Anomalous Diffusion of Water in [BMIM][TFSI] Room-Temperature Ionic Liquid

Anne-Laure Rollet,*,† Patrice Porion,‡ Michel Vaultier, | Isabelle Billard,§ Michael Deschamps,†Catherine Bessada,† and Laurence Jouvensal⊥

Centre de Recherche sur les Mate´riaux a Haute Tempe´rature (CRMHT)- CNRS 1D aVenue de la RechercheScientifique, 45071 Orle´ans Cedex 2 France, Centre de Recherche sur la Matie`re DiVisee (CRMD)- CNRS1bis rue de la Fe´rollerie, 45071 Orleans Cedex 2 France, Institut de Recherches Subatomiques de Strasbourg(IReS)- IN2P3, UMR 7500, CNRS/IN2P3 - ULP, Chimie Nucle´aire, Bat. 35, B.P. 28, 67037 StrasbourgCedex 2, France, UniVersitede Rennes 1, CNRS UMR 6510 (SESO), Campus de Beaulieu, 35042 RennesCedex France, and Centre de Biophysique Mole´culaire (CBM), CNRS, rue Charles Sadron,45071 Orleans Cedex 2 France

ReceiVed: July 10, 2007; In Final Form: August 29, 2007

We have studied the self-diffusion properties of butyl-methyl-imidazolium bis(trifluoromethylsulfonyl)-imide([BMIM][TFSI]) + water system. The self-diffusion coefficients of cations, anions, and water moleculeswere determined by pulsed field gradient NMR. These measures were performed with increased water quantityup to saturation (from 0.3 to 30 mol %). Unexpected variations have been observed. The self-diffusioncoefficient of every species increases with the quantity of water but not in the same order of magnitude.Whereas very similar evolutions are observed for the anion and cation, the increase is 25 times greater forwater molecules. We interpret our data by the existence of phase separation at microscopic scale.

Introduction

The room-temperature ionic liquids (RTILs) field has widelyexpanded since the early 1990s.1,2 Though their discovery datesback to 1914, they have been overlooked by scientists untilsynthetic organist chemists identified them as a new class ofsolvents. Since that moment, synthesis of new RTILs as wellas their use as solvents,3 reactants, and catalysts4 exponentiallyincreased. They have now applications in materials synthesis,5

biocatalysis,6 electrochemistry,7,8 extraction,9,10 etc. However,there is a need to collect data on the physical and chemicalproperties of RTILs because of a lag between the understandingof these solvents and their uses. For example, their sensibilityto the presence of additional compounds such as water11 isknown but few studies attempt to explain it. As a consequence,important discrepancies occur in literature data because of thepresence of neglected impurities in studied samples.12 In thispaper, we have studied how water influences the properties ofone of the most used systems, the butyl-methyl-imidazoliumbis(trifluoromethylsulfonyl)-imide, [BMIM][TFSI]. Its chemicalformula writes as follows:

Moreover, water is an omnipresent compound on the one handbecause of the intrinsic hygroscopy of these systems and on

the other hand because many of the processes (synthesis,extraction, etc.) involve water. We have chosen to address thisissue of water impact by focusing on the self-diffusion of everyspecies of the [BMIM][TFSI]+ water mixture. Self-diffusionrepresents the ability of a particle to move inside its environ-ment. This fundamental quantity is therefore involved in everytransport equation either individual or collective. Among all theexperimental techniques allowing us to get at the self-diffusioncoefficients, NMR pulsed field gradients is probably one of themost convenient and reliable. Indeed, it is noninvasive, thesystem is kept at equilibrium, and different elements of thesystem can be measured selectively. In our case, the self-diffusion coefficient of BMIM cation and water molecules wasdetermined via1H and the one of TFSI anion via19F.

Experimental Methods

The pulsed gradient spin-echo NMR (PGSE NMR) methodwas used to measure the1H (cation and water) and19F (anion)self-diffusion coefficients. Because of the difference betweenthe transverse relaxation time (T2) and the longitudinal relaxationtime (T1) (the T2 values are always shorter thanT1), we haveused a modified stimulated spin-echo sequence13 based on theCotts et al. sequence14 to improve the measurements. Self-diffusion coefficients were calculated by measuring the decreasein the NMR echo signal intensity through increasing magneticfield gradients. The self-diffusion coefficients were obtained bynonlinear least-square fitting of the echo attenuationE(q, ∆) as

whereI(q, ∆) andI(0, ∆) are the echo intensities, respectively,measured with and without the field gradient;q ) γgδ/2π,whereγ is the gyromagnetic ratio of the nuclei,g is the intensity

* To whom correspondence should be addressed. E-mail: rollet@cnrs-orleans.fr.

† Centre de Recherche sur les Mate´riaux aHaute Tempe´rature (CRMHT).‡ Centre de Recherche sur la Matie`re Divisee (CRMD).§ Institut de Recherches Subatomiques de Strasbourg (IReS).| Universitede Rennes 1.⊥ Centre de Biophysique Mole´culaire (CBM).

E(q, ∆) ) I(q, ∆)/I(0, ∆) ) exp[-4π2q2D(∆ - δ/3 - τ/2)]

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2007,111,11888-11891

Published on Web 09/21/2007

10.1021/jp075378z CCC: $37.00 © 2007 American Chemical Society

of the applied magnetic field gradient,δ is its duration,∆ isthe diffusing time,D is the self-diffusion coefficient, andτ isa gradient delay. All the1H self-diffusion measurements wereperformed on a DSX100 Bruker spectrometer equipped with amicroimaging probe (Micro5 Bruker), the maximum gradientvalue was 1.2 T/m, and all the data were recorded for∆ ) 50ms andδ ) 5 ms. The19F measurements were done on aDSX400 Bruker spectrometer on a 10 mm liquid probe (1H-19F/X), the maximum gradient value was 0.55 T/m, and all themeasurements were performed for∆ ) 50 ms andδ ) 4 ms.All the experiments were conducted at room temperature (298K).

After [BMIM][TFSI] synthesis, water has been carefullyremoved by pumping the sample under vacuum at 50°C.Increased water amounts have been then added to the samples.Finally, NMR tubes have been sealed to prevent sampleevolution over time. Experiments were performed several daysafter sample preparation to ensure the equilibrium state of thesample. Indeed, the demixion occurs slowly in this system as ithas been also observed by numerical simulations.15

Results and Discussion

All the data are gathered in Table 1. First, the self-diffusionof both anion and cation in the system of lowest water amountis very slow. The pertaining coefficients are 2 orders ofmagnitude lower than the one of bulk water (2× 10-9 m2/s).This result is in agreement with previous works16,17on this verysystem or similar systems.18,19 Moreover, these results areconsistent with the [BMIM][TFSI] viscosity12 that is 0.0635 Pacompared to 0.001 Pa for bulk water. Second, the anion andcation have close self-diffusion coefficients despite their verydifferent size and shape. This phenomenon arises from the factthat BMIM and TFSI are strongly associated and thereforepartially move together. Through the assumption of a fastexchange between free and associated species at NMR timesscale, the self-diffusion coefficient of one species can thus bewritten as

whereDfree represents the self-diffusion coefficient when thespecies moves alone,Dassociatedis when it moves together withthe counterion, andR is the proportion of free species.

[BMIM][TFSI] is known as being slightly hygroscopic andweakly miscible with water. At 298 K and atmospheric pressure,the maximal quantity of water in [BMIM][TFSI] is about 1.3mass %.20,21Usually and also in this work, the water amount isdetermined using Karl Fischer titration. This method gives theoverall amount of water but no insight of the mixture micro-structure. The water addition in [BMIM][TFSI] decreases theviscosity.22,12 This effect has been attributed to the screeningof electrostatic interactions by water, which induces a decreaseof RTIL cohesion.11 In this work, we have measured the self-diffusion coefficient of every species of the system [BMIM]-[TFSI] with increased amount of waterW. As presented inFigure 1 whereD(W)/D(W0) is plotted againstW, the variation

for both anion and cation are very similar, almost superimposed.This is somehow surprising because water is expected to risethe ion pair dissociation rate and as a consequence to cause agreater increase ofDanion as compared toDcation with respect totheir size (Rg anion< Rg cation). At the largest water amount,Danion andDcation are larger by a factor 1.3 than at the lowestwater amount. The amplitude of this variation is very close tothe decrease of viscosity12, that is, around 30%, observed inthe same conditions. These results indicate that the addition ofwater in [BMIM][TFSI] system does not lead to a significantincrease of anion-cation pair dissociation, that is, toR. Waterappears to interact quite weakly with ions pairs. Recent works23

suggest that water content is dependent on the interactionbetween the anion and water. The hydrophobicity of TFSI anionsprevents water from dissociating ions pairs and being incorpo-rated in RTILs in large amount.

We have also measured the self-diffusion coefficient of waterDwater using the1H nucleus. Here appears the striking result ofthis study: the evolution ofDwater is completely out ofcomparison with that of the ions. As it can be seen in Figure 2,Dwater rises 25 times quicker.

What hypothesis can be put forward to explain this phenom-enon? The thesis of the fluidizing effect of water can be rejectedbecause if it was valid, all the self-diffusion coefficients (waterand ions) would have been affected in the same order ofmagnitude. A second hypothesis would be to think of water asbeing linked to ions at low water amount; then, when increasing

TABLE 1: Self-Diffusion Coefficients of BMIM, TFSI, andH2O

water molarfraction Dcationm2/s (1H) Danionm2/s (19F) Dwaterm2/s (1H)

0.03 ()W0) 2.3× 10-11 2.0× 10-11 3.5× 10-11

0.12 2.6× 10-11 2.3× 10-11 13.4× 10-11

0.22 2.7× 10-11 2.5× 10-11 20.6× 10-11

0.3 2.9× 10-11 2.6× 10-11 26.8× 10-11

Dmeasured) RDfree + [1 - R]Dassociated

Figure 1. Relative self-diffusion coefficientsD(W)/D(W0) have beenplotted as a function of water molar fractionW. W0 is the lowest wateramount used in this work.Danion is represented by triangles andDcation

by diamonds.

Figure 2. Relative self-diffusion coefficientsD(W)/D(W0) have beenplotted as a function of water molar fractionW. W0) 0.03 is the lowestwater amount used in this work.Dwater is represented by circles,Danion

by triangles, andDcation by diamonds. The dotted line represents therelative self-diffusion coefficients of water calculated using the Stokes-Einstein relation.

Letters J. Phys. Chem. B, Vol. 111, No. 41, 200711889

the water amount water would be released and could thus diffusemuch more rapidly. Such a hypothesis implicates the followingevolution ofDwaterwith 2 domains: in the small water amount,Dwater should increase rapidly along withW and then reach apseudo-plateau whereDwater should increase in the same orderof magnitude asDcation and Danion. Indeed, one can write themeasuredDwateras

whereb(W) represents the proportion of bounded water mol-ecules.Dwater

linked is approximately equal toDcation and Danion.Dwater

free can be estimated thanks to the Stokes-Einstein rela-tion24,25 that links self-diffusion coefficient to viscosity. TheDwater

free values are about 10-11 m2/s, which is much slower thanour experimental values. In Figure 2, the variation ofDwater(W)/Dwater(W0) versus W, calculated using the Stokes-Einsteinrelation and assuming that the whole water is free, is plottedfor comparison. This figure clearly demonstrates that this secondhypothesis can also be rejected.

The hypothesis we suggest to explain the particular evolutionof the three species in [BMIM][TFSI]+ water systems as afunction of water amountW is that water and ions do not occupythe same domains. In other words, water is not homogenouslymixed with RTIL but forms small aggregates whose size andconnections increase withW. Figure 3 offers an artistic viewof this phenomenon. Recent numerical simulations on this haveshown the existence of a local water “pool” in several RTILs26,23

and particularly in [BMIM][TFSI].15

Our results show that these pools are connected and form aporous network at the local scale. According to Sieffert andWipff,15 water molecules are generally hydrogen-bonded to twoTFSI anions so as to form pore walls richer in TFSI than BMIM.Moreover they also found that this H-bond is stronger andshorter than the one between BMIM and water despite thatBMIM may have long lifetime hydration shell at high dilution27

(in the [BMIM][Br] + H2O system). When increasing the wateramount, the tortuosity of aqueous network is decreased. At 30%of water, the tortuosity28 θ is estimated usingDwater) θ-1 Dbulk

water and is about 10. Such values are comparable to thoseobtained in porous systems like Nafion ionomer membraneswhere the tortuosity is about 10 for 30% water volumefraction;29 one can notice that 30 mol % of water in [BMIM]-[TFSI] corresponds approximately to 8% in volume fractionindicating a great connectivity of the aqueous network. Above30 mol % of water, macroscopic demixion occurs between waterphase and RTIL phase. The method of pulsed field gradientsNMR allows us to investigate diffusion phenomena in the timerange from tens of milliseconds to a few seconds (time rangedepends on the sample), and the corresponding distances areabout a micrometer. By varying the observation time∆, onecan determine the characteristic size of the pores or the pseudo-pores (heterogeneity of pores organization as may occur inpolymer systems for example). If the volume explored by theprobe is bigger than this characteristic size, no variation ofDversus∆ is observed; in the reverse case,D decreases versus∆. We have performed a series ofD measurements with∆

ranging from 50 to 400 ms on the sample with the highest watercontent where the pores size is the biggest. No variation ofDversus∆ is observed indicating than the characteristic size ismuch smaller thanλ ) (2D∆)1/2 ) 5.2 µm.

The porous network formed by water in [BMIM][TFSI] canbe compared to bicontinuous phases (oil+ surfactant+ water)and could be defined as one of a particular kind. Indeed, thesegregation between oil and water in the three-componentbicontinuous phases is high and consequently the self-diffusioncoefficients of oil and water are proportional to the phase volumeeach element occupies.30 Thus, the self-diffusion coefficient ofwater increases along with the water amount, whereas the oilself-diffusion coefficient decreases. In the [BMIM][TFSI]+water system, there is an affinity between the two components,as shown by the hygroscopy of [BMIM][TFSI]. An increase ofDcationandDanionversus water amount is observed that indicatesthe presence of water molecules in the RTIL phase, that is, apartial phase segregation.

Conclusion

We have measured the self-diffusion coefficients of BMIM,TFSI, and water in [BMIM][TFSI]+ water system to studythe modification of translational dynamics properties of thisRTIL when water is added. The variation of the self-diffusioncoefficients versus water amount indicates that water does notinduce a significant increase of the ion pair dissociation butdisturbs the RTIL cohesion. Moreover, whereas very similarevolutions are observed for anion and cation (increase of 30%),in the same range of water molar fraction the increase ofDwater

is 25 times greater. It indicates that miscibility of water is notcomplete at the microscale and that the [BMIM][TFSI]+ watersystem shows a partial segregation between [BMIM][TFSI]+some water molecules phase and water+ some [BMIM][TFSI]ions phase.

Acknowledgment. The authors thank Herve´ Meudal, Anne-Marie Fauge`re, Alfred Delville, and Joe¨l Puibasset for theirhelpful discussions. This work has received support from GDRPARIS and ANR JCJC.

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