Pressure dependence of the ionic conductivity of poly(oxyethylene)–LiTFSI polymer electrolytes

Solid State Ionics 110 (1998) 15–20

Pressure dependence of the ionic conductivity of poly(oxyethylene)–LiTFSI polymer electrolytes Fannie Alloin, Joanna Bolton, Jean Louis Souquet, Michel Duclot* ´ ´ a` et des Interfaces ( LEPMI), ( UMR CNRS INPG No. 5631, Associee Laboratoire d’ Electrochimie et de Physicochimie des Materiaux ` , France l’ Universite´ Joseph Fourier Grenoble), ENSEEG BP 75, F 38402 Saint Martin d’ Heres Received 9 May 1997; accepted 20 March 1998

Abstract Variations in ionic conductivity of poly(oxyethylene)–LiTFSI complexes with pressure have been studied. In the 1–5000 bar range, the ionic conductivity decreases by about two orders of magnitude. The apparent activation volume DV *, 3 21 and does not experimentally determined by the relationship s(≠ ln s ) / ≠P)d T 5 2 (DV * ) /(RT ), is close to 25 cm mol significantly varies with LiTFSI concentration or polymer cross-linking. The ionic conductivity variations with pressure is interpreted by a decrease of the available free volume reducing the charge carrier mobility.  1998 Elsevier Science B.V. All rights reserved. Keywords: Salt polymer complexes; Ionic conductivity; Activation volume; Isostatic pressure

1. Introduction

straight lines whose slope allows a volume DV * to be determined by the relationship:

Advances in lithium battery research has raised the interest in lithium salts complexed by a polymeric matrix. The present study deals with linear or crosslinked poly(oxyethylene) (POE) chains in which is dissolved lithium trifluoromethanesulfonyl imide (LiTFSI) corresponding to the formula (CF 3 SO 2 ) 2 N 2 Li 1 . The use of LiTFSI and also cross-linking stabilise the amorphous character of these polymeric electrolytes. For most liquid, crystalline or glassy electrolytes, logarithmic variations in conductivity, ln s as a function of pressure at constant temperature define

≠ ln s DV * S]] D 5 2 ]] . ≠P RT

*Corresponding author: Tel.: 133 47682 6569; fax: 133 47682 6670; e-mail: [email protected]

T

(1)

This volume is commonly related to the local volume expansion required for ionic transport. When the transport mechanism implies an activation free energy barrier DG*, this volume is called activation volume and is thermodynamically defined by: ≠DG* S]] D 5 DV *. ≠P T

(2)

This activation volume is the difference in volume between a mole of the moving species in its activated transition state (at the top of the energy barrier) and its volume at normal equilibrium. In case of cationic conductive mineral glasses studied below their glass

0167-2738 / 98 / $19.00  1998 Elsevier Science B.V. All rights reserved. PII: S0167-2738( 98 )00123-4

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F. Alloin et al. / Solid State Ionics 110 (1998) 15 – 20

transition temperature, activation volume lies between 0.5 to 6 cm 3 mol 21 and is comparable to the molar volume of the moving cation [1,2]. All these results suggest that, in case of salt polymer complexes, the controlling factor for ionic transport would be the segmental motion of the polymer backbone. For salt polymer complexes it is known that ionic transport follows a V.T.F. behaviour rather than a classical Arrhenius type law. Nevertheless in a limited temperature range, conductivity variation with temperature may be reasonably compared to an Arrhenius type dependence and an apparent activation free energy and apparent activation volume may be defined. For this reason we will use the term of apparent activation volume for DV *. For its determination we have performed conductance measurements under isostatic pressure in the 10 2 4 –0.5 GPa (i.e. 1–5000 bar) range.

2. Experimental

2.1. Poly(oxyethylene) –LiTFSI complexes preparation 2.1.1. Preparation of POE 5 M complexes The solvating polymer is a linear POE 5 M (Aldrich) that is corresponding to a molecular weight ]] MW 5 5 3 10 6 . The dissolution of the lithium salts was made in a glove box under argon atmosphere by mixing the appropriate ratio of polymer and salt in dry acetonitrile and then stirring at room temperature for few hours. The conventional solvent casting method, using a glass ring on PTFE plate in a dry box, provides homogeneous films. Using this procedure two compositions of POE 5 M–LiTFSI complexes have been prepared corresponding to O / Li520 and O / Li56. Note that the intrinsic conductivity of the POE 5 M is three order of magnitude lower than the conductivity of complexes studied. 2.1.2. Preparation of cross-linked electrolytes 2.1.2.1. Polycondensation reaction The host polymer is prepared according to the following procedure. The polycondensation has been performed by reacting a stoichiometric amount of

]] polyethylene glycol, (MW51000), PEG1000, and 3-chloro-2-chloromethyl-1-propene, CCMP, in presence of pounded potassium hydroxide (KOH / PEG5 5) [3]. Both PEG1000 and CCMP from Aldrich have been used as received. A mixture of PEG1000 and CCMP was first heated to 408C in a round-bottomed flask equipped with mechanical stirring. The ground KOH was then added and the mixture left to react in air for 24 h. The resulting polycondensate has been dissolved in water. The aqueous solution has been then filtered using a Filtron Novacell unit of 150 ml size with a nominal molecular weight limit of 3000. This filtration allows removal inorganic by-products (KOH, KCl) as well as possible oligomers. The water was removed and the polymer thoroughly dried under vacuum for several days at 308C.

2.1.2.2. Network formation Cross-linking of the polymer was induced by freeradical initiation, using dibenzoyl peroxide. Using acetonitrile as common solvent, we have mixed the previous polycondensate and the dibenzoyl peroxide. The acetonitrile solution is casted in a glass ring on a PTFE plate. After acetonitrile removal, the membrane is heated up to 708C to induce the free-radical cross-linking of the polyether. In order to remove any peroxide traces as well as soluble polymers, the membrane is then swollen in a large volume of methanol for one day, the operation is repeated twice, then the membrane is thoroughly dried. Polymer electrolyte is obtained by swelling the film with acetonitrile solution of the salt in glove box in argon. After the solvent removal, the weight difference of the membranes makes it possible to determine the salt composition. Two membranes refereed as CLPC 1000 (Cross Linked PolyCondensate 1000) have been prepared with a LiTFSI concentration corresponding to O / Li516.4 and O / Li515.2. 2.2. High pressure conductivity cell The conductivity cell has been described in a previous paper [2]. The cylindrical pressure chamber (8 cm in diameter, 25 cm high) is joined to a hydrostatic press. A silicon oil (Total Equivis ZS 15) is used as the pressure fluid in the range 1–5000 bar. A heating element introduced in the chamber allows adjustment of the internal temperature between room

F. Alloin et al. / Solid State Ionics 110 (1998) 15 – 20

temperature and 1208C. Accurate measurements of the pressure and the temperature inside the chamber are determined by a piezoelectric pressure sensor and a Fe-constantin thermocouple. The polymer electrolytes samples are discs of about 13 mm in diameter and 0.1 to 0.4 mm thick. Electrodes are silver foils stacked to platinum leads with a silver paint. The polymer and the electrodes are then coated with an elastomeric silicon polymer (Rhodorsil CAF 4). Such a coating allows the isostatic pressure transfer to the sample, and protect it from the silicon oil and water. The conductance G of the sample is measured by an impedance technique using a Hewlett Packard 4192A Impedance Analyser in the frequency range 5 Hz–13 MHz. The electrical insulating property of the silicon polymer has been checked throughout the experimental temperature and pressure range. Each set of measurement for a given sample is made at a constant temperature near the room temperature. Inside the pressure chamber a constant temperature cannot be kept constant since each increase of pressure induce an instantaneous increase of temperature which cannot be controlled. Typically, an increase of pressure of 5310 2 2 GPa (500 bar) leads to an increase of 2 K and, inversely, a decrease in pressure lead to a small instantaneous decrease in temperature. It is the reason why, before any electrical measurement a delay of 10 to 20 min is necessary to return to the ambient temperature.

17

of 0.3 GPa 2 1 can be reasonably estimated for the corrective term xT / 3. In addition to this correction due to the polymer deformation the conductance measurements need to be compared at a same reference temperature. Since most of our measurements have been done near room temperature this reference temperature has been chosen as 298 K. Consequently each set of conductance measurement has been corrected to be reported at 298 K. For such a correction we need first to know the temperature conductivity dependence at constant pressure. For some selected compositions and pressures we have first verified that conductance variations with temperature obey a V.T.F. [5–7] equation:

S

D

B GT 5 A exp 2 ]]] . R(T 2 T 0 )

(4)

In Fig. 1 are represented the variations of the conductance temperature product GT as a function of temperature for four different pressures for a linear POE matrix. Fit to Eq. (4) for each pressure results from a least squares analysis procedure in which all three parameters (A, B and T 0 ) have no ‘a priori’ fixed values. Calculated values for B and T 0 are reported in Table 1 and Table 2. Using this procedure it is true that the relative variation of one

2.3. Measurement of DV* from experimental data According to Eq. (1) the slope of the isothermal variations ln s as a function of P allows the determination of apparent activation volume DV *. Since the pressure induces a variation in the cell parameters due to the polymer isothermal compressibility, xT , the pressure variation in electrical conductivity is related to measured variations in conductance by:

x ≠ ln s ≠ ln G S]] D 5S]]D 1 ] ≠P ≠P 3 T

T

T

(3)

where xT is the volumic compressibility of the polymer. The exact value of xT is not known, but for most of polymers is about 1 GPa 2 1 [4], and a value

Fig. 1. For different pressures, logarithmic variations of the conductance temperature product GT (SK) as a function of the reciprocal absolute temperature for the POE 5 M–LiTFSI complex (O / Li520). Parameters B and T 0 deduced from the best fit with Eq. (4) are reported in Table 1.

F. Alloin et al. / Solid State Ionics 110 (1998) 15 – 20

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Table 1 B and T 0 V.T.F. parameters as a function of pressure for POE 5 M–LiTFSI complex (O / Li520) P (GPa) 10

24

0.10 0.15 0.20

B (eV)

T 0 (K)

0.082 0.074 0.076 0.138

196 215 222 189

Table 2 B and T 0 V.T.F. parameters as a function of pressure for CLPC1000–LiTFSI cross linked complex (O / Li516.4) P (GPa) 10

24

0.10 0.20 0.30

B (eV)

T 0 (K)

0.094 0.126 0.113 0.147

201 171 183 155

parameter with another has no physical signification and only pressure independent mean values of parameter B and T 0 , have to be considered. Consequently for each sample, parameters B and T 0 can be determined from one set of conductance–temperature measurements and then, at constant pressure all conductances measured at temperature T can be corrected to 298 K using the following relation:

S

D

GT T B B G298 5 ]] exp 2 ]]]] 1 ]]] . 298 R(298 2 T 0 ) R(T 2 T 0 ) (5) In Fig. 2 are represented conductance variations as a function of pressure for a POE 5 M–LiTFSI complex with O / Li520. We may note the results reproducibility along a pressure cycle between 10 2 4 GPa (1 bar) and 0.5 GPa (5000 bar). In a logarithmic scale, the variation of the GP /G1bar ratio present a reasonably linear dependence with pressure from which we deduce a mean value of the apparent activation volume DV *. For this salt-polymer complex at 298 K, DV *527.6 cm 3 mol 21 . Conductance data shown in Fig. 2 have been reported to this temperature using Eq. (5) with B50.092 eV and T 0 5205 K which are average values of these parameters deduced from data in Fig. 1. Obviously the apparent activation volume DV *, depends on the numerical values of B and T 0 . Nevertheless, using for B two extreme values, B50.05 eV or B50.15 eV,

Fig. 2. At 298 K, logarithmic variations of the conductance GP /G1bar versus pressure for the POE 5 M–LiTFSI complex (O / Li520). At this temperature G1bar correspond to a ionic conductivity of 1.2310 2 5 S cm 2 1 . d Conductance data obtained with increasing pressure. n Conductance data obtained with decreasing pressure. Note the results reproducibility along a pressure cycle.

apparent activation volume value equals 26.4 cm 3 mol 21 and 28.1 cm 3 mol 21 respectively. Using this procedure for the four studied LiTFSI polymer complexes we have calculated apparent activation volumes at 298 K. Numerical results are reported in Table 3.

3. Discussion The pressure dependence on ionic conductivity for salt polymer complexes has been already studied on different systems. For alkali metal salts with POE, all DV * values lie between 9 to 60 cm 3 mol 21 . The highest values corresponding to alkali perchlorates and the lowest to alkali thiocyanates [8,9]. When NaSCN is complexed by poly(oxypropylene), POP, the individual activation volume for Na 1 cations and SCN 2 anion has been determined using 2 2 Na and 14 C radio tracers [9]. Interestingly, cationic and anionic apparent activation volume have exactly the same value DV *525 cm 3 mol 21 at 298 K. Our results on poly(oxyethylene)–LiTFSI complexes shows that the activation volume, of about 25 cm 3 mol 21 , does not varies significantly with salt concentration or polymer chain cross-linking. The (CF 3 SO 2 ) 2 N 2 anion is the predominant

F. Alloin et al. / Solid State Ionics 110 (1998) 15 – 20

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Table 3 Apparent activation volume DV * for different LiTFSI complexes Complex Composition

POE 5 M O / Li520

POE 5 M O / Li56

CLPC1000 O / Li516.4

CLPC1000 O / Li515.2

DV * (cm 3 mol 21 )

26.4

24.9

21.2

25.1

charge carrier (t 2 ¯0.9) [10,11]. This anionic conductivity may be expressed as a function of the concentration n 2 in anionic charge carriers and his mobility m2 :

s2 5 Fn 2 m2

(6)

In this expression n 2 is the concentration (mole cm 23 ) of anionic charge carriers. The microscopic nature of these charge carriers is not specified. They are probably not ‘free’ (CF 3 SO 2 ) 2 N 2 anions but more likely ‘clusters’ or ‘interstitial pairs’ like [(CF 3 SO 2 ) 2 N] 2 Li 2 . The pressure variation of the conductivity is expressed by the relation (7). ≠ ln n ≠ ln m ≠ ln s D 1S]] D. S]] D 5S]] ≠P ≠P ≠P 2

T

2

T

T

(7)

3.1. Pressure dependence of charge carriers concentration For salt–polymers complexes interpretation of conductivities data [12] or Raman spectroscopic studies [12,13] lead to conclude to a partial dissociation of the salt in the macromolecular network. Ionic dissociation would be an exothermic reaction associated to large decrease in entropy [12,15]. This drop in entropy would result from an important increase in the local order by the wrapping and the correlative immobilisation of the macromolecular chains around the charged species. These interactions would then lead to a decrease of the volume when the salt dissociate. Consequently an increase of pressure is expected to increase the number of charge carriers. Such a behaviour has been observed in poly(propylene glycol)–LiCF 3 SO 3 complexes for which in the 1 bar to 5000 bar pressure range, the number of charge carriers is found to increase by 50% approximately [16]. If we extend these results to LiTFSI complexes, the observed decrease in conductivity of two order of magnitude in the same

pressure range cannot be explained by the variations in charge carriers concentration.

3.2. Pressure dependence of charge carriers mobilities This conductivity decrease would be then a consequence of a mobility decrease with pressure. Charge carriers mobilities in salt polymer complexes are usually interpreted in terms of a free volume mechanism. The local displacement of a charge carrier around its equilibrium position in the macromolecule ¯ Above the ideal chain defines a cell of volume V. transition temperature T 0 , part of this average volume, V¯f is considered as free, that is redistributable without any enthalpic contribution. The displacement of a charge carrier over a distance of the same size as the cell diameter l requires a local minimal value of this free volume V *f . The probability p to locally reach this critical free volume is

S D

V *f p 5 exp 2 ] ] . Vf

(8)

Calling n0 the attempt frequency for a charge carrier to escape from its cell, the anionic charge carrier mobility m2 may be then rewritten as

S D

Fl 2 n0 V *f ]] m2 5 exp 2 ] ] 6RT Vf

(9)

where F and R have their usual values. Qualitatively an increase of pressure, decreasing the available free volume V¯f will significantly reduce the anionic mobility m2 and consequently the anionic conductivity [14]. A more quantitative interpretation would require the knowledge of the free volume–pressure dependence.

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F. Alloin et al. / Solid State Ionics 110 (1998) 15 – 20

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