Dielectric Relaxation Spectroscopy Shows a Sparingly Hydrated

Article pubs.acs.org/Langmuir

Dielectric Relaxation Spectroscopy Shows a Sparingly Hydrated Interface and Low Counterion Mobility in Triflate Micelles Filipe S. Lima,† Hernan Chaimovich,† Iolanda M. Cuccovia,† and Richard Buchner*,‡ †

Instituto de Química, Universidade de São Paulo, São Paulo, Brazil Institut für Physikalische und Theoretische Chemie, Universität Regensburg, Regensburg, Germany

‡

ABSTRACT: The properties of ionic micelles are affected by the nature of the counterion. Specific ion effects can be dramatic, inducing even shape and phase changes in micellar solutions, transitions apparently related to micellar hydration and counterion binding at the micellar interface. Thus, determining the hydration and dynamics of ions in micellar systems capable of undergoing such transitions is a crucial step in understanding shape and phase changes. For cationic micelles, such transitions are common with large organic anions as counterions. Interestingly, however, phase separation also occurs for dodecyltrimethylammonium triflate (DTATf) micelles in the presence of sodium triflate (NaTf). Specific ion effects for micellar solutions of dodecyltrimethylammonium chloride (DTAC), bromide (DTAB), methanesulfonate (DTAMs), and triflate (DTATf) were studied with dielectric relaxation spectroscopy (DRS), a technique capable of monitoring hydration and counterion dynamics of micellar aggregates. In comparison to DTAB, DTAC, and DTAMs, DTATf micelles were found to be considerably less hydrated and showed reduced counterion mobility at the micellar interface. The obtained DTATf and DTAMs data support the reported central role of the anion’s −CF3 moiety with respect to the properties of DTATf micelles. The reduced hydration observed for DTATf micelles was rationalized in terms of the higher packing of this surfactant compared to that of other DTA-based systems. The decreased mobility of Tf− anions condensed at the DTATf interface strongly suggests the insertion of Tf− in the micellar interface, which is apparently driven by the strong hydrophobicity of −CF3.

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INTRODUCTION The properties of ionic micelles depend upon, among other parameters,1−3 counterion condensation.4−9 The different properties of alkyltrimethylammonium micelles with bromide and chloride as counterions are one of the best known examples.10 Changing bromide to chloride for dodecyltrimethylammonium (DTA + ) micelles (DTAB and DTAC, respectively) leads to a small decrease in the aggregation number, Nagg,10 an increase in the critical micelle concentration, cmc,11 and an increase in the degree of counterion dissociation, α.2 In other systems, changes in micellar shape, such as those observed with naphthalenesulfonate,12 benzoate derivatives,13,14 and tosylate,15 are dramatic and seem to be related to the (limited) penetration of the anions into the micellar headgroup layer.16 Shape transitions of surfactant aggregates have also been associated with decreased micellar hydration and the formation of ion pairs at the micellar interface,17,18 highlighting the need to investigate these properties. Differences between interfacial and bulk water in micellar solutions have been probed with electron paramagnetic resonance (EPR),19 catalysis,20 chemical trapping,18 and dielectric relaxation spectroscopy (DRS).21 Also, molecular dynamics simulations have been used to analyze the dynamics of water in micellar systems,22,23 and the formation of ion pairs at the micellar interface was evaluated in theoretical models.24−26 DRS is sensitive to all dipole moment fluctuations27 and provides information on micelle and counterion hydration from © 2013 American Chemical Society

the analysis of the solvent modes contributing to the dielectric spectrum.28 The dynamics of the counterions surrounding the aggregates is probed by micelle-specific relaxation modes, yielding information on the location and mobility of the adsorbed counterions.21,29 Considering that counterion condensation at the micellar interface is also related to shape transitions17,18 and potentially to phase separation,30 DRS can be a used to examine the properties of micellar systems capable of undergoing phase transitions. Dodecyltrimethylammonium trifluoromethanesulfonate (DTA-triflate, DTATf) micelles have unusual properties. The degree of counterion dissociation, α, of DTATf micelles is considerably smaller than for DTAB or DTAC.31 The addition of 0.05 M sodium triflate (NaTf) also induces phase separation in DTATf micelles.31 The DTATf aggregates are disklike objects that are larger and more packed than DTAC, DTAB, or DTAMs (DTA+ with methanesulfonate (Ms) as the counterion) micelles.30 Although one has to keep in mind that the exact location of the used spin probes in the different aggregates was uncertain, electron paramagnetic resonance (EPR) spectra indicated that DTATf micelles are less hydrated than DTAC or DTAB.30,32 The unusual properties of DTATf micelles are probably related to the position and hydration of Received: May 13, 2013 Revised: July 10, 2013 Published: July 11, 2013 10037

dx.doi.org/10.1021/la401728g | Langmuir 2013, 29, 10037−10046

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the −CF3 group at interfaces.30,31,33,34 The affinity of Tf− for micellar interfaces is not limited to DTA-based systems, as Tf− seems to induce the formation of vesicles of the monoalkyl surfactant N-alkyl-3-boronopyridinium.35 Here we used DRS to investigate the hydration properties and counterion dynamics of dodecyltrimethylammonium triflate, methanesulfonate, bromide, and chloride micelles at 45 °C. The obtained hydration numbers indicated that for DTATf water−micelle interactions were weaker than for DTAC, DTAB, and DTAMs. The low mobility of the adsorbed counterions inferred from the micelle relaxations is compatible with the insertion of Tf− in the interfacial region of the micelle.

n

ε(̂ ν) =

i=1

(2)

where the “infinite frequency” permittivity, ε∞, summarizes the contributions from intramolecular polarizability and Si is the amplitude of mode i. The static permittivity is defined as εs = ε∞ + ∑i n= 1Si. The associated band shape functions, F̃i(ν), can be modeled with the Havriliak−Negami (HN) equation −β ̃ ⎣1 − (i2πντi)1 − αi ⎤⎦ i F( i ν) = ⎡

(3)

with relaxation time τi and shape parameters 0 ≤ αi < 1 and 0 < βi ≤ 1. Simplified variants of eq 3 are the Cole−Davidson (CD, αi = 0, 0 < βi ≤ 1), Cole−Cole (CC, 0 ≤ αi < 1, βi = 1) and Debye equations (D, αi = 0, βi = 1) equations.27 The spectra were analyzed by simultaneously fitting ε′ and ε″ to all conceivable relaxation models, following the selection criteria described in detail elsewhere.37 Electrode polarization, notable in the spectra at ν < 0.1 GHz, was corrected as described in section 3.4.2 of ref 36.

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MATERIALS AND METHODS Trifluoromethanesulfonic acid, sodium methanesulfonate, and DTAB were obtained from Sigma-Aldrich (purity ≥98%). DTATf and NaTf were prepared as previously described.31 DTAMs and DTAC were prepared by passing a solution of 5 g of DTAB in 30 mL of methanol through an ion-exchange resin column (Purolite, Purolite, SGA550OH, OH form) previously saturated with sodium methanesulfonate and chloride, respectively. Methanol was removed by rotoevaporation, and the surfactants were recrystallized from methanol/ether. All surfactants were dried at 40 °C under vacuum before the solutions were prepared. The electrical conductivity, κ, of the samples was measured at 45 ± 0.005 °C using a computercontrolled setup and a two-electrode capillary cell (cell constant of approximately 25 cm−1) calibrated with aqueous KCl. Solution densities at that temperature were measured with a vibrating-tube densimeter (Anton Paar DMA 5000 M) to ±0.05 kg/m3 uncertainty. Dielectric spectra at 45 ± 0.05 °C were combined from measurements with a waveguide interferometer covering the frequency range of 60 ≤ ν/GHz ≤ 89, two commercial open-ended coaxial reflection probes covering 0.2 ≤ ν/GHz ≤ 20 and 1 ≤ ν/GHz ≤ 50, respectively (Agilent), and a coaxial-line cutoff reflection cell for 0.02 ≤ ν/ GHz ≤ 0.5. The coaxial-line cell and reflection probes were connected to an Agilent E8364B vector network analyzer (VNA) with an electronic calibration module (Ecal, Agilent N4693A). Prior to the VNA measurements of the samples, the instrument was calibrated with air, mercury, and water as the primary standards. All reflection measurements were recorded at least twice with independent calibrations. The interferometer did not require calibration.

■

RESULTS The spectra of relative permittivity, ε′, and dielectric loss, ε″, for 0.1 M aqueous solutions of DTATf, DTAMs, and DTAC were dominated by a relaxation at ∼30 GHz (Figure 1) that, by

Figure 1. Spectra of relative permittivity, ε′(ν), and dielectric loss, ε″(ν), of 0.1 M aqueous solutions of DTAC (a), DTAB (b), DTAMs (c), and DTATf (d) at 45 °C. Symbols (●) show experimental data; solid lines represent fits with the D + D + D + D (a−c) and D + D + D (d) models (see the text); filled areas show the contributions of resolved modes 1−4 to ε″(ν). The dashed line represents pure water.

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PROCESSING OF DIELECTRIC SPECTRA Dielectric relaxation spectroscopy measures the response of the sample to an applied electric field of frequency ν.36 This response is conveniently expressed in terms of the total complex permittivity, η̂(ν), η (̂ ν) = ε(̂ ν) − iκ(c)/2πνε0

∑ SiFi (̃ ν) + ε∞

comparison to the spectrum of pure water at 45 °C, was assigned to the solvent (Figure 1a−d). Hereafter, we define this relaxation as mode 4, with parameters τ4 and S4 (eqs 2 and 3). Additionally, a contribution at ν < 1 GHz can be seen in all spectra. As with previous studies of ionic surfactant solutions,21,17−19 this broad low-frequency relaxation can be split into two micelle-specific modes, with the lower- and higher-frequency relaxations designated as modes 1 (τ1 and S1) and 2 (τ2 and S2), respectively. Additionally, a weak contribution at ∼10 GHz (mode 3, τ3 and S3) can be resolved by spectral decomposition for DTAC (Figure 1a), DTAB (Figure 1b), and DTAMs (Figure 1c). Thus, the DR spectra of the DTAC, DTAB, and DTAMs were best fitted by a sum of four Debye equations (n = 4, the D + D + D + D model), with

(1)

which can be split into a term arising from the dc conductivity, κ, and the complex (relative) permittivity, ε̂(ν) = ε′(ν) − iε″(ν). The latter includes all contributions that depend on frequency and thus monitor the cooperative dynamics of the sample.27 In eq 1, ε0 is the permittivity of vacuum, ε′(ν) is the relative permittivity, and ε″(ν) is the associated dielectric loss. Generally, the complex permittivity spectrum, ε̂(ν), can be formally described by a sum of n individual relaxations i, 10038


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Table 1. Amplitudes, Si (i = 1−4), Relaxation Times, τi, Static Permittivity, εs, Infinite-Frequency Permittivity, ε∞, and Corresponding Normalized Variance, χr2, of the Fits of 0.1 M DTAX Solutions, with X = Cl−, Br−, Ms−, and Tf−

a

X

S1

τ1/ns

S2

τ2/ns

S3

τ3/ps

S4

τ4/ps

εs

ε∞

χr2

Cl Br Ms Tf

2.34 2.53 2.96 8.01

1.77 1.75 1.66 2.94

11.27 10.74 12.04 6.63

0.29 0.30 0.40 0.58

3.68 2.03 2.52

14.4 14.4 13.4

61.66 63.43 62.88 64.98

5.07 5.27 5.32 5.26

81.73 81.51 83.18 82.4

4.75 5.50 5.42 4.85

0.192 0.095 0.225 0.124

a

a

See text.

peaking at ∼0.05 GHz (τ1 ≈ 3 ns) and ∼0.3 GHz (τ2 ≈ 0.5 ns). However, in contrast to the other surfactants, the amplitudes of the micelle-specific modes were inverted (i.e., S1 > S2) (Table 1). Additionally, the contribution at ∼10 GHz could not be resolved because trial fits with n = 4 yielded S3 ≈ 0 with considerable scattering in the other parameters. For the DTATf concentration series (0 < c/M ≤ 0.1), the low-frequency region of the recorded loss spectra is shown in Figure 2 and the associated fit parameters are summarized in Table 2. Although the amplitude of the bulk water mode, S4, decreased with surfactant concentration, the corresponding relaxation time, τ4, remained constant. Similar to the behavior reported for DTAB and DTAC at c < 0.3 M,28,29 the amplitudes of both low-frequency modes, S1 and S2, increased with DTATf concentration, whereas the corresponding relaxation times, τ1 and τ2, remained constant. In contrast to the other studied surfactants, S1 > S2 was found for the micellerelated amplitudes of DTATf at all investigated concentrations. The addition of up to 0.1 M NaTf to a solution of 0.1 M DTAB led to a progressive change in the spectra (Figure 3). In particular, the amplitude related to the lowest-frequency mode, S1, increased whereas that of the second mode, S2, decreased. Additionally, the corresponding relaxation times, τ1 and τ2, increased with [NaTf], approaching the values for 0.1 M DTATf (Table 1). Overall, with increasing [NaTf], the shape of the DTAB + NaTf spectra approached that observed for DTATf solutions (Figure 2). Additionally, as expected for the addition of salt,37 the amplitude of solvent mode 4, S4, decreased with [NaTf], but the corresponding relaxation time, τ4, remained unchanged. The marked changes in the low-frequency region of the spectra upon NaTf addition could only be qualitatively grasped by band fitting (Figure 3, Table 3). Nevertheless, a significant change in the counterion dynamics can be inferred. Although the D + D + D + D model is definitely the best fit for [NaTf] = 0 (i.e., pure DTAB), mode 3 could not be resolved any further for the NaTf-containing samples. Best fits were obtained with D + D + D for [NaTf] = 0.025 M, D + CD + D for 0.050 M NaTf, CD + CD + D for [NaTf] = 0.075, and D + D + D to [NaTf] = 0.1 M. Thus, at first relaxation 2 at ∼0.5 GHz became asymmetric, possibly swamping contribution 3 as a result. This

the parameters summarized in Table 1. This model gave values for the normalized variance, χr2, that were ∼10% smaller compared to fits with n = 3. Additionally, the obtained parameters could be reasonably interpreted (see below). For DTAC and DTAB (Figure 1a,b), the resolved modes peaked at ∼0.1 GHz (corresponding to a relaxation time of τ1 ≈ 1.5 ns), ∼0.5 GHz (τ2 ≈ 0.3 ns), ∼10 GHz (τ3 ≈ 15 ps), and ∼30 GHz (τ4 ≈ 5 ps). For DTAMs (Figure 1c), the second relaxation was shifted to ∼0.4 GHz (τ2 ≈ 0.4 ns) but the other peak frequencies/relaxation times and corresponding amplitudes, Si, were similar to those of DTAC and DTAB. In contrast to that, all recorded DTATf spectra (Figures 1d and 2) were best fitted

Figure 2. Dielectric loss spectra, ε″(ν), of DTATf solutions at 45 °C at concentrations (M) of 0.020 (■), 0.030 (red ▲), 0.045 (light green ●), 0.060 (blue ▼), 0.080 (green ⧫), and 0.100 (pink ▲). The dashed line represents pure water, and solid lines show the fits of the spectra (see text); arrows indicate the locations of modes 1 and 2.

with a sum of only three Debye equations (n = 3, the D + D + D model, eq 2). The bulk-water relaxation (∼30 GHz, τ4 = 5.4 ps) again dominated (Figure 1d), and the micelle-specific region at ν < 1 GHz could be split into two modes, now

Table 2. Amplitudes, Si (i = 1, 2, 4), Relaxation Times, τi, Static Permittivity, εs, Infinite-Frequency Permittivity, ε∞, and Corresponding Normalized Variance, χr2, of the Fits of DTATf Solutions at Concentration c c/M

S1

τ1/ns

S2

τ2/ns

S4

τ4/ps

εs

ε∞

χr2

0.020 0.030 0.045 0.060 0.080 0.100

2.40 3.45 4.97 6.23 6.98 8.01

2.91 3.22 2.80 2.98 2.72 2.94

1.12 1.84 2.77 3.10 4.39 6.63

0.47 0.64 0.48 0.49 0.50 0.58

68.02 67.43 67.02 66.60 65.77 64.98

5.43 5.20 5.43 5.24 5.27 5.26

74.33 75.50 77.54 78.71 79.92 82.4

5.66 4.76 5.60 4.89 4.87 4.85

0.051 0.096 0.064 0.086 0.104 0.124

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Thus, from its relaxation time and amplitude (Tables 1−3), the mode at ∼30 GHz dominating all recorded spectra was assigned to the cooperative relaxation of bulk water. In contrast to previous DRS studies28,29 of aqueous DTAB and DTAC at 25 °C, the fast water mode was not detected for the present samples because for the present temperature it was too far outside the covered frequency range. Following previous investigations,28,29 relaxations 1 and 2 (Tables 1−3 and Figure 1) were associated with the fluctuations of the diffuse counterion cloud surrounding the charged micelles and the lateral motion (surface hopping) of counterions adsorbed at the micellar interface, respectively. Likewise, relaxation 3 (Tables 1−3 and Figure 1) was assigned to water near the hydrophobic region of the micelle.21,28 Such “slow water”, which is reduced in its dynamics but not completely immobilized (“irrotationally bound”),27 was not present in aqueous DTATf (Figure 1d, Table 1) and apparently disappeared when NaTf was added to DTAB (Table 3). As expected from the increased temperature, the present τi values were lower than those reported for 25 °C.28,29 Solute Relaxation. The two micelle-related modes (1 and 2) of the dielectric spectra of ionic surfactant solutions are generally well described21,29 by Grosse’s model for charged spherical colloidal particles.40 This theory predicts that the relaxation times, τi, and amplitudes, Si, of the ion-cloud relaxation (i = 1) and the surface-hopping mode of the adsorbed counterions (i = 2), given as

Figure 3. Dielectric loss spectra, ε″(ν), of 0.1 M DTAB with NaTf added to the following concentrations (in M): 0 (●), 0.025 (red ▲), 0.050 (green ▼), 0.075 (blue ⧫), and 0.100 (green ▲). The dashed line represents pure water, and solid lines show the fits of the spectra (see the text); arrows indicate the trends of solute relaxations 1 and 2 with increasing NaTf concentration.

asymmetry of mode 2 suggests that a distribution of environments is probed in the NaTf-containing solution. On further increase in [NaTf] the lowest-frequency relaxation 1 also became asymmetric. However, at the highest NaTf concentration, modes 1 and 2 were again best described by Debye equations. Such behavior may indicate that at intermediate NaTf concentrations modes 1 and 2 are actually both superpositions of two relaxations each, where the lowerfrequency contributions, 1a and 2a, are defined by the τ1 and τ2 values of a pure DTATf solution and the corresponding τ1 and τ2 values of pure DTAB determine the location of the higherfrequency contributions, 1b and 2b. Unfortunately, at the noise level of the present spectra this hypothesis could not be verified because trial fits with the corresponding D1a + D1b + D2a + D2b + D4 model did not converge.

τ1 ≈

S1 =

R G2 D

⎡ 2χλ 16⎢⎣ κ(c)s

■

DISCUSSION Assignment of Spectra. The dielectric spectrum of pure water is dominated by a mode in the microwave region associated with the cooperative reorientation of H2O molecules within the hydrogen-bond network of this liquid. Additionally, a weak mode of unclear origin at a few hundred gigahertz (“fast water”) can be detected.38 At 45 °C, the corresponding relaxation times (amplitudes) of these bulk and fast water modes are τb = 5.31 ps (Sb = 66.19) and τf = 0.19 ps (Sf = 2.65) with an infinite-frequency permittivity of ε∞ = 2.68 and a corresponding static permittivity of ε = Sb + Sf + ε∞ = 71.52.39

S2

4

( ) ( + 1) + 2⎤⎥⎦ 2χλs κ(c)

9ϕmicεm

( = κ (c )( ε0εm

τ2

(4)

2λs Rκ(c)

εp

(5)

) + 2)

+2

εm

2λ s Rκ(c)

( = ⎡ + 2)( ⎣⎢( 9ϕmicεm

2

2λ s Rκ(c)

εp

εm

−

2λ s Rκ(c)

(6) εp 2

) ⎤ + 2)⎥ ⎦ εm

2

(7)

are defined by the same set of parameters, namely, the diffusion coefficient of free counterions, D; the location of the adsorbed counterions, RG (the Grosse radius); the volume fraction of the micelles, ϕmic; the static permittivities of the micelle core, εp (∼2), and the solvent, εm (= 71.52); the Debye length, χ−1; the dc conductivity of the solution, κ; and the surface conductivity

Table 3. Amplitudes, Si (i = 1−4), Relaxation Times, τi, CD Parameters, βi, Static Permittivity, εs, Infinite-Frequency Permittivity, ε∞, and Corresponding Normalized Variance, χr2, of the Fits of 0.1 M DTAB with Added NaTf

a

[NaTf]/M

S1

τ1/ns

β1

S2

τ2/ns

β2

S3

τ3/ps

S4

τ4/ps

εs

ε∞

χr2

0 0.025 0.05 0.075 0.1

2.53 4.16 8.11 11.18 14.66

1.75 2.01 2.52 2.95 3.30

1 1 1 0.85 1

10.74 9.89 7.21 5.89 4.77

0.30 0.41 0.49 0.56 0.46

1 1 0.61 0.54 1

2.03

14.4

63.43 64.38 63.67 63.07 62.86

5.27 5.34 5.33 5.37 5.33

81.51 81.21 81.77 82.92 85.07

5.50 5.45 5.35 5.63 5.45

0.095 0.129 0.191 0.252 0.311

a

a

a

a

a

a

a

a

See the text. 10040


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∼21 and 26, respectively, at 25 °C).28 Only the surface diffusion coefficient of Br− was significantly smaller than that observed for Cl− (Table 4), suggesting that bromide interacts more strongly with the micellar surface than does chloride. DTAMs micelles exhibit many properties comparable to those reported for DTAB and DTAC.30 At 45 °C, a 0.1 M solution of DTAMs forms micelles with αDTAMs = 0.3, cmc = 0.024 M (α45 and cmc46 were determined by conductivity), and Nagg = 43 (obtained from experiments performed according to procedures described elsewhere47), values close to those of DTAC and DTAB under the same conditions. Consequently, the DR spectra of DTAMs, DTAB, and DTAC are also similar (Figure 1). However, a closer look reveals differences for solute-related modes 1 and 2 (Table 1). In particular, mode 2 is shifted to lower frequencies, implying a smaller surface diffusion coefficient for counterions adsorbed to DTAMs micelles (Table 4). In part, this is probably due to the larger size of the methanesulfonate ion, but as discussed below, specific interactions between counterions and micelles also affect this value. Compared to the spectra of 0.1 M DTAC, DTAB, and DTAMs, ε′(ν) and ε″(ν) of 0.1 M DTATf were distinctly different. Not only did mode 3 (slow water) disappear but the relative magnitudes of modes 1 and 2, which are associated with fluctuations of the diffuse counterion cloud and the surface hopping of adsorbed counterions, respectively, also changed (Figure 1, Table 1). Although S1 was considerably larger, S2 decreased. The increased value of S1 can be rationalized by the considerably smaller (by factors of 3 and 5 compared to the values for DTAB and DTAC, respectively) degree of triflate dissociation from the micelle, αDTATf = 0.1,31 and thus the larger χDebye−1. Because of the higher density of adsorbed counterions, one would expect that S2 also increased for DTATf.40 However, it should be kept in mind that the surface conductivity of the micelles, λs, that enters into S1 (eq 6) and S2 (eq 8) is also sensitive to the binding strength of the condensed counterions to their adsorption sites, which is reflected by the surfacediffusion coefficient, Dsi (eq 9). Thus, the decreased S2 value for DTATf indicates a stronger binding of Tf− to the micelle surface compared to that of Br− and Cl−. The DR parameters of DTATf were used to estimate the Grosse radius, surface conductivity, volume fraction, and Debye length of the micelle. Note that these calculations can yield only estimates because Grosse’s theory is valid only for spherical micelles with RG ≫ χ−1 whereas DTATf micelles are definitely not spherical30 and the Debye length is comparable to the size of the micelle (Table 4). This is reflected in the large difference between the χ−1 value obtained from Grosse’s model (eqs 4−7) and the conventionally calculated Debye length (eq 9). The experimental aggregation number of 0.1 M DTATf, Nagg ≈ 260,30 was not compatible with RG derived from τ1. Also, other tested Nagg values (not shown) did not yield better agreement between experimental and calculated values for S1, S2, τ1, and τ2. Therefore, the maximum aggregation number for a 12-carbon chain surfactant forming spherical micelles, Nagg ≈ 55,44 was assumed for evaluating the micelle relaxations of DTATf. In doing so, the relaxation time of mode 2 was reproduced (Figure 4a) but the calculated τ1 values exceeded the experimental data by almost 20%. Also, the calculated amplitudes, S1 and S2, were much larger (Figure 4b). Clearly, the obtained data set for RG, λS, ϕmic, and χ−1 (Table 4) is not self-consistent, and this is mainly a consequence of the disklike shape of DTATf micelles. Nevertheless, some qualitative information can be extracted:

of the micelle, λs. The latter can be related to the surface diffusion coefficient, Ds, of the adsorbed counterions by Ds =

4πkBTλsR G 2 (1 − α)e0 2Nagg

(8)

where T is the Kelvin temperature, kB is the Boltzmann constant, and e0 is the elementary charge.21 The above equations are valid for spherical micelles in the limit of small ϕmic and RG ≫ χ−1. In this case, the Grosse radius, surface conductivity, volume fraction (via ϕmic = 4πRG3NA(c − cmc)/(3Nagg)), and Debye length of the micelle can be calculated from the experimentally determined values for the amplitudes, S1 and S2, relaxation times, τ1 and τ2, dc conductivity, and counterion diffusion coefficient in the bulk solution by simultaneously solving eqs 4−7. The obtained parameters for the 0.1 M surfactant solutions with the input data from Table 1 are summarized in Table 4. The Debye Table 4. Grosse Radius, RG, Surface Diffusion Coefficient, Ds, and Its Ratio to the Diffusion Coefficient of Free Counterions, Ds/D, Debye Length, χ−1, Adjusted from DRS Data Using Equations 4−8 and the Debye Length, χDebye−1, Using Equation 9 surfactant

RG/nm

Ds/10−9 m2·s−1

Ds/D

χ−1/nm

χDebye−1/nma

DTAC DTAB DTAMs DTATf

2.24 2.26 2.20 2.21

1.65b 1.08b 0.78c 0.45d,e

0.58 0.37 0.27 0.27

1.94 1.83 1.77 0.75

2.38 2.62 2.17 4.44

cmc and α values for DTAC, DTATf, and DTAB were taken from refs 2, 31, and 41, respectively; those for DTAMs are from this work. b Diffusion coefficients were taken from ref 42, and Nagg values were taken from ref 11. cThe diffusion coefficient was assumed to be equal to that of Br− because of similar values of conductivity, cmc, α, and Nagg. dUsing D = ((RT)/F2)(λ0/(|z|)) with λ0 of the triflate ion from ref 43. eNagg was assumed to be the theoretical limit for a spherical micelle formed by a 12-carbon chain surfactant.44 All D values were corrected to 45 °C as previously described.31 a

length calculated with the Grosse model, χ−1, was compared to the conventional definition (eq 9), ⎛ εmε0k T ⎞1/2 B ⎟ χDebye−1 = ⎜ 2 ⎝ 2NA e0 I ⎠

(9)

where NA is Avogadro’s constant and I is the ionic strength of the medium. The latter is defined by the concentration of free surfactant ions (∼cmc) and free counterions (α(c − cmc)). As generally found for spherical micelles,20,28 the χ−1 values of DTAB, DTAC, and DTAMs are comparable but somewhat smaller than χDebye−1 (Table 4). The large difference for DTATf is unusual and will be discussed below. The dielectric spectra of DTAB and DTAC at 0.1 M (Figure 1 and Table 1) were very similar28,29 and so are the results obtained by applying the Grosse model (Table 4) to the two surfactants. This is expected because the properties of DTAC and DTAB aggregates that are relevant to the dielectric spectra are comparable: with α values of 0.49 and 0.32,2,41 DTAC and DTAB form highly dissociated micelles. Also, the aggregation numbers are similar, with Nagg = 42 for DTAC and ∼52 for DTAB,11 and the diffusion coefficients of free Cl− and Br− anions in solution are similar.42 The number of water molecules hydrating DTAB and DTAC micelles is also similar (a total of 10041


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Table 5. Partial Charges (in Proton Charges) for Tf− and Ms− anion −

Tf Ms−

C

S

O

Xa

−SO3b

−CX3b

0.682 −0.588

1.403 1.291

−0.732 −0.776

−0.296 0.208

−0.793 −1.037

−0.206 0.036

X = F for Tf− and H for Ms−. bThe charge is the sum of the atomic charges in the respective group.

a

interestingly, Ms− exhibiting the more negative value. For −CF3 and −CH3, the magnitudes of the partial charges were significantly smaller than that of −SO3− and close to zero for −CH3 but somewhat negative for −CF3 (Table 5). Thus, the partial charges of Table 5, combined with the known strong hydrophobicity of −CF3, support the previously published hypothesis that Tf− is inserted into the interfacial region with the −CF3 group pointing toward the micellar core.30,31,33 One would expect that the diffusion of these inserted anions is rather slow, in line with the Ds value deduced from the present dielectric data (Table 4). Such a preferential orientation might also be possible for Ms− because of the small partial charge of the −CH3 group (Table 5). However, the present results for the micelle relaxations (Table 4) and the effective hydration numbers derived from the water mode (see below) as well as existing information from the literature30 indicate that the insertion of Ms− into the micellar interface is much less pronounced (i.e., Ms− is lessstrongly bound than Tf−). This is almost certainly due to the smaller hydrophobicity of hydrogenated groups compared to that of fluorinated groups.48,49 Ion pairing through Coulomb interactions can be excluded as the main reason for the stronger binding of Tf− versus Ms− and thus the low degree of counterion dissociation of DTATf micelles (αDTATf = 0.1 at 0.1 M compared to αDTAMs = 0.3) because the −SO3− moiety of Ms− is even more negative than that of Tf−. The postulated insertion of Tf− anions into the micellar interface also explains the drastic changes in the DR spectra on addition of NaTf to a 0.1 M aqueous DTAB solution (Figure 3). At low NaTf concentrations, anions Br− and Tf− will surround the micelle, with each of them binding to and diffusing on the micelle surface with its own characteristic times and strengths. In line with the reported 1H NMR spectra of these solutions,30 the changes in the dielectric spectra upon NaTf addition suggest an effective ion exchange between the bromide originally adsorbed on the micellar interface and the added triflate. The similarity between the spectra of pure 0.1 M DTATf and 0.1 M DTAB + 0.1 M NaTf, both from DRS and NMR experiments, suggests that for this DTAB/NaTf mixture the exchange between Br− and Tf− on the surface of the micelle is nearly quantitative. The aggregates present in this mixture are probably already very similar to pure DTATf micelles with regard to Nagg and the shape. Water Relaxation. For relaxations associated with dipole reorientation, such as the water-related modes (here 3 and 4), the generalized Cavell equation38,50,51 (eq 10)

Figure 4. Relaxation times, τ1 and τ2, (a) and amplitudes, S1 and S2, (b) of solute modes 1 (▲) and 2 (●) of DTATf solutions as a function of surfactant concentration at 45 °C. Lines correspond to predictions of the Grosse model for modes 1 and 2.

The Grosse model yielded a rather low but probably still overestimated (because of the larger surface area of the real micelle) surface-diffusion coefficient, Dsi, for Tf− (Table 4), which is a direct consequence of the increased relaxation time of mode 2, τ2 (Table 1), and the thus reduced surface conductivity, λS, of DTATf compared to that of DTAC and DTAB. This suggests strong interactions between the triflate anion and the micellar interface, in line with previous investigations.30,31,33 Interestingly, DTAMs also exhibited larger τ2 values than DTAC and DTAB whereas, in line with the α values of the three surfactants, similar amplitudes, S1 and S2, were found. Compared to Cl− and Br−, this leads to a reduced surface diffusion coefficient for Ms− (Table 4), indicating that, similar to Tf−, the interactions between Ms− and the micellar interface are also stronger than those involving Br− or Cl−. Unfortunately, because of the deviating shape of DTATf micelles, the surface diffusion coefficients of Tf− and Ms− summarized in Table 4 cannot be directly compared (see above) so that no inference with the binding relative strengths of both anions is possible. To obtain some information in this respect, quantum chemical calculations (Gaussian 03, B3LYP/ 6-31++G** basis set with solvent correction) were performed, yielding the partial charges of the two anions (Table 5). Both showed significant negative partial charges for −SO3− with,

ciapp(c) =

k Tε 3(ε(c) + (1 − ε(c))A) × B 0 NA ε(c ) ×

(1 − αĩ fi (c))2 μi 2

× Si(c)

(10)

relates the amplitude, Si, to the concentration, ci, of the relaxing species at solute concentration c. In eq 10, α̃ i is the 10042


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Table 6. Effective Hydration Numbers Zib, Zs, and Zt for 0.1 M Aqueous DTAC, DTAB, DTAMs, and DTATf 25 °Ca

a

45 °C

surfactant

Zib

Zs

Zt

DTAC DTAB DTAMs DTATf

12.1 ± 1.2 9.7 ± 0.8 n.d. n.d.b

14.3 ± 0.9 10.9 ± 1.8 n.d. n.d.b

26.4 ± 2.1 20.6 ± 2.6 n.d. n.d.b

Zib 9.8 9.1 7.3 11.3

± ± ± ±

Zs 1.5 1.5 1.4 1.5

29.3 ± 1.5 16.2 ± 1.5 19.6 ± 1.4 n.d.c

Zt 39.1 25.3 26.9 11.3

± ± ± ±

3.0 3.0 2.8 1.5

Values from ref 28. bThe Kraft temperature of DTATf is 37 °C.31 cSee the text.

and Ms−53 Zib = 0 was found (i.e., the interaction strength of these anions is not sufficient to freeze the reorientation of water molecules in their hydration shells). A value of Zib = 0 is also likely for triflate because this anion is known for its low hydration number.54 Additionally, for symmetrical tetraalkylammonium ions Zib = 0 was found.52 In ref 21, it was speculated that these frozen water molecules are trapped on the micellar surface because of their simultaneous interactions with the surfactant headgroups and the condensed counterions. Such a simultaneous interaction of water molecules with a cation and anion, which we may call cooperative binding, was also found by DRS for aqueous ionene bromides55 and in a Car−Parrinello study of 1-ethyl-3-methyl-imidazolium chloride + water mixtures.56 Apparently, a temperature rise of 20 °C had no notable effect on Zib, suggesting that the increased thermal motions at 45 °C were not yet sufficient to overcome the attractions exerted by the ions on the surrounding water molecules. However, Zs and thus Zt increased with temperature. It is known that bromide and chloride ions have Zs = 028 and thus, for DTAB and DTAC the slow water mode can be attributed to the water molecules close to hydrophobic groups of the surfactant cations. Because this comprises not only the small fraction of free cations but also the surfactant ions incorporated in the micelles,21,28 the aggregation number and thus the micellar shape must significantly affect the Zs values. Because the radius of a spherical micelle is basically defined by the number of carbon atoms in the hydrophobic chain,44 a smaller Nagg implies larger voids inside the micelle that could be accessed by water molecules and thus result in larger Zs values. This change in the ratio of micelle volume to aggregation number explains the decrease in Zs with rising DTAB concentration28 and thus increasing Nagg.57 Decreasing Zs with increasing Nagg was also observed for the present series of 0.1 M solutions of DTAMs, DTAB, and DTAC (Figure 5). Water−micellar core interactions also explain the increase in Zs with rising temperature observed for DTAC and DTAB as a larger fraction of the hydrophobic core is exposed with increased thermal motions (Table 6). This interpretation is supported by convincing theoretical58 and experimental59 evidence for contact between the hydrophobic moiety of the micellized monomers and water molecules arising from the disordered and fluid nature of the DTAB, DTAC, and DTAMs micelles.60 From this correlation between the accessibility of the hydrophobic core and Zs, the value of Zs = 0 can also be understood for all investigated DTATf solutions (Table 6 and inset of Figure 5): it has been reported that in DTATf micelles, which have aggregation numbers well above 100 for the investigated solutions, the monomers are more densely packed than in micelles of DTAB, DTAC, or DTAMs.30 Additionally, the present results for the micelle relaxations as well as the NMR results in ref 30 suggest that Tf− is inserted into the micellar interface (Figure 6). This dense packing of DTATf

polarizability, f i is the reaction field factor, and μi is the dipole moment of the relaxing species, i.51 For water, a spherical cavity field was assumed (i.e., A = 1/3) and factor f i was calculated as described in ref 51. For the evaluation of the bulk-water amplitude, eq 10 was also normalized to the pure solvent.52 Except for 0.1 M DTATf(aq) and the DTAB + NaTf mixtures, two water-related relaxations, modes 3 and 4, could be resolved (Figure 1). From the magnitudes of amplitude, S4, and relaxation time, τ4 (Tables 1−3), it is obvious that mode 4 represents the collective relaxation of (bulk) water molecules not affected by the solute. Mode 3 can be assigned to weakly bound water molecules that are retarded (hence slow water) but not frozen (irrotationally bound, ib) in their dynamics because of their interactions with the solute.27 Because the fast water mode at ∼400 GHz,27 not resolved for the present spectra, is strongly linked to the cooperative relaxation, its weak amplitude has to be included when calculating the bulk water concentration for the present samples. As shown previously, the latter is given to a good approximation as Sb(c) = S4(c) + ε∞(c) − ε∞(0),27 where S4(c) and ε∞(c) are the data in Tables 1−3 and ε∞(0) = 2.68 is the infinite-frequency permittivity of pure water from ultra-high-frequency measurements.39 From the thus-obtained values of Sb(c), corrected for kinetic depolarization with slip boundary conditions,37 the DRS-detectable bulk water concentration, cap b , at the solute concentration, c, was obtained with eq 10. The concentration of slow water, cap s , was directly obtained from S3. From the DRS-detected amount of slow water, the corresponding hydration number (Zs) (i.e., the number of weakly bound (slow) water molecules per mole of solute)

Zs =

csap c

(11)

is directly obtained. However, cbap + csap gives the total concentration of DRS-detectable water. The comparison of this number with the analytical water concentration, cw, thus defines a second effective hydration number Z ib =

c w − csap − cbap c

(12)

This Zib value represents the number of water molecules per equivalent of solute that are so strongly interacting that their dynamics is effectively frozen (ib) on the nano- to picosecond time scale of the DR experiment.21 The values of Zs and Zib and the resulting total hydration number Zt, where Zt = Zs + Zib, obtained for the 0.1 M solutions of DTAB, DTAC, DTAMs, and DTATf at 45 °C, are summarized in Table 6, together with data for DTAB and 0.1 M DTAC at 25 °C from elsewhere.28 For all studied surfactants, the Zib values were very similar (∼10) and clearly larger than zero, in line with previous findings for DTAB and DTAC at 25 °C.20,27 This is surprising because for Cl−, Br−,28 10043


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region of the micelles, is essentially the same for all four surfactant systems. The most likely explanation for these observations is the insertion of the trifluoromethyl moiety of Tf− into the micellar core as sketched in Figure 6 and postulated in ref 30 on the basis of the results from other techniques. Because the partial charge of the −SO3− moiety of Ms− is even more negative than that of Tf−, cation−anion pairing through Coulomb interactions is an unlikely reason for the observed strong Tf− condensation on the DTA+ micelle. The main driving force is probably the strong hydrophobicity of the −CF3 group. The hydration data suggest that with increasing aggregation number micelles become more compact and expose a less-hydrophobic surface. However, with the insertion of Tf− into the interfacial region of DTA+ micelles, leading to a shape transition from sphere to disk,30 the hydrophobic core apparently becomes completely shielded from water.

■

Figure 5. Hydration numbers of slow, Zslow (solid symbols), and frozen, Zib (open symbols), water molecules as a function of aggregation number, Nagg, for 0.1 M aqueous solutions of DTAC11 at 25 °C (▼, ▽) and 45 °C (■, □), DTAB11 at 25 °C (◆, ◇) and 45 °C (▲, Δ), and DTAMs at 45 °C (●, ○). The lines are a guide to the eye. (Inset) Zs as a function of Nagg with added data for the DTATf samples in Table 2.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS

■

ABREVIATIONS

■

REFERENCES

The financial support of FAPESP (project no. 2007/50970-5), CNPq, Instituto Nacional de Ciência e Tecnologia de Fluidos Complexos (INCT-FCx), and Núcleo de Apoio à Pesquisa de Fluidos Complexos (NAP-FCx) is gratefully acknowledged. F.S.L. is a FAPESP graduate fellow (project no. 2008/50041-7). Figure 6. Sketch of the interfacial regions of DTAB and DTATf micelles showing for DTAB slow water molecules interacting with the hydrophobic core and for DTATf the insertion of the strongly hydrophobic −CF3 moieties into the micelle. Arrows indicate water molecules cooperatively bound by an anion and a cation and thus frozen in their dynamics.

DTA+, dodecyltrimethylammonium cation; Cl−, chloride; Br−, bromide; Ms−, methanesulfonate; Tf−, trifluoromethanesulfonate, triflate; DRS, dielectric relaxation spectroscopy; α, degree of counterion dissociation; cmc, critical micellar concentration; Nagg, aggregation number; κ, electrical conductivity; ε0, permittivity of vacuum; ε̂(ν), complex relative permittivity; ε′(ν), relative permittivity; ε″(ν), dielectric loss; τi, relaxation time of mode i; Si, amplitude (relaxation strength) of mode i; RG, Grosse radius; D, diffusion coefficient of a free ion; ϕmic, volume fraction of micelles; εm (= 71.52), static permittivity of the solvent; εp (∼2), static permittivity of the hydrophobic core of the micelles; λs, surface conductivity of the micelle; Ds, surface diffusion coefficient of adsorbed counterion; χ−1, Debye length from Grosse’s model; χ−1 Debye, Debye length; Zs, number of weakly bound (slow) water molecules per mole of surfactant; Zib, number of strongly (irrotationally) bound water molecules per mole of surfactant; Zt, total hydration number

aggregates, both at the interface and in the core, prevents the penetration of water molecules by diminishing the available free space in the core and by providing a steric barrier at the surface. Such an interpretation of Zs is in line with the electron paramagnetic resonance results for DTATf, DTAB, and DTAC micelles,30 which indicate a smaller hydration of the triflatebased surfactant in comparison to that of the latter surfactants.

■

CONCLUSIONS The behavior of triflate as a counterion of DTA+ micelles is remarkably different from that of halide anions Br− and Cl−. It also differs from that of methanesulfonate, despite the similar structure of both anions. From the micelle relaxations analysis a considerably reduced mobility of Tf− on the micelle surface was inferred, which is in line with the reported tight packing and small mobility of the monomers within DTATf aggregates.30 Additionally, compared to that of DTAB, DTAC, and DTAMs, the total hydration number of DTATf is considerably smaller (Table 6). More precisely, no weakly bound (slow) water typical of hydrophobic hydration could be detected (Zs = 0) whereas the number of strongly bound (frozen) water molecules, associated with H2O molecules simultaneously interacting with anions and surfactant cations in the interfacial

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