Dielectric Relaxation of Dilute Aqueous NaOH, NaAl(OH)4, and NaB

11186

J. Phys. Chem. B 1999, 103, 11186-11190

Dielectric Relaxation of Dilute Aqueous NaOH, NaAl(OH)4, and NaB(OH)4 Richard Buchner,*,† Glenn Hefter, Peter M. May, and Pa´ l Sipos Chemistry Department, Murdoch UniVersity, Murdoch, W.A. 6150, Australia ReceiVed: July 23, 1999; In Final Form: September 22, 1999

The complex dielectric permittivity of aqueous NaOH (c e 2 M) and of dilute (e0.6 M) NaAl(OH)4 and NaB(OH)4 solutions in NaOH ([Na] ) 1 M) at 25 °C has been determined in the frequency range 0.2 e ν/GHz e 20. All spectra could be represented by a single Cole-Cole relaxation time distribution attributed to the cooperative relaxation of the solvent. The concentration dependence of the effective hydration number of OH- has been determined. For aluminate and borate solutions the deduced parameters: effective conductivity κe, static permittivity , relaxation time τ, and distribution parameter R suggest a 1:1 replacement of hydroxide by aluminate and borate, accompanied by a release of bound water. The lack of an ion-pair relaxation process despite notable ion association suggests that rapid proton exchange is important not only for the dynamics of OH- but also for Al(OH)4- and B(OH)4-.

1. Introduction The relatively strong binding of Na+ with a great variety of macrocyclic ligands has received considerable attention in recent years. However, the interactions of Na+ with weakly complexing anions is of much greater importance in many situations of biological,1 geochemical,2,3 and industrial interest.4 For example, in the well-known Bayer process for the recovery of alumina from its ores, the weak interactions between Na+ and the major anionic components (OH- and Al(OH)4-) of Bayer “liquors” appear to play a significant role.5 Even though its significance is often overlooked mainly because of the difficulties in quantifying it, weak ion pairing is likely to be important in any solution containing large amounts of sodium ions. Dielectric relaxation spectroscopy (DRS) probes the interaction of an electromagnetic wave of frequency ν with the sample. For an electrolyte solution of conductivity κ DRS determines the relative dielectric permittivity, ′(ν), and the total loss, η′′(ν), which is related to the dielectric loss ′′(ν) as

η′′(ν) ) ′′(ν) + κ/(2πν0)

TABLE 1: Molar Concentration, c, Effective Conductivity, Ke, Dielectric Relaxation Parameters, E, τ, r, and Variance of the Fit, s2, of aqueous NaOH solutions at 25 °Ca c

κe



τ

R

s2

0 0.1056 0.2027 0.4022 0.8171 1.033 1.211 1.598 2.007

0 2.293 ( 0.001 4.248 ( 0.009 7.94 ( 0.05 14.95 ( 0.03 17.88 ( 0.08 20.51 ( 0.02 25.25 ( 0.15 29.42 ( 0.17

78.33 76.83 75.25 71.92 66.29 64.42 62.06 58.78 55.87

8.21 8.17 8.14 8.11 8.06 8.19 8.07 8.21 8.32

0 0.013 0.017 0.004 0.014 0.033 0.045 0.068 0.104

0.002 0.06 0.06 0.17 0.33 0.29 0.76 0.81 1.12

a Units: c in mol dm-3; κ in Ω-1 m-1; τ in 10-12 s.  ) 5.6 preset e ∞ for all fits.

aqueous NaOH, NaAl(OH)4, and NaB(OH)4. The first two are directly relevant to the study of chemical speciation in Bayer “liquors”. Because of its larger stability range, the last is of interest as a model system for the more difficult aluminate solutions.

(1) 2. Experimental

0 is the permittivity of the vacuum. The accessible complex dielectric permittivity

ˆ (ν) ) ′(ν) - i′′(ν)

(2)

is directly related to the fluctuations of the total dipole moment of the sample, M B (t) ) ∑µ bj, which arise from the motions and interactions of the individual molecular dipole moments, b µj.6,7 Because of the long range of dipole-dipole and ion-dipole interactions, DRS can be used to gain information on the structure and the dynamics of cooperative motions in electrolyte solutions.8,9 Because DRS is sensitive to the magnitude of the dipole moments of dissolved species, it can, at least in principle, provide unique insights into the nature and stability of even relatively weak ion pairs.10 This paper presents a DRS study of * To whom correspondence should be addressed. † Permanent address: Institut fu ¨ r Physikalische und Theoretische Chemie, Universita¨t Regensburg, D-93040 Regensburg, Germany. E-mail: [email protected].

The spectra of dielectric permittivity, ′(ν), and total loss, η′′(ν), were recorded with a HP 85070M dielectric probe system in the frequency range νmin e ν/GHz e 20 at (25.00 ( 0.02) °C. The instrument was calibrated with air, mercury, and water as described in ref 11. This allows an accuracy of 2% in ′ and η′′ relative to the static permittivity of the sample, , to be achieved. For each sample at least two spectra were recorded using independent calibration runs. νmin was adapted to the conductivity of the sample and ranged from νmin ) 0.2 GHz for the dilute solutions to 1.4 GHz at 2 mol dm-3 NaOH. Solutions were prepared in volumetric flasks using concentrated (ca. 20 M) carbonate-free NaOH, analytical grade B(OH)3 (“99.5%+” grade, Ajax, Australia), and concentrated sodium aluminate stock solutions prepared from Al wire (“99.999%” grade, Goodfellow, U.K.) as described elsewhere.12 3. Data Analysis Each spectrum was analyzed separately to determine the slightly calibration-dependent effective conductivity, κe, of each

10.1021/jp992551l CCC: $18.00 © 1999 American Chemical Society Published on Web 11/24/1999

Relaxation of NaOH, NaAl(OH)4, and NaB(OH)4

J. Phys. Chem. B, Vol. 103, No. 50, 1999 11187

Figure 1. Dielectric dispersion, ′(ν), and loss spectrum, ′′(ν), of NaOH in water at 25 °C. Experimental data (symbols) are fitted to a Cole-Cole relaxation process (solid lines): 1, pure water; 2, 0.2027 mol dm-3; 3, 0.8171 mol dm-3.

experiment. Tables 1-3 summarize the average values of κe and their maximum deviations for the NaOH, NaAl(OH)4, and NaB(OH)4 solutions, respectively. After correction of η′′ for the Ohmic loss, κ/(2πν0), the individual complex permittivity spectra were combined and fitted to various conceivable relaxation models. Typical spectra for NaOH(aq) are shown in Figure 1. Similar results were obtained for the other two electrolytes. For all electrolyte solutions it was found that ˆ (ν) is best fitted by a single Cole-Cole equation,

ˆ (ν) )

 - ∞ 1 + (i2πντ)1-R

+ ∞

(3)

with “static” permittivity , relaxation time τ, and relaxationtime distribution parameter 0 e R < 1. As in ref 11 the “infinite frequency” permittivity ∞ ) limνf∞ ′, which is reached far outside the accessible frequency range, was fixed to the value of pure water, ∞(0) ) 5.6, to reduce the number of adjustable parameters. This was found to be necessary because for solutions with κ > 20 Ω-1 m-1 the usable frequency range is limited to 1.4-20 GHz and the spectra become markedly distorted. Consequently, the reproducibility of  deteriorates from (0.1 for κ< 10 Ω-1 m-1 to (0.4 for κ around 20 Ω-1 m-1 to (0.8 for the highest NaOH concentration. For τ the reproducibilities rise from (0.05 to (0.1 to (0.4 ps. The covered conductivity range, 8.6 e κ/(Ω-1 m-1) e 15.9, also determines the error limits of  and τ for the aluminate and borate solutions. It should be noted that because of the limited frequency range no conclusions can be drawn for the shape of the spectra at ν > 20 GHz. The weak concentration dependence of τ in the case of NaOH/H2O and its smooth behavior for the aluminate and borate solutions only suggest that the amplitude variation of the high-frequency process known to exist in water13 must be small compared to  - ∞. 4. Results and Discussion 4.1. NaOH Solutions. In the investigated concentration range, c e 2 mol dm-3, the spectra are best fitted by a single ColeCole equation, eq 3. The variance of the fit, s2, the relaxation parameters, , τ, and R, and the average effective conductivity, κe, are summarized in Table 1. From the magnitude of the relaxation time it is obvious that the observed process is due to water. Compared with the data tabulated by De Wayne and Hamer,14 obtained by conventional conductivity measurements, κe is about

2-5% smaller. Even with precise low-frequency ac bridges, conductivity measurements in concentrated NaOH solutions are difficult, as can be seen from a comparison of literature data14-16 which show variations up to 40% (but < 2.5% for c e 2 mol dm-3). However, the major reason for the deviation of the DRS data from the conductivity values is the implemented equivalentcircuit model of the probehead/sample interface, which is not fully appropriate for such high conductivities. As discussed in ref 11 this deficiency does not affect the accuracy of ′(ν) nor the precision of ′(ν) and η′′(ν). However, the large value of κe causes problems as it reduces the accessible frequency range (for c ) 2 mol dm-3 at 1 GHz the conductivity loss is κe/(2πν0) ) 540) and the precision of ˆ (ν) at high concentrations. It was found that with the present instrumentation excessive conductivity prevented the investigation of aqueous NaOH for c > 2 mol dm-3. Table 1 shows that the relaxation time of the solutions does not depend on c within the error limits, yielding an average of τ ) (8.16 ( 0.08) ps. Comparable to NaCl solutions11 the relaxation-time distribution parameter, R, increases for c > 1 mol dm-3. The permittivity of the NaOH solutions decreases significantly with increasing concentration following the polynomial

 ) 78.6 ( 0.2 - (20.9 ( 0.8)c + (6.7 ( 0.5)c3/2 (4) with c in mol dm-3. Following the route outlined in ref 11 the apparent concentration of water in the solution was obtained as

(0)(2(c) + ∞(c)) Seq(c) cap s ) cs(0) (c)(2(0) + ∞(0)) (0) - ∞(0)

(5)

from the equilibrium amplitude of the solvent dispersion

Seq(c) ) (c) - ∞(c) + ∆kd(c)

(6)

where the kinetic depolarization term, ∆kd, is given by

(0) - ∞(0) τ(0) 0 (0)

∆kd(c) ) ξκ(c); ξ ) p

(7)

In eq 7 κ is the conductivity of the sample; the factor p accounts for the hydrodynamic boundary conditions of stick (p ) 1) or slip (p ) 2/3) ionic motion.17,18 The magnitude of kinetic depolarization predicted by theory is still a matter of discussion.19 However, recent experimental investigations suggest that eq 7 with a slip hydrodynamic boundary holds for aqueous electrolytes, whereas the stick limit yields physically impossible negative values for the effective solvation number:

ZIB(c) ) (cs - cap s )/c

(8)

The assumption of negligible kinetic depolarization, ξ ) 0, predicts unrealistically large ZIB.11,20,21 Note that ZIB is the average number of water molecules per equivalent of electrolyte which are (at a given time) unable to contribute to the solvent relaxation process, i.e., are irrotationally bound. ZIB is not necessarily identical to the average number of water molecules in the primary solvation shells of the ions (the coordination number deduced by simulation studies or scattering experiments) because of possible fast water exchange. This gives the rationale behind the assumption ZIB(Cl-) ) 0, which permits the splitting of the experimental data into ionic contributions.11

11188 J. Phys. Chem. B, Vol. 103, No. 50, 1999

Buchner et al. TABLE 2: Molar Concentration of Aluminium, [Al], Effective Conductivity, Ke, Dielectric Relaxation Parameters, E, τ, r, of a Cole-Cole Fit and Variance of the Fit, s2, of Aluminate Solutions in Aqueous NaOH at [Na] ) (1.00 ( 0.03) mol dm-3 and 25 °Ca [Na]

[Al]

[Al]/[Na]

κe



τ

R

s2

0.977 0.999 0.989 1.001 1.003 0.999

0.097 0.199 0.299 0.403 0.502 0.599

0.099 0.199 0.302 0.403 0.501 0.600

15.66 ( 0.04 14.33 ( 0.06 12.78 ( 0.03 11.37 ( 0.03 9.98 ( 0.03 8.59 ( 0.04

66.23 66.54 67.95 68.19 68.98 69.71

8.29 8.32 8.46 8.60 8.71 8.80

0.031 0.026 0.037 0.039 0.043 0.045

0.295 0.222 0.201 0.132 0.114 0.093

a Units: [Na] and [Al] in mol dm-3; κ in Ω-1 m-1; τ in 10-12 s.  e ∞ ) 5.6 preset for all fits.

TABLE 3: Molar Concentration of Boron, [B], Effective Conductivity, Ke, Dielectric Relaxation Parameters, E, τ, r, of a Cole-Cole Fit and Variance of the Fit, s2, of Borate Solutions in Aqueous NaOH at [Na] ) (1.002 ( 0.005) mol dm-3 and 25 °Ca Figure 2. Effective solvation number, ZIB, of NaOH in water at 25 °C calculated on the assumption of negligible kinetic depolarization (kd), b and curve 1, and for kd due to slip translational motion of Na+ aq, curve 2. The effective solvation number of OH-, Zslip IB (OH ), curve 3, + 20 is calculated from curve 2 and Zslip IB (Na ), curve 4.

For the investigated NaOH solutions, stick kinetic depolarization can be ruled out because Zstick IB < 0. Furthermore, the assumption of slip motion for Na+ and OH- yields Zslip IB (NaOH) + < Zslip IB (Na ), whereas the neglect of kinetic depolarization results in apparently realistic effective solvation numbers; see curve 1 of Figure 2.22 This inconsistency is resolved by assuming that only the slowly moving hydrated cations induce kinetic depolarization. This is reasonable because charge transport by OH- occurs via proton exchange with the solvent on a 0.11-ps time scale23 and is governed by quantum dynamics;24,25 i.e., the process is faster than the relaxation rate of water. The contribution of the cations to the solution conductivity, κ(Na+), was calculated from the data of De Wayne and Hamer14 and transference numbers interpolated from ref 26. Insertion of κ(Na+) into eq 7 for p ) 2/3 yields effective solvation numbers which can be fitted in the investigated concentration range by the expression -3 Zslip × c 2] IB (NaOH) ) 1/[(0.100 ( 0.003) + (7 ( 2) × 10

dm-3.

See curve 2 of Figure 2. c is in mol Subtraction of +), curve 4, Figure 2,20 yields the effective solvation Zslip (Na IB number of the hydroxide ion given by curve 3. The available literature data for the solvation number of OHjustify this procedure. The intercept of Zslip IB (OH ) ) 5.5 ( 0.5 compares favorably with the OH- coordination number, CN ) 6.6 obtained by Balbuena et al.27 from a classical molecular dynamics (MD) simulation. It is also in excellent agreement with the ab initio MD simulation result of Tuckerman et al., CN ) 5.8.28 The effective OH- hydration numbers of 5.9 (determined from the entropy of hydration), 6.6 (compressibility), and 4.0 (activity coefficients) given by Marcus are also similar.29 4.2. Solutions of Sodium Aluminate and Borate in 1 M NaOH. For fitting the complex permittivity spectra of the Al(OH)3/NaOH/H2O and B(OH)3/NaOH/H2O systems a single Cole-Cole equation, eq 3, is again sufficient. The relaxation parameters , τ, and R are summarized in Tables 2 and 3 together with the variance of the fit, s2, and effective conductivity, κe.

[Na]

[B]

[B]/[Na]

κe



τ

R

s2

1.007 1.008 1.003 1.002 1.000 0.994

0.1018 0.2008 0.3006 0.4008 0.5014 0.5977

0.1011 0.1992 0.2996 0.3999 0.5014 0.6011

15.85 ( 0.08 14.40 ( 0.07 12.88 ( 0.05 11.43 ( 0.04 9.97 ( 0.03 8.58 ( 0.04

65.99 66.57 67.68 68.76 69.80 70.71

8.17 8.29 8.33 8.38 8.45 8.48

0.038 0.030 0.026 0.030 0.038 0.044

0.233 0.180 0.148 0.112 0.079 0.089

a Units: [Na] and [B] in mol dm-3; κ in Ω-1 m-1; τ in 10-12 s.  e ∞ ) 5.6 preset for all fits.

TABLE 4: Parameters of eq 9 for the Dielectric Permittivity, E, Relaxation Time, τ/ps, and Relaxation-Time Distribution Parameter, r, of Sodium Aluminate and Borate Solutions in Aqueous NaOH at [Na] ) 1.00 mol dm-3 and 25 °C y

y(0)

b

Al

 τ/ps R

64.76 ( 0.24 8.14 ( 0.02 0.027 ( 0.002

8.7 ( 0.7 1.11 ( 0.07 0.029 ( 0.006

B

 τ/ps R

64.53 ( 0.11 8.14 ( 0.02 0.029 ( 0.003

10.5 ( 0.3 0.60 ( 0.06 0.016 ( 0.010

Only the dielectric relaxation of water is detectable. There is no indication of any ion-pair relaxation process. Both aluminate and borate solutions show a linear increase

y ) y(0) + b[M]/[Na]; M ) Al, B

(9)

of y ) , τ, and R with increasing concentration ratios of aluminium to sodium, [Al]/[Na], or boron to sodium, [B]/[Na]. Intercepts and slopes of eq 9 are summarized in Table 4. The effective conductivity, κe, of both electrolytes is equal within the probable error limits and decreases linearly with [M]/[Na]. The intercept is κe(0) ) (17.20 ( 0.05) Ω-1 m-1 and the slope is b ) -(14.40 ( 0.13) × 10-3 m2 Ω-1 mol-1. The linear change of κe suggests a 1:1 replacement of hydroxide by aluminate or borate according to

OH- + M(OH)3 f M(OH)4;

M ) Al, B

where the single-ion conductivities λ(Na+), λ(OH-), and λ(M(OH)4 ) do not depend on the concentration. Subtraction of κe(0) from the solution conductivity, which can be expressed as

κ ) λ(Na+)[Na] + λ(OH-)[OH] + λ(M(OH)4 )[M]

(10)

Relaxation of NaOH, NaAl(OH)4, and NaB(OH)4

J. Phys. Chem. B, Vol. 103, No. 50, 1999 11189

thus yields the difference

λ(OH-) - λ(M(OH)4) ) (14.40 ( 0.13) × 10-3 m2 Ω-1 mol-1 In eq 10 [M] is the concentration of aluminate or borate, [Na] ) 1.00 mol dm-3 is the constant concentration of Na+, and [OH] ) [Na] - [M] is the concentration of OH-. From the data of refs 14 and 26 the single-ion conductivity of hydroxide in 1 M NaOH is obtained as λ(OH-) ) (16.2 ( 0.2) × 10-3 m2 Ω-1 mol-1. This yields λ(M(OH)4 ) ) (1.8 ( 0.3) × 10-3 m2 Ω-1 mol-1 as the single-ion conductivity of borate and aluminate. The quoted error is based only on the standard deviations of slope b and λ(OH-). The effect of the systematic error in κe should be largely compensated by the subtraction of κe(0). The above value of λ(M(OH)4-) significantly exceeds the value of (1.0 ( 0.1) × 10-3 m2 Ω-1 mol-1 deduced from λ0(M(OH)4-) ) (3.21 ( 0.05) × 10-3 m2 Ω-1 mol-1 30 and the single-ion conductivities of Na+ at infinite dilution, λ0(Na+) ) 5.011 × 10-3 m2 Ω-1 mol-1, and in 1 M NaOH, λ(Na+, 1 M) ) 1.70 × 10-3 m2 Ω-1 mol-1, but nevertheless seems reasonable. Therefore, the ratio of the effective hydrodynamic radii of M(OH)4- and Na+ may be estimated from these data to be rhyd(M(OH)4-)/rhyd(Na+) ) λ(Na+)/λ(M(OH)4-) ) 0.94. Because the crystallographic radius of Al(OH)4- (0.29 nm31) is between the radii of the bare (0.098 nm) and the hydrated Na+ ion (0.38 nm) and because the latter is the the moving species in water,11 we may conclude that aluminate and probably also borate are not strongly hydrated. As will be shown below, this is corroborated by the analysis of the static permittivity, . As for the NaOH/H2O system, it is reasonable to assume that OH- does not contribute to kinetic depolarization in the investigated aluminate and borate solutions; thus,

κ′ ) λ(Na+)[Na] + λ(M(OH)4-)[M(OH)4-]

(11)

was inserted into eq 7 for slip conditions. If it is assumed for simplicity that the effective solvation number of the cation in 1 + M NaOH, Zslip IB (Na , 1 M) ) 3.95, does not change upon substitution of OH- by M(OH)4-, the linear relations

ZIB ) (5.16 ( 0.11) - (6.6 ( 0.3)[Al]/[Na]

(12)

Figure 3. Ratio ZIB/[OH ] of the effective solvation numbers of sodium aluminate (1) and sodium borate (2) solutions in aqueous NaOH ([Na] ) 1.00 mol dm-3) at 25 °C, as a function of [M]/[Na] ratio, M ) Al,B. [OH] ) [Na] - [M] is the formal concentration of OH-. Aluminate data shifted by +1 for clarity.

For both NaAl(OH)4/H2O and NaB(OH)4/H2O there is a small but significant increase of the relaxation time (Tables 2 and 3). According to the kinetic model, the experimental relaxation rate of these solutions should be given by

τ

-1

n+[Na] n-[OH] nM[M] cap s ) + + + csτ+ csτcsτM csτ0

1/τM is the relaxation rate of water in the hydration shell of aluminate or borate. n+, n-, and nM are the numbers of water molecules around Na+, OH-, and M(OH)4-, which differ in their relaxation time from bulk water. These “dynamic hydration numbers” are not necessarily identical to effective hydration numbers or coordination numbers, although one may assume + 11 n+ ) Zslip IB (Na ). + The assumption that Zslip IB (Na ) is independent of [M], which was also used in the analysis of , allows elimination of the cation contribution by subtracting the relaxation rate, 1/τ(0), of 1 mol dm-3 NaOH and yields

and

1/τ([M]) - 1/τ(0) ) a[M] + b[M] ZIB

) (5.29 ( 0.06) - (7.9 ( 0.2)[B]/[Na]

(13)

are obtained for the effective solvation numbers of the anions, ZIB, in the aluminate and borate solutions, respectively. Interestingly, eqs 12 and 13 extrapolate to ZIB < 0 well before complete substitution of OH- by M(OH)4-. This suggests not only negligible hydration (in the sense of irrotational bonding) of aluminate and borate but also the release of bound water in these systems, as can be seen by the decreasing ratios ZIB/[OH] of Figure 3. Probably, this effect, which is more pronounced for borate, is due to the overlap of the ion co-spheres. Within the error limits the water relaxation time does not depend on the concentration in NaOH/H2O (Table 1). This prevents further analysis of the data, but according to the kinetic model proposed in ref 11, the relaxation rates of water in the bulk, 1/τ0, and around OH-, 1/τ- are similar and significantly larger than that of water in the hydration sphere of Na+, 1/τ+.

(14)

(15)

with -1 a ) (nMτ-1 M - n-τ- )/cs

and ap cap s ([M]) - cs (0) b) csτ0

With correlation coefficients of 0.98 for aluminate and 0.94 for borate 1/τ([M]) - 1/τ(0) is reasonably linear. This is also ap 10 true for cap s ([M]) - cs (0), where data yield b ) 1.491 × 10 dm3 s-1 mol-1 for M ) Al and b ) 1.644 × 1010 dm3 s-1 mol-1 for M ) B if τ0 ) 8.14 ps and cs ) 55.42 mol dm-3 are inserted. Note that the analytical concentration of water does not change significantly with [M]. The consequence of two linear terms in eq 15 is that a must also be independent of [M]. The value of

11190 J. Phys. Chem. B, Vol. 103, No. 50, 1999 acs ) -(3.05 ( 0.05) × 1012 s-1 is obtained for aluminate, whereas for borate acs ) -(1.40 ( 0.02) × 1012 s-1. Without independent data, either for the dynamic hydration numbers (nM, n-) or for the corresponding relaxation times (τM, τ-), the quantitative analysis cannot be pursued further. However, the finding of constant a values suggests that these four parameters do not depend on the concentration of aluminate or borate. If it is assumed that nAl ≈ nB, we may also deduce τB < τAl. This result seems to be compatible with the observation that water release is more pronounced for borate than for aluminate (Figure 3). 4.3. Question of Ion-Pair Formation. A major goal of our experiments was to look for ion-pair formation in the investigated systems. There is firm evidence for ion association from potentiometric data. For NaB(OH)4 standard-state stability constants of β0 ) 1.91 (ref 3) and β0 ) 1.66 (ref 32) have been reported. Investigations in this laboratory using sodium amalgam electrodes indicate weak but definite associations for both NaOH and NaAl(OH)4 with apparent β values of 0.6 M-1 5 and 2.0 M-1 33 in a 5 M (Me4NCl) medium. Although these equilibrium constants are small, similar systems have been successfully investigated with DRS.10,20 However, it was not possible to extract an ion-pair relaxation process from the the present complex permittivity spectra. Nevertheless, when the activity coefficients are neglected, the amplitude of the solute relaxation process for a possible ion-pair species may be estimated from the above data.34 For a 0.2 mol dm-3 NaOH solution SCIP ≈ 0.16 is obtained for contact ion pairs (CIP), SSSIP ≈ 0.83 for solvent-separated, and S2SIP ≈ 1.97 for doubly solvent-separated ion pairs (2SIP). SCIP is definitely below the noise level of the presented dielectric experiments, but SSIP and definitely 2SIP should be detectable if they were formed, provided the lifetime of the ion pairs is at least comparable to their reorientation time. Because of the larger radius of B(OH)4- and Al(OH)4- compared to that of OH-, even CIP should be easily detectable for borate and aluminate solutions. For these systems reorientation times of at least 50 ps are expected. Therefore, the separation of solute and solvent contributions to ˆ (ν) should not pose numerical problems, in contrast to NaOH. Thus, the lack of a detectable solute relaxation process suggests that for NaOH/H2O, Al(OH)3/NaOH/H2O, and B(OH)3/NaOH/H2O the ion-pair lifetimes are comparable or even smaller than the water relaxation time. Because one would expect a lifetime in the order of 25 ps for an ion-pair decay controlled by “conventional” Brownian diffusion, this possibly means that rapid proton exchange not only governs the dynamics of aqueous NaOH but also is important for aluminate and borate solutions. Acknowledgment. The authors thank Judith Nagy and Stephen Capewell for assistance in the preparation of the samples. This work was funded by the Australian alumina industry and the Australian Research Council through the Australian Mineral Industries Research Association Project P380B. Support by the Deutsche Forschungsgemeinschaft for R.B. is gratefully acknowledged.

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