheme of ZnCl2 ion complexes. This scheme leads also to noticeable high-frequency dispersion in the sound velocity cs (Figure 8, inset). The relaxation of the CuCl2 solution has been assigned to the equilibrium 12257



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fields of the small ions. Because of this packing the protonaround-proton motions of the water molecules surrounding the bivalent cations are slowed and thus the B+m values are positive. These values also nicely reveal the effect of ion radius on the reorientational mobility: the B+m value for Mg2+ (= 0.45 (mol/ kg)−1), for instance, is 2.5 times larger than that for Ba2+ (= 0.18 (mol/kg)−1).52 In contrast, the B+d values for the alkaline earth metal ions are negative. At first sight this is a surprising result because of the quite strong effect of dielectric saturation around the cations mentioned before. Also the residence time of water molecules in the dielectrically saturated region will be too large to account for the significantly negative shifts in the dielectric relaxation time. In fact negative hydration occurs beyond the layer of radially orientated dielectrically saturated water molecules. Because of the effect of electrostriction within this layer its surface area will feature a comparatively dense array of positively charged hydrogen sites of water molecules and will thus provide a large concentration of partners for the formation of new hydrogen bonds. Within the context of the wait-and-switch model of dielectric relaxation such a defect in the water structure involves a reduction in the waiting period and thus of the relaxation time at all.

Figure 8. Ultrasonic excess attenuation spectra for aqueous solutions of some salts at 25 °C: (□) ZnCl2, 0.2 mol/L;66,67 (◊) CuCl2, 0.5 mol/L;66 (●) SrCl2, 1 mol/L.68 The inset shows the sound velocity spectrum of a solution of ZnCl2 in water at 25 °C (■, 0.4 mol/L67).

[Cu+Cl−]aq ↔ [Cu+(H 2O)Cl−]aq

4. CONCLUSIONS The cationic and anionic contributions B+κ and B−κ , respectively, to the relative molal shifts in the adiabatic compressibility of electrolyte solutions are useful measures of the effects of ions on the structure of their surrounding water. The B±κ values can be easily derived from κS data without any assumptions. This advantage over the frequently used hydration numbers Zhκ, which are calculated presuming a vanishing adiabatic compressibility κS,h of the hydration water, is opposed by an only marginally less descriptive meaning of the relative shifts. The primary advantage of using B±κ values is their direct comparability with the equivalent relative molal shifts B±d and Bm± in the principal dielectric relaxation times and the intramolecular proton magnetic relaxation rates, respectively, of water. Both quantities are related to the reorientational dynamics of water in lieu of its structure and thus complement the insights into the properties of water in electrolyte solutions. B±d and B±m likewise simply result from measurements without essential presumptions. Similar to aqueous solutions of nonionic solutes the B+κ and B−κ values of the electrolyte solutions are negative throughout. Solutes in general reduce the high compressibility of water. Hence changes from solutions exhibiting predominantly positive hydration to such revealing mainly negative hydration or changes from the latter to predominant hydrophobic solutes are not associated with a change in the sign of the B±κ values, but the magnitudes |B±κ | depend on the size of the ions, on their overall charge, as well as on the structure of the solute. An example is the significantly smaller |B+κ | value for the ammonium ion than for the equally sized rubidium ion. Another one is the large |B−κ | value for tetrafluoroboronate that does not fit into the trend shown by the halide ions, the |B−κ | values of which substantially decrease when going from the positively hydrated fluorine ion to the iodide ion that features significant effects of negative hydration. In correspondence with results for nonionic hydrophobic solutes the |B+κ | values for some series of organic cations increase less strongly with number nC of methyl groups per ion than the B+d values. For the tetraalkylammonium ions |ΔB+κ / ΔnC| = (0.016 ± 0.001)(mol/kg)−1 is found, in contrast to

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between the contact ion pair and the outer-sphere complex.66 As verified by the (αλ)exc spectrum for a SrCl2 solution (1 mol/L68) alkaline earth halides may also feature ultrasonic relaxations. Their amplitudes A, however, are distinctly smaller (A/c = 0.58 × 10−3 (mol/L)−1, SrCl2) than those of transition metal halides (A/c = 15.2 × 10−3 (mol/L)−1, CuCl2). Because of the minor concentration of ion complexes, which likely follows from the small amplitudes of ultrasonic relaxation terms, the following discussion will be restricted to alkaline earth metal ions. Hence marginal effects from ion association will be neglected. Figure 9 shows the B+κ and B+d data for alkaline earth metal ions along with the corresponding relative molal shifts B+m of

Figure 9. Cationic contributions B+x to the relative molal shifts in the adiabatic compressibility (x = κ31), the principal dielectric relaxation time (x = d65), and the intramolecular proton magnetic relaxation rate (x = m52) of aqueous solutions of alkaline earth halides at 25 °C.

proton magnetic relaxation rates of water. As expected intuitively the B+κ values for Mg2+, Ca2+, Sr2+, and Ba2+ solutions are negative and the absolute values are roughly twice those for the alkali metal ions (Figure 6). This reduction in the compressibility of the water is again a result of the dense packing and alignment of water molecules in the Coulombic 12258



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|ΔB+d /ΔnC| = (0.056 ± 0.003)(mol/kg)−1. This remarkable difference in the increments indicates again the noticeable sensitivity that the microdynamics reveals to structural changes of water.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 551 39 7715, Fax: +49 551 39 7720. E-mail: uka@ physik3.gwdg.de. Notes

The authors declare no competing financial interest.

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