Electrolytic conduction in amorphous salt complexed polyethers

Solid State lonics 24(1987) 155-167 North-Holland, Amsterdam

ELECTROLYTIC C O N D U C T I O N I N A M O R P H O U S SALT C O M P L E X E D P O L Y E T H E R S Jeremy R.M. GILES Materials and Structures Department, Royal Aircraft Establishment, Farnborough, Hampshire, GUI 4 6TD, UK

Received 26 August 1986; in revised version 24 March 1987; accepted for publication 3 April 1987

phosphate ester extended and crosslinked poly(ethylene glycol)s were prepared from reaction of the glycolswith chlorophosphates. Fully amorphous electrolytesformed with lithium trifluoromethanesulphonateshowed enhanced conductivity over comparable poly(ethylene oxide) electrolytesin the temperature range 293-373 K. With O/Li= 27.6, a = 5.2 × 10-6 S cm-~ at 293 IC A conductivity maximum was detected at ca. 1 mol dm -3 concentration consistent with the increase in charge carrier density opposed by medium viscosity.For all complexesthe temperaturedependenceof conductivity obeyedthe Vogel-Tamman-Fulcher and Williams-Landel-Ferry equations, with/'8(onset) for the parent polymer as the ideal glasstransition temperature. Activation energy parameters from use of the VTF equation and Adam-Gibbs configurational entropy model showed a linear dependence on salt concentration.

1. Introduction

Recently, interest in solid polymeric electrolytes has increased and a number of potential areas of application have been suggested, including for solidstate batteries, electrochemical displays and sensor devices. Most attention has been concentrated on alkali metal salt solvates formed with polyethers such as poly(ethylene oxide) (PEO) or poly(propylene oxide) (PPO) while a few reports on the investigation of polyester-salt complexes have appeared [ 1 ]. One of the earliest papers on this class of material described a study of the variation in damping constant and shear modulus for poly(propylene oxide)s containing incremental quantities of lithium perchlorate [ 2 ]. Various crystalline complexes of PEO have been characterised using X-ray and other spectroscopies; usually the alkali metal ion has been assigned to cavities in tight helical polyether environments, strongly solvated by the oxygen atoms [ 3 ]. Latterly emphasis has been placed on the property of ion conduction which is thought to be dominated by the amorphous components of the material and the presence of highly resistive crystalline phases of varying salt content is detrimental. Such behaviour is consistent with results recently obtained from an oxymethylene-oxyethylene copolymer complexed with lithium trifluoromethanesulphonate [4]. In

addition to salt-rich crystalline and semi-crystalline regions in PEOxLiCF3SO3 films a further phase consisting of essentially crystalline PEO is present below ca. 333 K ( x > 3 . 5 ) and is responsible for the poor conductivities measured at 298 K of ca. 10- s S c m - l [ 5,6 ]. A successful route to overcome the problems of crystallisation and increase ambient temperature conductivity has been the introduction of flexible linking groups in sufficiently high concentration along the PEO molecule such that crystallisation is prevented [ 7 - 9 ]. Here results are presented from an ac impedance and calorimetry study of amorphous complexes of LiCF3SO3 with phosphate ester extended and crosslinked a-bydro-to-hydroxypoly(oxyethylene)s [poly(ethylene glycol)s] which show considerable improvements in conductivity throughout the temperature range examined, in comparison with typical PEO electrolytes.

2. E x p e r i m e n t a l

2.1. Materials

Polymers were prepared by phosphate ester bond formation using either phosphoryl chloride or ethyl phosphorodichloridate (ethyl dichlorophosphate) in reaction with poly(ethylene glycol). For example:

156

J.R.M. Giles~Conductionin amorphouspolyetherelectrolytes

3H (OCH2 CH2) nOH + 2 POCI3 --, [(OCH2CH2)nO]3[PO]2 + 6 HCI.

Commercially available distillation mixtures of low molar mass ( 300 or 400 g tool- 1) glycols were used and dried before reaction by azeotropic distillation with benzene or toluene as solvent. The individual polymers are identified throughout by a Roman numeral and their preparation is described below. All manipulations of the resultant polymers were carded out under dry-air glovebox conditions ([H20] < 10 ppm).

Polymer I Phosphoryl chloride (2 mol) was added dropwise over one hour to the azeotropically dried poly(ethylene glycol) (3 tool) of average molar mass 400 [abreviated to PEG(400)] in benzene solution (ca. 1.5 tool dm -3) under a nitrogen atmosphere at 298 K. The reaction mixture was raised to 353 K and dried (P2Os)N2 gas passed through the solution at a moderate rate until gelation occurred, ca. 2.5 h. Reaction was allowed to continue at lower temperatures and remaining solvent and volatile components removed under reduced pressure for an extended period. The product was a colourless gel. Polymer II Polymer II was prepared in a similar manner except that the gel formed was washed briefly with dried ethanol and then exposed to high vacuum for an extended period. Polymer III Polymer III was prepared by first adding phosphoryl chloride dropwise to PEG(300) in toluene (ca. 1.5 tool dm -~) at 298 K under a N2 atmosphere, over a 30 min interval, starting [ OH ] / [ CI ] = 1.12. The resulting solution was stirred for 16 h at 298 K and then heated to 358 K for ca. 8 h to achieve initial gelation during which time N2 was passed through the solution. Heating was discontinued, volatile components removed and further reaction allowed to occur at close to 293 K over several days, during which Tg(onset) increased from 200 K to 232 K.

Polymer IV Polymer IV was synthesised by a similar route to that of polymer III. Polymer V Ethyl phosphorodichloridate (1 mol) was added dropwise (I 5 rain) to azeotropically dried PEG(400) (1 tool) in benzene (ca. 1.5 mol dm -3) under a N2 atmosphere and stirred for 2 h, then refluxed for 2 h to generate a linear oligomeric material. The product was a colourless, transparent viscous oil. Gel permeation chromatographic analysis of a typical product showed a broad mass distribution from ca. 5000 downwards. High molar mass and gelled products were formed by the addition of phosphoryl chloride (0.2 mol) to the reaction mixture and heating under reflux. If aliquots were removed, after ca. 45 rain of reflux, then exposed to high vacuum and cast into moulds, transparent, colourless rubbery films were formed after further solid-state reaction. Continued reflux of the original reaction mixture led to gelation (polymer VI) in the usual way. Z2. Impedance measurements Electrolyte complexes were prepared by partition of lithium trifluoromethanesulphonate between acetone solutions and the solution swollen gels, excess solution was removed and the gels dried under high vacuum for ca. 16 h. ac impedance measurements (Solartron 1250 Frequency Response Ananlyser and 1186 Electrochemical Interface) were performed over a frequency range of 50 kHz to 0.1 Hz using equivalent, parallel, steel blocking electrodes contained in an argon atmosphere within a variable temperature cell ( + 0.5 K). Polymeric films were pressed in situ and cycled within the range 2 7 8 - 3 7 3 K . The electrolyte film may be considered as a parallel resistance-capacitance arrangement in series with the double-layer capacitance. The resistance was measured at the frequency corresponding to the minimum in double-layer reactance, this usually occurred at or near the 50 kHz frequency maximum, for the films examined, typically 100 am in thickness.

2.3. Calorimetry Differential scanning calorimetry (DSC) experi-

J.R.M. Giles~Conductionin amorphouspolyetherelectrolytes ments were performed using a Du Pont 1090 Thermal Analyser, where samples were hermetically sealed in aluminium pans and quenched (cooling rate ca. 30 K m i n - ~) from 298 to 152 K and heated to 423 K at 10 K rain-re.

3. Results and discussion

3.1. Synthesis The synthetic method described for the formation of the amorphous polyethers represents a simple preparative procedure to electrolyte forming polymers. The major by-product in the condensation is hydrogen chloride which may be readily removed by a gas purge, as used here, by addition of a suitable base, or by carrying out the reaction at reduced pressures. Rapid removal of the hydrogen chloride by a suitable method is preferred, hindering side-reactions and displacing the equilibrium to product formation. Relevant phosphorus chemistry has been discussed by Kosolapoff [ 10 ]. By suitable choice of reagents and their reaction order the method is capable of easy and wide variation. The crosslink density and nature of the crosslinks may be varied by changing the glycol, using more than one glycol in a stepwise procedure, or by generating linear phosphate ester oligomers prior to a crosslinking step. For example, reaction at ca. 293 K of phosphoryl chloride with a low molar mass glycol in the appropriate mole ratio can lead to the formation of a tetrafunctional crosslinking agent for use in further condensation reactions. Usually the ease of product formation from reaction of ROH with POC13 decreases in the order ROP(O)CI2> (RO)2P(O)CI> (RO)3PO, where R = primary alkyl [ 10 ]. A problem with the preparation of relatively high molar mass linear esters is the high degree of polymerisation required; this may be overcome by the inclusion of trifunctional reagents. In the limit of one reagent being present in only a trifunctional form with the other difunctional the extent of reaction necessary for gelation is only 70.7%. It is advantageous to use an excess of starting glycol to avoid unreacted P-C1 groups in the final product.

157

3.2. Calorimetry 3.2.1. Polymers The thermal events detected for each polymer depended on the synthetic procedure adopted. A maximum of three transitions were present, a welldefined glass transition, crystallisation exotherm and corresponding melting endotherm. The temperature recorded for the onset of each event is labelled Tv Tc and Tm respectively (table 1). For the gels (I and II) prepared by the reaction of phosphoryl chloride and PEG at 353 K, without an initial step of extended ambient temperature reaction, all three thermal events were detectable showing the presence of a crystalline component with a melting region near.273 K (fig. 1). Enthalpies for the cold crystallisation and melting transitions were similar, ca. 30 J g-m indicating approximately 15% crystallisation, and that the majority of the crystalline material was formed during the heating cycle. Attempted extraction using acetone of any glycol remaining did not affect the transitions detected. By comparison with the parent glycol for I [ PEG(400)], for which only a melting event ( Tr,=273 K, peak at

u

213

Fig.

253

293

T/l(

I. DSC curve for I, as prepared, heated at 10 K rain- ~from

153 K after quenching from 298 K.

158

J.R.M. Giles~Conduction in amorphous polyether electrolytes

Table 1 Calorimetry data, conductivity (tr) values and VTF equation parameters for representative polymers formed from glycol mixtures of average molar mass (M). Polymer

I

M

O/Li a)

Ts (K)

Tc (K)

Tm (K)

400

~ 41.4 35.8 27.6 13.7 oo 18.6 13.8 9.7 8.0 oo co 32.8 21.4 14.0 7.0 5.9 4.8 ~ oo oo

229 a~ 237 236 239 245 221 c~ 240 240 249 254 232 210 o 223 227 229 238 239 241 226 227 214

254

277

II

400

III IV

300 300

V VI VII

400 400 400

244

268

_

_

252 227

274 g~ 263

106×tr(293 K) b) ( S c m -~)

Ea (kJ mol -t )

A(S cm -t K 1/2)

T~ (K)

T~ c) (K)

dE Arrheniu~ (kJ t o o l - ' )

4.5 4.4 5.2 2.5 1.1X 10 -2 h~ 4.0 1.1 0.4

3.7 3.9 4.0 4.5 3.6 5.1 5.3 6.1 6.4

0.08 0.10 0.15 0.20 7.3× 10 -5 h~ 0.45 0.54 0.32

297.3 293.0 294.5 293.0 302.0 298.9 285.2 295.3 298.5

238 220 211 230 228 220 225 227 224

30.0 31.1 31.3 39.4 22.5 3319 33.4 38.6 40.5

Values relate to the oxygen atom content derived from the polyethers,

b Data obtained using the VTF equation.

c Values found using equation (6). d Mid-point of the heat capacity step at 232 K. c Mid-point of the heat capacity step at 224 K. f Ts(onset) extrapolated to zero heating rate was 207.5 K. s The melting feature had two poorly resolved components. " An accurate value is unknown due to an error in the measurement of the polymer film thickness.

288 K AH= 130 J g- 1) was detectable after a similar quenching and heating cycle, the kinetics of crystallisation for the polymers were slow. If an initial ambient temperature reaction stage were included in the polymer synthesis (products III and IV) then the final materials were fully amorphous and only Ts was detected. Thus by allowing a more efficient early reaction stage, initially an end-capping step, the crystalline component was essentially eliminated. This is consistent with crystallisation being the result of defect, hydroxyl group terminated side-chains, in relatively high concentration for I and II; and correspondingly the suppression of crystaUisation by the presence of phosphate ester groups in the final polymers at the resulting concentration dictated by the chain-lengths of the starting glycols used. This is also supported by the absence of crystallisation inVI. The absence of any effect on the DSC events for the gel samples after acetone washings, and the differences

in thermal transitions and their occurrence, between the products and the starting glycols demonstrate that residual glycol contents were negligible. In the preparation of III the rise inTg after initial gelation could be followed by DSC, when further reaction was allowed at continue at near ambient temperature. The product formed at first was similar tO a highly plasticized gel, and Tg increased from ca. 200 K to a final value of 232 K. A similar depression of the glass transition could be achieved by the addition of glycol to the final product. Tg for the networks is expected to depend on crosslink density in a usual way, with Tg inversely proportional to the number average molar mass between crosslinks (Me). Entanglements [ 11 ] probably make a negligible contribution as a result of the high crossslink densities achieved and low mass ranges of the glycols used. The gels may be considered to be close to model crosslinked polymers, in that for fully reacted examples

J.R.M. Giles~Conduction in amorphous polyether electrolytes

the chain length distribution of the starting glycol should determine that between crosslinks in the resultant polymer and is thus well defined and of a relatively narrow range. In addition, Me should be closely related to Mn of the glycol. The narrow chain length distribution between crosslinks for the products is reflected in the well-defined heat capacity steps detected at T8. Similarly the width of the loss tangent peak from dynamic mechanical measurements usually increases as the breadth of the chain length distribution increases [12] and is related to the distribution of relaxation times. In addition, using a ball and spring system immersed in a medium of uniform viscosity as a model for a polymer chain, the distribution of relaxation times for viscoelastic behaviour in a three-dimensional solid (or crosslinked polymer) has been predicted to be narrower than for the linear chain analogue [ 13]. The networks described here are thus close to ideal for the investigation of ion mobility. In terms of simple free volume concepts the dependence of Ts on molar mass and crosslink density may be expressed as T8 = r ~ - g / M ,

(l)

where T~° is the glass transition temperature for the polymer with infinitely high molar mass, M is the average molar mass and K is a constant which may be composed of contributions from the different structural elements in the polymer if additivity of free volumes is assumed [ 11 ]. A description by Chompff [ 14] treats the network as a ternary system of chain ends, chain segments and crosslink points, which can be reduced to an expression similar to that above if M = M ¢ . Here K was interpreted in terms of molecular parameters. For phosphate ester gels a copolymer effect is introduced because of the differing structure of the crosslinking group to that of the polyctber chain segment. This also applies to the difunetional chain linking groups in VI. The effect depends on the flexibility of the crosslinking group and increases as the molar volume of the group is increased. For example, ROPO3(R=Me, Et) is a highly flexible group, in part as a consequence of the P - O bond lengths. The structural unit -(Me2)SiO- is excellent in this respect consistent with the very low Tg of high molar mass linear poly(dimethyl siloxane) of ca. 150 K

159

[ 15 ]. The Tgs for ethyl siloxane and phosphate ester crosslinked PEG(400) prepared by similar routes (I and VII) are given in table 1. While retaining the simple form of eq. (1), the copolymer effect can be allowed for by replacing T ~ with that for the equivalent copolymer of infinite molar mass. 3.2.2. Electrolytes

When I and II contained electrolyte salt, within the O/Li molar ratios used (42 > O/Li> 8), polymer crystallisation and melting events were not detected, so that presence of the salt inhibited polymer crystaUisation. Secondly, for all the complexes examined (42 > O/Li > 4.5), formation of any crystalline or semi-crystalline salt containing complexes did not occur during the timescale of the experiments. Thus the electrolytes may be considered to be fully amorphous. As the salt concentration was increased Tg moved to higher values (table 1), consistent with a reduction in polymer chain mobility. The dependence for I, II and IV for low concentrations is given in fig. 2. The polymer-salt complex may be treated as a random copolymeric system formed between coordinated and uncoordinated segments. Using this analogy Tg should depend linearly on the salt mole fraction as can be shown, and Tg(complex) = Ts (polymer) + fixs[ ~c _ Ts(polymer) ] ,

(2)

where xs is the mole fraction of coordinated ethylene oxide units if a 1:I complex [i.e. (CH2CH20)iLii ~ ] were formed with the salt, (~) is the average coordination number for the lithium ion in the solvate and T~¢ is the glass transition temperature for the corresponding stoichiometric complex, i.e. when vLrs= 1. ~i may vary with salt concentration and trial values may be used to estimate T~. The same arguments would apply to higher salt aggregates such as ion pairs, triple ions and so on. The above equation is satisfactory for low salt concentrations, however at higher values the probability of the occurrence of solvate-solvate diads, in the copolymer analogy, increases. There is evidence to suggest that for the alkali metals individual ions are solvated preferentially by a single PEO chain [ 16 ] and consequently

J.R.M. Giles~Conduction in amorphous polyether electrolytes

160

253

Tg/K

233

? 213

I

I

/,

8

I

102xl.i/0

12

Fig, 2. Glass transition onset temperatures, obtained by DSC (10 K rain- t ) plotted against Li/O ratio for added LiCF3SO3; points ( • ) from I, ( [] ) from II and ( × ) from IV.

the solvation environment around the ion may not be too dissimilar to that of crystalline forms. An effective solvation number of 6-12 is probable [ 16 ]. If this situation is correct then a change in the dependence of TB on salt content would be expected for an amorphous, single phase material as the concentration is increased beyond that which correponds to the average stoichiometry for the solvate at low concentrations. This would correspond to the formation of solvate-solvate diads and probably a change in ion solvation. The rate of increase in Ts against Li/O may be expected to decrease as the relative decline

in chain mobility would be less in comparison with the initial effects of salt addition. If the solvation number were 6-12 and the average chain segment length or chain length between crosslinks were of this order, then it would also correspond to the increasing presence of segments containing more than one solvate. Thus for the polymers described here a change in gradient is expected in the Ts plot as O/Li is reduced below ca. 8. From the results obtained with IV (table 1 ) the decline in gradient occurs at O/Li ca. 13 (the data for higher salt concentrations are not shown in fig. 2). This difference may be attributed to the presence in the polymer of a relatively high content of short chain-length oxyalkane sequences which are possibly not involved in ion solvation at these concentrations. For II no change in gradient in fig. 2 was detected for O/Li>~8; however the preexponential factor, A, in the VTF equation, proportional to the charge carder concentration declined markedly for O / L i = 8 indicating the change in solvation. The behaviour described here may be compared with the result of Moacanin and Cuddihy [2] for poly(propylene oxide) (PPO) complexes with lithium perchlorate. The damping constant and modulus for low molar mass (2025) PPO containing increased amount of LiCIO4 (O/Li >/6) were interpreted in terms of copolymer behaviour with the observed properties a result of a superposition from both free and coordinated polyether segments, giving rise to changes in the distribution of relaxation times as the salt concentration was varied. However, using high molar mass, amorphous PPO in PPOxLiC104 with 1 0 < x < 7 0 the results were consistent with block copolymer formation in that two damping curves were detected as the temperature was increased for a fixed applied torsional frequency; the peak at lower temperature corresponded to the free polymer, the second to that of the solvated polymer. The intensity of the latter relaxation increased at the expense of the former as the salt mole fraction was increased. These effects may result from an increased stability of coordinated helical conformations. As O/Li was reduced below l 0 single phase behaviour returned, there being no free polyether remaining.

J.R.M. Giles~Conduction in amorphouspolyether electrolytes

161

Variation of o(293 K) with O/Li ratio showed a broad maximum for values around 30 corresponding to a concentration of ca. 1 mol dm-3. At these concentrations in a medium of low relative permittivity (cf. 4.5 at ca. 298 K for PEO) ion association phenomena are expected to dominate [ 17 ], with ion pair and triple ion species in high relative abundance. Fuoss and Krauss [ 18] have discussed, the equilibria for triple ion formation and their increased presence as electrolyte concentration is increased, the importance of solvent relative permittivity and the dominance of coulombic forces. If equality in the equilibrium constants for formation of the triple ion species from the ion pair is not assumed, then either the cationic or anionic triple ion may dominate and so the simple counter ion may then be present at a higher concentration than found before the extensive formation of triple ions. The effect is a result of

3.3. Impedance measurements

The conductivity (~r/S c m - 1) values found for the electrolytes examined, were higher over the whole temperature range investigated than for comparable poly(ethylene oxide) LiCF3SO3 complexes. Typical results are displayed in fig. 3 and compared with PEOeoLiCF3SO3 [6 ]. The superiority of the gels is particularly apparent at temperatures below ca, 340 K, as a result of the high crystallinity of the PEO material. If electrolyte salt was not added to an ester (for example, II) then the observed conductivity was strongly diminished, so that conduction as a result of the dissociation of residual hydroxyl groups or other impurities was unimportant. In parallel, the pre-exponential term in the VTF equation (eq. ( 3 )), which depends on the carrier concentration, decreased by several orders of magnitude.

-3.0

00

FE

•

• -4.0

w

O

v

® •

v o

O •

® •

v O

o

v

o v

®

• v

•

o

•

v

®

•

-§.0

•

O O

v

• V

* 2.6

J

t 3.0

Y

J . 103T.I/K_ 1

I 3.4

Fig. 3. Arrheniusplots ofloglo (o/S cm- 1) versusreciprocaltemperaturefor I complexedwith LiCF~SO3,O/Li= 27.6 (Q) or 13.7 ( • ). Results from PEO20LiCF3SO3,secondheatingcycleare also shown ( ~ ) [6].

162

J.R.M. Giles~Conduction in amorphous polyether electrolytes

The temperature dependence of tr, within the range of O/Li ratios examined, did not follow Arrhenius equation dependence, however the results could be interpreted by use of the Vogel-Tamman-Fulcher (VTF) eq. (3).

the requirement of charge balance and the existence of the ion-pair dissociation equilibrium. Blomgren [ 19] has described the spectroscopic (UV-VIS, ESR, NMR, IR and Raman) evidence for the presence of solvent separated or contact ion pairs and triple ions in electrolytes formed from dipolar aprotic solvents, and in particular has discussed the data and theoretical predictions for lithium perchlorate ( ~< 1 mol dm-3) in T H F solution. For most solvents containing a simple dissolved binary salt the maximum in conductivity occurs within a 1.0-2.0 mol dm -3 range at 298 K [20]. The peak in conductivity with increasing electrolyte concentration can be interpreted as the interplay between the rise in carrier ion concentration opposed by a rapid increase in solution viscosity and consequent decrease in average ion mobility. The phosphate ester polymeric electrolytes showed a similar effect.

a = ( A / T ~/2) exp[ - E a / R ( T - To)] .

(3)

This empirical relationship has been applied to conduction in molten salts and originally To was an adjustable parameter [ 21,22 ]. T is the absolute temperature, A a constant and Ea an apparent activation energy. Derivations for the equation may be given within a configurational entropy model (where To is considered to be an equilibrium glass transition temperature, typically Tg- To ~ 50 K) or a modified Free Volume Theory, for ion transport in an amorphous medium. From plots of log a T i/2 against ( T - To) where To is the temperature for the onset of the glass

-2.0

-3.0 I--

0 p

Ot 0 ..p

-4.0

I I0

I

IO$/(T-To)

,

! 14

Fig. 4. Data from fig. 3 for complexesof I with LiCF3SO3replotted accordingto the VTF equation (|Oglo~T t/2 against ( T - To)- a/K- a) with 7"0=229K, O/Li=27.6 (Q) or 13.7 (O).

ZR.M. Giles~Conductionin amorphouspolyetherelectrolytes

transition for the parent polymer, excellent straight line fits were obtained (fig. 4). Both E, and A values thus found increased linearly with lithium salt concentration (fig. 5); A is expected to be proportional to the number of charge carriers and the apparent activation energy should increase with increasing salt content. An exception for the above dependence of A was that of II, O/Li=8, this may result from a change in salt solvation and carrier types as discussed under Calorimetry. The above and caflier [ 9 ] use of the VTF equation with To= Ts(onset) for the parent polymer is unconventional. Usually either To is equated with Ts for the electrolyte or values for E,, A and To are optimised in the linearisation of the conductivity data for each electrolyte, consequently

163

imparting less significance to the results. Using the latter method, there is an isolated report [28] of application of the VTF equation for amorphous PEOsLiCIO4, where after such curve fitting To nearly coincided with the glass transition temperature of the parent polymer. Unfortunately, the corresponding apparent activation energy was equated with the activation energy for the backbone rotational relaxation in PEO, which should be compared with Au of the Adam-Gibbs model as described later. The temperature dependences of the viscoelastic behaviour [23 ] of polymers may be described using the empirical Williams-Landel-Ferry Equation (eq. (4)) where cm and c2 are constants and aT is a ratio of the chosen variable at temperature T and arbitrary reference temperature 7",. -log ar=c~ (T - T,)/[c2+ (T - T,)]

100 50 I I

20 I

10 I

(4)

O/Li

7",may be varied and pairs of the constants c~ and c2 found. However, it can be shown that

8.0 i

-

0

-

0

o

0.5

E

13

-

0

iJ

5.0

U~

[] 0.3

/..0

0.1

I

I

/,

8

I lOZxLi/O

12

I 4

8 . lOZxLi/O

12

Fig. 5. (a)VTF apparent activation energies (E./kJ tool- ' ) as a function of salt concentration expressed as Li/O ratio, for the LiCF3SO3 complexes of I (O) and II (O); (b) VTF equation pre~xponential factor (A/S cm-~K ,/2) plotted against Li/O ratio for LiCF3SO~ complexes of I ( • ) and II ( [] ) . . . . .

J.R.M. Giles~Conduction in amorphous polyether electrolytes

164

T~-c2 = T',- c~= Too, a constant and secondly, c~c2=c;c~= a further constant. Too is equivalent to

To from the VTF equation and is the temperature at which log ar~OV. Here eq. (4) has been applied to the temperature variation of conductivity and from the linear dependence of ( - l o g a t ) -~ against ( T - T,)- I (fig, 6) the constants were evaluated. (For each complex T, was chosen from the position of an experimental point near 298 K and then corrected to T'~= 298 K using eq. (5) and (6) [23]; log (~T/er~) = - - log aT. Fig. 7 shows the variation of log a T = - - l o g ( a T i l T , ) against ( T - T , ) with T~=293 K for electrolytes prepared from I.) cl =cl c2/ [ c~ - ( Ts - T'~)] ,

(5)

c~=c2-(T~-T's)

(6)

.

Most importantly, there was no apparent dependence of Too on salt concentration for the complexes examined (see table 1) and again the values were close ( ~ + 10 K) to T~(onset) for the parent polymer. Thus for the temperature range examined the

important characteristic temperature for ion mobility is that of the glass transition of the parent polymer. The WLF equation may be derived using a configurational entropy model [24] considering the temperature dependence of the size of a region capable of undergoing a cooperative rearrangement, and particularly the minimum critical size of such a region. The average probability of transition is given by, I~(T) =A exp(-AI~c/kTSc),

(7)

where A is an essentially temperature independent factor, A/z is the potential energy barrier or enthalpy per mol hindering the cooperative rearrangement, the critical configurational entropy required by the region and Sc the macroscopic configurational entropy. A minimum of two possible configurations are needed and s* = kin 2 may be used. As the glass transition is approached the rate of molecular relaxation slows as the number of configurations available declines such that equilibrium cannot be maintained (glass formation) and eventually the

3.0

y-t

2.0

1.0

I

I

I

I

50

Io3/(T- T~)

loo

Fig. 6. Graph of [log~o (eTle~;)] -* = y - ~ against ( T - T,) -~/K- ~used to find the constants cl and c2 in the WLF equation. Data refer to II complexed with LiCF3SO3 having O/Li = oo ( • ) , 18.6 ( [ ] ) and 8.0 ( • ) with T~= 302.0, 298.9 and 298.5 K respectively.

J.R.M. Giles/Conduction in amorphous polyether electrolytes

165

0

%, 0

0

V

-0.5

0 0

g"

0

o

~o 0 •

-1.0

O

•

O v

0 I 10

I 20

I 30

~IIT-Ts~/K

I ~0

Fig. 7. Plot of the WLF equation shift factor [log,oar= -log (or/a r,)] against ( T - T,)/K for I eomplexedwith LiCFaSO3and O/Li= 13.7 (O), 27.6 (O), 35.8 (XT)and 41.4 ( , ) . Here/',=293 K.

(extrapolated) dynamic configurational entropy reaches zero, now the whole sample represents the minimum rearranging region. At this point a secondorder thermodynamic transition is defined occurring at a temperature T2, which is often found to be ca. 50 K below the experimentally observed Ts, corresponding to log a r = l o g ( z r / z r , ) - * o v , i.e. Too. The relaxation time (z) is inversely related to I~'(7") and using S o ( T 2 ) = 0 and ACp as the configurationally derived heat capacity difference between the equilibrium melt a n d glass at Tg, a WLF-like equation can be found giving rise to expressions for the corresponding constants am and a2" aj = 2.303Al~c/ACpkTs In( T J T 2 ) ,

(8)

a2 = T~ln( T J T 2 ) / [ 1 + ln(Ts/T2)].

(9)

a2 is slightly temperature dependent so that eq. (9) is an approximation *./'2 can be found using either * As c,c~ is a temperature invariant constant of the system,then a, should also be temperature dependent. (ref. [29 ].)

T'~- ¢2 = Too, as above, or by use of eq. (9). With a value for T2, a~ can be used to find (Ap/ACp). The ratio is plotted along with the corresponding c~ values (T's=298 K) for II as a function of Li/O in fig. 8. If a typical [ 24 ] range for ACp is 50-150 kJ toolthen A/z is in the region of values consistent with molecular conformational rearrangement activation energies (ca. 15 kJ t o o l - l ) . Furthermore, if the backbone rotational relaxation activation energy [ 25 ] for PEO (10.3 El mol - t ) is taken as a minimum for Au then this value should be approached when O / L i = or. Using a direct substitution in the example of II where O / L i = oo then a value for ACp may be found. From fig. 8, ACp ~ 100 J K - ~tool- ~. The linear dependence of (A/dACp) with Li/O can be understood as the presence of an increasing potential energy barrier for ion motion consistent with lowered polymer chain flexibility, increased viscosity and coulombic interaction between the ions of the electrolyte. Both Ap and ACp would be expected to increase as effective interactions between polymer

J.R.M. Giles~Conduction in amorphous polyether electrolytes

166

200

(.cp)

4.0

100

I

/,

i

8

I

12

102xLi/O

Fig. 8. WLFequationconstantc'( T~=298 K) plottedagainst LifO for LiCFaSO3complexesof II (D). For the same set of electrolytesthe variation of (&u/ACo)/Kwith Li/O is given ( , ) . chains increase. Thus cl from the WLF equation has an activation energy component and this is more obvious if the expression is rearranged - l o g aT =CI( T - - Ts)/( T - Too) , or

log aT = E ' + F' /( T - Too) , where E' = - c , and F' =c,c2. The salt concentration dependence of c'~ parallels that of Ea from the VTF equation. A further set of activation energies can be determined from the near-linear temperature dependence in fig. 3 shown by the electrolyte conductivities above 333 K. The Arrhenius equation can now be applied and the values found (AE) are listed in the table. A similar linear dependence of AE on Li/O to that of Ea and c'~ is apparent. All the activation energy data here refer to single phase systems and therefore can be considered of greater significance than values obtained from electrolytes formed from high molar mass poly(ethylene oxide) where the results are complicated by the presence of several phase equilibria, and thus the apparent values measured should reflect the combined

effects of crystalline phase dissolution equilibria, carrier concentrations and ion mobilities. A number of temperature domains characterised by the dependence of conductivity of the polymeric electrolytes may be defined. Firstly, a high temperature region, beginning above Ts(polymer) + 100 K, in which Arrhenius or near-Arrhenius behaviour is found, as just described. Next a region of dependence where the apparent activation energy is t e m perature dependent and the WLF and VTF equations may be used. Here To= Too= T2 = Ts(onset) of the parent polymer. As the temperature is reduced divergence from VTF equation dependence must occur, as In a T ~ / 2 - . - o v when ( T - T o ) - * 0 . In this third region the conductivity will be higher than predicted by the VTF equation, and a return to Arrhenius dependence may be expected. At the glass transition for the complex a decrease in gradient for the Arrhenius plot should occur as the medium becomes rigid, so that the material passes from what may be considered as a soft-framework conductor to an ion-hopping conductor. Miyamoto and Shibayama [26] have examined the behaviour of polystyrene and poly(methyl methacrylate) samples at near the glass transition temperature and found such Arrhenius or near-Arrhenius behaviour. In conclusion, a series of amorphous LiCF3SO3 complexed poly(ethylene glycol) phosphate esters have been examined as electrolytes by DSC and ac impedance methods and found to possess superior ionic conductivitics, particularly at ambient temperatures, when in comparison with related PEO solrates. Similar behaviour is shown by siloxane bridged poly(ethylene glycol) s [ 8 ], and related ABA triblock copolymeric electrolytes have been described [27 ].

4. Summary Phosphate ester chain extended and crosslinked poly(ethylcnc glycol) oligomers and gels have been prepared by a condensation reaction route using chlorophosphates. The preparative method allows ready control of the polymer structure and crosslink density. Thin-film electrolyte complexes formed with lithium trifluoromethanesulphonate were fully amorphous and showed enhanced conductivity over comparable PEO solvates in the temperature range

J.R.M. Giles~Conduction in amorphous polyether electrolytes

293-373 K. A conductivity maximum was seen at concentrations of ca. 1 tool dm -3 consistent with the interplay of increased charge carrier densities opposed by increased medium viscosity. The temperature dependence of conductivity for each O/Li ratio used, obeyed the Vogel-Tamman-Fulcher and Williams-Landel-Ferry equations with Ts(onset) for the parent polymer as the ideal glass transition temperature, demonstrating the importance of polymer chain cooperative rearrangements in the mechanism of ion conduction. The activation energy parameters from use of the VTF equation and the Adam-Gibbs configurational entropy model showed a wellbehaved linear dependence on salt concentration.

Acknowledgement The author wishes to thank Mr. M.P. Greenhall for his assistance with the preparation of polymers while a vacation student at the Royal Aircraft Establishment.

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