.
Angewandte
Communications
Table 1: Second-order rate constants for the nucleophilic substitution of [Ar3Pic][Cl] at 294.3 K in a range
of 1-alkyl-3-methylimidazolium ILs.
This can then be combined to
give Equation (3), where Vp is the
volume of the polar domain and Vtot
is the total volume of the system.
The full derivation of this expres-
sion and the underlying assump-
tions made can be found in the
Supporting Information.
Rate constants [ꢀ10ꢁ4 mꢁ1 sꢁ1 [a]
]
IL
Water
Methanol
Ethanol
1-Propanol
1-Butanol
Benzyl alcohol
[C2MIM][NTf2]
[C4MIM][NTf2]
[C6MIM][NTf2]
[C8MIM][NTf2]
[C10MIM][NTf2]
17.0ꢀ0.5
20.6ꢀ0.3
31.9ꢀ1.1
43.3ꢀ0.5
45.5ꢀ0.9
33.8ꢀ0.4
46.5ꢀ1.9
57.5ꢀ1.3
68.6ꢀ7.6
70.5ꢀ3.6
12.5ꢀ0.4
16.6ꢀ0.1
20.5ꢀ0.9
24.7ꢀ0.5
24.3ꢀ1.4
12.7ꢀ0.3
16.7ꢀ1.4
20.2ꢀ0.8
23.2ꢀ0.8
25.4ꢀ0.3
14.1ꢀ0.8
17.3ꢀ1.2
22.4ꢀ0.5
24.2ꢀ1.9
26.0ꢀ1.3
5.8ꢀ0.2
8.0ꢀ0.6
8.7ꢀ0.2
11.2ꢀ0.3
12.1ꢀ1.1
kpðVtotÞ ½ROHꢂtot½Ar3Picꢂtþot
2
[a] Rate constants were obtained by dividing the pseudo-first-order rate constants by the initial
concentration of nucleophile (0.515m for all reactions). Reported errors are standard deviations of at
least three replicate experiments.
À
Á
r ¼
ð3Þ
Vp KVtot þ Vpð1 ꢁ KÞ
As the total volume of the
the hydrogen bond strength caused by utilizing 1-butyl-2,3-
dimethylimidazolium bis(trifluoromethanesulfonyl)imide
system was maintained at 1.05 mL for all reactions, only the
volume of the polar domains is required in order to fit this
model to the observed bimolecular rate constants. The
volume of the nonpolar domains was estimated by a group
contribution method where the volume of a CH2 group was
treated as 17.2 mLmolꢁ1, a value that has previously been
found for imidazolium ILs,[9] and the CH3 group was assigned
a volume of 25.49 mLmolꢁ1 based on the findings of
Plyasunov et al. regarding aliphatic esters.[10]
Fitting these data to the Vp values estimated by this
method led to the plots in Figure 1. As can be observed, R2
values greater than 0.92 were obtained for all nucleophiles in
Figure 1 with excellent fits obtained in most cases, particularly
given the relative simplicity of the model. In addition, the
fitted K parameters obtained were consistent with values that
could be anticipated in light of literature precedence. The
fitted K value for water was zero (within error), indicating it
does not partition into the nonpolar domains, as has been
predicted through molecular dynamics (MD) simulations and
determined spectroscopically.[11]
The value of K increased with the length of the side chain
for the aliphatic alcohols, consistent with the increased
hydrophobicity leading to more favorable partitioning into
the nonpolar domains. The K values for the alcohols also
suggest significant interactions with both domains, as have
been predicted by MD.[11a] The K value obtained for benzyl
alcohol was similar to that for methanol rather than for
a longer chain alcohol and might arise from the quadrupolar
interactions between the polar domain of the IL and the
aromatic ring, as has been found for other aromatic systems in
ILs, thereby favoring benzyl alcoholꢁs solvation in the polar
domain.[12]
It is worth discussing that the rate constant obtained in
[C4MIM][NTf2] with water as a nucleophile (Vp = 0.85 mL)
lies significantly below that predicted by the fitted model.
[C4MIM][NTf2] has been found to possess a nonpolar domain;
however, owing to the bulk of the [NTf2] anion, this domain is
not a continuous microphase like that found for imidazolium
ILs with longer alkyl side chains.[3c] In addition, water has
been found to reduce the cohesion of [C4MIM][NTf2] even at
very low mole fractions[13] which suggests that the anomalous
result for [C4MIM][NTf2] with water employed as the
nucleophile may arise from the reduced cohesion of the IL
which already possesses weakly aggregated nonpolar
domains. The reduced dissociating power of the aliphatic
([C4MMIM][NTf2]) as a solvent rather than [C4MIM][NTf2]
has been found to yield a reaction rate constant for hydrolysis
of (36.5 ꢀ 0.8) ꢀ 10ꢁ4 mꢁ1 sꢁ1.[6,5c] This means that the rate
increase observed when the alkyl side chain is changed from
butyl to octyl is larger than that obtained when the hydrogen-
bond acidity of the medium is significantly reduced.[5c]
Furthermore, the larger rate enhancement for water
relative to the aliphatic alcohols or benzyl alcohol suggests
that the effect is more pronounced for more polar molecules.
The most logical explanation for such behavior arises from
the nanostructural heterogeneity of the solvent, that is, the
reactants concentrate in the polar domains which are
relatively smaller in volume as the alkyl side chain of the IL
increases. This phenomenon, that is, the pseudo-encapsula-
tion of reactants in the polar domains of the IL, changes the
effective concentrations of the reagents. Such effects have
been observed in micellar kinetics,[7] where the concentration
of reagents within the micelle can significantly affect reaction
rates. The aforementioned rate effects in micellar systems led
to the development of a pseudophase model for the inter-
pretation of kinetic data, where the two phases were defined
as the aqueous phase and the interior of the micelle.[8]
Applying such a pseudophase treatment to this non-
micellar, but domain-based reaction system involves separat-
ing the rate law into the rates within both the polar and
nonpolar domains, as shown in Equation (1), where [ROH]p
r ¼ kp½ROHꢂp½Ar3Picꢂþp þ knp½ROHꢂnp½Ar3Picꢂþ
ð1Þ
np
and [Ar3Pic]+p refer to the concentrations of alcohol or water
and substrate in the polar domains, respectively, and [ROH]np
and [Ar3Pic]+ refer to the corresponding concentrations in
np
the nonpolar domains.
Given the proposition above that [Ar3Pic]+ partitions
exclusively into the polar domains, then [Ar3Pic]+np ꢃ 0 and
the contribution of the nonpolar domain to the rate can
therefore be ignored. However, this assumption is not
necessarily true for the nucleophile, so it is necessary to
define a partition coefficient, K, to describe the proportion of
nucleophile, ROH, in the nonpolar relative to polar domains
and this is formalized in Equation (2).
½ROHꢂnp
K ¼
ð2Þ
½ROHꢂp
ꢀ 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2012, 51, 11483 –11486