Raman spectroscopy is employed to examine vibrations of ions in polymeric electrolytes because triflate anions CF₃SO₃⁻ are very sensitive to coordination state. Three bands at 1,033, 1,043 and 1,053 cm⁻¹ are assigned to free anions, ionic couples and ionic aggregates, respectively. Free ions dominate in solutions of LiCF₃SO₃ in H-[OCH₂CH₂]_n-OH (n = 1–4), while the number of ionic couples is small due to the presence of ionic associates [28].

The Raman spectrum of pristine LiCF₃SO₃ at room temperature is shown in Figure SI.5 (supporting information) and the peaks of corresponding vibrations are listed in the Table 1. From the spectra of pure LiCF₃SO₃ (Figure SI.5) the symmetric vibration of anion SO₃⁻ at 1,034 cm⁻¹ is the most interesting. Nonperturbed CF₃SO₃⁻ ion has pyramidal symmetry (C_3v) with the sum of the normal vibrational modes 3A₁+A₂+6E. Seven vibrations, which are observed for LiCF₃SO₃ solutions in (EG)₁₁DME in Raman spectra are shown in Figure 2. The vibration of SO₃⁻ is very sensitive to the medium due to the characteristic band of free CF₃SO₃⁻ near 1,032 cm⁻¹ in a strongly diluted LiCF₃SO₃.

Raman bands of SO₃⁻ in LiCF₃SO₃ + (EG)_nDME with n = 2 and 11 in the range from 289 K to 363 K are shown in Figure 3. Both bands are broad with a distinct peak near 1,047 cm⁻¹ and shoulders at 1,034 cm⁻¹ with both chain lengths (n = 2 and 11). Raman band of SO₃⁻ in LiCF₃SO₃ + (EG)₂DME acquire a shoulder near 1,053 cm⁻¹ at the highest temperature 363 K (Figure 3(A)) and near 1,058 cm⁻¹ with n = 11 (Figure 3(B)).

The bands become broader with lower intensity due to the temperature increase, indicating formation of ionic aggregates. Raman spectra of LiCF₃SO₃ + (EG)_nDME (n = 2 and 11) at a concentration of EO/Li from 10 to 30 at room temperature show a relatively broad band with two maxima in the range of 1,025 cm⁻¹ to 1,050 cm⁻¹ (Figure 4). Both bands with LiCF₃SO₃ + (EG)_nDME (n = 2 and 11) exhibit maximum shoulders near 1,037 cm⁻¹ and near 1,043 cm⁻¹ (Figure 4(A) and 4(B)). The intensity of LiCF₃SO₃ + (EG)₂DME band at 1,045 cm⁻¹ increases with the receding of EO/Li from 30 to 10 (Figure 4(A)), while the band of LiCF₃SO₃ + (EG)₁₁DME at 1,043 cm⁻¹ is shifted to 1,047 cm⁻¹ at EO/Li = 15 and to 1,047 cm⁻¹ at EO/Li = 10 (Figure 4(B)), indicating changes in the number of free ions, ionic pairs and aggregates.

In LiCF₃SO₃ + (EG)₁₁DME at EO/Li = 10 additional peaks appear at 1,045 cm⁻¹ and 1,054 cm⁻¹, which are assigned to ionic pairs and associates like {CF₃SO₃⁻…Li⁺}, {Li⁺…CF₃SO₃⁻…Li⁺} and {CF₃SO₃⁻…Li⁺…CF₃SO₃⁻} (Figure 5). Based on the literature, the triplet, which is observed at 1,045 cm⁻¹ is attributed to free ions, ionic pairs and ionic aggregates at the higher frequency region [24]. Therefore, one can deduce that the concentration of free anions (i.e., CF₃SO₃⁻ and SO₃⁻) in LiCF₃SO₃ + (EG)₁₁DME at EO/Li = 10 and EO/Li = 30 is increased [31]. The Raman frequencies of (EG)_nDME (n = 2 and 11) with interpretations are listed in Table 2 (supporting information) and are in a good agreement with the literature [22,23,32,33].

Free ions, ionic pairs and ionic aggregates can be studied in polyethylene oxide doped LiCF₃SO₃ by examination of the shape of Raman bands. For instance, spectral vibrations of anion SO₃⁻ become broader if the temperature is increased from 289 to 363 K, indicating ionic aggregates. Later, the Raman spectral bands of either free or aggregated tetrahedral SO₄²⁻anions, surrounded by Li⁺ or Na⁺ cations, are studied at a higher temperature region of 328 to 573 K.

Raman Spectra of Li₂SO₄ at Different Temperatures

Single lattice Li₂SO₄ contains 28 atoms, which correspond to the 84 degrees of freedom vibrations. All of the two or three-dimensional presentations split up the one-dimensional presentation A due to the low side symmetry (C₁). Group factor C_2h transforms any group presentation into A_g+B_g+A_u+B_u. The minimal structure presentation of the vibrational modes in Li₂SO₄ can be introduced as follows (Equations 1–4).

Translational and rotational degrees of freedom become lattice modes in the crystal Li₂SO₄. For a Li⁺ ion any translational degree of freedom corresponds to A, and the correlation group factor is considered as the minimal presentations of Li⁺ ion movement (Equation 5).

The most intense peak (Ag) in Raman spectra is assigned to _ν1SO₃⁻ at 1,014 cm⁻¹ [34]. Less intense peaks (Ag) at 1,127, 1,123 and 1,194 cm⁻¹ and three peaks (Bg) symmetry at 1,116, 1,150 and 1,204 cm⁻¹ are attributed to the free _ν3SO₃⁻ ion. The intramolecular movement ν₄ generates two modes in Ag presentation at 617 and 666 cm⁻¹ and three modes in Bg symmetry at 623, 649 and 666 cm⁻¹. Shoulder at 650 cm⁻¹ is assigned to Ag geometry of scattering. It is difficult to find the differences between effects of shift and peak positions at ∼650 and ∼666 ccm⁻¹ in both (Ag and Bg) presentations. The intramolecular mode ν₂ of E symmetry in the isolated ion split into two Ag and Bg modes in the crystal. There are two modes at 513 and 446 cm⁻¹ in Ag presentation and those at 516 and 451 cm⁻¹ in the Bg scattering symmetry. The intensities of Ag modes, which are observed in the XY geometry, are much weaker than those in YY [23]. The bandwidths corresponding to Ag and Bg at higher frequencies (i.e., 513 and 516 cm⁻¹, respectively) of ν₂ vibrations are broader than those which correspond to the other intramolecular modes in Li₂SO₄. In addition, the bands at 513 and 516 cm⁻¹ are relatively high for ν₂ components in comparison to other sulfate crystals. Normally ν₂ components are in the region of 460 to 480 cm⁻¹ in the Li₂SO₄·H₂SO₄, LiNaSO₄ and LiKSO₄, where one of the Ag components is observed at 513 cm⁻¹ and of Bg components is at 516 cm⁻¹. Several translational modes of Li⁺ ion can be connected due to their presence in the region of 400–450 cm⁻¹ and the appearance of a group factor component ν₂ with the corresponding symmetry.

Figure 6 shows the dependence of ν₁ (469 cm⁻¹), ν₂ (646 cm⁻¹) and ν₃ (1,123 cm⁻¹) vibrations of Li₂SO₄ on temperature in the range from 55 to 300 °C. As the temperature increases, the vibration bands are shifted to the lower frequency range. The bandshifts of ν₁ and for each ν₂ and ν₃ vibrations are 9 and 17 cm⁻¹.

Free tetrahedral SO₄²⁻ ion has four types of fundamental vibrations _ν1SO₄, _ν2SO₄, _ν3SO₄, _ν4SO₄ with corresponding wavenumbers (Table 3). The most intense bands of SO₄²⁻ ion vibrations are the following: i) 994 cm⁻¹ for the all components of _ν1SO₄ tensor; ii) 450 and 456 cm⁻¹ for the YY and ZZ components of polarization _ν2SO₄ tensor, respectively; iii) 1,103, 1,133 and 1,156 cm⁻¹ for the XY, YZ and ZX components of polarization _ν3SO₄ tensor, respectively; iv) 633 and 651 cm⁻¹ for the ZX and YZ components of polarization _ν4SO₄, respectively [35].

In the table, XX, YY, ZZ, XY, YZ, ZX indicate a symmetry of vibration, which is determined from the investigation of experimental tensors of Raman spectra. The characteristics of the bands intensity are illustrated in arbitrary units: ‘vw’ (very weak, <10³), ‘w’ (weak, 1–2 × 10³), ‘m’ (medium, 4–8 × 10³), ‘ s’ (strong, 8–10 × 10³) and ‘vs’ (very strong, >10 × 10³). The vibrations of the crystal lattice are given as ‘T’ (translational) and ‘L’ (libratory), while that of SO₄²⁻and Na atom are indicated by an ‘S’ and an ‘A’, respectively. The vibrations of SO₄² are assigned by _ν1SO₄ as the most intense and fully symmetric nondegenerate, _ν2SO₄ and _ν3SO₄ are twice and thrice degenerate vibrations, while _ν4SO₄ is ascribed as a deformation vibration.

The symmetry of vibrations in the Table 3 is determined from experimental tensors of Raman spectra (Equation 6).

(6) α ν = ( I x x I x y I x z I y x I y y I y z I z x I z y I z z )where I_ij is the scattering intensity with i and j as combinations of x, y and z from experimental data and tensor components α_v, which cannot be directly determined. The intensity I_ij (i and j indicate the directions of excited and scattered light) is measured for each vibration v. For example, I_xx indicates the direction coincidence of the excited and scattered light E⃗. The investigation of components of Raman tensor requires an application of linearly polarized and excited light as well as an analysis of the polarization state of scattered light relative to crystallographic orientations of the sample under study [35].

The components of the tensor are relative intensities of Raman bands for different crystal orientations, positions of the analyser and polarizers (Table 4).

The symmetry of A_g, B_1g, B_2g and B_3g vibrations is shown in Equation 7.

Free isolated SO₄²⁻ion is a tetrahedron of T_d symmetry. Both the theory and experiments mark out four fundamental vibrations v₁(A₁) = 983 cm⁻¹, v₂(E) = 450 cm⁻¹, v₃(F₁) = 1,105 cm⁻¹ and v₄(F₂) = 611 cm⁻¹, which are observed in Raman and Infra-red spectra (e.g., A₁ and E only in Raman and F₂ in both Raman and Infra-red). The interaction between SO₄²⁻ ions and neighboring cations yields the change of SO₄²⁻ vibration symmetry due to the degeneration of vibrations in the lower symmetry. The crystal Na₂SO₄ has D_2h symmetry, while SO₄²⁻ ion is positioned with the D₂ local symmetry [35], yielding a vibration symmetry change and the splitting of bands. For example, ν₂(E)→2A_g; ν₃(F₁) → B_1g + B_2g + B_3g and ν₄(F₂)→B_1g+B_2g+B_3g (Table 4), which are observed in Raman and only 2A_u with B_1u + B_2u + B_3u —in Infra-red spectroscopy. Band splits of ν₂(E) and ν₄(F₂) are observed by Raman spectra, which are more informative than those in Infra-red with only a ν₃(F₁) band.

When the temperature increases from 55 to 300 °C the vibration bands of SO₄²⁻ are shifted to a lower frequency range, indicating interactions between sulfate groups and Li⁺ cations as well as the presence of aggregated species. In addition, the vibration symmetry of SO₄²⁻ changes with the bands splitting due to interaction with neighboring cations. Later the mobility of Li⁺ cations is modeled in polyelectrolytes at room temperature and experimentally examined in solid electrolytes within a temperature range of 20 to 227 °C.

The modeling of polyelectrolytes is introduced by the examination of the movements of Li⁺ ion along the polymeric chain [CH₂-CH₂-O]₄ through a quantum mechanical calculation in order to determine the conductivity mechanism of polymeric electrolytes (LiCF₃SO₃+(EG)_nDME, n = 2 and 11). From the beginning, the positions of Li⁺ ion are considered nearby the first oxygen (model A in Figure 7). The configuration of the ‘A’ system is stable because it is a state at local minimum energy (E_A = −3,287.18 kkal·mol⁻¹). If the polyelectrolyte chain is deflected to the right or left, up or down, the configuration becomes unstable and the Li⁺ ion either goes back or approaches its initial position. Later the Li⁺ ion sits between the first and second oxygen atom (i.e., it is shifted to intermediate position in the model B). This new configuration is stable due to the local minimum of energy (E_B = −3,304.13 kkal·mol⁻¹). Later Li⁺ is positioned close to the second oxygen atom (model C) with acorresponding minimum of energy E_C= −3,286.61 kkal·mol⁻¹. Later Li⁺ passes a number of stable configurations with the local minimum of energies (E_D= −3,304.63 kkal mol⁻¹, E_E= −3,286.82 kkal mol⁻¹, E_F= −3,304.61 kkal·mol⁻¹, Eg= −3,286.60 kkal·mol⁻¹, E_H= −3,319.30 kkal·mol⁻¹, EJ= −3,318.75 kkal·mol⁻¹ and E_K= −3,330.75 kkal·mol⁻¹) when lithium ion moves along the polymeric chain. The models which are described above are shown in Figure 7.

In addition, there are non-operating transitions (L and M) which exist between the intermediate states (B, D, F, H and K) (Figure 8). Li⁺ ions move by changing the states with the local minimum of energy due to the states with the local maximum of energy (model L and M) with the close values (E_L= −3,283.80 kkal·mol⁻¹ and E_M= −3,287.19 kkal·mol⁻¹). Li⁺ ions move actively along the polymeric chain due to the rotations of polymer (i.e., carbon permanently rotates around hydrogen, hydrogen rotates around carbon, both carbon and hydrogen rotate around oxygen, etc.). Therefore Li⁺ ion transports along the polymeric chain by passing through the non-operating positions (L and M) due to intrapolymeric rotations. Li⁺ ion acquires energies of E_L and E_M when carbon atoms get a perpendicular position relatively to each other at the position of a Li⁺ ion. One requires to transform an additional energy of E1= −3.31 kkal·mol⁻¹ in order to move Li⁺ from the position with E_A to E_B through E_L and similarly one donates the Li⁺ by E₂= −19.28 kkal·mol⁻¹ for transportation from E_B to E_C through E_M. The calculations of the minimum energy corresponding to the most probable positions of a Li⁺ ion nearby the atoms (C, H and O) of polymeric chain allow increasing the conductivity of polyethylene oxide with impurities.

The conductivity of Li₂SO₄ versus temperature is measured by a technique reported elsewhere [36]. Conductivity increases with the temperature rise because the Li⁺ ion becomes more mobile due to weaker bonding with other atoms (Table 5). The high mobility of Li⁺ ion can be explained by the mechanism of a ‘paddle-wheel’, where Li⁺ diffuses into the crystal lattice via an adhesion of sulfate ions in the rotation [37]. This phenomenon results in band shifts to the low frequency region.

Lithium trifluoromethanesulfonate (LiCF₃SO₃, 99.995%), dimethyl ethylene glycol ([EG]_nDME, n = 2, 3 and 11), lithium sulfate dihydrate (Li₂SO₄·2H₂O, ≥99.99%), sodium sulfate dihydrate (Na₂SO₄·2H₂O, ≥99.99%) were purchased from Sigma-Aldrich (Munich, Germany).

Li₂SO₄ and Na₂SO₄·crystals were grown by slow evaporation at different temperatures. The aqueous solutions were heated until 80 °C, filtered, slowly cooled with a step 5–10 °C until 30 °C and dried; but not completely in order to avoid possible contamination by the rest of the impurities contained in the bulk of the material. These formed crystals are colorless with a morphology at the mm scale.

Polymeric electrolytes, which are produced on the basis of dimethyl ethylene glycol ((EG)_nDME) were dried in vacuum in order to remove water traces. LiCF₃SO₃ was dried at 120 °C under vacuum (10⁻³ bar) during 24 hours. The mixture of LiCF₃SO₃ in ethylene glycol was prepared at 50 C in a micro chamber under argon atmosphere. LiCF₃SO₃ was dissolved in oligomers (EG)_nDME with n = 2 and 3. The molar ratio of Li/EO (LiCF₃SO₃ to ethylene oxide) was varied from 0 to 0.4.

Li₂SO₄ crystals (4 × 10⁻³ g) and KBr (846 × 10⁻³ g) were ground into a powder and pressed to form a pellet (0.47% of Li₂SO₄ crystals) by putting the mixture into a press-shape (150 kg·cm⁻²) with a diameter of 12 mm under high pressure (150 atm). The pellets and Li₂SO₄ crystals were kept in a waterproof reservoir in order to avoid contact with air. The Fourier transformed infrared spectra (FTIR) of prepared Li/KBr pellets were measured employing the Bruker IFS66 Fourier spectrometer with Raman module FRA106 in the middle infra-red region (2.5–25 μm) with a spectral resolution 2 cm⁻¹ at a laser (1,064 nm) power of 3 × 10⁻⁵ V. 400 scans. A 10 min scan was added for each spectrum, in order to get a good signal/noise ratio. Raman intensities were determined as integral intensities. The ν(CO) and ν(CC) bands of pure polymer at 1,032 cm⁻¹ were subtracted from the reaction spectra. Raman bands were factorized into Gaussian-Lorentz function and a linear baseline in the spectral range 740 cm⁻¹.

The temperature dependence of Raman spectra was measured employing a temperature add-on device R495 from Bruker (Figure SI.2, supporting information) and a special home made thermostat set-up for this purpose (thermo-isolator box with a metallic net inside, Figure SI.3, supporting information). The voltage power supply in the in-built electro-heater (85 W) was completely on or off in a range of 0 to 12 V, while the temperature was increased from 22 °C to 250 °C with a stability ±3 °C. The calibration curves of the thermocouple (thermo electromobile force, EMF, versus temperature) in the temperature add-on device and special home made thermostat are shown in Figure SI.4 (supporting information).

The MNDO method is based on stationary Schrödinger equations. MNDO (Modified Neglect of Differential Overlap) is a modified method of NDDO (Neglect of Diatomic Differential Overlap) and semi-empirical method, which is oriented to the correct reproduction of electron characteristics such as dipole moments, non-transformation heat and geometry of molecules. The atomic orbital is of spherical symmetry in the calculations of electron-electron repulsion integrals. The orientation of p-orbitals is considered in the calculation of n-centered (n = 1–4) integrals of atomic orbital repulsion of the same atom. The self-descriptiveness of MNDO is due to information not only from the geometry of the molecule, but also dipole moments, the heat of the formation, the order of bonds, and spinning and density ratios among other factors.

MNDO is employed for a more accurate description of the repulsion between unshared electronic couples [38]. One of the main advantages of MNDO is the calculation of unsaturated compounds and molecules, which contain unshared electronic couples within neighboring atoms (for polar molecules). In addition, valent angles and the consistency of molecular orbital levels are accurately calculated through this method. MNDO correctly reproduces a relative stability of isomers, which contain double and triple bonds, and is widely used for a calculation of the oscillation frequency and structure of linear polymers. Moreover, MNDO is applied to polyyne and paracyclophan molecules, yielding high results for fluorine compounds (e.g., F-O, F-N, etc.) as well as a good reproduction of oscillation frequency. The disadvantages of MNDO are as follows: i) an incorrect description of hydrogen bonds; ii) an inaccurate calculation of internal rotation barriers in the conjugate molecules (e.g., benzylideneaniline, stilbene and azobenzene); iii) a disability to calculate four-termed cycles (they are too planar and stable); and, iv) a systematic overstating of ionization potentials in compounds, which contain Cl⁻ and Br⁻ anions Despite these disadvantages, MNDO/d (modified version of MNDO) is applied to model the interactions between Li⁺ and polyethylene oxide.