Closed-shell ion pairs: Cation and aggregate dynamics of tetraalkylammonium salts in a ion-pairing solvent

Article abstract of DOI:10.1021/ja9723139

Tetrabutylammonium ion (1) forms tight ion pairs with small anions (Cl^-, BH₄^-) in GDCl₃ solution. These ion pairs aggregate as a response to increasing solution concentration with little temperature dependence. Maximum aggregate size is approximately four ion pairs, as measured by comparing self-diffusion coefficients of the aggregates with that of an internal nonaggregating standard of the same shape and nominal size, tetrabutylsilane (2). The magnitudes of steady state interionic ¹H{¹H} NOEs observed between 1 and the BH₄^- anion in CDCl₃ as a function of temperature in solutions of fixed concentration are well fit to the standard theoretical expression by assuming a single aggregate size that is independent of temperature. A simplified model-free analysis was applied to steady state ¹⁵N{¹H} NOE and ¹⁵N T₁ measured at several magnetic field strengths, using ¹⁵N-labeled 1 to obtain estimates for reorientational correlation times for the ion aggregates. A similar analysis of ¹³C{¹H} NOE and ¹³C T₁ gives local effective correlation times for C-H bond vectors of the 1-CH₂ carbon of 1 and order parameters relating the local motion to overall cation motion. Comparison of these correlation times with those obtained from analysis of ²⁹Si{¹H} NOE, ¹³C{¹H} NOE, and ¹³C T₁ for silane 2 provides an estimate of aggregate size which is independent of that obtained by diffusion, with good agreement between the different approaches.

Full text of DOI:10.1021/ja9723139

11666
J. Am. Chem. Soc. 1997, 119, 11666-11673
Closed-Shell Ion Pairs: Cation and Aggregate Dynamics of
Tetraalkylammonium Salts in an Ion-Pairing Solvent
Huaping Mo, Anping Wang,† Patricia Stone Wilkinson,‡ and
Thomas C. Pochapsky*
Contribution from the Department of Chemistry, Brandeis UniVersity,
Waltham, Massachusetts 02254-9110
ReceiVed July 11, 1997. ReVised Manuscript ReceiVed September 26, 1997X
Abstract: Tetrabutylammonium ion (1) forms tight ion pairs with small anions (Cl-, BH4-) in CDCl3 solution.
These ion pairs aggregate as a response to increasing solution concentration with little temperature dependence.
Maximum aggregate size is approximately four ion pairs, as measured by comparing self-diffusion coefficients of
the aggregates with that of an internal nonaggregating standard of the same shape and nominal size, tetrabutylsilane
(2). The magnitudes of steady state interionic 1H{1H} NOEs observed between 1 and the BH4- anion in CDCl3 as
a function of temperature in solutions of fixed concentration are well fit to the standard theoretical expression by
assuming a single aggregate size that is independent of temperature. A simplified model-free analysis was applied
to steady state 15N{1H} NOE and 15N T1 measured at several magnetic field strengths, using 15N-labeled 1 to obtain
estimates for reorientational correlation times for the ion aggregates. A similar analysis of 13C{1H} NOE and 13C
T1 gives local effective correlation times for C-H bond vectors of the 1-CH2 carbon of 1 and order parameters
relating the local motion to overall cation motion. Comparison of these correlation times with those obtained from
analysis of 29Si{1H} NOE, 13C{1H} NOE, and 13C T1 for silane 2 provides an estimate of aggregate size which is
independent of that obtained by diffusion, with good agreement between the different approaches.
Introduction
contact between the anion and the protons on the methylene
group adjacent to the quaternary nitrogen of the cation. We
also used steady-state 11B{1H} and 10B{1H} NOEs as well as
10B and 11B relaxation measurements to characterize the motions
Ion pairing is a phenomenon of considerable interest to
physical scientists in a variety of fields, and has been under
intense investigation since Bjerrum first introduced the concept
in the early part of this century.1-3 Much of what is known or
conjectured concerning ion pairs is the result of measuring
electrical and colligative properties of ion pair-containing
solutions.4 However, as spectroscopic methods, particularly
magnetic resonance techniques, have become more sophisti-
cated, it has become possible to obtain more direct information
concerning the structure and dynamics of ion pairs.5-10 We
have previously described the use of steady-state 1H{1H} nuclear
Overhauser effects (NOEs) to characterize the time-average
structure of tetraalkylammonium tetrahydridoborate (R4N+,
BH4-) ion pairs in nonpolar solvents.11,12 This structure places
-
of the BH4 anion in these ion pairs.12 We found that in
solutions of tetrabutylammonium tetrahydridoborate (1a) in
CDCl3, the anion reorients rapidly (τc ∼ 10-12 s) relative to the
overall motion of the ion pair. Furthermore, anion reorientation
is sufficiently fast to average the local electrical environment,
suppressing quadrupolar relaxation of the boron nucleus to a
large extent. 10B and 11B relaxations for 1a do not show
significant differences when measured in nonpolar and dis-
sociative solvents (such as water), so ion pairing does not appear
to significantly affect the electronic environment of the boron.12
The motion of the cation, as well as the overall motion of
the ion pair, is somewhat more complicated. The results of
interionic NOE measurements for 1a and for the related
compounds tetraisoamylammonium tetrahydridoborate (1b) and
tetraoctylammonium tetrahydridoborate (1c) in chloroform over
a range of temperatures suggested to us that these ion pairs
aggregate in nonpolar solution.13 NMR self-diffusion measure-
ments performed with solutions of 1a in CDCl3 support the
conclusion that ion pairs formed by 1a aggregate in chloroform
and also confirm that the ion aggregate is the primary diffusing
species.14 Self-diffusion measurements for tetrabutylammonium
chloride (1d) permitted us to estimate aggregate size by
comparing the self-diffusion of the cation to that of a nonionic
internal reference of similar shape and nominal mass, tetra-
butylsilane (2).14 Similar estimates were made for for 1a as
well.15
-
the BH4 anion in a trigonal pyramidal site created by three
alkyl chains of the tetraalkylammonium ion, and shows close
† Current address, General Electric Inc., Waterfront, NY.
‡ Current address, Bruker Instruments, Inc., Billerica, MA.
X Abstract published in AdVance ACS Abstracts, November 15, 1997.
(1) Bjerrum, N. K. Dan. Vidensk. Selsk. 1926, 7, No. 9.
(2) Szwarc, M. Ions and ion pairs in organic reactions; Wiley-
Interscience: New York, NY, 1972 and 1974; Vols. 1 and 2.
(3) Reichardt, C. SolVents and SolVent Effects in Organic Chemistry,
2nd ed.; VCH: Weinheim, 1988.
(4) Copenhafer, D. T.; Kraus, C. A. J. Am. Chem. Soc. 1951, 73, 4557.
(5) Grutzner, J. B.; Lawlor, J. M.; Jackman, L. M. J. Am. Chem. Soc.
1972, 94, 2306.
(6) Chen, N.; Witton, P. J.; Holloway, C. E.; Walker, I. M. J. Coord.
Chem. 1988, 19, 113.
(7) Honeychuck, R. V.; Hersh, W. H. J. Am. Chem. Soc. 1989, 111,
6056.
(8) Kessler, H.; Feigel, M. Acc. Chem. Res. 1982, 15, 2.
(9) Miller, J. M.; Clark, H. H. J. Chem. Soc., Chem. Commun. 1982,
1318.
The present work is aimed at characterizing the motions of
the tetrabutylammonium (TBA+) cation and ion aggregates in
(10) Radley, K. Mol. Cryst. Liq. Cryst., Lett. Sect. 1989, 6, 203.
(11) Pochapsky, T. C.; Stone, P. M. J. Am. Chem. Soc. 1990, 112, 6714-
6715.
(12) Pochapsky, T. C.; Wang, A.-P.; Stone, P. M. J. Am. Chem. Soc.
1993, 115, 11084-11091.
(13) Stone, P. M.; Pochapsky, T. C.; Callegari, E. J. Chem. Soc., Chem.
Commun. 1992, 178-179.
(14) Pochapsky, S. S.; Mo, H.; Pochapsky, T. C. J. Chem. Soc., Chem.
Commun. 1995, 2513-2514.
(15) Mo, H.; Pochapsky, T. C. J. Phys. Chem. B 1997, 101, 4485.
S0002-7863(97)02313-5 CCC: $14.00 © 1997 American Chemical Society

Tetraalkylammonium Salts in Ion-Pairing SolVents
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11667
Table 1. Self-Diffusion Coefficients D Determined in CDCl3 at
298 K by Pulsed Field Gradient NMR Experiments As Described in
Refs 14 and 15 for Salts 1a, 1d and 1ea
anion in both salts diffuse at similar rates in moderately
concentrated solutions, as expected for tight ion pairs (see Table
1).15 However, only very small interionic NOEs are observed
between the acetate methyl protons and cationic protons of 1e.
This indicates that the carboxylate group of the anion interacts
most strongly with the tetrabutylammonium ion, and the methyl
group of the acetate is relatively far from the cationic center.
This is not suprising, since the driving force for ion pairing is
mainly electrostatic. The similar self-diffusion coefficients for
both the cation and anions of 1e appear to rule out extensive
solvent separation of the ions as the reason for this lack of
interionic NOE.
compd (concn, M)
ion
D (×10-10 m2/s)
N
-
1a (0.2)
1a (0.2)
1d (0.09)
1e (0.08)
1e (0.08)
BH4
5.34 ( 0.22
4.99 ( 0.14
6.20 ( 0.11
8.6 ( .2
4.2
5.2
3.5
TBA+
TBA+
TBA+
acetate
8.1
a Aggregation numbers N are calculated as the inverse cube of the
ratio of diffusion coefficients of the aggregating species and internal
reference tetrabutylsilane (2). Detailed descriptions of experiments are
given in refs 14 and 15. Errors are calculated from the maximum
deviations of diffusion coefficients calculated by using individual
resonances to the average coefficient for the molecule.
Cation and Aggregate Dynamics from NOE and T1
1
Relaxation. For a two-spin (I ) /2) system, the steady-state
NOE at spin I upon saturation of spin S may be expressed as:
solutions of 1a and 1d in nonpolar solvents. To accomplish
this, we fit the temperature dependence of homonuclear inte-
rionic NOEs using Solomon’s theoretical treatment, assuming
a single aggregate size.16 We have also measured 13C{1H} and
15N{1H} NOE and 15N and 13C nuclear relaxation parameters
in ion pairs formed by the tetrabutylammonium ion, and analyze
these data using a simplified version of the model-free approach
of Lipari and Szabo.18,19 Finally, we analyze 29Si{1H} NOE,
13C{1H} NOE, and 13C relaxation data for the reference
compound tetrabutylsilane (2) to obtain an estimate of aggregate
size independent of that obtained from NMR self-diffusion
measurements.
γS σIS
NOE ) fI{S} )
(1)
γI FIS + F*
where σIS is the dipolar cross-relaxation rate constant and FIS is
the total dipolar relaxation rate constant for spin I. If relaxation
pathways other than dipole-dipole (dd) exist, they attenuate
the NOE, and are represented by F*. The spin-lattice relaxation
rate constant for spin I, R1I, is given by:
R1I ) T-1I1 ) FIS + F*
(2)
Results and Discussion
Multiplication of eqs 1 and 2 yields:
General Considerations. Both the tetrahydridoborate 1a and
chloride 1d salts of TBA+ were used in the work described
γS
γI
NOE
T1I
)
σIS
(3)
-
here. Cl- and BH4 have the same charge and similar ionic
-
radii (1.9 Å for BH4 and 1.81 Å for Cl-). Both have
advantages and disadvantages for the present studies. Samples
of 1a have limited lifetimes in CDCl3 due to decomposition of
BH4-, whereas samples of 1d in chloroform can be prepared
and stored in sealed tubes indefinitely. 35Cl and 37Cl have
deficiencies as NMR probes, and the sensitivity of the interionic
Note that the expression on the right-hand side of eq 3 is also
the I{S} NOE buildup rate at short mixing times, which is linear
with respect to the cross relaxation rate constant σIS. The dipolar
relaxation rate constants FIS and σIS are related to spectral
densities and other experimental variables as follows:
-
1H{1H} NOE makes BH4 by far the preferred counterion for
TBA+ in experiments where interionic contacts or reorientations
of interionic vectors are to be examined. Nevertheless, there
is some indication (see Table 1) that at similar concentrations
and temperature, 1a aggregates to a somewhat greater extent
than 1d, and some caution is required when making comparisons
between results obtained with the two salts.
1
20
σIS ) k2[6J(ωI + ωS) - J(ωI - ωS)]
(4)
1
20
FIS ) k2[J(ωI - ωS) + 3J(ωI) + 6J(ωI + ωS)] (5)
Self-Diffusion of Ion Pairs. We have described the mea-
surement of self-diffusion coefficients for ion pairs formed by
1a and 1d in CDCl3 solution using pulsed field gradient-
stimulated echo NMR experiments.14,15 Using tetrabutylsilane
(2) as an internal reference, we showed that the aggregation of
ion pairs formed by 1d in CDCl3 is primarily a response to
solution crowding. Mean aggregate size increases with increas-
ing 1d concentration to an apparent maximum of ca. 4 ion pairs
per aggregate over the concentration range we have studied (up
to 0.1 M).14 Aggregation of 1d shows little temperature
dependence at a fixed concentration, indicating that aggregation
is enthalpically neutral under these conditions. Because of
sample stability considerations, temperature variation experi-
ments were not performed for solutions of 1a in CDCl3.
However, the concentration dependence of diffusion for 1a was
similar to that of 1d, so it is likely that similar thermodynamic
considerations are valid in both cases.
µ0
k ) γIγSr-IS3
4π
(6)
where µ0 is the magnetic permeability of vacuum, rIS is the
internuclear distance between spins I and S, and the γ are the
gyromagnetic ratios of the spins.16,17
If the overall motion of the internuclear I-S vector is isotropic
and can be described by a single correlation function, the spectral
density J(ω) can be expressed as:
2τc
J(ω) )
(7)
1 + ω2τ2c
where τc is the overall correlation time. Combination of eqs
1-7 gives:
The results of NMR self-diffusion measurements on 1a and
tetrabutylammonium acetate (1e) in CDCl3 show that cation and
(17) Abragam, A. Principles of Nuclear Magnetism; Clarendon Press:
Oxford, 1961.
(18) Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546.
(19) Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4559.
(16) Solomon, I. Phys. ReV. 1955, 99, 559.

11668 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Mo et al.
γS
γS
γI
NOE )
×
NOE )
×
γI
6
1
6
1
-
-
1 + (ωI + ωS)2τc2 1 + (ωI - ωS)2τ2c
1 + (ωI + ωS)2τc2 1 + (ωI - ωS)2τ2c
1
3
6
10F*
k2τc
(8)
1
3
6
10F*
+
+
+
+
+
+
+
1 + (ωI - ωS)2τc2 1 + ωI2τc2 1 + (ωI + ωS)2τ2c
1 + (ωI - ωS)2τ2c 1 + ω2I τc2 1 + (ωI + ωS)2τ2c k2s2τc
(12)
1
1
T1I )
×
T1 )
×
1
1
k2τc
k2s2τc
10
10
1
1
1
3
6
10F*
k2τc
(9)
1
3
6
10F*
+
+
+
+
+
1 + (ωI - ωS)2τc2 1 + ωI2τc2 1 + (ωI + ωS)2τ2c
1 + (ωI - ωS)2τ2c 1 + ω2I τc2 1 + (ωI + ωS)2τ2c k2s2τc
(13)
Phenomenologically, eqs 12 and 13 are equivalent to eqs 8 and
9, with k2s2 replacing k2. For the purposes of data analysis we
rewrite eqs 12 and 13 as:
Equations 8 and 9 describe the relationship between the
observables NOE and T1 with the motional behavior represented
by the correlation time τc, estimates for which are obtained by
fitting experimental data. To accomplish this fit, reasonable
values for k2 and F* are required. An a priori estimate of F*
is difficult to obtain, since by definition, multiple mechanisms
may contribute to this rate constant and their origins may be
NOE )
6
1
-
γS
γI
1 + (ωI + ωS)2τc2 1 + (ωI - ωS)2τ2c
quite complicated. The parameter k2 is proportional to rI-S6
.
c1
1
3
6
However, when dealing with large numbers of nuclei which
may be contributing to the dipolar relaxation of the observed
nucleus, the appropriate value of rIS is not obvious, and both
F* and k must be treated as fittable parameters.
+
+
+
1 + (ωI - ωS)2τc2 1 + ωI2τc2 1 + (ωI + ωS)2τ2c
τc
(14)
T1 )
c2
The fitting as described above also requires an assumption
of isotropic motion in which one correlation time is sufficient
for describing all motion in the system. The model-free
formalism of Lipari and Szabo allows the consideration of more
than one type of motion affecting relaxation.18,19 In this
approach, the overall molecular motion is isotropic and char-
acterized by a correlation time τc, while the motion of the
internuclear I-S vector has an effective correlation time τeff.
The local motion is described by τeff, which correlates to some
extent with τc. The order parameter s is used to represent this
correlation, with s ) 1 representing complete correlation (τc )
τeff) while s ) 0 indicates that the local motion is completely
uncorrelated with the overall motion of the molecule. (Situa-
tions where s ) 0 are expected to be rare intramolecularly, but
might apply in the present case when considering the relationship
1
τc
c1
1
3
6
+
+
+
1 + (ωI - ωS)2τc2 1 + ωI2τc2 1 + (ωI + ωS)2τ2c
τc
(15)
The ratio of the two expressions eliminates the leakage term
c1/τc:
τc γS
NOE
T1
6
1
)
-
(16)
2
2
2 2
c γ
(
)
2
I 1 + (ωI + ωS) τc 1 + (ωI - ωS) τc
The ratio NOE/T1 provides information concerning the cross
relaxation rate between I and S. For small molecules in
nonviscous solvents, the extreme narrowing limit (ω2τc2 , 1)
holds, and NOE/T1 is directly proportional to τc. As the
temperature is lowered, the correlation time becomes longer and
the absolute value of NOE/T1 becomes larger. However, once
the system begins to move away from the extreme narrowing
limit, the factors containing the inverse ω2τc2 terms become
important, and the absolute value of NOE/T1 decreases. There-
fore, as a system moves from the extreme narrowing limit into
a broadening regime, a maximum or minimum in the curve of
NOE/T1 versus τc (or temperature) is expected, depending on
relative signs of the gyromagnetic ratios of the spins involved.
This phenomenon is observed for ion pairs discussed here (vide
infra).
-
between the motion of the ion aggregate and the BH4 anion,
which appears to be uncorrelated, see ref 12.) According to
this approach,
s2τc
(1 - s2)τ
J(ω) ) 2
+
(10)
2
2
2
2
(
)
1 + ω τc
1 + ω τ
where τ-1 ) τ-c 1 + τ-1
.
eff
If internal motion is very fast compared with overall orienta-
tion of the molecule, in the limit of τeff f 0 and s not very
small, J(ω) can be simplified as:18
s2τc
1 + ω2τc2
1
Aggregation Effects on Interionic Steady State H{1H}
J(ω) ) 2
(11)
NOEs: Evaluation of Aggregate Rotational Correlation
Times. We previously reported that steady-state interionic
BH4--{1-CH2} NOEs observed for ion pair 1a and related ion
pairs in CDCl3 are profoundly temperature sensitive. As the
temperature is decreased from 298 K the observed NOE
becomes smaller, finally becoming zero around 223 K in a 7.05
This result differs from eq 7 by only a factor of s2, which means
that fast internal motion makes dipolar relaxation less efficient.
Now combining eqs 7-9 and 11 gives the following
expressions for the NOE and T1 with s2 included:

Tetraalkylammonium Salts in Ion-Pairing SolVents
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11669
Table 2. Values of NA and c1 Obtained from Nonlinear
Least-Squares Fitting of Experimental NOE Data for Interionic
BH4--{1-CH2} NOEs Observed for 1a As Shown in Figure 1
Bo (T)
NA
c1 (s)
7.05
11.74
2.39 ( 0.05
2.45 ( 0.05
(2.6 ( 0.1) × 10-9
(1.7 ( 0.1) × 10-9
Figure 1. Nonlinear fit of steady-state interionic BH4--{1-CH2} NOEs
observed as a function of temperature for 0.2 M 1a in CDCl3 as
described in refs 12 and 13. Coarse dashed line fits data obtained at
11.74 T, and fine dashed line fits data obtained at 7.05 T. Best-fit values
of parameters NA and c1 are shown in Table 2.
T field (300 MHz 1H).13 Because the observed interionic NOEs
deviate from what is predicted from eq 8 on the basis of the
estimated correlation time of a single ion pair, it was concluded
that ion pairs of type 1 aggregate in CDCl3, at least at low
temperatures and moderate concentrations (0.2 M), with ωτc ≈
1.12 at 223 K. At that time, we made no attempt to fit the
interionic NOE data to eq 8, as we assumed that average
aggregate size would change as a function of temperature.
However, the observation from self-diffusion measurements that
the apparent aggregation state of ion pair 1d is little affected
by temperature, but appears to be almost completely a response
to increasing concentration, has made it reasonable to attempt
to fit the homonuclear interionic NOE to a single aggregate
size.14 Before data analysis was begun, a complementary
steady-state BH4--{1-CH2} NOE data set was obtained at 11.74
T (500 MHz 1H). The higher field changes the value of ωτc at
a particular temperature for a given sample and improves
confidence in the fitting routine (vide infra). The results of
both experimental runs are shown in Figure 1.
Figure 2. Nonlinear fit of steady-state 15N{1H} NOEs observed as a
function of temperature for 0.2 M 15N-labeled 1d in CDCl3. Errors bars
define 10% error in the observed data. Fit was obtained simultaneously
for data at all field strengths. The coarse dashed line fits data obtained
at 7.05 T (diamonds), the fine dashed line fits data obtained at 9.39 T
(stars), and the solid line connects data obtained at 11.74 T (squares).
Best-fit values of parameters are NA ) 3.81 ( 0.14 and c ) 2 × 10-13
2
s/(rad‚T2), where cBo ) CSA as explained in the text.
monomers. The corrected correlation time, including the
correction for aggregation, is:
τc ) NA4πηr3/3kT ) NAτs
(18)
Assuming a monomeric radius of 5 Å for ion pair 1a, and
using experimentally determined values for solvent viscosity,21
the interionic BH4--{1-CH2} NOEs a observed at two field
strengths, 7.05 and 11.74 T, were fitted to eq 14 by varying
NA and c1, the best-fit values of which are listed in Table 2.
Experimental data and fitted curves are shown in Figure 1. It
can be seen from Table 2 that similar NA values are obtained
at both magnetic field strengths. Two conclusions can be
reached from this. First, the data are well fit with a single value
of NA (see Figure 1), so the aggregation number does not appear
to change significantly as a response to temperature. Secondly,
if A is a number near 1, the mean aggregate size is unlikely to
be very large. Both of these conclusions are in agreement with
those reached on the basis of our diffusion measurements on
1a and 1d in CDCl3. c1 is also similar at both field strengths,
and an explicit field dependent term was not required to obtain
a good fit for this parameter. This is not true for relaxation
and NOE involving 15N in the ion pairs under study here (vide
infra).
To incorporate aggregate size into an expression for the
steady-state NOE (or for nuclear spin relaxation), a relationship
is needed between aggregation state and the rotational correlation
time, τc. The Stokes-Einstein equation is commonly used for
predicting the correlation time as a function of experimental
parameters:
τs ) 4πηr3/3kT
(17)
where η is the viscosity of the solution, r is the radius of the
molecule, k is Boltzmann’s constant, and T is the absolute
temperature. It has been found that the correlation time
predicted by eq 17 (referred to hereafter as τs) is often larger
than that measured experimentally, except for small polar
molecules.20 To adjust for such discrepancies in our fitting of
Overall Cation Reorientation: 15N- and 29Si -{1H}NOE
and T1 Measurements for 1d and 2. The reorientation of any
internuclear vector through the central nitrogen of the tetra-
butylammonium ion correlates strongly with the overall τc for
the cation. Relaxation and NOE parameters for 15N are therefore
expected to report on the rotational motion of the cation. We
synthesized 15N-labeled 1d and performed a series of steady-
state 15N{1H} NOE and 15N T1 measurements as a function of
temperature and magnetic field intensity. Steady-state 15N{1H}
1
the H{1H} NOE data for 1a, we multiply τs by a correction
factor A. A is expected to be a number not far from unity and
a constant for molecules of similar size and shape (such as 1a
and 2), and will also correct for any inaccuracies in the value
used for the molecular radius r. We also assume that the volume
of the aggregate increases linearly with aggregation number,
N. This is justified by noting that the correlation time is directly
proportional to the volume of a spherical species. In this case,
the overall correlation time of the aggregate will be N times
that of the monomer, assuming no interpenetration of the
NOE was obtained by broad-band presaturation of 1H, and 15
N
T1 values were measured with the inversion recovery method.
(20) Gierer, A.; Wirtz, K. Z. Naturforsch. A 1953, 8, 532.
(21) Phillips, T. W.; Murphy, K. J. Chem. Eng. Data 1970, 15, 304.

11670 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Mo et al.
Both 15N{1H} NOE and 15N T1 decrease in magnitude with
decreasing temperature. However, the ratio NOE/T1, which
removes the field-dependent term c1 from the fit, is more
sensitive to the precise value of NA than the NOE term by itself.
As τc increases with decreasing temperature, FIS increases while
σIS also increases at first, then begins to decrease, as expected
from eq 16. As the system moves out of the extreme narrowing
regime with increasing correlation time, the ratio NOE/T1 goes
through a minimum (at least for 15N, because of the negative
sign of the gyromagnetic ratio). The position of the minimum
is very sensitive to the value of NA used for the fit of NOE/T1
(see Figure 3). A value of NA ) 2.5 gives the best fit to eq 16
for the position of the minimum as a function of temperature at
all three fields (see Figure 3). However, the data at the extremes
of temperature are not well fit to eq 16, particularly at 11.74 T.
The assumption of an inverse temperature dependence of NA
improves the fit, so it is possible that there is a small favorable
enthalpic contribution to aggregation of ion pairs formed by
1d (see Figure 4, parts a-c), although such an effect is not
observed in self-diffusion measurements for 1d.14 So it may
be that some other as yet unknown consideration is still missing
from the analysis.
Figure 3. Plot of eq 16 for 15N{1H} NOE/ 15N T1 expected at 11.74
T for ion pair 1d in CDCl3 as a function of temperature for three values
of NA at an arbitrary value of c2. Calculations were performed as
described in the text assuming that NA is independent of temperature.
The dotted line (‚‚‚) is for NA ) 1.5, the broken line is for NA ) 2,
and the solid line is for NA ) 2.5, the best fit value. For comparison,
the experimental values of the ratio measured at 11.74 T are shown as
filled squares.
To analyze the results of 15N experiments, it was necessary
to use a two-spin approximation, treating all of the protons in
the molecule as a single nucleus. If 1H is not decoupled during
relaxation, the 15N spin-lattice relaxation (T1) is biexponen-
tial: one rate constant being FIS + σIS and the other being FIS
- σIS. Considering the fact that FIS is at least twice σIS, and
that F* does not contribute to the cross-relaxation rate σIS, we
assume that the rate of T1 relaxation is FIS - F* so that a single
exponential rate constant may be used to describe this process.
For this reason, the value of T1 calculated by using a single
exponential fit is expected to have ∼10% error. In fact, a single
exponential fit works quite well in the present case. 15N{1H}
NOE buildup experiments were also performed to provide an
To extract an estimate of aggregation number N from the
values of NA shown in Tables 2 and 3, a value of NA for a
non-aggregating species of similar size and shape to the TBA+
ion is needed. We measured 29Si{1H} NOE and 29Si T1 for
tetrabutylsilane (2, 0.2 M in CDCl3), which has the same shape
and size as the tetrabutylammonium ion but is uncharged and
so is expected to have an aggregation number of N ) 1. To a
first approximation, the motional behavior of interatomic vectors
originating at the silicon atom of 2 and at the quaternary nitrogen
in 1d will have similar constraints. Steady-state 29Si{1H} NOEs
observed for 2 at 11.74 T with use of broadband 1H decoupling
are essentially constant over the temperature range 253 to 298
K (measured fractional enhancements of -2.35 at 253 K and
-2.37 at 298 K), with a maximum theoretical enhancement of
-2.52. These values are consistent with an NA ) 1.1 ( 0.1
for 2, which, when compared to the corresponding 15N{1H}
NOEs for 1d, yields an aggregation number for 1d of N ) 3.2
( 0.2, a value similar to that obtained from diffusion measure-
ments (see Table 1). A comparison of NOE/T1 for 1d and 2 is
more problematic. 29Si T1 relaxation for 2 is quite long, ranging
from 44 s at 298 K to 12 s at 253 K, and the measurement is
difficult due to the insensitivity and low natural abundance of
29Si. However, measurements of 13C{1H} NOE and 13C T1 for
both 1d and 2 provide alternate means of measuring aggregation
(vide infra).
Local Motions of Alkyl Groups in 1d and 2: 13C{1H}-
NOE and 13C T1. In contrast to 15N or 29Si relaxation described
in the previous section, in which protons are not directly bonded
to the relaxing nuclei and other relaxation mechanisms might
compete significantly, methylene 13C relaxation in 1d and 2 is
dominated by dipolar interactions with the attached protons.
Good fits of 13C NOE/T1 are obtained for the relaxation of the
1-CH2 (directly attached to the central heteroatom) with both
compounds. Since broadband decoupling of 1H was performed
during the 13C T1 relaxation experiments, T-1 1 ) FIS in theory.17
However, T1 is still assumed to be subject to 10% experimental
error.
independent estimate of the weighted average N-H distance
-3
NH
r
for calculating σIS.
Interestingly, an explicit magnetic field dependence for c1 is
required for fitting the steady state 15N{1H} NOE. At a given
temperature, 15N T1 decreases with increasing field strength, and
the magnitude of the NOE (which is negative in sign) also
decreases with increasing field strength. This field dependence
suggests that chemical shift anisotropy (CSA) provides an
alternate pathway for 15N T1 relaxation. This is intriguing in
that, although CSA is often an important mechanism for 15N
T1 relaxation, it might not be expected to contribute significantly
in the present case since the TBA+ cation is symmetric. For
example, ∆σ for the ammonium ion in the solid state is 0.22
One likely explanation for the observed field dependence of
15N T1 relaxation is that the Cl- anion is bound in one of the
trigonal pyramidal sites provided by the TBA+ cation with a
mean lifetime long enough to induce anisotropy in the local
environment of the 15N nucleus. The CSA is included in the
calculations by assuming that it is the only contributor to F*,
2
and replacing F* with cBo in which Bo is the magnitude of
field strength and c represents the magnitude of the CSA. The
extreme narrowing limit is assumed to apply for 15N CSA
relaxation, which is dependent only on ωN (τc < 10-10 s), and
does not change over the temperature range studied. Figure 3
shows fitted experimental data for the 15N{1H} NOE at 7.05,
9.39, and 11.74 T, respectively. The data are best fit by using
NA ) 3.81.
Fitting NOE/T1 data for the 1-CH2 methylene carbon of 1d
to eq 16 in a manner similar to that described in the previous
section yielded the fits shown in Figure 5. The simplified
Lipari-Szabo treatment was used for data fitting (see eq 11).
The corresponding data for silane 2 gave a best fit value of NA
) 0.54. Dividing this into the values of NA obtained for 1d
(22) Gibby, M. G.; Griffin, R. G.; Pines, A.; Waugh, J. S. Chem. Phys.
Lett. 1972, 17, 80.
(23) Harbison, G.; Herzfeld, J.; Griffin, R. G. J. Am. Chem. Soc. 1981,
103, 4752.

Tetraalkylammonium Salts in Ion-Pairing SolVents
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11671
Figure 5. Fitting of NOE/T1 data for the 1-CH2 methylene carbon of
1d (0.2 M in CDCl3) to eq 16. The dashed line fits data obtained at
7.05 T, the solid line connects data obtained at 11.74 T. Table 3 lists
best-fit values of NA and c2.
Table 4. Values of NA and Fitting Constant c2 Obtained from
Nonlinear Least-Squares Fitting of 13C NOE and Relaxation Data
for 1-CH2 Carbons of 1d and 2
compd
Bo (T)
7.05
11.74
NA
c2 (×1010 s)
3.63 ( 0.09
4.58 ( 0.01
5.7 ( 2.0
1d
1d
2
1.80 ( 0.09
2.38 ( 0.13
0.54 ( 0.21
7.05/11.74
Table 5. Correlation Times τ at 298 K for Various Types of
Motion in Ion Pairs of Type 1 Shown in Figure 6a
compd
type of motion
anion reorientationb
effective for 1-CH2 local motion
τ (ps)
1a
1d
1d
4
160
260
overall cation/aggregate reorientation
a Values of τ were calculated by using the values of NA obtained
from nonlinear least-squares fitting of experimental NOE and relaxation
data. b See ref 12 for complete description.
Discussion
The experimental data and analysis presented here provide
insight into the molecular motions of cations and ionic ag-
gregates in closed shell ion pairs formed in nonpolar solvents
by lipophilic quaternary ammonium ions with small anions.
Table 4 provides a summary of motional behavior in terms of
correlation times calculated by using the values of NA deter-
mined here. Figure 6 provides a graphical representation of
the types of independent motions which can occur.
Figure 4. (a) Fit of 15N{1H} NOE/ 15N T1 measured at 7.05 T as a
function of temperature for ion pair 1d (0.2 M in CDCl3). The fit was
made assuming an inverse temperature dependence of N as described
in the text. Values of NA and c2 are shown in Table 3. (b) Fit of 15N-
{1H} NOE/ 15N T1 measured at 9.39 T as a function of temperature for
ion pair 1d (0.2 M in CDCl3). The fit was made assuming an inverse
temperature dependence of NA and c2 as described in the text. Values
of NA and c2 are shown in Table 3. (c) Fit of 15N{1H} NOE/ 15N T1
measured at 11.74 T as a function of temperature for ion pair 1d (0.2
M in CDCl3). The fit was made assuming an inverse temperature
dependence of NA as described in the text. Values of NA and c2 are
shown in Table 3.
Order parameters for the motion of the 1-CH2 bond vectors
in 1d and 2 may be estimated by comparing best-fit values of
NA calculated from 13C NOE/T1 to those obtained from the 15
N
and 29Si relaxation parameters. The relaxation behavior of the
central atom in each species reflects the overall correlation time
of the ion pair (or aggregate) τc. In the simplified Lipari-Szabo
treatment used here, the spectral density at the extreme
narrowing limit which accounts for local motion is given by
s2τs, where s is the order parameter correlating local motion to
the overall motion of the molecule (see eq 11). Thus, the ratio
of values of NA obtained for the same species from relaxation
of the central atom (spectral density determined by τs) and the
adjacent carbon atom (spectral density determined by s2τs)
should yield an estimate for the order parameter. The ratio of
the value of NA for 2 obtained from 29Si{1H} NOE to that
obtained from the 13C NOE/T1 for the same species is 0.6,
yielding an order parameter of s ) 0.77 for the local motion of
the C-H bond in the 1-methylene of the silane. The corre-
sponding calculation for ion pair 1d with use of the values of
NA obtained from 15N{1H} NOE yields an order parameter of
Table 3. Values of NA and c2 Obtained from Least-Squares Fitting
of Experimental 15N NOE/T1 Data Observed for 1d As Shown in
Figures 4a-c
NA
Bo (T)
298 K
223 K
c2 × 108
2.07 ( 0.05
2.00 ( 0.06
1.66 ( 0.06
7.05
9.39
11.74
1.77 ( 0.08
2.09 ( 0.14
2.07 ( 0.16
2.36 ( 0.08
2.80 ( 0.14
2.76 ( 0.22
from the corresponding experiments yields an aggregation
number of 3.2 ( 0.6, the same as that calculated from the 15
N
and 29Si experiments described in the previous section.

11672 J. Am. Chem. Soc., Vol. 119, No. 48, 1997
Mo et al.
closed shell ion pairs of this type, since the lifetimes of these
discrete ion binding modes are long relatiVe to bond-making
and bond-breaking processes. In this light, the study of ion
pair solution structure is particularly relevant when considering
the mechanism of phase-transfer reactions and selective phase
transfer catalyst design.
The general agreement between the agreggation numbers
calculated by NMR diffusion experiments and those calculated
with relaxation data supports our earlier conclusions that
aggregate size is limited to less than five ion pairs even in the
fairly concentrated solutions of ion pairs used in these experi-
ments. This is not in agreement with the rather large aggregate
sizes for these types of ion pairs calculated with freezing point
depression methods.4 Furthermore, although self-diffusion is
a translational phenomenon rather than rotational, the size of
the aggregate formed appears to determine both rotational and
translational motion, which suggests that the aggregates are
roughly spherical, the shape for which both the diffusional and
rotational forms of the Stokes-Einstein equation are best suited.
We are currently preparing selectively labeled samples of 1d
to determine the time-average shapes of these ion aggregates
using interionic NOEs.
Figure 6. Types of motion in closed shell ion pairs of type 1. (a)
Local motion of bond vectors, reflected in the relaxation behavior of
alkyl carbons. (b) Reorientation of the anion, reflected in 10B and 11B
relaxation in 1a. (c) Overall isotropic reorientation of the ion pair (or
aggregate) reflected in the relaxation of the quaternary nitrogen and
interionic NOE.
Experimental Section
Synthesis of 15N-Labeled 1d. A 200-mg (3.67 mmol) sample of
15NH4Cl (CIL) was mixed with 5 mL of ethyl acetate, along with 2.7
g (14.7 mmol) of butyl iodide and 2.5 g (14.7 mmol) of 1,2,2,6,6-
pentamethylpiperidine (PMP) in a 100-mL sealable bomb. The mixture
was purged briefly with N2 gas, and the bomb was sealed under N2.
The reaction mixture was then heated to 90 °C, and held there for 2
weeks. It was found to be critical that the reaction not be allowed to
heat over 100 °C, or byproducts were formed which rendered the
purification more difficult. As the reaction proceeds, PMP hydroiodide
salt and product precipitate from the reaction mixture. After cooling,
the precipitate (which contains the product) was filtered and washed
with a mixture of hexane and ethyl acetate to remove unreacted alkyl
halide. The solid material was then washed three times with 5 mL of
acetone, which selectively dissolves the product tetrabutylammonium
iodide. After removal of the acetone by rotary evaporation, the crude
product was recrystallized from hot water. The exchange of chloride
for iodide was accomplished as described by Ford-Moore.24 Into a
10-mL round-bottom flask was placed 0.92 g of AgNO3 and 3 mL of
distilled water. This solution was heated to boiling and 0.75 mL of
concentrated hydrochloric acid was added dropwise with stirring. After
the mixture was stirred for 30 min, the supernatant liquid was decanted,
and the solid silver chloride was resuspended in 10 mL of distilled
water and heated to 60 °C. A solution of 0.8 g of the mixed
tetrabutylammonium chloride/iodide was dissolved in 3 mL of methanol
and added dropwise to the silver chloride. A yellow precipitate of
AgI forms as the addition proceeds. The mixture was stirred at reflux
for another hour and then allowed to cool with stirring for half an hour.
The precipitate was filtered and washed with hot water, and the filtrate
was concentrated under vacuum to yield a white solid, 15N-1d. The
completeness of the alkylation reaction and purity of the product were
confirmed by NMR. The final yield was 15% of theoretical.
s ) 0.81. The consistency of these values suggests that the
observed differences in NA obtained by the various techniques
are not an artifact of the analysis or the experiment, but reflect
real differences in the types of motion being measured.
Comparison of Motional Correlation Times of the Ag-
gregate, the Cation, and the Anion in 1a and 1d. Table 5
lists correlation times for various types of motion in ion pairs
1a and 1d based on the present results. In a previous
publication, we described the use of 10B and 11B relaxation and
10B{1H} and 11B{1H} NOE to characterize the motional behavior
-
of the BH4 anion in ion pairs formed by 1a in CDCl3. Our
conclusion from that work was that the anion was reorienting
rapidly within a discrete binding mode (τc on the order of ps),
averaging the electronic environment quickly enough to average
out any electric field gradients due to the nearby cation, thereby
suppressing the quadrupolar relaxation of both boron nuclides
to a large extent. The observation of a field dependence for
15N relaxation at the nominally symmetric quaternary am-
monium nitrogen suggests that some residual chemical shift
anisotropy exists in the tight ion pair. Given that anisotropies
even for nonsymmetric quaternary ammonium ions are very
small (∆σ ≈ 10 ppm, see ref 23), it is unlikely that the
anisotropy introduced by the presence of the anion is larger than
100 ppm. When this number is used to estimate a slow-
exchange limit at 11.74 T, the lifetime of the chloride anion
occupying a discrete binding mode is probably longer than 10-5
s, since CSA is incompletely averaged on the time scale of
relaxation processes. This reduces the range of discrete binding
mode lifetimes considerably from our earlier range of between
10-8 and 10-2 s. These previous estimates were based on the
dominance of the correlation time of the aggregate upon the
Synthesis of Tetrabutylsilane (2). Tetrabutylsilane (2) used in
NMR experiments was either distilled from commercially available
material (Lancaster) or prepared according to the method of Gilman
and Clark.25 Into a dry three-necked 25-mL round-bottom flask fitted
with a condenser and N2 inlet was add 3 mL of anhydrous diethyl ether.
The flask was placed in an ice bath, and 5 mL (0.043 mol) of
tetrachlorosilane (Petrarch) was introduced by syringe. Then, 65 mL
of a 1.6 M butyllithium solution in diethyl ether (0.104 mol) was added
dropwise with stirring. A white precipitate formed as addition
continued. After addition was complete, the ice bath was removed
and the reaction mixture brought to reflux and held there for 30 min.
1
sign and intensity of the interionic H{1H} NOE for 1a, the
absence of differential relaxation effects between 10B and 11B
in the same samples, and the observation of only averaged
chemical shifts for all species in these studies.12 If these new
range estimates are correct, then this suggests that the structure
and dynamics of discrete binding modes are important consid-
erations in determining the outcome of reactions involving
(24) Ford-Moore, A. H. Organic Synthesis; John Wiley & Sons: New
York, 1963; Collect. Vol. IV, p 84.
(25) Gilman, H.; Clark, R. N. J. Am. Chem. Soc. 1947, 69, 967.

Tetraalkylammonium Salts in Ion-Pairing SolVents
J. Am. Chem. Soc., Vol. 119, No. 48, 1997 11673
After cooling, the reaction mixture was hydrolyzed by the addition of
dilute HCl. The ether and water layers were separated, and the ether
layer was washed once with 15 mL of concentrated H2SO4 and three
times with 30 mL of water. The ether layer was dried over anhydrous
sodium sulfate and concentrated under vacuum to yield a clear liquid.
This liquid was fractionally distilled with use of a Vigeroux column,
and the fractions obtained between 85 and 145 °C were collected. This
fraction was redistilled, and the fractions obtained beteen 120 and 145
°C were recollected. Purity of the product was confirmed by NMR.
NMR Spectroscopy. Experiments were performed on one of three
instruments. The 7.05 T experiments were performed on a Varian XL-
300 (Brandeis University) equipped with a broad band probe, the 9.39
T experiments were performed on a Bruker ARX-400 (Bruker Instru-
ments, Billerica, MA), and the 11.74 T experiments were performed
on a Bruker AMX-500 (Brandeis University). Both the ARX-400 and
AMX-500 are equipped with broadband tunable probes. As a function
spectra were obtained in a similar fashion, but without the 1H
presaturation. NOE was measured by integrating the signal intensity
of the X resonance in the presence of H saturation, subtracting the
signal intensity without saturation, and dividing the diffference by the
signal intensity without saturation.
1
X T1. Heteronuclear T1 values were measured by using a standard
inversion recovery sequence delay-π-τ-π/2-acq, where τ is the
variable relaxation delay. Eight values of τ ranging from 0 to 2 s were
used. For 15N and 29Si T1 measurements, 1H decoupling is applied only
during acquisition. For 13C T1, 1H decoupling was applied during the
delay prior to the beginning of the sequence as well as during
acquisition.
Data Fitting. All data fitting was performed as described in the
text with use of the nonlinear regression analysis package available
with Mathematica 3.0 (Wolfram, Inc.), and values of the fitting
parameters obtained from these analyses were used to calculate the
fitting curves shown in all figures. All plots of data and fitting curves
were also prepared with use of Mathematica 3.0. Previously reported
viscosity data21 for chloroform as a function of temperature were fit
by using a linear least-squares routine in Mathematica 3.0 to yield the
following expression:
1
of magnetic field strength (7.05, 9.39, and 11.74 T), H resonates at
300, 400, and 500 MHz, respectively, 15N resonates at 30.4, 40.5, and
50.7 MHz, respectively, 13C resonates at 75.4, 100.6, and 125.7 MHz,
respectively, and 29Si resonates at 59.6, 79.5, and 99.3 MHz, respec-
tively.
Sample Preparation. Samples were prepared for spectroscopy in
CDCl3 (Cambridge Isotopes Laboratories) that had been passed over
activated neutral alumina to remove traces of acid. Tetrabutylammo-
nium tetrahydridoborate was obtained from Aldrich, tested for purity
by elemental analysis, and used without further purification. Samples
to be used in NOE experiments were freeze-thaw degassed multiple
times to remove traces of oxygen.
log η ) -3.646 + 584.9t-1 + (7.22 × 10-3)t - (8.26 × 10-6)τ2
Values for chloroform viscosity calculated with use of this expression
were then substituted into the fitting equation to obtain τs as a function
of temperature.
Steady State X{1H} NOE. The experimental conditions for
measurement of the selective interionic 1H{1H} NOE have been
described previously.12 Steady state heteronuclear NOEs were measured
by using broadband composite pulse saturation of 1H during a
preaquisition delay time set to approximately five times the T1 relaxation
time in order to ensure steady state, followed by a read pulse on X and
Acknowledgment. This work was supported in part by a
grant from the NSF (CHE-9510131). T.C.P. also acknowledges
support from the NSF Young Investigators Program (CHE-
9257036) and the Camille and Henry Dreyfus Teacher-Scholar
Program.
1
direct observation of the X nucleus with H decoupling. Reference
JA9723139