© Copyright 1997 by the American Chemical Society
VOLUME 101, NUMBER 23, JUNE 5, 1997
LETTERS Self-Diffusion Coefficients of Paired Ions Huaping Mo and Thomas C. Pochapsky* Department of Chemistry, Brandeis UniVersity, Waltham, Massachusetts 02254-9110 ReceiVed: January 24, 1997; In Final Form: April 15, 1997X
The self-diffusion coefficients of the cation and anion of tetrabutylammonium tetrahydridoborate, (C4H9)4N+BH4-, were measured simultaneously at several concentrations in CDCl3 solution using an NMR stimulated echo experiment incorporating pulsed field gradients. A nonionic species of similar size and shape to the tetrabutylammonium ion, tetrabutylsilane, was included as an internal reference. In the first direct measurement of self-diffusion of both cation and anion in an ion pair, it was observed that self-diffusion of BH4- is only slightly faster than that of the (C4H9)4N+ ion, with the self-diffusion rate of tetrabutylsilane being significantly greater than that of either BH4- or (C4H9)4N+. These results indicate that the tight ion pair is the primary diffusive species, and the diffusion of free BH4- is not an important contributor to the measured self-diffusion coefficient of the anion. The aggregation states of the paired ions were estimated from ratios of the selfdiffusion coefficients of the tetrabutylammonium ion and tetrabutylsilane.
Introduction Ion pairing in solution remains an incompletely understood phenomenon, even for relatively simple ion pairs.1,2 In particular, the measurement of relative motions of ionic species has often been a problem, and information concerning such motion had to be extracted from experimental observations that are affected by other unrelated and often poorly understood phenomena.3,4 NMR methods provide an elegant alternative for extracting information concerning relative motions of ions in solution. Nuclear relaxation by paramagnetic ions in aqueous systems as a function of the relative diffusion of cations and anions has been examined.5 The effects of charge on the diffusion of organic species has also been studied.6 Recently, we described the use of pulsed field gradient NMR methods to measure self-diffusion coefficients for aggregates of ion pairs formed by tetrabutylammonium chloride 1a in CDCl3.7 Using * E-mail:
[email protected]. Website: http://tucano.chem.brandeis.edu. X Abstract published in AdVance ACS Abstracts, May 15, 1997.
S1089-5647(97)00311-8 CCC: $14.00
a nonaggregating species tetrabutylsilane 2 as an internal reference, we estimated aggregation numbers (numbers of ion pairs per aggregate) for 1a and showed that ion aggregation in this system is primarily a response to solution crowding rather than any favorable enthalpic change, since aggregation number shows little temperature dependence but changes considerably as a function of concentration of 1a. At very low concentrations of 1a (∼0.0001 M), single ion pairs predominate, but aggregates are formed as the concentration of 1a is increased, with an apparent maximum aggregation number of ∼4 observed at higher concentrations.7 However, it was still not clear from these experiments whether both cation and anion diffuse at the same rate or whether there is a significant increase in dissociation of individual ion pairs into cation and anion at lower concentrations. We now show that diffusion of the small tetrahydridoborate anion (BH4-) in CDCl3 solutions of tetrabutylammonium tetrahydridoborate 1b is strongly affected by the formation of ion pairs. As far as we have been able to ascertain, this is the first direct measurement of self-diffusion for both cation and anion in an ion pair. © 1997 American Chemical Society
4486 J. Phys. Chem. B, Vol. 101, No. 23, 1997
Letters
TABLE 1: Self-Diffusion Coefficients of 1a and 2 Measured as a Function of Concentration in CDCl3a 1a concentration (M) 2 × 10-1 4 × 10-2 8×
10-3
2 × 10-3 5×
10-4
TBA+
D (×10-10 m2/s) BH4-
4.99 ( 0.14 5.34 ( 0.22 (5.58 ( 0.23) 6.83 ( 0.21 7.35 ( 0.16 (7.43 ( 0.16) 8.10 ( 0.07 8.42 ( 0.13 (8.46 ( 0.16) 8.48 ( 0.13 8.73 ( 0.16 (8.84 ( 0.12) 8.34 ( 0.11 8.64 ( 0.42 (9.36 ( 0.38)
2
D2/ aggregation DTBA+ number
8.64 ( 0.23 1.73
5.2
10.3 ( 0.3
1.51
3.4
10.5 ( 0.2
1.30
2.2
10.6 ( 0.2
1.25
2.0
10.5 ( 0.2
1.26
2.0
a All experiments were performed at 298 K. The aggregation number of 1a is taken as the cube of D2/DTBA+ (see text and footnote 9). Errors are estimated as maximum deviations from the average of the values calculated from individual resonances. Diffusion coefficients for BH4are corrected for decomposition during the experiment. Values listed in parentheses are the same diffusion coefficients for BH4- uncorrected for sample decomposition (see footnote 8). Note that decomposition increases apparent diffusion coefficients.
Experimental Section and Results The experimental procedure and data analysis used in the present work are identical to those described previously for tetrabutylammonium chloride 1a.7,8 Self-diffusion coefficients were measured for both tetrabutylammonium (TBA+) and BH4using samples with concentrations ranging from 2 × 10-1 to 5 × 10-4 M of 1b and similar concentrations of tetrabutylsilane 2 as a nonaggregating internal standard. Measured self-diffusion coefficients as a function of concentration for TBA+ and BH4as well as for the standard 2 are listed in Table 1. In all cases, it was found that BH4- diffuses only slightly faster than TBA+ despite their considerable size difference. The self-diffusion coefficient of a spherically symmetric species is proportional to the inverse of its radius of gyration,9 and TBA+ is estimated to have an effective radius of gyration of ∼5 Å, while BH4has an ionic radius of 1.9 Å.2 It is clear from these results that a tight ion pair is the primary diffusive species for 1b in CDCl3 even at very low concentrations, and separate ions or solventseparated ion pairs are not important contributors to selfdiffusion in this system. As previously reported for tetrabutylammonium chloride 1a in CDCl3, the self-diffusion coefficients of TBA+ and BH4decrease faster than that of 2 as concentration is increased.7 As with 1a, we interpret this observation as evidence for ion aggregate formation and have used the ratio of the self-diffusion coefficients of 2 and TBA+ to estimate aggregate size, assuming that the ratio of the diffusion coefficients is inversely proportional to the cube root of the relative volumes of the species. Due to limited sample stability, we did not attempt to measure temperature effects on aggregation for 1b. However, the similarity between the concentration effects on aggregate size for 1a and 1b suggests that similar thermodynamic considerations might apply in both cases. It has been argued that charge and solvation effects may also be responsible for differences in self-diffusion between neutral and ionic species of similar sizes and shapes.6 However, two
pieces of evidence indicate that this is not true for the present case. First, we note that as concentration of 1a decreases, its self-diffusion coefficient approaches that of 2, and they become equal at very low concentrations.7 A similar concentration dependence is observed in the present experiment (although the coefficients do not become equal even at the lowest concentrations of 1b and 2). If solvation alone were responsible for these differences, the effect should not be concentration dependent. Our conclusion is further supported by the observation that TBA+ has the same self-diffusion coeffient as 2 in solutions of 1a in methanol, a dissociative solvent which should strongly solvate an ionic species (H. Mo, unpublished results). However, these observations do not generally rule out solvation effects on diffusion, and concentration studies are required in order to rule out such effects in any given case. Acknowledgment. This work was supported in part by a grant from the National Science Foundation (CHE-9510131, T.C.P.). T.C.P. also acknowledges support through the NSF Young Investigator (CHE-9257036) and the Camille and Henry Dreyfus Teacher-Scholar programs. The authors thank Prof. Ernest Grunwald for valuable discussions. References and Notes (1) Pochapsky, T. C.; Stone, P. M. J. Am. Chem. Soc. 1990, 112, 6714. (2) Pochapsky, T. C.; Wang, A. P.; Stone, P. M. J. Am. Chem. Soc. 1993, 115, 11084. (3) Harned, H. S.; Nuttall, R. L. J. Am. Chem Soc. 1947, 69, 736740. (4) Fries, P. H.; Patey, G. N. J. Chem. Phys. 1984, 80, 6253-6266. (5) Fries, P. H.; Jagannathan, N. R.; Herring, F. G.; Patey, G. N. J. Chem. Phys. 1984, 80, 6267-6273. (6) Cohen, Y.; Ayalon, A. Angew. Chem., Int. Ed. Engl. 1995, 34, 816818. (7) Pochapsky, S. S.; Mo, H.; Pochapsky, T. C. J. Chem. Soc., Chem. Commun. 1995, 2513. (8) Samples of 1a and 2 in CDCl3 were prepared as described previously, using a series of dilutions of the more concentrated samples to prepare samples of lower concentration.1 A series of stimulated echo NMR experiments incorporating pulsed field gradients7 were performed on a Bruker AMX-500 equipped with a three-axis gradient probe, with gradient strength increasing from 0.5 G/cm to 15.5 G/cm in steps of 1.0 G/cm. Upon completion of the series, the first experiment of the series (0.5 G/cm) was repeated in order to permit correction for sample decomposition during the experiment. The number of free induction decays acquired per experiment depended on concentration (16 acquisitions per experiment at the highest concentration to 256 acquisitions per experiment at the lowest concentrations). A postacquisition relaxation delay of 5 s was used prior to the beginning of the next pulse train. All data sets were processed as described previously,7 and self-diffusion coefficients were calculated as the slope of a plot of the negative log of normalized signal intensity versus K2(∆ δ/3), where ∆ is the intergradient diffusion delay in the pulse sequence, δ is the length of the gradient pulse, and K ) γGδ, with γ the gyromagnetic ratio of 1H and G the gradient strength. Correction for decomposition of BH4- during the experimental series was accomplished by measuring the signal integration for the BH4- signals in the two identical experiments performed at the beginning and end of each series. The value of the integrated BH4- signal for each experiment was then corrected for the amount of decomposition which was expected to have occurred by that time in the experimental series, assuming that decomposition is linear as a function of time. The precise nature of the BH4- decomposition reaction is unknown, but the appearance of gas bubbles in older samples suggests that the first step of the decomposition is the deprotonation of CDCl3 with BH4as the hydride source, resulting in H2 evolution. (9) The Stokes-Einstein equation relates the self-diffusion coefficient D of a spherical species to the radius of that species r, the absolute temperature T, and solvent viscosity η by D ) kBT/6πηr.
