Correlation among transport properties in ionically conducting cross-linked networks

Solid State lonics 14 (1984) 231-237 North-Holland, Amsterdam

CORRELATION AMONG TRANSPORT PROPERTIES IN IONICALLY CONDUCTING CROSS-LINKED NETWORKS * A. KILLIS, J.F. LE NEST, A. GANDINI, H. CHERADAME Ecole Franfaise de Papeterie, B.P. 65, 38402 St. Martin d'Hdres, France and

J.P. COHEN-ADDAD Universitd Scientifique et Mddicale de Grenoble, B.P. 53 X, F-38401, Grenoble, France

Received 4 July 1983 Revised manuscript received 2 February 1984

Examination of the quantitative correlation between the ionic conductivity and the dynamic mechanical properties of cross-linked polyether networks filled with an inorganic salt supports the assumption that mobile ions and chains segments need the same free volume fraction for their diffusion. The spin-spin relaxation time of the different nuclei belonging either to the macromolecular chains or to the ionic species exhibits the same free volume dependence. From the study of the conductivity variations with respect to salt concentration it is concluded that its dissociation is probably complete even at relatively high concentration.

1. Introduction Interest in research concerning solid electrolytes is growing due to potential applications of these materials in electrochemical primary or secondary generators. Numerous studies have been carried out on linear high molecular weight polyethers filled with inorganic salts, and particularly on their electrical properties, their electrochemical properties [ 1 - 8 ] , and their structure [9-11]. We wish to deal here with a new class of solid amorphous electrolytes consisting of polyurethane networks filled with inorganic salts. We have been involved in a systematic study of the relationship of the conductivity of such materials with their viscoelastic properties and the spin-spin relaxation times by NMR spectroscopy, in order to determine the fundamental parameters governing the conductivity. The main purpose of the present work is first to establish a correlation among the above transport properties in ionically conducting networks, * This paper was presented at the 4th Conference on Solid State Ionics, Grenoble, 4-8 July 1983.

and then to reach a better understanding of the state of the inorganic salts, i.e. their degree of dissociation and aggregation.

2. Experimental 2.1. Polyurethane synthesis

These preparations used the classical technology of polyurethane synthesis, the polyethers studied behag polyoxyethylene, M -- 400 and 1000, polyoxypropylene M -- 425, the crosslinking agent p, p', p" trisocyanate-triphenylmethane and the salts: sodium tetraphenylborate NaBPh4, lithium perchlorate LiC10 4 and lithium trifluoromethanesulfonate LiCF3SO 3. After the salt dissolution into the polyether with the help of small amount of dichloromethane, the isocyanate is added in stoichiometric quantity, in the presence ofO.1 ml of stannic dibutyldilaurate, under dry nitrogen. The reaction medium is then placed in a mould which is made up by two glass plates separated by a silicone-rubber joint of known

232

A. Killis et al./Correlation among transport properties in ionically conducting cross-linked networks

thickness. After the reaction medium is transformed into a more or less tough membrane, it is dried under nitrogen at room temperature, then at 60°C in vacuum.

5

100 lla/O 0 Q52 1.03 1.71 3A4

I ~ aT

4 3

a 0 v

* •

2

2.2. Characterisation o f networks

1 0

Conductivities were obtained b y complex impedance measurements (transfer function analyser Schlumberger Solartron 1174). The viscoelastic measurements were made with a Rh6ovibron DDVII viscoelasticimeter. NMR spectra were run on a Brucker W.P. 100 spectrometer. Glass transition temperatures were determined with a differential scanning calorimeter (Dupont 990).

3. Results and

-1 -2 ql

IT-TQ)'I:

,

*3

~a ! -25

o

| 50

2~1

Fig. 2. Variation of the shift factor log a T with the reduced temperature T - Tg for PEO-based networks containing different amounts of NaB(C6Hs) 4. The line was drawn following calculations based on the WLF relation wih C1 = 12.5 and C2 = I00.

discussion

3.1. As shown in fig. 1 the frequency-temperature principle o f equivalence is observed with our networks (taking the glass transition temperature as reference temperature). A good agreement is observed between the experimental shift factor log a T and the theoretical one given b y the well known Williams, Landel and Ferry (WLF) relationship [12]:

log E"

:¢

=7///

f

loga T = -CI(T-

Tg)/(C 2 + T -

Tg),

when C 1 = 12.5 and C 2 = 100 (figs. 2 and 3). 3.2. The Arrhenius plots o f the conductivity o f the same polyether networks Idled with NaBPh 4 are shown in figs. 4 and 5. It is clear that the conductivity o f these materials does not follow an Arrhenius behaviour in the temperature range studied. In a previous paper, we showed that the conductivity o f our materials follows instead free volume behaviour [13]. A similar study has been initiated b y other authors in the case of high molecular

,....,o,. 100. ~ ' / 0

5t I*°~r 4

2

A

A

~

0 1.03

• •

S.I 4

v

1 o -1 -2 -3

Fig. 1. Storage modulus isotherms versus frequency and the master curve obtained with TO = 26°C and (100 Na/O) = 1.03 for PEO-based networks.

~T-~I ~:

Fig. 3. Same as fig. 2, but for PPO-based networks.

A. Kiilis et al./Correlation among transport properties in ionically conducting cross.linked networks

b

• NalO

233

o

501 344

-5 171

o -5

1(}3

052 075

-7

i

I

2.5

I

I

2.7

I

i

.

2.9 ~3 [x'~

Fig. 4. Arrhenius plot for the conductivity of PEO 400-based networks containing different amounts of NaB(C6Hs) 4.

weight polyethers Idled with inorganic salts [3,14-16]. The free volume concept has been applied by Cohen and Tumbull [17] to diffusion processes in polymers as follows:

i

2.5

I

I

2.7

4

l

~ooo/'r I~ )

for the diffusing particle. As usual, if it is assumed that the free volume varies as: f=fg + or(T- Tg),

where fg is the free volume fraction at the glass transition temperature, and ~ is the free volume thermal expansion factor, then D = D 0 T exp [-Tf*/(fg + 0/(T - Tg)].

where

Eq. (1) can be written in the reduced form:

A and B being constants characteristic of the system studied,f* the critical free volume fraction, i.e. the volume necessary for the movement of the considered particle or i o n , f the mean free volume fraction at T, and 7 a geometrical factor taking into account the overlapping of free volume elements. In the case of networks the viscosity r/loses physical significance and must be replaced by the local friction coefficient

I

Fig. 5. Arrhenius plot for the conductivity of PPO 425-based networks containing different amounts of NaB(C6Hs) 4.

D = BRT/r/,

= A exp [(Tf*)/f] ,

I

2.9

(1)

log(D T Tg/DTg 70 = (Tf* /2.3 fg)

× T - rg/[(fg/a) + T - Tg] = - l o g a T , where log a T is the WLF shift factor loga r = - C l ( T -

Tg)/(C 2 + T - Tg),

with C 1 = 7f* /2.3fg and C 2 = fg/~.. In the case of our networks Filled with an inorganic salt three diffusing species must be considered:

234

A. KiUis et al./Correlation among transport properties in ionically conducting cross-linked networks

(a) polymer chain segments whose diffusion is characterised by a free volume fraction fl~, (b) cations, characterised by a critical free volume fraction fc, (c) anions, characterised by a critical free volume fraction fa" fg, a, Tg and 3' can be assumed to be independent of the nature of the species involved in a diffusion process. Then eq. (1) in the case of chain segments becomes: log(Dp, r Tg/Dp, r gT) = (3"fp /2.3fg) X T-

Tg/[Oeg/OO + T -

Tg] .

(2)

The mobility of chain segments with temperature can be expressed following the WLF law, determined by the dynamic mechanical properties as: log(Dp, T Tg/Dp, Tg T) = -log(aT) m .

(3)

Combining eqs. (1), written for cation diffusion, (2) and (3) we obtain: l°g(Oc, T Tg/Dc, Tg 7") = -- ( f c / f p ) l°g(aT)m

we obtain:

Or/Org = Oa" rg(ar)mJa~*V* Jp + Dc ' Tg(ar)- f,*V* c Jp

x W~ rg + Dc, rg)- 1

When the conduction is the result of the predominant migration of one ionic species, eq. (6) becomes:

log(oT/OTg ) = _ ( f * /f p) log(aT)m . It must be noticed that if the free volume fractions fa and fc have about the same magnitude eq. (6) becomes: £ */~*

Or/arg = K ( a r ) m J

JP .

Fig. 6 shows the variation of the logarithm of the conductivity as a function of the mechanical shift factor. The linearity of this plot suggests the following conclusions: the conductivity and the dynamic mechanical properties are correlated through the same dependence on the free volume. The characteristic pa-

(4) % Na/O : 3.44

and l°g(Oa, T

(6)

TglDa, rgT) = -Oralf p) log(aT)m .

(5)

Ionic conductivity is a transport process initiated by the presence of an electric field. At low values of the field thermal fluctuations control the ionic mobility and thus a free volume theory describes adequately the ionic diffusion. The well-known Nernst-Einstein relationship defines the conductivity of a given species at concentration n i and with a diffusion coefficient D i and charge q:

ai =Diniq21RT. Taking into account cationic and anionic conductivity, the preceeding relationship gives

-5

o~ - 6 0

-7

/

cr = ( D a + D c ) n q 2 / R T .

Assuming that the influence of the temperature on the charge carriers concentration is negligible, by comparison with its influence on the diffusion, it follows that

aT/OTg = (D a + De) T Tg/(D a + Dc)Tg T. Introducing eqs. (4) and (5) in the above expression

!

I

3

4

- l o g ( a T ) rn

Fig. 6. Correlation between the logarithm o f the ionic conductivity and the WLF shift factor determined from d y n a m i c mechanical data for a PEO 400-based network containing NaB(C6Hs)4 .

A. Killis et al./Correlation among transport properties in ionically conducting cross-linked networks Table 1 Characteristics of the examined networks.

4

Polyether

Na/O (%) a)

Tg/*C

dlog o d log(aT) m

PEO 400 b)

0 0.52 1.03 1.71 3.44 5.01 0 1.03 1.70 3.39 5.14

25 23 26 31 40 45 40 46 57 65 69

0.53 0.60 0.86 1.25 1.08 1.10 0.91 0.72 0.74 0.62 0.69

PPO425 c)

a) Percentage of Na + ions to ether O atoms. b) Polyethyleneoxide glycol/d-'- 400. c) Polypropyleneoxide glycol I~= 425; for all other symbols see text.

rameters of the linear correlations are shown in table 1. The slopes are close to unity in most eases: this means that mobile ions and chain segments need the same free volume fraction for their diffusion.

3.3.

NMR experiments give information on the dynamics of the mobile species. We have studied spinspin relaxation times T 2 against temperature for different nuclei. Fig. 7 shows the variation of the 713 NMR linewidth in a network based on POE 400 containing 13C104. When the temperature increases

II

°e

o

3

v~

'2

235

B

2-

~O_o

-2

•

~

-100

•

0

~ooo

T-lo

(K'~I

100

Fig. 8. Free volume plot of 7Li linewidth, with To = 323 K, for a PEO 400-based network containing LiCIO4 (LifO = 0.034).

a narrowing is observed due to increased ionic mobility. The variation of the reciprocal logarithm of the reduced linewidth [log(8 To/8 T)] -1 against 1/(T- TO) for a reference temperature T O = 323 K is shown in fig. 8. The observed linearity is the consequence of the free volume dependence expressed as a WLF relationship. It follows that there is a linear correlation between the conductivity and the 7Li NMR linewidth as shown in fig. 9. Using the same technique the mobility of polymer and anions was studied in the case of a network based on POE 400 containing LiCF3SO3, and compared to the lithium ion mobility as shown in fig. 10. From this study it can be concluded that the three species behave in the same way with respect to temperature variations. It can be concluded that the movements of chain segments allow the same relaxation time variations through free volume fluctuations.

T Ixl

3.4. Study of the salt dissociation Fig. 7. Variation of the 7Li and IH linewidth with temperature for POE 400-based network containing LiCIO4.

In order to allow a complete study of the eonduc-

A. KiUis et al./Correlation among transport properties in ionically conducting cross-linked networks

236

m

o

I 1

log

I 2

ST"

6T

Fig. 9. Correlation between the reduced ionic conductivity and the reduced linewidth at TO = 323 K for a PEO 400based network containing LiC10 4 (Li/O = 0.034).

•

1H

•

19 F

•

7Li

•

tivity properties of our materials the dissociation state of the salt must be known as well as the respective ionic transport numbers. The dissociation can be studied by conductivity measurements. Calling Va and Vc the respective mobility of the anions and cations, assuming the same valence, the conductivity can be written as o = n(V a + Vc)q, where n is the number o f charge carders, equal to C0a , a being the degree of dissociation of the salt. Then o = C 0 a ( V a + Vc) q. It must be noticed from the above study that the mobility must not vary when considering the conductivity at constant reduced temperature T - Tg, at least in the range where a WLF behaviour is observed. The conductivity variations with salt concentration are shown in fig. 11 on a log-log ptot. We observe a direct proportionality between conductivity and concentration at constant reduced temperature since the slope of the straight lines obtained is close to unity.This result implies that the degree of dissociation is constant over the range where the proportionality is observed and independent o f the salt concentration. The simplest interpretation o f this result is that the dissociation of the salt is complete or nearly complete despite the relatively low dielectric constant of POE (e ~- 8).

•

T-Tg

.~

i

i

-4

a m

t~ o •

m u

-5

Q

oO° -6

,~/"r tiC-'t; Fig. 10. Variation of the 1H, 19F and 7Li linewidth with temperature for POE 1000-based network containing CFaSOaLi.

log ¢ Fig. 11. Log-log plots of the ionic conductivity versus the salt concentration at constant T - Tg for POE 400-based networks containing LiCIO4.

A. Killis et al./Correlation among transport properties in ionically conducting cross-linked networks

1, ~

SO*c

~

Y

4 ~

237

segments are correlated through free volume fluctuations. This means that the same free volume allows the movements of the chain segments, the anions and the cations. The dissociation o f the salt is complete at least at concentrations lower than ~1 mole/kg. At higher concentration the systems begins to suffer phase separations which drastically reduces the mobility o f the chains.

Acknowledgements The Soci6t6 ELF-AQUITAINE and the Direction des Recherches Etudes et Techniques are thanked for financial support. - I

-0.5

0 log

OS

c

Fig. 12.7Li NMR peak area (A) and ionic conductivity (tr) at 60°C versus salt concentration (c) for POE 1000-based networks containing LiC104.

Networks based on POE 1000 exhibit a drastic conductivity fall when the salt concentration reaches a value o f 1 mole Li+ per kg (Li+/O = 0.05). It is worth noting that this concentration corresponds to one cation per chain of POE 1000. We postulate that above this salt concentration a new phase is formed corresponding to chain segments associated with more than one cation. This assumption is supported by the appearance o f a second peak on the curves showing the variations o f the loss tangent against temperature when Li/O > 0.05. The variation of the NMR peak area for the 7Li nuclei versus salt concentration, fig. 12, also shows that when the Li/O ratio is higher than 0.05 there is a change o f the relaxation conditions in the network.

4. Conclusion This work aimed at elucidating the mechanism which is at the origin of the peculiarities of the transport phenomena in polyether networks containing ionisable salts. Another goal was the determination o f the dissociation state o f the salts. We have shown that the conductivity, the viscoelastic properties and the spin-spin relaxation times o f nuclei belonging either to the salts or to the chain

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