Conformational isomerism and phase transitions in tetraethylammonium bis(trifluoromethanesulfonyl)imide Et4NTFSI

Journal of Molecular Structure 783 (2006) 145–156 www.elsevier.com/locate/molstruc

Conformational isomerism and phase transitions in tetraethylammonium bis(trifluoromethanesulfonyl)imide Et4NTFSI M. Herstedt a, W.A. Henderson b, M. Smirnov c, L. Ducasse a, L. Servant a, D. Talaga a, J.C. Lasse`gues a,* a

Laboratoire de Physico-Chimie Mole´culaire, UMR 5803, CNRS, Universite´ Bordeaux I, 351 Cours de la Libe´ration, 33405 Talence Cedex, France b Department of Chemistry, US Naval Academy, 572 M Holloway Road, Annapolis, MD 21402, USA c Institute of Physics, Saint Petersburg State University, Saint Petersburg 199155, Russian Federation Received 29 July 2005; accepted 22 August 2005 Available online 17 October 2005

Abstract Solid phase transitions are detected by DSC at 277 and 322 K in the tetraethylammonium bis(trifluoromethanesulfonyl)imide salt (Et4NTFSI) before the melting point at 377 K. Over this temperature range, the experimental Raman spectra of the solid and liquid phases of Et4NTFSI can satisfactorily be reproduced using the calculated frequencies and intensities of the cation in its all-trans (D2d) or trans–gauche (S4) conformation, and of the anion in its transoid (C2) or cisoid (C1) conformation. The Raman spectra of the low-temperature ordered phase III show that the cation and anion adopt the D2d and C2 conformations, respectively, predicted by DFT calculations to be of lower energy than the corresponding S4 and C1 ones. Above the first order phase transition near 277 K, w70% of the cations are transformed into the S4 conformation while the population of C2 anions decreases progressively (phase II). Another disordered phase seems to occur between 322 and 377 K where the cations and anions reach comparable populations of their two possible conformations. In this phase I, the cation D2d form is found to be more stable than the S4 form by 4.4G0.3 kJ molK1 and the anion C2 form is more stable than the C1 form by 7G1 kJ molK1. In the liquid phase, the cation keeps comparable populations of the D2d and S4 conformers, whereas w70% of the anions adopt the C1 conformation. Finally, by quenching the liquid or the disordered phases, a supercooled solid phase II’ is easily obtained. It is composed of C2 anions and a mixture of w80/20 S4/D2d cations that corresponds roughly to the extrapolation of the phase II populations. q 2005 Elsevier B.V. All rights reserved. Keywords: Phase transitions; Tetraethylammonium bis(trifluoromethanesulfonyl)imide; Conformation; Raman; DFT calculations

1. Introduction The tetraethylammonium bis(trifluoromethanesulfonyl) imide salt, (C2H5)4NC(CF3SO2)2NK, abbreviated as Et4NTFSI, is formed of cationic and anionic species that each have two conformational states of rather close energy. Quantum mechanical calculations on the free TFSIK anion [1,2], or LiCTFSIK ion-pairs [3,4] and structural results on a variety of TFSI salts [5–11], have shown that the anion can adopt a transoid or cisoid form. The former, of C2 symmetry, has the CF3 groups on opposite sides of the S–N–S plane and a dipole moment of 0.67 debye; the latter, of C1 symmetry, less stable by 2–3 kJ molK1, has the CF3 groups on the same side of the * Corresponding author. Tel.: C33 5 40 00 63 55; fax: C33 5 40 00 84 02. E-mail address: [email protected] (J.C. Lasse`gues).

0022-2860/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2005.08.028

S–N–S plane and a dipole moment of 5.42 debye (Fig. 1(a) and (b)). We have recently shown that these two conformers can be distinguished by vibrational spectroscopy [2]. The transoid form exhibits, for example, an intense IR absorption at 618 cmK1 which is replaced by two weaker bands at 596 and 646 cmK1 for the cisoid form. In the Raman spectra, the distinction can be made either from a doublet at 629 and 653 cmK1 for the transoid or cisoid form, respectively, or from the region around 330 cmK1. Experimental studies have shown that the Et4NC cation exists essentially under the two forms represented in Fig. 1(c) and (d): a quasi-planar all-trans conformation with D2d symmetry or a quasi-pyramidal trans–gauche conformation with S4 symmetry [12]. This is in agreement with the theoretical prediction of four equilibrium structures of D2d, S4, C1 and C2 symmetries having relative energies of 0.0, 3.3, 14.6 and 28.5 kJ molK1, respectively [13]. Considering the relative energies and multiplicities of these conformers, only the former two have significant gas-phase populations at room temperature.

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Fig. 1. Projections of the TFSIK conformers: (a) transoid C2 and (b) cisoid C1, and of the Et4NC conformers along their pseudo C4 axis: (c) D2d and (d) S4.

The Et 4N C D 2d and S4 conformers can hardly be distinguished by NMR [13,14], but they are easy to identify by Raman spectroscopy using for example the intense and nondegenerated ns(NC4) stretching vibration [12]. For a large series of Et4NX salts, this vibration gives a line located either in the 675–681 cmK1 region for the D2d conformers or in the 662– 664 cmK1 region for the S4 conformers at room temperature. In aqueous or organic solutions, the D2d form is found to be more stable than the S4 one by w4 kJ molK1 [12,14]. In the solid state, various situations are encountered as a function of the temperature, depending upon the crystal structure and local packing effects induced by the anion. The case of the Et4NTFSI salt is particularly intriguing since the population of cation D2d conformers was found to decrease between 340 and 260 K, before all the cations switch suddenly to the D2d conformation below 260 K [12]. As progresses have been made in the spectroscopic identification of the anion geometry [2], we have extended our previous Raman study of the Et4NTFSI salt to a larger temperature range and performed differential scanning calorimetry (DSC) measurements to follow the conformational state of the two ions and the phase transitions as a function of the temperature. Ab initio calculations have also been used to predict Raman spectral regions where one ion isomerism can be studied without overlapping bands from the counter ion.

2. Materials and methods In the previous Raman experiment [12], Et4NTFSI was purchased from Sigma-Aldrich. This commercial product (O

99%, melting temperature 381–383 K) was used as received. For the present work, Et4NTFSI has been prepared by the metathesis reaction of Et4NBr and LiTFSI. The salts were dissolved in deionized water. The solutions were combined and stirred together at room temperature producing a precipitate of Et4NTFSI. The salt was washed three times with deionized H2O, melted in boiling water and recrystallized twice. It was then filtered and heated on a hot plate to remove residual water. Acetone and activated carbon (Darco-G60, Aldrich) were added and the hot slurry was stirred on a hot plate overnight. The mixture was filtered through an activated alumina (acidic, Brockmann I, Aldrich) column. The acetone was removed by heating on a hot plate. The Et4NTFSI was dried under high vacuum at 100 8C for 24 h and then 130 8C for 6 h. It was stored and handled in a dry room (!0.2% RH, 20 8C). The Et4NTFSI is a clear, colorless liquid in the melt and a white, crystalline solid at room temperature. The Raman spectra of the commercial and synthesized Et4NTFSI salts proved to be identical. The DSC measurements were performed with a TA Model 2910 calorimeter calibrated using cyclohexane (185.95 and 279.54 K), n-octane (216.24 K), indium (429.60 K) and tin (504.93 K). The Et4NTFSI sample was hermetically sealed in an Al crucible. For the Raman experiment, the Et4NTFSI sample was placed inside a glass tube sealed under vacuum or inside a quartz cell in argon atmosphere. The spectra were recorded using a Labram HR800 Jobin-Yvon spectrometer equipped with an air-cooled CCD detector (ANDOR). Two different

M. Herstedt et al. / Journal of Molecular Structure 783 (2006) 145–156

laser wavelengths were used: (i) an argon laser (514.5 nm) using a grating of 1800 groves/mm and a hole of 50 mm, resulting in a spectral resolution of w1 cmK1 or (ii) a kryton laser (752.45 nm) using a grating of 600 groves/mm and a hole of 100 mm, resulting in a spectral resolution of w2 cmK1. The laser power was adjusted normally to 15 mW at the sample. The sample temperature was regulated between 123 and 393 K using a Dilor cryostat (accuracy of G1 K) during the measurements. Cooling and heating cycles were performed to check for thermal hysteresis and for a better comparison with the DSC results. In a particular experiment, the sample was first melted in an oven, then directly immersed in liquid nitrogen and finally introduced in the cryostat to be cooled down as quickly as possible. In this way, a metastable solid phase could be studied at low temperature. Peak fittings were performed using GRAMS/32 (Galactic). The quantum–mechanical calculations have involved the geometry optimisation and the vibrational states simulations of the free TFSIK and Et4NC ions in different conformations. The density functional theory in the Becke’s threeparameter hybrid method using the Lee–Yang–Parr correlation functional (B3LYP) [15,16] together with the 6-31G** basis set was chosen in the present study. It was previously shown that this method provides quite realistic molecular geometry and vibrational frequencies for the TFSIK ion [2]. The calculations were performed using the GAUSSIANK98 program [17]. 3. Results and discussion 3.1. DSC measurements The Et4NTFSI sample was cooled (10 K/min) to 173 K, heated (10 K/min) to 253 K and annealed (5 min), cooled (10 K/min) to 173 K and finally heated (5 K/min) to 473 K.

Fig. 2. DSC plot for the last heating cycle between 173 and 473 K (see experimental part). The onset and peak temperatures (K) and the enthalpy (J/g) are indicated for each peak.

147

Three endothermic transitions are reported from the last heating cycle (Fig. 2). The first solid–solid phase transition (TIII–II) is observed at 277 K. In a simple cooling process starting from room temperature, TIII–II was found to be shifted to about 260 K in the first DSC run as well as in the previous Raman experiments. Strong hysteresis effects have already been reported for derivatives of the (Et4N)2MCl4 family (MZ Fe, Zn, Cd) where first-order solid phase transitions occur between 200 and 300 K [18]. Note that the baseline after the first endothermic peak differs from that before the peak, indicating a heat capacity (Cp) change analogous to what occurs when an amorphous glass changes to a liquid state. The weak thermal transition around 322 K (TII–I) is of unknown origin. It could not be observed in the previous Raman experiment as heating was stopped just above this temperature. Nevertheless, we suppose for convenience that two distinct disordered phases exist below and above TII–I. The melting temperature (Tm) is measured at 376.8 K (peak), to be compared to the value of 381–383 K indicated for the commercial product. 3.2. Ab initio calculations on the free cation and anion The ab initio calculations previously performed on the Et4NC cation [13,14] and on the isoelectronic Et4C molecule [19,20], lead to very similar results in terms of nature and relative energies of the equilibrium geometries. As previously pointed out, amongst the possible D2d, S4, C1 and C2 conformers, the former two have predominant gas phase populations at room temperature. We have repeated these calculations in order to check and extend the literature results. In particular, it is crucial for our study to calculate the vibrational frequencies and intensities of the Et4NC conformers, as we did recently for the TFSIK anion [2]. The electronic energies, dipole moments and Mulliken charges of the D2d, S4 and C1 conformers of the cation and of the C2 and C1 conformers of the anion are reported in Table 1. The net Mulliken charges on a given ion do not depend very much upon the conformational state and are reported only for the lowest-energy conformer. Note that both nitrogen and carbon atoms are negatively charged, whereas every hydrogen atom carries a positive charge of about 0.15 eK (Table 1). Thus, the cation charges are distributed according to a rather isotropic and symmetric cloud with a low dipole moment for any conformation. On the other hand, the anion dipole moment is very sensitive to the conformation (0.67 debye for C2 and 5.42 debye for C1), owing to the distribution of negative charges on the F, O and N atoms in the 1:2:3 ratio, respectively, and of positive charges on the C and S atoms in the 1:2 ratio (Table 1). The vibrational frequencies and intensities (IR and Raman) of the free TFSIK conformer with C1 and C2 symmetries have previously been calculated and compared to the experimental spectra [2]. The vibrational frequencies and intensities (IR and Raman) of the free Et4NC conformers are calculated using the same B3LYP/6-31g(d, p) method and reported in Tables 2 and 3 for the two conformers of lower energy. Each cation

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Table 1 Electronic energies Eel (a.u.), electronic energies corrected for zero-point energy EZPE (a.u.), relative energies DEZPE (kJ molK1), multiplicities (m), dipole moments m (debye) and net Mulliken charges of the D2d, S4 and C1 conformers of Et4NC and of the C2 and C1 conformers of TFSIK using the DFT/6-31g(d, p) approach Et4NC

Eel EZPE DEZPE m m Net Mulliken charges

TFSIK

D2d

S4

C1

C2

C1

K371.455163 K371.176019 0 3 0.46 qNZK0.41 qC(Et)ZK0.07 qC(Me)ZK0.36 qH(Et)ZC0.16 qH(Me)ZC0.15

K371.453906 K371.174780 3.25 6 0.42

K371.449964 K371.171051 13.03 24 0.96

K1827.204975 K1827.151952 0 2 0.67 qNZK0.71 qSZC1.11 qOZK0.55 qCZC0.58 qFZK0.25

K1827.204103 K1827.150637 3.45 4 5.42

Only the charges on non-equivalent atoms of the lowest energy conformer are reported.

conformer has 81 internal vibrational modes classified according to: GðD2d ÞZ 12A1 ðR; pol:Þ C 8A2 C 9B1 ðIR; RÞ C 20EðIR; RÞ

(1)

GðS4 Þ Z 20AðR; pol:Þ C 21BðIR; RÞ C 20EðIR; RÞ

(2)

In Tables 2 and 3, the modes calculated for the two conformations are compared to the experimental values observed for two types of systems: the solid salts Et4NBr and Et4NI where the cation is known to adopt the D2d and S4 conformations, respectively, and an aqueous solution of Et4NOH where comparable amounts of the two conformers

Table 2 Calculated wavenumbers and infrared and Raman intensities of the Et4NC vibrations and experimental wavenumbers of the Raman lines observed for the solid salts Et4NBr (D2d) and Et4NI (S4) and for a 2.3 M Et4NOH aqueous solution at 210 K Calc. all-trans (D2d)

B1 E A2 A1 E B1 B2 A2 B1 E A1 B2 E A1 A2 E B1 E B2 E A1 B2 E A2 A1 B1 B2 E A2 B1

Exp. Raman

n/cm

IR

R

78.0 109.1 129.4 196.4 268.0 273.3 296.4 355.4 356.0 369.0 407.1 411.7 526.0 667.8 778.1 778.3 822.9 892.2 908.0 1003.9 1031.3 1054.9 1087.4 1114.9 1138.7 1181.6 1185.4 1221.8 1306.9 1330.5

0.0 1.2 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.0 1.2 0.0 0.0 0.0 68.6 0.0 1.6 0.0 45.4 0.0 12.9 7.4 0.0 0.0 0.0 24.5 2.0 0.0 0.0

0.4 0.0 0.0 0.2 0.2 0.1 0.0 0.0 0.3 0.0 7.8 4.6 0.2 9.5 0.0 4.8 0.9 3.2 6.1 9.0 2.5 0.3 6.2 0.0 8.2 0.1 2.8 0.0 0.0 25.1

K1

Et4NBr

211 w

Calc. Trans–gauche (S4) Solution

203 vw

368 w

356 w

422 s

417 s, p

679 vs

674 vs, p

788 m

788 w

909 m 1004 m

905 m 1001 s 1026 sh

1068 w 1114 s

1120 s, p

1174 w

1176 m

1302 s

1301 s

E B A B B A E A E A B E B A E B A B E B A E A E B A E B A E

Exp. Raman

n/cm

IR

R

116.2 116.8 137.1 200.9 250.7 255.6 256.3 313.7 350.2 381.8 387.0 467.8 561.4 656.9 793.2 798.7 830.0 888.6 895.5 1009.5 1021.4 1031.4 1087.8 1098.7 1141.0 1176.0 1209.3 1223.4 1327.1 1331.8

0.8 0.3 0.0 0.2 0.0 0.0 0.2 0.0 0.0 0.0 0.3 4.4 0.0 0.0 22.0 26.0 0.0 3.2 1.0 29.7 0.0 37.2 0.0 8.2 0.8 0.0 23.2 3.2 0.0 18.0

0.2 0.2 0.3 0.4 0.1 0.2 0.4 0.4 0.4 4.9 0.4 3.6 1.2 11.8 2.8 2.7 0.5 2.9 9.0 4.1 1.3 4.4 5.7 5.8 5.3 0.6 1.4 0.8 18.5 0.6

K1

Et4NI

Solution

203 vw

259 vw 325 m 345 vw 392 s

313 w 389 m, p

475 s 561 m 664 vs 795 m 800 sh 823 vw

467 w 558 w 664 vs, p

894 s 1003 m

894 m 1001 s 1026 sh

1030 vw 1077 s

802 sh 823 sh

1071 s, p

1120 m 1184 w

1120 s, p 1156 w, p 1187 w

1308 m

1301 s

˚ 4 amuK1 (Raman). The experimental intensities are reported using the usual nomenclature: vs (very The calculated intensities are expressed in km molK1 (IR) and A strong), s (strong), m (medium), w (weak), vw (very weak), sh (shoulder) and p stands for polarized.

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149

Table 3 Same as Table 2 for the region above 133 cmK1 Calc. all-trans (D2d)

E E B2 A1 E A1 B2 E B2 A2 B1 E A1 E B2 A1 A1 E B2 E B2 A1 E A1 B1 B2 E A2 A2 B1 E

Exp. Raman

n/cm

IR

R

1367.9 1401.9 1419.8 1436.8 1442.6 1446.0 1460.9 1488.9 1506.9 1513.7 1515.4 1515.9 1516.3 1532.2 1535.1 1541.4 3074.2 3074.3 3074.5 3108.5 3116.0 3118.2 3143.0 3143.3 3143.9 3146.0 3151.7 3152.6 3162.2 3171.9 3172.5

3.2 29.2 0.0 0.0 65 0.0 1.6 21.2 21.1 0.0 0.0 1.6 0.0 26.4 41.0 0.0 0.0 2.2 5.0 5.2 10.7 0.0 0.4 0.0 0.0 19.3 9.0 0.0 0.0 0.0 41.2

0.8 1.0 3.0 6.9 3.4 12.4 4.1 0.0 0.0 0.0 62.0 8.6 46.3 2.0 0.0 0.2 392.9 18.8 2.8 10.4 77.5 225.4 61.6 22.4 24.6 71.0 277.8 0.0 0.0 7.0 23.2

K1

Et4NBr

1392 w

1465 s

Calc. trans–gauche (S4) Solution

1391 s, p

1464 vs

1492 w 1499 w 2900

2922 2943

2902 s, p

2951 vs, p

2969

2996

3000 vs

B B E A A B E A E B E B B A E A E A B B E A A E B B E A E B A

Exp. Raman

n/cm

IR

R

1381.9 1398.6 1415.1 1423.3 1444.9 1445.9 1450.5 1495.7 1506.8 1510.3 1512.1 1521.8 1523.0 1524.1 1527.6 1539.5 3075.5 3075.8 3076.0 3107.5 3109.9 3114.8 3143.3 3144.2 3144.4 3147.3 3153.5 3155.3 3171.5 3173.3 3175.5

0.1 8.6 0.0 0.0 0.0 40.7 30.4 0.0 18.4 18.2 44.6 0.2 1.0 0.0 22.8 0.0 6.2 0.0 2.0 2.1 13.4 0.0 0.0 13.0 0.0 0.0 5.6 3.9 28.2 20.2 0

9.4 1.4 1.2 1.2 3.7 10.3 7.8 39.6 4.6 0.1 2.8 53.0 3.1 15.0 2.0 2.0 16.8 391.6 12.3 11.6 48.8 232.0 21.4 142.4 52.5 20.3 118.8 127.6 8.8 14.7 7.1

K1

Et4NI

Solution

1413 m 1447 vs

1445 m

1459 m 1471 m

1464 vs 1493 m

2879 2900

2902 s, p

2915 2930 2943

2951 vs, p

2974

2984 2997

3000 vs 3000 vs

The correspondence between the calculated and experimental results is more difficult to establish, particularly in the region of the poorly resolved methyl and methylene bending and stretching vibrations.

are in equilibrium. In aqueous solution, the cations are closer to the ‘free’ state than in the solid state, but the distinction between the two conformers is sometimes difficult. In Fig. 3(a) and (b), the Et4NC and TFSIK calculated wavenumbers have been multiplied by scaling factors between 1.01 and 1.04, depending upon the considered spectral range and compound, for a more convenient comparison with the experimental Raman spectrum of Et4NTFSI at room temperature (Fig. 3(c)). This comparison is used to identify the spectral ranges where the cation conformation can be studied without too many overlapping bands of the anion and vice versa. The spectra in the regions above 800 or below 250 cmK1 are not represented because they are less favorable for the distinction between the cation and anion contributions. It is clear from Fig. 3(a) that the two Et4NC conformers give well separated lines in two different spectral regions, near 660 and 400 cmK1. As TFSIK lines occur also around 400 cmK1 (Fig. 3(b)), we have selected the region near 660 cmK1 for the investigation of the Et4NC conformational state. We also calculated the Raman spectra of the C1 conformer of Et4NC. The results are not reported in Table 2 for simplicity, but if we consider the ns(NC4) mode, the DFT calculation predicts a Raman line at 658.5 cmK1 with an intensity of 10.4. This line

should be situated between the D2d component calculated at 667.8 cmK1 (9.5) and the S4 line at 656.9 cmK1 (11.8) (Table 2). The TFSIK spectrum is characterized by a very intense and narrow line near 741 cmK1. The calculations indicate that the frequency shift between the C1 and C2 forms for this vibration is only w3 cmK1. Less intense features are better separated in the 620–650 and 300–350 cmK1 regions, the latter being free from any significant cation contribution. 3.3. Identification of the Et4NC and TFSIK conformers in the Raman spectra Raman spectra have previously been reported in the 148– 340 K temperature range for the commercial Et4NTFSI product [12]. These preliminary results are extended here to lower and higher temperatures using the newly synthesized salt and a better spectral resolution. In addition, cooling and heating cycles are performed for a better comparison with the DSC results. When the sample is heated or cooled through TII–I and Tm, its Raman spectral response is reversible. This is not the case for cooling and heating cycles below room temperature through the first order phase transition at TIII–II. As already pointed out in the previous Raman experiment [12]

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Fig. 3. Calculated and scaled Raman spectra for (a) Et4NCD2d (solid line) and S4 (dotted line), (b) TFSIK transoid C2 (solid line) and cisoid C1 (dotted line), compared to (c) experimental Raman spectrum of Et4NTFSI recorded at 296 K using a laser wavelength of 514 nm. The FWHM of the individual calculated bands is 10 cmK1 and the multiplicative scaling factors are 1.01 for Et4NC and 1.036 for TFSIK.

and observed in the DSC runs, the first cooling cycle may quench the room temperature situation if the cooling rate is fast, or shift TIII–II to 260 K for slower cooling rates. The first order phase transition is observed at 277 K only after a first cooling/heating cycle. 3.3.1. The Et4NC conformational state The Raman spectra of several reference compounds are first compared with the calculated spectra in the region of the ns(NC4) stretching vibration (Fig. 4). Let us recall that the Et4NC conformation is known to be D2d in Et4NBr and S4 in Et4NI from the crystal structures of these salts [12]. The ns(NC4) stretching vibrations observed at 679 cmK1 in Et4NBr and 664 cmK1 in Et4NI are in good agreement with the calculated values of 667.8 cmK1 for the D2d form and 656.9 cmK1 for the S4 form (Table 2). The calculated values become 674.5 and 663.5 cmK1, respectively, by applying a scaling factor of 1.01. Thus, the narrow line at 675 cmK1 observed from 122 to 258 K for Et4NTFSI in its phase III (Fig. 4(c)) indicates that most of the cations adopt the D2d conformation. On the other hand, the doublet observed for Et4NTFSI in its disordered phases II and I from 263 to 368 K (Fig. 4(d)) or in the liquid phase at 388 K (Fig. 4(e) and (f)), can easily be assigned to a mixture of the two isomers. A closer examination of the ns(NC4) profile of Et4NTFSI in phase III reveals the presence of a weak additional component at 671 cmK1. This may be due to some overtone or combination, but may also result from an incomplete transformation into the D2d form, i.e. to a ‘defect’ conformation of lower symmetry. Thus, an Et4NC conformation of C1 symmetry is more energetic than D2d by about 15 kJ molK1, but this can be partly compensated at high temperatures by a multiplicity of

Fig. 4. Calculated and scaled Raman spectra for (a) Et4NCD2d (solid line), S4 (dotted line), compared to the experimental Raman spectra of (b) Et4NBr (solid line) and Et4NI (dotted line) at room temperature, (c) Et4NTFSI at 122 K (solid line) and 258 K (dotted line), (d) Et4NTFSI at 263 K (solid line) and 368 K (dotted line) and (e,f) liquid Et4NTFSI at 388 K. In (a), the FWHM of the individual calculated lines is arbitrarily set to 6 cmK1. In (c), the asterisk indicates the weak band at 671 cmK1 (see text). In (e) and (f), two or three lorenzian components have been fitted, respectively, to the same experimental profile.

24, compared to 3 for D2d [13,14,19]. In thermodynamical equilibrium above room temperature, the Et4NCC1 form can easily reach populations of a few percents and this form may be partly quenched in the cooling process. In Fig. 4(e) and (f) two fitting examples of the experimental doublet of the liquid phase at 388 K are compared to show that the agreement is satisfactory with or without introducing a third component at 664 cmK1. The existence of this third component originating from a C1 conformer is supported by the DFT calculations that predict a ns(NC4) Raman line for C1 situated between the D2d and S4 ones. Let us remark that whatever the assignment of the 671 cmK1 weak band is, the conclusion is unchanged of an Et4NTFSI low-temperature ordered phase III composed essentially of the D2d form of the cation associated with the main band at 675 cmK1. Similarly, even if a third component at 664 cmK1 due to the C1 conformer is taken into account in the liquid state spectrum, we will see below that it corresponds to a small population of C1 forms compared to the D2d and S4 ones. Finally, the experimental features illustrated in Fig. 4 have been fitted by two Lorenzian components, the peak position and full-width at half-maximum (FWHM) of which are reported in Fig. 5. It is interesting to note that the positions (Fig. 5(a)) vary little in the 260–390 K temperature range: from 663 to 661 cmK1 for the S4 component and from 673 to 672 cmK1 for the D2d one. The FWHM of the latter is nearly

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Fig. 5. Temperature dependence of the (a) position and (b) FWHM for the ns(NC4) line of the D2d (open circles) and S4 (crosses) conformers of the cation in Et4NTFSI.

constant: 7.7G0.4 cmK1 whereas the FWHM of the S4 component increases from 6 to 10 cmK1 (Fig. 5(b)). None of these parameters present a discontinuity at TII–I and there is just a small change at Tm. In contrast, the ns(NC4) profile changes drastically below the first order phase transition TIII–II: as pointed out above, the S4 component disappears and the D2d component is observed at 675 cmK1. In the fitting procedure, the integrated intensities of the various components are also determined and we will see below how they can be used to predict relative populations of the two conformers. 3.3.2. The TFSIK conformational state Let us first consider the strong TFSIK line observed at w741 cmK1. We have shown earlier that the position and shape of this line are influenced more by ionic interactions than by conformational isomerism [2]. Considering the calculated Mulliken charges reported in Table 1, one can infer that the ionic interactions between one TFSI K anion and the surrounding Et4NC cations are weak and isotropic. This is confirmed experimentally by the fact that a temperature variation between 100 and 400 K (Fig. 6) leaves the peak position in the 740–742 cmK1 interval, i.e. within a range of typical values for TFSIK anions involved in solvent-separated ion-pairs; contact ion-pairs would produce a shift to higher frequencies (typically R746 cmK1) [2,9,21]. In other words, the cation–anion interactions in Et4NTFSI are similar to those occurring between TFSIK and aprotic solvents. Nevertheless, the anion is not insensitive to molecular packing and dynamics as can be seen from discontinuous variations in position and/or FWHM occurring at the phase transitions and melting temperatures (Fig. 6). In more detail, the peak moves always to lower wavenumbers and broadens when the temperature increases, but there is a clear discontinuity in these two

151

Fig. 6. Temperature dependence of the (a) position and (b) FWHM of the most intense TFSIK line.

parameters at the first order phase transition TIII–II. The variations are then continuous between TIII–II and Tm through TII–I. The transition to the melt state is simply characterized by a small jump in the FWHM increase. We have recently shown that the conformational state of TFSIK can be better investigated in the Raman spectra at lower wavenumbers [2]. The above presented Raman results were recorded using the argon laser at 514.5 nm. We found that the detection in the low-frequency region is significantly improved using a krypton laser at 752 nm. In addition, the 260–360 cmK1 region is free from any cation contribution (Fig. 3), while presenting well-separated features for the two conformers of TFSIK [2]. In the low-temperature phase (Fig. 7(b) and (c)), the Raman spectra are characterized by the same four main lines as those calculated for the C2 conformer (Fig. 7(a)) with only some small frequency and intensity differences for the two middle lines. This situation is maintained over a very large temperature range extending up to room temperature (Fig. 7(d)). Thus, one can conclude that in phase III the D2d conformation of the cation is associated with a C2 conformation of the anion. At the first-order phase transition, we have seen that a large number of cations switch suddenly to the S4 conformation. In contrast, the anion keeps its C2 conformation just above TIII–II and it is necessary to heat above TII–I to detect a broad feature coming from C1 at about 325 cmK1 (Fig. 7(e)). Finally, this C1 band has a much stronger intensity in the liquid state above 375 K (Fig. 7(f)) and the observed spectra can be reproduced only by combining comparable amounts of the C1 and C2 contributions (Fig. 7(g)). This qualitative description can be made a bit more quantitative by fitting all the components of the C2 and C1 conformers present in the 260–360 cmK1 spectral range and by using the integrated intensity of these components. However, as illustrated in Fig. 7(f), the disordered solid phase and the liquid phase need a minimum of eight components to reproduce

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proportionality factor a between the integrated intensities Ai and the corresponding populations ni, scattering cross-sections si and multiplicities mi (iZa or b): Aa Z ana sa ma

(4)

Ab Z anb sb mb

(5)

a also includes instrumental corrections common to the two lines and the transformation from concentrations Ci to populations ni. The populations of the two conformers are related by the simple sum rule: na C nb Z 1

Fig. 7. (a) Calculated Raman spectra for TFSIK of conformation C2 (solid line) or C1 (dotted line) with GAUSSIAN contours of 1.5 cmK1 FWHM and a multiplicative scaling factor of 1.055, compared to the experimental Raman spectra of Et4NTFSI at (b) 123 K, (c) 247 K, (d) 296 K, (e) 328 K and (f) 388 K. The latter has been fitted with eight Lorenzian components. A calculated spectrum (g) resulting from the sum of the C1 and C2 contributions and using a GAUSSIAN contour of 8 cmK1 FWHM is also reported in dotted line for a better comparison with the liquid state spectrum.

the 360–260 cmK1 region and the accuracy of the quantitative measurements is lower than for the ns(NC4) doublet of the cation. 3.4. Thermodynamical parameters of the TFSIK and Et4NC conformational isomerism Let us recall that the dynamic equilibrium between two conformations a and b can be described by the ratio of their concentrations, or equilibrium constant KZCa/Cb, related to the free energy, enthalpy and entropy differences, DG0, DH0 and DS0, respectively, according to the classical expression:       KDG0 KDH0 KDS0 K Z exp Z exp exp (3) RT RT RT where T is the absolute temperature and R the gas constant (8.3145 J KK1 molK1). If the a and b conformers can be characterized, as those of Et4NC and TFSIK can, by two Raman lines separated by only a few tens of cmK1, it is not necessary to apply a temperature correction factor of the [1K exp(Khcni/kBT)] form because the intensities of the two lines are similarly affected. This correction is included instead in a

(6)

The multiplicities come from the introduction of a conformational entropy term DSZR ln(ma/mb) in (3). Their values for the cation conformers are m(D2d)Z3 and m(S4)Z6, as previously described for the parent Et4C molecule [19]. For the anion conformers, m(C2)Z2 and m(C1)Z4. Indeed, the C2 conformation has two equal gauche torsional angles [1] and can occupy the states gCgC or gKgK, whereas the C1 conformation has one trans and one gauche angle [1] and can occupy the states tgC, tgK, gCt or gKt. Generally, DH0, DS0, sa and sb are supposed to be constant in the investigated temperature range and the last three terms are often unknown. DH0 is then determined from the slope of a ln(Aa/Ab)Zf(1/T) plot. Indeed, by combining (3) to (5), the following equation can be obtained:     A s m DS 0 DH (7) ln a Z ln a a K 0 K 0 Ab sb mb R RT where the first two terms of the right hand side are considered as constant. Application of the above expressions supposes that a dynamic conformational equilibrium takes place. This is obviously not the case for Et4NTFSI at temperatures lower than TII–I where the conformational state either depends on the thermal history of the sample or even reduces to a single form in phase III. Above TII–I, a reversible spectral response was observed during cooling or heating cycles. Unfortunately, we could study the sample only up to 393 K which means that only a few data points are available for the liquid state. Van’t Hoff plots for the two conformers of the cation and anion are shown in Fig. 8. The choice of the characteristic Raman lines of the D2d and S4 cation conformers is obvious and has already been illustrated in Fig. 4. A672 and A662 are the fitted integrated intensities of the two Lorenzian components near 672 and 662 cmK1, associated with the D2d and S4 conformers, respectively. According to the results of Fig. 8, in the 328– 378 K interval corresponding to the disordered solid phase of Et4NTFSI, the D2d conformer of Et4NC is more stable than the S4 one by 4.4G0.3 kJ molK1, i.e. very close to the value of 4.1G0.3 kJ molK1 found for Et4NC in aqueous solution [12]. Note however that the three data points reported for the liquid phase in Fig. 8 are not in the continuity of the solid state line. As far as a slope can be defined from only three points, the DH value in the liquid state would be about 8 kJ molK1. This surprisingly high value might be explained by the fact that

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Fig. 8. Determination of DH0 for the conformational equilibria of the cation (black circles) and of the anion (open circles and crosses) in phase I and in the liquid phase of Et4NTFSI. The black circles come from the ratio of the integrated intensities A672 and A662 for the cation conformations D2d and S4, respectively. The open circles come from the ratio of the integrated intensities A340 and A(321C326) for the anion conformations C2 and C1, respectively, and the crosses simply use the peak heights at 340 and 326 cmK1.

the conformational equilibrium is no longer limited to the D2d5S4 exchange above the melting point. We have already commented on the possible contribution of less symmetric and more energetic conformers such as the C1 form of multiplicity 24. We have seen that the Raman spectra of liquid Et4NTFSI in the 650–690 cmK1 region are satisfactorily fitted by two or three Lorenzian components (Fig. 4). The present spectra of the liquid state are too broad and noisy to be sure of the existence of a third component at w664 cmK1 due to the C1 form. Let us recall that a small population of C1 can give a component of non-negligible intensity because of the high multiplicity of this conformer. We have seen that the identification of the TFSIK conformers can be attempted in the 260–360 cmK1 spectral range (Fig. 7). The low temperature spectra can be fitted with the four C2 components, whereas a minimum of eight lorenzian components is needed to reproduce the observed features at high temperature (Fig. 7(f)). Most of these components result from mixed contributions of the two conformers, but the band at 340 cmK1 comes only from the C2 conformer, whereas a couple of bands at about 321 and 326 cmK1 seem to be due only to the C1 conformer. Intensity measurements have been performed by using either the integrated intensities of the 340 cmK1 band, A340, and the sum of the integrated intensities at 321 and 326 cmK1, A321CA326, or simply from the heights at 340 and 326 cmK1. This second method gives less scattered points in the Van’t Hoff plot (Fig. 8) and a DH0 value of 7.0G 0.5 kJ molK1, compared to 8G1 kJ molK1 with the first method. These values are much higher than the theoretical gas phase value of 2–3 kJ molK1. Again, there is a striking change in the relative intensities at the melting temperature and the DH0 value in the liquid state, although non measurable,

153

Fig. 9. Populations of D2d conformers for the Et4NC cation (black circles) and C2 conformers for the TFSIK anion (open circles) as a function of the temperature.

seems to decrease. Instead of postulating additional conformer contributions at high temperature, as for Et4NC, one is tempted here to suppose that the TFSIK conformational isomerism is limited to the C1 and C2 forms, but is more strongly hindered in the high temperature solid phase than in the liquid phase. The next step is to evaluate the populations of the respective conformers in the liquid and solid states. As pointed out above, the knowledge of the scattering cross sections is necessary. The well-defined symmetric stretching vibration ns(NC4) of the D2d and S4 conformers is an ideal case where the ratio s(D2d)/s(S4) is expected to be close to one. Indeed, one can infer that this non-degenerated vibration that occurs at frequencies separated by only 10 cmK1 is very similar in the two conformers. The ab initio calculations confirm this hypothesis since, they give s(D2d)Z9.5 and s(S4)Z11.5 for the two lines situated at 667.8 and 656.9 cmK1, respectively (Table 2). Therefore, we assume that s(D2d)Zs(S4) for the ns(NC4) vibration. Using these values and m(D2d)Z0.5m(S4), in Eqs. (4) and (5), the total number of molecules is found to be proportional to (A672C 0.5A662) and all the spectra can be normalized by this factor. It follows that the population of cations having the D2d conformation is given by: nðD2d Þ Z

A672 ðA672 C 0:5A662 Þ

(8)

and, similarly, the population of anions in the C2 conformational state can be calculated according to: nðC2 Þ Z

A340 ðA672 C 0:5A662 Þ

(9)

The results are reported in Fig. 9. As already commented, the Raman spectra of the low-temperature phase indicate clearly the presence of the D2d form for the cation and the C2 form for the anion. The fact that n(D2d) is not strictly equal to one comes from the presence, in addition to the main 675 cmK1

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band, of the previously discussed weak component at 671 cmK1, possibly due to a quenched C1 conformer. At the transition from phase III to phase II, nearly w70% of the cations change suddenly from D2d to S4, while the population of C2 anions decreases progressively. Then, between TIII–II and the next phase transition (TII–I) at 323–328 K, the D2d fraction increases from 30–50% as if the D2d conformation was less stable than the S4 one. The decrease of the C2 population down to w50% is more in line with the respective energies of the isolated anion conformers. Obviously, intermolecular forces and packing effects in the solid state are of the same order of magnitude as the energy difference between the two isolated conformers and they have a different influence on the cation and anion conformational states. The D2d conformer is more stable than the S4 one in the gas state and it occupies a slightly smaller volume. One can infer that above the first order transition at TIII–II, tumbling and internal motions of Et4NC are released. The consecutive onset of these motions on heating has been detected in tetraethylammonium halides by NMR [22]. The free volume offered to the ions may suddenly be increased in phase II and the cation may prefer to adopt the S4 conformation as it does in Et4NI, but not in Et4NBr. However, there are no clear general rules to predict the cation conformation in tetraethylammonium derivatives. A recent data base analysis by Alder et al [20] has shown that amongst 208 reported structures, there are 45 S4 conformations and 163 D2d conformations. In phase I, between TII–I and Tm, the apparent relative stability of the two cation conformers is again reversed, D2d becoming the form of apparent lower energy. The S4 population increases slightly with the temperature, in a similar way as found for other Et4NX salts and Et4NC cations in solution [12]. The data points for the anion are very scattered; they simply indicate similar populations for the C2 and C1 conformers. One can infer that solid phase I is a highly disordered liquid-like one. Furthermore, the data obtained from several temperature runs coincide, showing that no thermal hysteresis is present. In the liquid state, the population of anions in the C2 form drops to w30% while equivalent

populations of D2d and S4 conformers are maintained for the cation. We have seen, however, that we reach the limits of the Raman analysis since conformers of lower symmetry than D2d or S4 may contribute to the ns(NC4) profile of liquid Et4NTFSI. Interestingly, this does not modify the main populations very much because the multiplicity of the less symmetric conformers is very high (24 for C1). As an example, the fitting with two components at 388 K in Fig. 4(e) gives 53% D2d and 47% S4, whereas the fitting with three components (the additional 664 cmK1 one in Fig. 4(f) being assigned to C1) gives 58% D2d, 38% S4 and 4% C1. 3.5. A supercooled Et4NTFSI disordered phase If the liquid phase above 377 K or the disordered solid phases I or II are cooled very rapidly down to liquid nitrogen temperature, a supercooled disordered phase is obtained. The Raman spectra of the ordered and supercooled low-temperature phases are compared in Fig. 10. The anion lines in the 260– 360 cmK1 region are those of the C2 conformation, irregardless of the cooling rate, even if they have different relative intensities, presumably due to orientation effects, and are slightly broader for the supercooled phase. However, the most intense anion line near 740 cmK1 takes a strange shape (Fig. 11): in addition to the w743 cmK1 component predicted from the evolution reported in Fig. 6 and effectively observed for the ordered phase III, the supercooled phase exhibits a new component at 745 cmK1. We have at present no assignment to propose for this new line, but the presence of a doublet indicates that some kind of conformational disorder of the anion has been quenched. The cation lines for the supercooled phase are essentially those of the S4 conformation. For example, the ns(NC4) profile at 100 K is composed of an intense line of S4 at 666 cmK1, accompanied by a much less intense satellite line of D2d at 676 cmK1. By fitting these two components and using Eq. (8), the D2d population at 100 K is found to be w20% instead of about 100% in the ordered solid phase. This value of 20% corresponds roughly to an extrapolation in phase III of the D2d population measured in

Fig. 10. Comparison of the Raman spectra of Et4NTFSI at 100 K in its ordered phase III (solid line) or in the supercooled solid phase II’ obtained by quenching (dotted line).

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transition states, as well as the relative energies, can be strongly modified by intermolecular forces in condensed states. The present experimental results on Et4NC show that the liquid state situation is not too far from the gas-phase calculated one, but strong changes and unexpected behaviors occur in the solid state. No information is available on the transition states between the two anion conformers. Recent crystallographic results indicate a possible pathway through a new disordering C24C2 mode [23] and the present spectroscopic data show that an easy interconversion towards the C2 state occurs at low temperature whatever the cooling rate used. The metastability of the Et4NTFSI system seems to be mainly ascribed to the cation which is less easy to bring to its stable low-temperature form. More theoretical work is needed to determine the anion potential energy surfaces and to confirm that its interconversion barrier is lower than that of the cation. Fig. 11. Same as Fig. 10 in the region of the most intense TFSIK line.

phase II (Fig. 9). Similarly, the C2 anion population of about 100% in the supercooled phase follows the evolution observed in phase II (Fig. 9). A further illustration is provided by considering the results of Fig. 5 where the position and FWHM of the ns(NC4) is reported: the 666 cmK1 line observed for S4 in the supercooled state at 100 K (Fig. 10) could have been predicted by extrapolating the S4 curve in Fig. 5(a). It must be pointed out that the results just described have been obtained several times with excellent reproductibility by quenching either the liquid phase or the room temperature disordered phase. The supercooled phase could be called II’ to indicate that it involves conformations of the anion and cation corresponding to a metastable phase II. Some of us have recently studied an Et4NTFSI crystal cooled to 100 K at a rate of 0.5 K/min by X-ray diffraction [23]. The structure is that of a quenched disordered solid phase II’ as the asymmetric unit cell contains four cations (two ordered S4 and two disordered S4/D2d and S4/C1 cations giving a total of 83% S4 forms) and four anions, all in the C2 conformation. The crystal structure indicates, in addition, the existence of an anion disordering between two C2 conformations in the supercooled phase. Further work is necessary to see whether this disordering can be reconciled with the Raman doublet reported in Fig. 11 for the supercooled phase. The interconversion from one conformer to another is known to depend upon several other factors than the simple gas-phase relative energies. First of all, the mechanism of this interconversion has to be considered. One possible approach is the calculation of potential energy surfaces and of transition states. Brand et al. [13] looked for the lowest energy paths between the D2d to S4 conformers of Et4NC via ethyl torsions and found that all barriers were %54 kJ molK1. Luzhkov et al. [14] predicted a two-step interconversion with a torsion barrier of 40 kJ mol–1. In the case of the Et4C molecule, Alder et al. [20] used molecular mechanical calculations to describe the D 2d to S4 interconversion by two-step or three-step torsional pathways. They found interconversion barriers of w30 kJ mol–1. The

4. Conclusions In molten Et4NTFSI at 388 K, both cations and anions are involved in conformational equilibria. The Et4NC cations exchange between comparable amounts of conformers having D2d and S4 symmetries, with the possible contribution of a few percents of some less symmetric forms (such as C1). The anions adopt conformational states of C1 or C2 symmetry (w70% C1). In phase I, between 377 and 322 K, these conformational equilibria are maintained with comparable populations for the two couples D2d/S4 and C2/C1. In this highly disordered phase I, the cation D2d form is found to be more stable than the S4 form by 4.4G0.3 kJ molK1 and the anion C2 form more stable than the C1 form by 7G1 kJ molK1, in agreement with the relative energies predicted by ab initio calculations. Another disordered phase (phase II) seems to occur between 322 K and a first order transition occurring near 260 K in the first cooling cycle (instead of 277 K in the next heating cycle). In phase II the conformer populations change suddenly: the anion C2 population increases from 50 up to w90% whereas the anion D2d population decreases from 50 down to w30%. The latter behavior is unexpected since D2d is theoretically predicted to be more stable than S4 in the gas phase and indeed found to be more stable in the liquid and high-temperature disordered solid phases. Intermolecular forces must play an important role and reverse the apparent relative energies of the two cation conformers. They are likely to be at least of the same order of magnitude as the intrinsic energy difference between the two couples of conformers. These ionic interactions are modulated by thermal amplitude variations, crystal packing effects, ion reorientations, etc. in an unpredictable way. The Raman spectra give the net result of the competition between these different effects. Below the first-order TIII–II transition, two very different evolutions can be observed depending upon the thermal history: in a slow cooling process, phase II transforms into ordered phase III, even if TIII–II is shifted to 260 K. Phase III is composed essentially of C2 anions and D2d cations; fast cooling quenches phase II into a supercooled phase II’ composed of C2

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anions and w80% S4 cations. To understand the mechanisms of these thermodynamic and kinetic processes, further experimental information is needed, in particular the structure of the ordered phase III, but a theoretical study of the transition states and conformational pathways would also be helpful. Acknowledgements The CNRS (Chemistry Department), Conseil Re´gional d’Aquitaine and European FEDER funds are greatfully acnowledged for their financial support of the Raman and infrared equipment. M.H. is indebted to Fred T. Andersons donationsfond for financial support. Part of the calculations were performed thanks to computing time made available by the SiMoA (Simulation et Mode´lisation en Aquitaine, France) and by the intensive calculation pole ‘M3PEC-MESOCENTRE’ of the University Bordeaux I-DRIMM, partly financed by the Conseil Regional d’Aquitaine. References [1] P. Johansson, S.P. Gejji, J. Tegenfeldt, J. Lindgren, Electrochim. Acta 43 (1998) 1375. [2] M. Herstedt, M. Smirnov, P. Johansson, M. Chami, J. Grondin, L. Servant, J.C. Lasse`gues, J. Raman Spectrosc. 36 (2005) 762. [3] R. Arnaud, D. Benrabah, Y. Sanchez, J. Phys. Chem. 100 (1996) 10882. [4] S.P. Gejji, C.H. Suresh, K. Babu, S.R. Gadre, J. Phys. Chem. A 103 (1999) 7474. [5] J.L. Nowinski, P. Lightfoot, P.G. Bruce, J. Mater. Chem. 4 (1994) 1579. [6] Y.G. Andreev, P. Lightfoot, P.G. Bruce, Chem. Commun. (1996) 2169. [7] Z. Zˇa´k, A. Ruzˇicˇka, Ch. Michot, Z. Kristallogr. 213 (1998) 217. [8] R.E.A. Dillon, C.L. Stern, F. Shriver, Solid State Ion. 133 (2000) 247.

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