Dissociation and Charge Transport in Salts of Dendronized Ions in

Apr 5, 2011 - The ion dissociation and transport properties of a series of tetrabutylammonium salts (TBA+) of rigidly dendronized anions with various ...
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Dissociation and Charge Transport in Salts of Dendronized Ions in Solvents of Low Polarity Konstantinos Mpoukouvalas,† David T€urp,† Manfred Wagner,† Klaus M€ullen,† Hans-J€urgen Butt,† and George Floudas*,‡ † ‡

Max Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany Department of Physics, University of Ioannina, 451 10 Ioannina, Greece and Foundation for Research and Technology-Hellas, Biomedical Research Institute (FORTH-BRI)

bS Supporting Information ABSTRACT: The ion dissociation and transport properties of a series of tetrabutylammonium salts (TBAþ) of rigidly dendronized anions with various sizes have been investigated in toluene, THF, and chloroform for a range of concentrations with dielectric spectroscopy and diffusion ordered spectroscopy (DOSY)-NMR. This is one of the first cases that one can study salts in low polarity solvents. The new synthetic approach increases the solubility and allows for investigation of both steric hindrance as well as electronic effects in producing weakly coordinating anions. We found that steric effects promote ion dissociation. In addition, fluorine substitution in the dendritic corona screens the electrostatic interactions and leads to increased dissociation. From the degree of dissociation and the measured diffusion coefficients, the free anion and cation diffusion coefficients were extracted and compared for the different dendrimer generations.

1. INTRODUCTION The high lattice enthalpies of salts make them insoluble in most solvents. In addition, even when they are soluble, they only partly dissociate in nonpolar solvents. The reason is the high free energy of dissociation, which for two monovalent charge carriers is1 EC ¼

e2 4πε0 εS rc

ð1Þ

Here, e is the elementary charge, ε0 is the permittivity of free space, rc is the distance separating a point-like cation from a point-like anion, and εS is the dielectric permittivity of the surrounding medium. For liquids of low polarity (εS e 11)2 and for inorganic salts such as NaCl, KCl, and KNO3, the energy of dissociation is many times kBT, where kB is Boltzmann’s constant and T is the temperature. One consequence of the low degree of dissociation is that dispersions in nonpolar solvents cannot be stabilized by electrostatic or electrosteric repulsion.3 Another consequence is the low electrical conductivity of nonpolar liquids.4 This is important when pumping, for example, hydrocarbons through pipes since high electric potentials can built up leading to spark discharges and explosions, a process known in petroleum handling as flow electrification. To circumvent electrification, suitable molecules are added that effectively increase the conductivity of the liquid to a predefined value.5 From a thermodynamic viewpoint, charging in a liquid is controlled by the Bjerrum length, λB = e2/4πε0εSkBT, giving the characteristic separation between two ions at which Coulombic interactions are balanced by the thermal energy. In liquids of low r 2011 American Chemical Society

polarity such as toluene or even THF, the Bjerrum length is 20.4 and 7.4 nm, respectively. Ion dissociation in such solvents is limited unless the ion size approaches the “escape distance” set by λB. Hence extensive research was made on increasing the size and bulkiness of molecular anions that led to a new class of compounds known as weakly coordinating anions (WCAs).614 However, until recently steric hindrance prevented the direct synthesis of much larger structures and WCAs were limited to relatively small constituents.15 A recent investigation reported16 a novel synthetic strategy toward a number of extremely large and rigid molecular ions with dimensions approaching the Bjerrum length in nonpolar solvents. Among the different WCAs, rigidly dendronized ions based on polyphenylenes constitute a new class of materials because of their large size and shape persistence. In addition to the increase of the anion size, another approach emphasized the effect of delocalization of the anion charge.6 It is thought that the spreading of the anion charge to a larger area is responsible for the weaker coordination. The electron-withdrawing ability of fluorine atoms is well-known and it serves to delocalize the negative charge. However, it is still unknown how the large size, shape, and selective anion functionalization with fluorine atoms at the anion core and dendritic corona affect the dissociation and eventually the transport properties of ions. To Received: February 10, 2011 Revised: March 28, 2011 Published: April 05, 2011 5801

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Figure 1. Schematic representation of the samples investigated herein. Notice that all dendritic molecules share the same cation, i.e., tetrabutylammonium (TBAþ), but the anion size varies. The sample codes and sample characteristics are summarized in Table 1.

Table 1. Molecular Characteristics of the Samples Investigated in the Present Studya sample codes

a

compound abbreviations þ



chemical formula

Mw (g/mol)

1

TBA (BPh4)

2

TBAþ (B-G1)

C160H136BN

2083.6

3

TBAþ (B-G1F)

C160H56BF80N

3522.9

4 5

TBAþ (BF-G1) TBAþ (BF-G22)

C160H120BF16N C400H280BF16N

2371.5 5415.3

6

TBAþ (BF-G24)

C640H440BF16N

8459.1

C40H56BN

561.7

Mw corresponds to the total molecular weight, i.e., anion and cation.

this end, dielectric spectroscopy is the method of choice, because of its inherent ability to provide both the degree of ion dissociation and transport through the measured dc conductivity.17,18 In the present study the ion dissociation and transport properties of a series of tetrabutylammonium salts (TBAþ) of rigidly dendronized anions with various sizes (with diameters up to 5 nm) have been investigated in solution and as a function of the solvent polarity. This is one of the first cases that one can study salts in low polarity solvents since one is confronted with severe solubility problems. Here, the choice of the molecules with the ever larger anions promote solubility and allows investigating both the effects of steric hindrance (produced by the presence of bulky polyphenylenes) as well as electronic effects (due to selective fluorination) in producing weakly coordinating anions.

2. MATERIALS AND METHODS Samples. The synthesis of the TBAþ salts of rigidly dendro-

nized anions (Figure 1) is described in detail elsewhere16 and the molecular characteristics of all samples are summarized in

Table 1. These borate anions are perfectly defined and reach diameters up to 6 nm. In the present study solutions with concentrations of 6.15  105, 0.0001, 0.0005, 0.001, and 0.002 M were prepared with the upper and lower limit given by the solubility (of compound 1) and signal-to-noise ratio, respectively. Different solvents were employed with a range of polarities i.e. toluene, chloroform, and tetrahydrofuran (THF). The static dielectric permittivities of the three solvents at 25 °C are 2.38, 4.81, and 7.58 for toluene, chloroform and THF, respectively and the expectation is that the increased solvent polarity will promote ion dissociation (i.e., eq 1). Rheology. An advanced rheometric expansion system (ARES) equipped with a force-rebalanced transducer was used in the steady mode to measure the viscosity. A Couette geometry with a cup diameter of 27 mm, a bob diameter of 25 mm, and a bob length of 32 mm was employed. The solvent viscosities were measured by means of isothermal scans for temperatures in the range of 173.15293.15 K and rate sweeps between 200 and 2000 s1. The measured solvent viscosity, as expected, was found to follow the VogelFulcherTammann (VFT) equation: η = η0 exp(B/(T  T0)), where η0, B, and T0 are respectively the viscosity in the limit of very high temperatures, the activation parameter, and the “ideal” glass temperature. The following VFT parameters were used for chloroform and toluene: η0 = 1  104 Pa s, B = 332 K and T0 = 120 K. For THF, the reported19 dependence within the temperature range from 203 to 298 K conforms to an Arrhenius equation instead: η = η0 exp(E/T), where η0* = 2.134  104 Pa s and E = 910 K. NMR. The diffusion (DOSY, diffusion ordered spectroscopy) experiments were done with a 5 mm BBI 1H/X z-gradient probe and a gradient strength of 5.516 [G/mm] on the 700 MHz spectrometer and with a 5 mm BBFO z-gradient probe and a 5802

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Table 2. Maximum Extension of the Anion and Cation, Experimental Diffusion Coefficients from DOSY-NMR, Ion Dissociation (r), and Calculated Diffusion Coefficients for Dissociated Anion (Dc) and Cation (Dcþ)a 10 10 sample/generation concentration (M) r (nm)a rþ (nm)a Dexp (m2/s)b Dexp (m2/s)b   10 þ  10

Rb

Dc  1010 (m2/s)c Dcþ  1010 (m2/s)d

1/G0

0.005

0.56

0.52

8.91

8.51

0.30

9.61

8.30

2/G1

0.005

1.40

0.52

4.47

6.92

0.63

4.42

8.32

3/G1

0.005

1.44

0.52

4.07

7.94

0.67

3.60

9.19

4/G1 5/G2

0.005 0.001

1.40 2.28

0.52 0.52

4.17 2.75

7.08 6.17

0.55 0.47

3.74 2.06

9.00 7.13

6/G2

0.001

2.28

0.52

2.00

6.17

0.51

1.64

9.76

d c exp exp exp Theoretical values. b In THF at 25 °C. c Dc = [Dexp   D0(1  R)]/R. {Dþ = [Dþ  D0(1  R)]/R} where D0 = {[Dþ þ D  (σdckBT/ 2 pq )]/[2(1  R)]}. a

Figure 2. Frequency-dependence of conductivity σ* = σ0 þ iσ00 , (σ0 shown in symbols and σ00 with lines) shown for the different dendrimers in 0.001 M solutions in THF at 223.15 K. The frequency-independent part of σ0 was used in extracting the dc-conductivity (σdc). Note that 3 has the highest dc conductivity among the dendrimers.

gradient strength of 5.350 [G/mm] on the 500 MHz system. For the calibration of the gradient strength, a sample of 2H2O/1H2O was measured at a defined temperature and compared with the literature diffusion coefficient of 2H2O/1H2O. The diffusion delay was in the range from 200 to 350 ms depending on the investigated dendrimers (working with smaller diffusion time, e. g., 20 ms gave the same results; Supporting Information, Figures S1S3). The gradient pulse length was varied between 600 and 1200 μs. The gradient strength was varied in 32 or 64 steps from 2% to 100%. The diffusion coefficients were measured with a double stimulated echo for convection compensation.20 Hereby a decrease of lock power was implied in every experiment for reduction of an extra power source in form of heat. The error in the determination of the diffusion value was calculated from the standard deviation of decay curves for selected peaks using the Bruker Simfit program and appropriate diffusion fit functions. The relative standard deviations were always in the range of 1  103. Inside the measurement volume the temperature was kept constant at 298.3 K with a maximum drift of (0.1 K regulated by a standard 1H methanol NMR sample using the topspin 2.1 software (Bruker). The thus obtained diffusion coefficients (Dexp þ and Dexp  ) are included in Table 2. Dielectric Spectroscopy (DS). The liquid sample cell (Novocontrol BDS1308) consisted of two electrodes, 20 mm in diameter. Teflon spacers having a thickness of 25, 50, 100, 240, and 310 μm were used between the electrodes. For each

measurement approximately 0.5 mL of solution was necessary to fill the sample cell. Different electrodes were employed: brass, gold-coated, and stainless steel electrodes. Once the solution was placed in the liquid sample cell, the temperature was immediately dropped to 173 K to avoid any possible solvent evaporation. The dielectric measurements were performed in a cryostat at different temperatures in the range from 173.15 to 273.15 K at atmospheric pressure, and for frequencies in the range from 102 to 106 Hz using a Novocontrol High Resolution Alpha Analyzer. Temperature was controlled by a Novocontrol Quatro Cryosystem, which uses N2 to heat and cool the sample with an accuracy of (0.1 K. The complex dielectric function, ε* = ε0  iε00 , where ε0 is the real and ε00 is the imaginary part, is in general, a function of frequency f (or the radial frequency ω = 2πf), temperature T, and pressure P, ε* = ε*(ω,T,P). ε*(ω), is related to the complex electric conductivity, σ*(ω), through17 0

0

σðωÞ ¼ σ0 þ iσ0 ¼ iωε0 εðωÞ w σ0 ¼ ωε0 ε0 , σ 0 ¼ ωε0 ε0

0

ð1Þ 0

For pure electronic conduction no contribution arises to ε while ε00 (ω) = σdc/ε0ω increases linearly with decreasing frequency. The “transition” from dc to ac conductivity is given by a frequency independent to a frequency-dependent σ0 (ω).

3. RESULTS AND DISCUSSION The dc conductivity of an ion-containing medium is expressed as the sum of the individual contributions of all charge carriers: σ dc ¼

n

∑ pi μi qi i¼1

ð2Þ

Here, pi, μi, and qi are the number density, the mobility, and the charge of the ith type of charge carrier, respectively. An underlying assumption is that all charge carriers move independently of each other with a constant mobility. In the present case there are two monovalent charge carriers, i.e., the cations (TBAþ) and respective anions. Therefore, the dc conductivity of the fully dissociated ions can be expressed as σdc ¼ pþ μþ e þ p μ e

ð3Þ

Figure 2 gives the measured complex conductivities as a function of frequency for the different salts at 223.15 K and a 0.001 M concentration in THF. The dc-conductivities correspond to the frequency-independent part of the σ0 curves and are different by a factor of 2. Among the different dendrimers, sample 3 has the highest dc conductivity. The decrease of conductivity at lower frequencies is due to the accumulation of charges at the electrode/sample interface, a process known as electrode 5803

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Figure 3. Degree of ion dissociation R as a function of inverse temperature for the different dendrimers at 0.001 M concentration in THF. Note that 3 has many more ions available for conduction as, e.g., 1.

polarization.2123 Subsequently, the dc conductivity was measured as a function of temperature (Figure S4, Supporting Information) and concentration (Figure S5, Supporting Information). The temperature dependence for all concentrations conforms to σdc = σ0 exp(Eσ/kBT), where σ0 is the limited conductivity and Eσ is the activation energy for ion transport (Eσ = 7.3, 8.1, 8.3, 8.4, 8.3, and 8.4 kJ/mol for 16, respectively). On the other hand, the linear concentration dependence of the dc conductivity implies an increasing number of mobile charge carriers at a fixed degree of ion dissociation, within the investigated concentration range. The degree of ion dissociation can be extracted from the ratio of the measured dc-conductivity and the calculated conductivity that assumes complete ion dissociation as σ meas ð4Þ R¼ σ calc also known as the Haven ratio (HR).24 Based on the above definition, complete ion dissociation corresponds to R = 1, whereas any value below unity means that a fraction of mobile carriers does not contribute to the conductivity, i.e. forms ionpairs. The denominator in eq 4 can be calculated from the mobility, μi = e/6πηri, and eq 3 as   pS e2 1 1 σ calc ¼ þ ð5Þ 6πη r þ r  where ri are the radii of maximum extension rmax for the anion and cation (the values are listed in Table 2; for the definition see Supporting Information) and ps is the total ion concentration from the stoichiometry. The measured dc conductivity differs from the calculated one according to eq 5, because the paired charges do not contribute to the conduction mechanism. The obtained degrees of ion dissociation based on eq 4 are plotted in Figure 3 for the different salts in THF as a function of inverse temperature for a concentration of 0.001 M. Dendrimer 1 with the smallest anion size (radius of 0.56 nm) bears the lowest degree of dissociation. This is to be expected, as the small anion/ cation radii do not facilitate dissociation (rc (eq 1) is much smaller than the Bjerrum length). Dendrimer 2, bearing a larger anion (2 with a radius of 1.4 nm is the larger tetraphenylborate species ever synthesized), shows a higher dissociation as a result of the lower Coulomb energy, EC. On the other hand, 3 with the higher dc-conductivity has also the higher ion dissociation despite bearing approximately the same anion size with 2. We note here, that in 3, the fluorine atoms cannot delocalize the

Figure 4. Degree of ion dissociation for 4 (concentration 0.001 M) plotted as a function of temperature for toluene (squares), chloroform (spheres), and THF (up triangles).

boron charge because of the presence of the (twisted) phenyl rings in between that disrupt charge conjugation. Thus, the reason for the higher dissociation in 3 is not the boron charge delocalization but is a composite effect. First, the 80 fluorine atoms in the corona, being more bulky than their hydrogen counterparts, effectively screen the electrostatic interactions. Second, fluorination inevitably gives rise to the fluorophobic effect,25 i.e., to unfavorable interactions between the fluorinated corona and the cation hydrocarbon chains. Both of these factors lead to the observed higher ion dissociation. These screening effects have more profound consequences on the ion dissociation and transport than the mere steric hindrance (1 vs 2) or the delocalization of the anion charge by fluorination at the anion core. However, differences in ion dissociation among the three dendrimers bearing fluorine atoms in the vicinity of the anion (46) are small and within the experimental uncertainty. The effect of solvent polarity, as suggested through eq 1, is strong. Figure 4 provides the dissociation constant of 4 in THF (εS = 7.58 at 25 °C), chloroform (εS = 4.81), and toluene (εS = 2.38). Additional results for 2 in THF are given in Figure S6 of the Supporting Information. The three solvents represent the low polar (5 e εS e 11) and nonpolar (εS e 5) regimes.2 Ion dissociation is inversely proportional to the Coulomb energy, and depends on the static dielectric constant, εS, in the solutions by means of eq 1. As expected, ion dissociation is promoted in THF whereas in toluene the vast majority of ions form pairs. In view of the results presented in Figures 3 and 4, the diffusion coefficients measured by DOSY-NMR (Dexp) at 25 °C and reported in Table 2 are not the diffusion coefficients of the free ions but represent some average of the fully dissociated and paired states.2628 This is evident, for example, by comparing the ratio of the measured diffusion coefficients with the ratio of the ionic radii. According to the StokesEinstein equation (Di = k B T/6πηr i ), the ratio of the diffusion coefficients is inversely proportional to the ionic radii of the species. However, this is not the case here as can be readily verified from the NMR data of Table 2. Nevertheless, knowledge of the measured (NMR) diffusion coefficients together with the degree of ion dissociation allows calculating the diffusion coefficients of the free ions. The NMR diffusion coefficients are related to the coefficients of 5804

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exp Figure 5. NMR anion (Dexp  ) (open squares) and cation (Dþ ) (open circles) diffusion coefficients plotted for the different generations (G0, G1, and G2) plotted as a function of the anion size. The calculated anion (filled squares) and cation (filled circles) diffusion coefficients corresponding to free ions are also plotted for comparison. The solid and dashed lines through the calculated and measured data are guides for the eye.

the fully dissociated cation/anion (D cþ, Dc) states, as exp

Dþ ¼ D0 ð1  RÞ þ RDcþ

ð6Þ

c Dexp  ¼ D0 ð1  RÞ þ RD

ð7Þ

Here D0 is the diffusion coefficient of the neutral complex is the diffusion coefficient as (cation/anion pairs), D exp ( measured by NMR, and Dc( is the calculated diffusion coefficient of the free cation/anion. To obtain the three molecular properties, i.e., D0 , D cþ, and Dc, eqs 6 and 7 are combined with the NernstEinstein equation, relating the measured conductivity to the ionic diffusion coefficients as D = σdck B T/p s e 2 , where the degree of dissociation has been taken into account as σ dc ¼

RpS e2 c ðD þ Dc Þ kB T þ

ð8Þ

The result for the calculated diffusion coefficients corresponding to the free ions are included in Table 2. Figure 5 compares the measured and calculated diffusion coefficients for the different anion sizes/generations at 25 °C. The calculated diffusion coefficients of the free ions are reasonable; First, the free cation diffusion is the fastest (Dþ ≈ 8.6  1010 m2/s) being nearly independent of the compound, except from 1 where the anion and cation are of comparable size. Second, free anion diffusion exhibits a stronger dependence on the anion radii than the measured values. As a result, the ratio of the diffusion coefficients better corresponds to the ratio of ionic radii, an expectation bornout by the StokesEinstein (SE) equation. Despite this, some deviations from the SE relation are still present for the larger anions and this can have different origins (the assumptions for temperature-independent ionic radii in eq 5, as well as uncertainties in the viscosity and conductivity values entering, eq 5 and 4, respectively). Summarizing, the NMR diffusion coefficients underestimate/ overestimate the respective cation/anion diffusion coefficients with regard to the free ions, but when coupled with independent conductivity measurements they result in the transport properties of the unassociated species.

4. CONCLUSION In the present study the ion dissociation and transport properties of a series of tetrabutylammonium salts (TBAþ) of rigidly dendronized anions with various sizes have been investigated in solution for a range of concentrations, temperatures and as a function of the solvent polarity with dielectric spectroscopy. In particular, the effect of fluorine substitution at the anion core and corona as well as the steric effects produced by the polyphenylene groups have been investigated. Ion dissociation is promoted by fluorine substitution away from the boron position in the corona. This shows that the reduction of the electrostatic interactions is more effective in producing WCAs than the mere delocalization of the anion charge produced by fluorination of the core. However, in the absence of fluorine substitution, steric effects gain importance and result in a higher dissociation. In addition, increasing solvent polarity greatly promotes ion dissociation. Furthermore, knowledge of the degree of ion dissociation allowed calculating the anion/cation diffusion coefficients corresponding to the unpaired ions. A synthetic approach that utilizes even larger anions -with sizes that are comparable to the characteristic Bjerrum length- and selective fluorination can lead to the best, i.e. superweak anions. ’ ASSOCIATED CONTENT

bS

Supporting Information. Temperature and concentration dependence of dc conductivity and degree of dissociation for 2 in different solvents. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: gfl[email protected].

’ ACKNOWLEDGMENT Technical support by A. Hanewald (MPI-P) is acknowledged. We gratefully acknowledge financial support of this work by the Deutsche Forschungsgemeinschaft (DFG) within the frame of Sonderforschungsbereich (SFB) 625. The research project is cofunded by the European Union - European Social Fund (ESF) & National Sources, in the framework of the program “HRAKLEITOS II” of the “Operational Program Education and Life Long Learning” of the Hellenic Ministry of Education. D.T. thanks the Graduate School of Excellence “Material Science in Mainz” (MAINZ) for a scholarship. ’ REFERENCES (1) Fuoss, R. M.; Kraus, C. A. J. Am. Chem. Soc. 1933, 55, 1019–1028. Kraus, C. A.; Fuoss, R. M. J. Am. Chem. Soc. 1933, 55, 21. (2) van der Hoeven, P. H. C.; Lyklema J. Adv. Colloid Interf. Sci. 1992, 42, 205. (3) Briscoe, W. H.; Horn, R. G. Langmuir 2002, 18, 3945–3956. Hsu, M. F.; Dufresne, E. R.; Weitz, D. A. Langmuir 2005, 21, 4881. Roberts, G. S.; Sanchez, R.; Kemp, R.; Wood, T.; Bartlett, P. Langmuir 2008, 24, 6530. (4) Kitahara, A.; Karasawa, S.; Yamada, H. J. Colloid Interface Sci. 1967, 25, 490. (5) Klinkenberg, A.; der Minne, J. L. Electrostatics in the Petroleum Industry; Elsevier: Amsterdam, 1958. 5805

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’ NOTE ADDED AFTER ASAP PUBLICATION This paper was published ASAP on April 5, 2011. Table 2 footnotes were updated. The revised paper was reposted on April 11, 2011.

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