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The conductivity mechanism is studied in the LiCF_{3}SO_{3}doped polyethylene oxide by monitoring the vibrations of sulfate groups and mobility of Li^{+} ion along the polymeric chain at different EO/Li molar ratios in the temperature range from 16 to 90 °C. At the high EO/Li ratio (
The physics and chemistry of solid electrolytes requires expanding investigations in a new way due to the fabrication of devices of which they are the basis. Solid electrolytes (superionic conductors or solids with rapid ionic conductivity) are solids, which exhibit ionic conductivity comparable with that of electrolyte solutions or melted salts. Solids with rapid ionic conductivity have various applications from direct fuel cells [
Common ionic crystals or semiconductors (e.g., NaCl, AgCl,
Solid electrolytes or ionic superconductors (e.g., αAgI, αLi_{2}SO_{4}, metal containing complexes of phosphates and silica phosphate, sour sulfates of base metals,
Polymeric electrolytes with conductivity in the 10^{−3} to 10^{−1} S·cm^{−1} region due to the transport of impurity cations along the polymeric chains with structural disorders [
As the first class of solid electrolytes is well studied [
Polyethylene oxide (PEO) as a simple polyether can be chosen as the polymeric matrix due to its low molecular weight and an ease of solubility in water. The solubility of the polymer in water is decreased with the increase of molecular weight, firmness and melting temperature. This fragment of structural formula of PEO is shown in
The physicochemical properties of lithium and sodium salts are actively studied with the large interest in phase transitions of LiASO_{4} with A as the base cation (e.g., Li, Na, K, Rb and Cs) [
The investigation of high temperature phases of the Li_{2}SO_{4} structure is very interesting due to the fact that Li_{2}SO_{4} is a monohydrate crystal with a monoclinic system at room temperature. The crystal belongs to the space group with symmetry
The main factor which limits the ionic conductivity of such a conductor is the nature of coupling and aggregation of ions in polymeric electrolytes [
The main purpose of our work is to study ionic species (e.g., SO_{4}^{2−} and Li^{+}) in two conductive systems—polymeric and solid electrolytes. The vibrations of sulfate groups are examined by Raman and Infrared spectroscopy in the temperature region from 65 to 355 ° C. At room temperature the presence of free ions or ionic aggregates is studied at different molar ratios of ethylene oxide to LiCF_{3}SO_{3} salt (EO/Li) in the polymeric electrolyte with 2, 3 and 11 chain lengths of dimethyl ethylene glycol ((EG)_{n}DME). The mobility of the Li^{+} cation is modeled by a modified quantum mechanical method of molecular and atomic orbitals in the polyelectrolyte and spectroscopically studied solid electrolytes in the temperature region from 293 to 500 K.
Raman spectroscopy is employed to examine vibrations of ions in polymeric electrolytes because triflate anions CF_{3}SO_{3}^{−} 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 LiCF_{3}SO_{3} in H[OCH_{2}CH_{2}]_{n}OH (n = 1–4), while the number of ionic couples is small due to the presence of ionic associates [
The Raman spectrum of pristine LiCF_{3}SO_{3} at room temperature is shown in
Raman bands of SO_{3}^{−} in LiCF_{3}SO_{3} + (EG)_{n}DME with n = 2 and 11 in the range from 289 K to 363 K are shown in
The bands become broader with lower intensity due to the temperature increase, indicating formation of ionic aggregates. Raman spectra of LiCF_{3}SO_{3} + (EG)_{n}DME (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} (
In LiCF_{3}SO_{3} + (EG)_{11}DME 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 {CF_{3}SO_{3}^{−}…Li^{+}}, {Li^{+}…CF_{3}SO_{3}^{−}…Li^{+}} and {CF_{3}SO_{3}^{−}…Li^{+}…CF_{3}SO_{3}^{−}} (
Free ions, ionic pairs and ionic aggregates can be studied in polyethylene oxide doped LiCF_{3}SO_{3} by examination of the shape of Raman bands. For instance, spectral vibrations of anion SO_{3}^{−} 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 SO_{4}^{2−}anions, surrounded by Li^{+} or Na^{+} cations, are studied at a higher temperature region of 328 to 573 K.
Raman Spectra of Li_{2}SO_{4} at Different Temperatures
Single lattice Li_{2}SO_{4} contains 28 atoms, which correspond to the 84 degrees of freedom vibrations. All of the two or threedimensional presentations split up the onedimensional presentation
Translational and rotational degrees of freedom become lattice modes in the crystal Li_{2}SO_{4}. For a Li^{+} ion any translational degree of freedom corresponds to
The most intense peak (
Free tetrahedral SO_{4}^{2−} ion has four types of fundamental vibrations _{ν1}SO_{4}, _{ν2}SO_{4}, _{ν3}SO_{4}, _{ν4}SO_{4} with corresponding wavenumbers (
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: ‘
The symmetry of vibrations in the
The components of the tensor are relative intensities of Raman bands for different crystal orientations, positions of the analyser and polarizers (
The symmetry of
Free isolated SO_{4}^{2−}ion is a tetrahedron of
When the temperature increases from 55 to 300 °C the vibration bands of SO_{4}^{2−} 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 SO_{4}^{2−} 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 [CH_{2}CH_{2}O]_{4} through a quantum mechanical calculation in order to determine the conductivity mechanism of polymeric electrolytes (LiCF_{3}SO_{3}+(EG)_{n}DME, n = 2 and 11). From the beginning, the positions of Li^{+} ion are considered nearby the first oxygen (model A in
In addition, there are nonoperating transitions (L and M) which exist between the intermediate states (B, D, F, H and K) (
The conductivity of Li_{2}SO_{4}
Lithium trifluoromethanesulfonate (LiCF_{3}SO_{3}, 99.995%), dimethyl ethylene glycol ([EG]_{n}DME, n = 2, 3 and 11), lithium sulfate dihydrate (Li_{2}SO_{4}·2H_{2}O, ≥99.99%), sodium sulfate dihydrate (Na_{2}SO_{4}·2H_{2}O, ≥99.99%) were purchased from SigmaAldrich (Munich, Germany).
Li_{2}SO_{4} and Na_{2}SO_{4}·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)_{n}DME) were dried in vacuum in order to remove water traces. LiCF_{3}SO_{3} was dried at 120 °C under vacuum (10^{−3} bar) during 24 hours. The mixture of LiCF_{3}SO_{3} in ethylene glycol was prepared at 50 C in a micro chamber under argon atmosphere. LiCF_{3}SO_{3} was dissolved in oligomers (EG)_{n}DME with n = 2 and 3. The molar ratio of Li/EO (LiCF_{3}SO_{3} to ethylene oxide) was varied from 0 to 0.4.
At Room Temperature
Li_{2}SO_{4} 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 Li_{2}SO_{4} crystals) by putting the mixture into a pressshape (150 kg·cm^{−2}) with a diameter of 12 mm under high pressure (150 atm). The pellets and Li_{2}SO_{4} 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 infrared 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 GaussianLorentz function and a linear baseline in the spectral range 740 cm^{−1}.
In the Temperature Range from 22 °C to 250 °C
The temperature dependence of Raman spectra was measured employing a temperature addon device R495 from Bruker (
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 semiempirical method, which is oriented to the correct reproduction of electron characteristics such as dipole moments, nontransformation heat and geometry of molecules. The atomic orbital is of spherical symmetry in the calculations of electronelectron repulsion integrals. The orientation of porbitals is considered in the calculation of ncentered (n = 1–4) integrals of atomic orbital repulsion of the same atom. The selfdescriptiveness 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 [
Normally nuclei are considered to be static, while electrons are mobile. Given these considerations, it is possible to solve the Schrödinger equation for the oneelectron system only. For this reason the most applied method is the method of selfconsistent fields (SCF) or HartreeFock in quantumchemical theory. In this method any electron moves in the field of atomic nuclei and in the effective averaged field of other electrons. Multielectron wave function is considered as an asymmetric product of spinorbitals (
Restricted, the HartreeFock method (RHF) is used for systems with closed shells (without unpaired electrons), where each electron MO
Molecular orbitals
The group of atomic orbitals (AO),
This system of linear equations below is used to find the minimum of full molecule electron energy
This system of
Polyethylene oxide acquires the properties of a conductor and becomes a polymeric electrolyte when it is doped by LiCF_{3}SO_{3}. This conductivity can be controlled by monitoring the vibrations of SO_{3} groups at EO/Li molar ratio from 10 to 30 in LiCF_{3}SO_{3} + (EG)_{n}DME (n= 2,3, 11). At the high EO/Li ratio the intensity of bands increases and a triplet appears at 1,045 cm^{−1}, indicating the presence of free anions, ionic pairs and aggregates. The existence of free ions in the polymeric electrolyte is also proven by red shift of bands in Raman spectra within a temperature range of 16 to 90 °C. In addition, a shift of bands in the monocrystal Li_{2}SO_{4}·2H_{2}O to the low frequency region is observed in the Infrared at 65 < T < 355 °C, as measured by the home made temperature device located inside the spectrometer. In the Raman spectra of Na_{2}SO_{4} the symmetry of SO_{4}^{2−} vibrations is changed due to an interaction with neighboring cations resulting in the disposal of a degeneration of vibrations, leading to a band split.
From the quantum mechanical modelling (method MNDO/d), the energies (minimum and maximum) corresponding to the most probable and stable positions of Li^{+} are calculated in order to gain deeper insight into the conductivity of polymeric electrolytes. While being transported along the polymeric chain, Li^{+} ion overcomes intermediate states (minimum energy) through nonoperating transitions (maximum energy) due to permanent intrapolymeric rotations (rotation of C, H and O atoms around each other). The conductivity of the monocrystal Li_{2}SO_{4}·2H_{2}O increases with a temperature rise of 20 to 227 °C. Li^{+} ions become more free and mobile resulting in an increase of the conductivity of a pelletsample Li_{2}SO_{4}·2H_{2}O.
The results of this present work can be of practical interest for the direct production of small and effective devices in science and industry that use polymeric electrolytes, which are formed by combining polyethylene oxide and LiCF_{3}SO_{3} as well as solid electrolytes (e.g., Li_{2}SO_{4}).
The diagram illustrating conductivity σ (S·cm^{−1}), which compares polyethylene oxide with other materials.
Raman spectra of LiCF_{3}SO_{3} + (EG)_{11}DME (EO/Li = 10) at room temperature. (EG)_{11}DME is dimethyl ethylene glycol with the chain length n = 11 and EO/Li = 10 is the inverse molar ratio of LiCF_{3}SO_{3} to elements of ethylene oxide oligomer. Where ‘vs’, ‘s’ and ‘m’ are spectral bands with ‘very strong’, ‘strong’ and ‘medium’ intensity, respectively. The assignments ‘sh’ indicates a band shoulder, ‘w’—a bandwidth, ‘
Raman spectra of dimethyl ethylene glycol with the chain lengths 2 (
Raman spectra of dimethyl ethylene glycol with chain lengths 2 (
Band decomposition of symmetric valence vibration of SO_{3}^{−} in LiCF_{3}SO_{3} + (EG)_{11}DME at EO/Li = 10 at room temperature.
The dependence of Li_{2}SO_{4} ν_{1} (469 cm^{−1}), ν_{2} (646 cm^{−1}) and ν_{3} (1,123 cm^{−1}) vibrations on temperature in the range from 55 to 300 °C.
The quantum mechanical modeling (MNDO/d method) of the Li^{+} ion locations along the polymeric chain of polyethylene oxide with the chain fragment [CH_{2}CH_{2}O]_{n} (n = 4). The capital letters A, C, E, G and J are assigned to the states of Li^{+} ion with the local minimum energy (
The quantum mechanical calculation of the Li^{+} ion local energies with the nonoperating transitions L and M (E_{L}= −3,283.80 kkal·mol^{−1} and E_{M}= −3,287.19 kkal·mol^{−1}) which exist between the intermediate states (B,
Vibrations of pure LiCF_{3}SO_{3} at room temperature.
314_{s}  
349_{s}  
524_{w}  
575_{m}  
758_{s}  
1034_{vs}  
1230_{sh} 
Assignment of frequencies (cm^{−1}) in Raman spectra of Na_{2}SO_{4} crystal.
 

—  87w  87w  87w  87w  —  TAS 
140w  140w  140w  140w  140w  140w  — 
166vw  166vw  161w  166w  —  166w  LA 
—  —  456w  456w  _{ν2}SO_{4}  
472m  472w  —  469w  469w  469w  _{ν2}SO_{4} 
—  622w  —  625w  625w  —  _{ν4}SO_{4} 
639w  —  639m  —  —  _{ν4}SO_{4}  
—  650w  650w  651w  —  _{ν4}SO_{4}  
_{ν1}SO_{4}  
—  1106w  —  1103w  1103vw  _{ν3}SO_{4}  
—  1136w  1136w  1133w  1133vw  _{ν3}SO_{4}  
1156w  —  1156m  1156w  1156w  _{ν3}SO_{4} 
Components of a polarization tensor.
α_{456} 

B_{3g}, _{ν2}SO_{4} 
α_{639} 

B_{2g}, _{ν4}SO_{4} 
α_{650} 

B_{3g}, _{ν4}SO_{4} 
α_{994} 

A_{g}, _{ν1}SO_{4} 
α_{1106} 

B_{1g}, _{ν3}SO_{4} 
α_{1133} 

B_{3g}, _{ν3}SO_{4} 
α_{1156} 

B_{2g}, _{ν3}SO_{4} 
The dependence of the conductivity of Li_{2}SO_{4} on the temperature.
20  3.4  −4.1 
50  3.1  −3.3 
78  2.9  −2.8 
227  2.0  −1.6 
This work is supported by the FP6EU Project. The author thanks S. N. Shashkov from Department of Physics in Belarusian State University (BSU, Minsk, Belarus) for useful discussions and supporting materials. A. Kulak (BSU, Department of Physics, Minsk, Belarus) is acknowledged for careful reading the manuscript.