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Entropy effects on conductivity of the blend-based and composite polymer solid electrolytes
SOLID STATE
Solid State lonics 53-56 (1992) 1064-1070 North-Holland
IONICS Entropy effects on conductivity of the blend-based and composite polymer solid electrolytes Wtadystaw Wieczorek Institute (2flnorganic Technology, Warsaw UniversiO~qf Technology. ul. Noakowskiego 3, 00-664 Warszawa. Poland
The Meyer-Neldel rule is applied to describe the relation between the pre-exponential factors c~oand activation energies of various blend-based and composite polymeric electrolytes for which the temperature dependence of the conductivity satisfies the Arrhenius law. It is shown that for these electrolytes changes of ionic conductivity come from the variation of the migration entropy term. The correlations between the entropy of ion migration, phase structure and phase transitions are discussed. The physical meaning of the temperature TD calculated from the Meyer-Neldel equation is proposed.
1. Introduction
In o0 = A S , 1 , / k + l n K v o .
(2b)
It was previously found that for a wide range of fast ionic conductors the magnitudes of the pre-exponential factor and activation energy are connected by the M e y e r - N e l d e l rule [ 1-4 ] which can be written in the following form:
For a range o f materials, the entropy o f ion migration and enthalpy o f activation are related according to the following equation:
In o0 =c~Ea +[3.
This equation was originaly developed by Dienes, and the value TD represented for metals the melting point of the metal concerned. For fast ionic conductors this temperature usually corresponds to o r d e r - d i s o r d e r transitions in the mobile ion sublattice. By combination o f e q s . ( 2 b ) and (2c) we obtain
(1)
The M e y e r - N e l d e l equation (often called the C o m p e n s a t i o n Law) was firstly applied by Dienes to describe the dependence between the diffusion frequency factors and the activation energies for atomic diffusion in metals [5 ]. Recently A l m o n d and West [1] described the application of the rule for a description of the correlation between the pre-exponential factors and activation energies, calculated from the Arrhenius equation (2), for various solid ionic conductors: ~=aoT
]exp(-Ea/RT)
.
(2)
The pre-exponential factor cro can be described by the following equation: ao = Kvo exp A S m / k ,
(2a)
where K is the concentration term, k is the Boltzmann constant, Vo is the ionic oscillation frequency, ASm is the entropy o f ion migration, and hence
E J TD = ASm .
In a0 = E a / k T D + In Kvo = c~E~, + [3,
(2c)
il)
where c~= 1/kT~ and f l = l n Kv0. It was previously shown by the authors [6] that the rule is also valid for some composite polymeric electrolytes based on the P E O - N a l system with dispersed SiO2 particles. Since various blend-based and composite polymer solid electrolytes also satisfy the Arrhenius equation (especially at temperatures lower than the melting point of the crystalline PEO phase ) I would like to examine the applicability of the M e y e r - N e l d e l dependence in such systems. The aim o f the present paper is to correlate the effects of entropy on the conductivity with the phase structure of the polymeric electrolyte. The physical meaning of
0167-2738/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
W. Wieczorek/ Polymersolid electrolyte the Dienes temperature To calculated from the dependence described is also discussed.
1065
chemical potentials of a particle (i) belonging to the amorphous and crystalline phases at temperature T= TD are described by the equations (4a) and (4b) respectively:
2. Experimental
TD
Polymer electrolytes were prepared in the form of thin films by a casting technique. Details of the preparation procedure were described elsewhere [6,7]. The ionic conductivities of the samples were measured by impedance spectroscopy. The electrolytes were pressed between stainless-steel blocking electrodes. The experiments were performed in a frequency range from 5 Hz to 500 kHz and the temperature of the samples varied from ambient temperature up to about 373 K. All the experimental data were analyzed using an IBM PC XT microcomputer.
3. Physical background According to the assumption of Almond and West [ 1 ] the Dienes temperature TD is the temperature at which the difference between the free-energy of ions belonging to the ordered and disordered phases falls Io zero. In respect to semicrystalline polymeric electrolytes this means that the chemical potential of the ionic particles belonging to the crystalline phase becomes equal (at TD) to that of the particles belonging to the amorphous phase. The temperature dependence of the chemical potential of an ionic particle (i) is described by the following formula: T
,u,(T)=,u,(To)- j S,dT,
(3)
TO
where #,(T) and #,(To) are the chemical potentials of the particle i at temperatures T and To respectively and S, is the partial molar entropy of the substance (i) in the described phase. [Eq. (3) is valid for p, (, ~=const, where 0 is the Galvani potential and p, ( have their usual meanings. ] I intend to assume a very simple physical model and describe separately the chemical potential of the species in the amorphous and crystalline phases. I presume the temperature To to be equal to the glass transition temperature of the electrolyte 7g. Then the
#~a(TD)=,Uia(Tg ) - f S~adT-=flia(Tg ) Tm
TD
- f Si~dT- fSi~dT,
(4a)
Tm
TD
,ux(TD)=#,~(Tg)- f S,i~dT- f S2,~dT, (4b) 7~
7"~
where Sia is the partial molar entropy of a particle belonging to the amorphous phase, S~i~, $2,c are the partial molar entropies of a particle belonging to the crystalline phase at temperatures below Tm and above T,, respectively. (Tm is the melting temperature of the crystalline electrolyte phase). Since at TD ,U/a( T D ) = ,U,c( T D )
(5)
then Tm
ID
7~
7m
#,~( T~)Tm
TD
7g
Tm
(6) Assuming the abovementioned definitions of molar entropies for electrolytes with unmodified amorphous phases [ofa flexibility ( Tg value) comparable with the pristine PEO amorphous phase] S,a=S2,c and hence Tm #ia(Tg)--
Tm
f StadT=~ic(Tg)-
f SlicdT
rg
Tg
(7)
it implies that #ta(Tin) --#it(Tin) and hence TD= T~. The same mathematical procedure should be performed for all kinds of charged and uncharged species of the system described and, as can be easily recognized, leads to the same conclusions. For systems in which Sia#S2i c the eq. (6) can be rewritten in the following form:
Hi Wieczorek/Polvmersolidelectrolvte
1066
,8) l~,
l'm
Assuming that S,a and Sxi~ are constant in a temperature range between TD and Tin, the formula describing the Dienes temperature can be written in the following form:
Tr~=Tm+[lZi~(T.n)-IL,.(Tm)]/(S:,c-S,.).
(9)
In a quasi-equilibrium conditions
,u,":~.(T) =,u*. (T)
(10)
]l,* is the electrochemical potential of the ionic particle (i) which is equal to:
l~Ta(T) =/t,a(T) +zFO,a
( 1 la)
,a,*~(T)=.a,~ (T) +zFO,~
(1 lb)
for amorphous and crystalline phases respectively. According to these equations as well as eq. (5) O,,=O,c
(at T = T ~ ) .
(12)
Eq. ( 12 ) ilustrates that at TD the galvanic potentials of the amorphous and crystalline phases become equal. This assumption is in good agreement with the impedance spectroscopy data showing a distortion of the high-frequency semicircle for semicrystalline polymeric electrolytes. The distortion may be connected with the occurence of interfacial capacitance which comes from differences between the Galvani potentials of ions belonging to the crystalline and amorphous phases. For systems with a single amorphous phase or semicrystalline electrolytes at temperatures exceeding the melting point of the crystalline phase, such distortions are usually not observed. In my opinion, this oversimplified model indicated that the Meyer-Neldel rule should be generally valid for semicrystalline polymeric electrolytes. This assumption results from the fact that the differences between the melting temperatures for a set of electrolytes consisting of the same components but of different composition are small (indicated by the results included in table 1 ). Moreover for systems for which 7]~4: T..., the differences of molar entropies are also negligible which can be confirmed by the small differences of the glass transition temperatures. In
the experimental section I would like to examine the applicability of the Meyer-Neldel rule to the number of semicrystalline polymeric electrolytes with modified and unmodified amorphous phase.
4. Results and discussions
In the first step, changes of In ~ as well as thermodynamic function values after addition of an inert polymer [poly (methylmethacrylate)-PMMA] to PEO-alkali metal salt matrices are analyzed. Fig. la and Ib represent the relations between In a~ and the activation energy for PEO-PMMA blend-based polymeric electrolytes doped with LiCIO4 and Nal respectively. As can be seen, both systems satisfy the Meyer-Neldel dependence. Fig. 2a and 2b show the changes of room-temperature conductivily, activation energy, migration entropy and pre-exponential factor versus concentration of added PMMA for systems doped with LiCIO4 and Nal respectively. As can be seen, samples of the highest room-temperature ionic conductivity are characterized by the lowest values of AS,l, E,~ and In ~o- Similar relations were also found for other systems studied (see table l ). The values of the migration entropy found for PEOPMMA-LiC104 systems are about 50-100 J K ~ lower than for the analogous NaI-doped electrolytes. This fact can be connected with the values of the room-temperature conductivity, which for LiCIO4doped electrolytes were about 5-7 times higher. Fig. 3 shows evidence for the Meyer-Neldel relation for PEO-NaI-0-AI203 "'mixed phase" electrolytes. An Arrhenius plot of the temperature dependence of the conductivity for the samples used in the calculations is shown in fig. 4. Fillers of different grain sizes were used as additives. As is evident from fig. 4, the conductivity decreases with increasing size of the particles used. The value of 7"~ calculated from the Meyer-Neldel equation is equal to 358 K, which is 15-20 K higher than the melting point of pristine PEO phase in PEO-Nal electrolytes. The explanation of this behaviour should concern the two following observations: (i) the strong dependence of the structure and transport parameters on the size of particles used: (ii) the facilitation of ionic transport in an electrolyte containing 0-A1203 of grains lower than 2 lam.
V~ Wieczorek / Polymer solid electrolyte
1067
Table 1 Thermodynamic parameters of the studied blend-based and composite polymer solid electrolytes. Sample studied
(PEO)IoNal acetonitrile a) (PEO) ~oNaI nitromethane a) (PEO)IoNaI CH3OH+CH3CN .i PEO-PMMA 9:1 + 10% mol LiC104 PEO-PMMA 8 : 2 + 10% mol LiCIO4 PEO-PMMA 7:3 + 10% tool LiCIO4 PEO-PMMA 6 : 4 + 10% mol LiCIO4 PEO-PMMA 5 : 5 + 10% mol LiCIO4 PEO-PMMA 9 : 1 + 10% mol Nal PEO-PMMA 8 : 2 + 10% tool Nal PEO-PMMA 7 : 3 + 10% mol Nal PEO-PMMA 6 : 4 + 10% mol Nal PEO-PMMA 5 : 5 + 10% mol Nal PEO-SPMMA 7 : 3 10% mol LiCIO4 PEO-IPMMA 7 : 3 10% mol LiCIO4 PEO-IPMMA 8:2 10% mol LiCIO4 (PEO) ioNaI + 10% wt 0-A1203 grain size 2 ~tm (PEO)toNaI+ 10% wt 0-A1203 grain size 4 ~m (PEO) i oNaI + 10% wt 0-AI203 grain size 7 ~tm ( PEO ) ~0LiCIO4 30% wt plast, b) ( PEO ) ~oLiCIO4 40% wt plast, b) ( PEO ) joLiCIO4 50% wt plast, b)
E~ (eV)
Sa (JK
In ao
7~ (K)
CrRT ( S c m ~)
T~ (K)
Tm (K)
1.28
356
35.5
346
1.5X 10 v
249
338
1.05
293
27.2
346
4.0 X 10- 7
249
341
1.50
418
42.2
346
1.1 X 10 -7
249
339
1.19
341
32.0
337
2 . 4 X 10 - 6
0.82
234
19.0
337
3.0 X 10 -6
240
338
0.72
205
16.0
337
7 . 3 X 10 - 6
248
336
0.68
196
14.8
337
1.0× 10 -5
260
336
0.69
197
14.2
337
3 . 8 X 10 _6
0.92
273
22.0
324
1 . 8 X 10 - 7
1.04
311
26.5
324
2.0X 10 -7
1.04
309
25.7
324
1 . 2 X 10 - 7
0.98
293
22.6
324
4.7X 10 -8
0.86
257
18.9
324
1 . 6 X 10 - 7
0.55
156
10.3
341
1.4X l0 -5
249
338
0.49
132
9.8
361
9.0)< 10 -5
220
330
0.62
165
13.6
361
3.8X 10 -5
216
328
0.70
189
15.5
358
1.4)< I0 -5
328
0.95
259
22.7
358
3.3 X 10 -7
326
1.40
375
35.5
358
2.0X 10 8
325
0.80
209
19.9
371
6.1 X 10 - 6
0.78
203
19.3
371
9 . 9 × 10 - 6
0.60
156
13.8
371
5.1X 10 5
')
a) Solvents used for the preparation of PEO-based electrolytes. 6) Plasticizing phase consisting of grafted PEO-PMMA copolymer obtained by hot rolling of both components at 453 K. Ea = activation energy of conduction process; Sa = migration entropy of charge carriers In ao= logarithm of the pre-exponential factor calculated from the Arrhenius equation To = characteristic temperature calculated from the Meyer-Neldel relation; aRT = room temperature ionic conductivity of the studied samples Tg=glass transition temperature; Tm = melting temperature of the crystalline electrolyte phase.
1068
I4/~ Wieczorek / Polymer solid electrolyte tn~olSK/cm] In ~o[SK;cm]
z, ~,
/
36
(b)
6
,/
(a)
/ 40
30
// //'
3O
Q
20
o
c~'
14,
'90
2O
I
0i7
i
1.0
1.3
~
,
1.5 E ~ [ ~ , ;
,
1.0
ll.4
12
i
1.6 E~[~V]
Fig. 1. Plots of log conductivity pre-exponential factor against activation energy for: (a) PEO-PMMA-LiCIO4; (b) PEO-PMMA-Nal blend-based polymeric electrolytes of various blend compositions. The concentration of alkali metal salts is equal to 10 tool% with respect 1o the ethylene oxide molecular unit concentration.
(b)
i m~oISK
c~l
35
(a)
40
'°~ ........ o
tgg [s/cm]
3C
-66 o o
-5.0
o
30
o
o
-7,0
o
o
20 o
o
o
o
o o
o
20
o
-6.(]
o
14 1'0
3•
o
50' [ °'°wt "m~.tM~t
10 '
3'0
-7.6
50 ' [°'o wt P~4 MAI "
3'0
10 '
5 0.
°.'owt . pMMA; .
10 . S,
i Eo [ ~
340
o
300
So
.
50 °,o~qP & A}
30
J,K
iJ;Kt
:,t
1.6
360
13
300 1.C x
o
o
o
1.0 0.7
¢7 10 '
310
200 50' {eewt PMMA] ~
ll0
x
"x
310
510 [e/ewt PM MA]
o o 110
220
3;
50:%
.....
10
3'0
5101°/° wt P MMA]
Fig. 2. Composition dependence of: ionic conductivity at 293 K, log conductivity pre-exponential factor, activation energy, activation entropy for: (a) PEO-PMMA-LiC104; (b) PEO-PMMA-Nal blend-based polymeric electrolytes. The concentration of alkali metal salts is equal to 10 tool% with respect to the ethylene oxide molecular unit concentration.
W.. Wieczorek / Polymer solid electrolyte In ~[.gf( I¢ m ]
1069 tn ~ o l S K / c m l
/
44 4C
o/
36
30
/
20
/ /
/
20
,°,j
10
/
i
0.7
110
L
1.3
116 E.l,v]
Fig, 3. Plots of log conductivity pre-exponentialfactor against activation energyfor (PEOjoNaI-10 wt% of 0-A1203 polymer electrolytes of various grain sizes, of ceramic powder. l Log ~[S-cm-,] -3 "
A
oe D o •
-4
o•
o
o" •
-5 .6
o o
D fl
-6
o t~
&
-7
A A
2~
'
~o
'
3'.2
'
3:,.
IKxJ-
lOOO/T
Fig. 4. Changes of ionic conductivity versus reciprocal temperature for (PEO)~0NaI-10 wt% of 0-A1203 polymer electrolytes of various grain sizes of ceramic powder: ( © ) grain size 2 pm, conductivity measured two weeks after preparation of electrolyte; ( • ) grain size 2 lam, conductivity measured four weeks after preparation of electrolyte; ( [ ] ) grain size 4 lain, conductivity measured two weeks after preparation of electrolyte; (/x ) grain sizes 7 ~tm, conductivity measured two weeks after preparation of electrolyte.
As can be seen from table 1, the activation energy and migration entropy change drastically with increasing grain size of 0-A1203 powder used. Assuming these facts, one can stress that above the melting point of pure PEO, the properties of the amorphous phase previously present in the electrolytes are still
1.0 1.3 E, [evl O5 Fig. 5. Plots of log conductivity pre-exponential factor against activation energy for: (a) (©) PEO-PMMA-LiCIO4 blend-based electrolytes (PMMA of various tacticity); (b) ( × ) PEO-LiC104 electrolyte containing various amounts of plasticizing phase prepared by hot rolling of PEO-PMMA blend.
affected (in the case of great 0-A1203 additives) by inorganic fillers. Hence thermal activation is required to equalize the chemical potentials of the ions in the primary amorphous phase and the secondary (formed after melting of crystalline PEO). Fig. 5 presents a comparison of the functions of In ao versus Ea for blend-based electrolytes containing syndio and atactic PMMA (curve a) with those calculated for PEO-isotactic PMMA blend-based electrolytes. As was previously shown for PEO-APMMA (atactic PMMA) systems, the values of TD are close to the melting point of the crystalline PEO phase. The same is valid also for PEO-SPMMA (syndiotactic PMMA)-LiC104 systems. However, the activation energies and migration entropies in these electrolytes are smaller than in their APMMA analogues. In comparison to the above-described systems, the values of To calculated for PEOIPMMA (isotactic PMMA) blend-based electrolytes are higher and equal to 361 K. As is evident from table 1, these electrolytes are characterized by the highest value of room-temperature ionic conductivity and the lowest activation energy and migration entropy from all systems included in table 1. Moreover, the values of Tg found for these systems from DSC investigations are comparable with these characteristics of pure PEO in spite of the fact that ad-
1o 7 o
14~ Wieczorek / Polymer solid electroh'te
dition of a salt usually increases the stiffness of the polymer hosts. Assuming these observations, it seems to be clear that the properties of the amorphous phase of P E O - I P M M A - L i C I O 4 electrolytes are different from that characteristic of the PEO phase. In addition, they are also profitable for fast ionic transport. It can be assumed then that the a m o r p h o u s phase formed after melting o f PEO is not so flexible as the initial a m o r p h o u s blend phase and hence the temperature at which the free-energy of ions existing in the systems studied becomes the same is higher than 7",,7. Similar observations were made for P E O - L i C104 electrolytes (curve c in fig. 5) containing a plasticizing P E O - P M M A phase formed during hot rolling o f both polymers at 180°C. The product of this operation was a d d e d to the PEO-LiC104 electrolytes, Also in this case TD was about 2 5 - 3 0 K higher than the melting point of pure crystalline PEO, evidencing the facilitating structure o f the amorphous blend phase.
5. Conclusions It was shown that for various blend-based and composite p o l y m e r solid electrolytes the temperature dependence of the ionic conductivity satisfies the Arrhenius law. The function o f the pre-exponential factor a0 against the activation energies can be described in the terms o f the M e y e r - N e l d e l equation. The validity of the M e y e r - N e l d e l rule implied that both the migration entropy and activation energy of the conduction process played a crucial role on the conductivity of the studied systems. Other parameters, and particularly the concentration o f mobile species, seemed to be of less importance. It should be emphasized that the highest values of r o o m - t e m p e r a t u r e conductivity were found for samples characterized by the lowest entropy o f ion migration and low activation energy, ca. 0.4-0.6 eV. The value of 7"D calculated from the M e y e r - N e l d e l law was attributed to the t e m p e r a t u r e at which almost all ions present in the system were free to move. For the pristine P E O - a l k a l i metal electrolytes, TD is equal to
the melting point of pure crystalline PEO. The same is also true for blend-based and composite systems in which addition of the second c o m p o n e n t does not modify the properties of the a m o r p h o u s phase leading only to changes of crystallinity o f the studied electrolytes. For the systems containing modified (e.g. much more stiff or flexible a m o r p h o u s phase than PEO) TD usually differs from the melting point o f pure crystalline PEO. In general, high values o f 7"f~ and low entropy of ion migration and low activation energy were evidence o f fast ion transport in the studied polymeric electrolytes.
Acknowledgements l would like to thank Prof. Wactaw Jakubowski who as the referee of my Ph.D. Thesis brought the M e y e r - N e l d e l rule to my attention. I would like to thank Dr. Katarzyna Such for making available the results o f her Ph.D. work. This work was financially supported by the H e a d m a s t e r of the Warsaw University of Technology according to the 5 0 3 / 1 6 4 / 2 2 0 / 1 research programme. The author wishes to thank the Batory Foundation for a travel Scholarship which enabled him to attend the SSI-8 Meeting and present the above work.
References [ 1] D.P. Almond and A.R. West, Solid State lonics 18/! 9 ( 1986 ) 1105. [2] D.P. Almond and A.R. West, Solid State lonics 23 (1987) 27. [3] J. Garbarczyk, P. Kurek, J. Nowifiski and W. Jakubowski, Solid State lonics 36 (1989) 239. [4] A.S. Nowick, W-K. Lee and H. Jain, Solid State Ionics 2830 (1988) 89. [5] G.J. Dienes, J. Appl. Phys. 21 (1950) 1189. [ 6 ] W. Wieczorek, K. Such, J. Ptocharski and J. Przytuski, Proc. 2nd Intern. Syrup. on Polymeric Electrolytes (Siena, 1989) ed. B. Scrosati (Elsevier Sequoia, Lausanne, 1990) pp. 339346. [ 7 ] J. Ptocharski, W. Wieczorek, J. Przytuski and K. Such, Appl. Phys. A 49 (1989) 55.
Solid State lonics 53-56 (1992) 1064-1070 North-Holland
IONICS Entropy effects on conductivity of the blend-based and composite polymer solid electrolytes Wtadystaw Wieczorek Institute (2flnorganic Technology, Warsaw UniversiO~qf Technology. ul. Noakowskiego 3, 00-664 Warszawa. Poland
The Meyer-Neldel rule is applied to describe the relation between the pre-exponential factors c~oand activation energies of various blend-based and composite polymeric electrolytes for which the temperature dependence of the conductivity satisfies the Arrhenius law. It is shown that for these electrolytes changes of ionic conductivity come from the variation of the migration entropy term. The correlations between the entropy of ion migration, phase structure and phase transitions are discussed. The physical meaning of the temperature TD calculated from the Meyer-Neldel equation is proposed.
1. Introduction
In o0 = A S , 1 , / k + l n K v o .
(2b)
It was previously found that for a wide range of fast ionic conductors the magnitudes of the pre-exponential factor and activation energy are connected by the M e y e r - N e l d e l rule [ 1-4 ] which can be written in the following form:
For a range o f materials, the entropy o f ion migration and enthalpy o f activation are related according to the following equation:
In o0 =c~Ea +[3.
This equation was originaly developed by Dienes, and the value TD represented for metals the melting point of the metal concerned. For fast ionic conductors this temperature usually corresponds to o r d e r - d i s o r d e r transitions in the mobile ion sublattice. By combination o f e q s . ( 2 b ) and (2c) we obtain
(1)
The M e y e r - N e l d e l equation (often called the C o m p e n s a t i o n Law) was firstly applied by Dienes to describe the dependence between the diffusion frequency factors and the activation energies for atomic diffusion in metals [5 ]. Recently A l m o n d and West [1] described the application of the rule for a description of the correlation between the pre-exponential factors and activation energies, calculated from the Arrhenius equation (2), for various solid ionic conductors: ~=aoT
]exp(-Ea/RT)
.
(2)
The pre-exponential factor cro can be described by the following equation: ao = Kvo exp A S m / k ,
(2a)
where K is the concentration term, k is the Boltzmann constant, Vo is the ionic oscillation frequency, ASm is the entropy o f ion migration, and hence
E J TD = ASm .
In a0 = E a / k T D + In Kvo = c~E~, + [3,
(2c)
il)
where c~= 1/kT~ and f l = l n Kv0. It was previously shown by the authors [6] that the rule is also valid for some composite polymeric electrolytes based on the P E O - N a l system with dispersed SiO2 particles. Since various blend-based and composite polymer solid electrolytes also satisfy the Arrhenius equation (especially at temperatures lower than the melting point of the crystalline PEO phase ) I would like to examine the applicability of the M e y e r - N e l d e l dependence in such systems. The aim o f the present paper is to correlate the effects of entropy on the conductivity with the phase structure of the polymeric electrolyte. The physical meaning of
0167-2738/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
W. Wieczorek/ Polymersolid electrolyte the Dienes temperature To calculated from the dependence described is also discussed.
1065
chemical potentials of a particle (i) belonging to the amorphous and crystalline phases at temperature T= TD are described by the equations (4a) and (4b) respectively:
2. Experimental
TD
Polymer electrolytes were prepared in the form of thin films by a casting technique. Details of the preparation procedure were described elsewhere [6,7]. The ionic conductivities of the samples were measured by impedance spectroscopy. The electrolytes were pressed between stainless-steel blocking electrodes. The experiments were performed in a frequency range from 5 Hz to 500 kHz and the temperature of the samples varied from ambient temperature up to about 373 K. All the experimental data were analyzed using an IBM PC XT microcomputer.
3. Physical background According to the assumption of Almond and West [ 1 ] the Dienes temperature TD is the temperature at which the difference between the free-energy of ions belonging to the ordered and disordered phases falls Io zero. In respect to semicrystalline polymeric electrolytes this means that the chemical potential of the ionic particles belonging to the crystalline phase becomes equal (at TD) to that of the particles belonging to the amorphous phase. The temperature dependence of the chemical potential of an ionic particle (i) is described by the following formula: T
,u,(T)=,u,(To)- j S,dT,
(3)
TO
where #,(T) and #,(To) are the chemical potentials of the particle i at temperatures T and To respectively and S, is the partial molar entropy of the substance (i) in the described phase. [Eq. (3) is valid for p, (, ~=const, where 0 is the Galvani potential and p, ( have their usual meanings. ] I intend to assume a very simple physical model and describe separately the chemical potential of the species in the amorphous and crystalline phases. I presume the temperature To to be equal to the glass transition temperature of the electrolyte 7g. Then the
#~a(TD)=,Uia(Tg ) - f S~adT-=flia(Tg ) Tm
TD
- f Si~dT- fSi~dT,
(4a)
Tm
TD
,ux(TD)=#,~(Tg)- f S,i~dT- f S2,~dT, (4b) 7~
7"~
where Sia is the partial molar entropy of a particle belonging to the amorphous phase, S~i~, $2,c are the partial molar entropies of a particle belonging to the crystalline phase at temperatures below Tm and above T,, respectively. (Tm is the melting temperature of the crystalline electrolyte phase). Since at TD ,U/a( T D ) = ,U,c( T D )
(5)
then Tm
ID
7~
7m
#,~( T~)Tm
TD
7g
Tm
(6) Assuming the abovementioned definitions of molar entropies for electrolytes with unmodified amorphous phases [ofa flexibility ( Tg value) comparable with the pristine PEO amorphous phase] S,a=S2,c and hence Tm #ia(Tg)--
Tm
f StadT=~ic(Tg)-
f SlicdT
rg
Tg
(7)
it implies that #ta(Tin) --#it(Tin) and hence TD= T~. The same mathematical procedure should be performed for all kinds of charged and uncharged species of the system described and, as can be easily recognized, leads to the same conclusions. For systems in which Sia#S2i c the eq. (6) can be rewritten in the following form:
Hi Wieczorek/Polvmersolidelectrolvte
1066
,8) l~,
l'm
Assuming that S,a and Sxi~ are constant in a temperature range between TD and Tin, the formula describing the Dienes temperature can be written in the following form:
Tr~=Tm+[lZi~(T.n)-IL,.(Tm)]/(S:,c-S,.).
(9)
In a quasi-equilibrium conditions
,u,":~.(T) =,u*. (T)
(10)
]l,* is the electrochemical potential of the ionic particle (i) which is equal to:
l~Ta(T) =/t,a(T) +zFO,a
( 1 la)
,a,*~(T)=.a,~ (T) +zFO,~
(1 lb)
for amorphous and crystalline phases respectively. According to these equations as well as eq. (5) O,,=O,c
(at T = T ~ ) .
(12)
Eq. ( 12 ) ilustrates that at TD the galvanic potentials of the amorphous and crystalline phases become equal. This assumption is in good agreement with the impedance spectroscopy data showing a distortion of the high-frequency semicircle for semicrystalline polymeric electrolytes. The distortion may be connected with the occurence of interfacial capacitance which comes from differences between the Galvani potentials of ions belonging to the crystalline and amorphous phases. For systems with a single amorphous phase or semicrystalline electrolytes at temperatures exceeding the melting point of the crystalline phase, such distortions are usually not observed. In my opinion, this oversimplified model indicated that the Meyer-Neldel rule should be generally valid for semicrystalline polymeric electrolytes. This assumption results from the fact that the differences between the melting temperatures for a set of electrolytes consisting of the same components but of different composition are small (indicated by the results included in table 1 ). Moreover for systems for which 7]~4: T..., the differences of molar entropies are also negligible which can be confirmed by the small differences of the glass transition temperatures. In
the experimental section I would like to examine the applicability of the Meyer-Neldel rule to the number of semicrystalline polymeric electrolytes with modified and unmodified amorphous phase.
4. Results and discussions
In the first step, changes of In ~ as well as thermodynamic function values after addition of an inert polymer [poly (methylmethacrylate)-PMMA] to PEO-alkali metal salt matrices are analyzed. Fig. la and Ib represent the relations between In a~ and the activation energy for PEO-PMMA blend-based polymeric electrolytes doped with LiCIO4 and Nal respectively. As can be seen, both systems satisfy the Meyer-Neldel dependence. Fig. 2a and 2b show the changes of room-temperature conductivily, activation energy, migration entropy and pre-exponential factor versus concentration of added PMMA for systems doped with LiCIO4 and Nal respectively. As can be seen, samples of the highest room-temperature ionic conductivity are characterized by the lowest values of AS,l, E,~ and In ~o- Similar relations were also found for other systems studied (see table l ). The values of the migration entropy found for PEOPMMA-LiC104 systems are about 50-100 J K ~ lower than for the analogous NaI-doped electrolytes. This fact can be connected with the values of the room-temperature conductivity, which for LiCIO4doped electrolytes were about 5-7 times higher. Fig. 3 shows evidence for the Meyer-Neldel relation for PEO-NaI-0-AI203 "'mixed phase" electrolytes. An Arrhenius plot of the temperature dependence of the conductivity for the samples used in the calculations is shown in fig. 4. Fillers of different grain sizes were used as additives. As is evident from fig. 4, the conductivity decreases with increasing size of the particles used. The value of 7"~ calculated from the Meyer-Neldel equation is equal to 358 K, which is 15-20 K higher than the melting point of pristine PEO phase in PEO-Nal electrolytes. The explanation of this behaviour should concern the two following observations: (i) the strong dependence of the structure and transport parameters on the size of particles used: (ii) the facilitation of ionic transport in an electrolyte containing 0-A1203 of grains lower than 2 lam.
V~ Wieczorek / Polymer solid electrolyte
1067
Table 1 Thermodynamic parameters of the studied blend-based and composite polymer solid electrolytes. Sample studied
(PEO)IoNal acetonitrile a) (PEO) ~oNaI nitromethane a) (PEO)IoNaI CH3OH+CH3CN .i PEO-PMMA 9:1 + 10% mol LiC104 PEO-PMMA 8 : 2 + 10% mol LiCIO4 PEO-PMMA 7:3 + 10% tool LiCIO4 PEO-PMMA 6 : 4 + 10% mol LiCIO4 PEO-PMMA 5 : 5 + 10% mol LiCIO4 PEO-PMMA 9 : 1 + 10% mol Nal PEO-PMMA 8 : 2 + 10% tool Nal PEO-PMMA 7 : 3 + 10% mol Nal PEO-PMMA 6 : 4 + 10% mol Nal PEO-PMMA 5 : 5 + 10% mol Nal PEO-SPMMA 7 : 3 10% mol LiCIO4 PEO-IPMMA 7 : 3 10% mol LiCIO4 PEO-IPMMA 8:2 10% mol LiCIO4 (PEO) ioNaI + 10% wt 0-A1203 grain size 2 ~tm (PEO)toNaI+ 10% wt 0-A1203 grain size 4 ~m (PEO) i oNaI + 10% wt 0-AI203 grain size 7 ~tm ( PEO ) ~0LiCIO4 30% wt plast, b) ( PEO ) ~oLiCIO4 40% wt plast, b) ( PEO ) joLiCIO4 50% wt plast, b)
E~ (eV)
Sa (JK
In ao
7~ (K)
CrRT ( S c m ~)
T~ (K)
Tm (K)
1.28
356
35.5
346
1.5X 10 v
249
338
1.05
293
27.2
346
4.0 X 10- 7
249
341
1.50
418
42.2
346
1.1 X 10 -7
249
339
1.19
341
32.0
337
2 . 4 X 10 - 6
0.82
234
19.0
337
3.0 X 10 -6
240
338
0.72
205
16.0
337
7 . 3 X 10 - 6
248
336
0.68
196
14.8
337
1.0× 10 -5
260
336
0.69
197
14.2
337
3 . 8 X 10 _6
0.92
273
22.0
324
1 . 8 X 10 - 7
1.04
311
26.5
324
2.0X 10 -7
1.04
309
25.7
324
1 . 2 X 10 - 7
0.98
293
22.6
324
4.7X 10 -8
0.86
257
18.9
324
1 . 6 X 10 - 7
0.55
156
10.3
341
1.4X l0 -5
249
338
0.49
132
9.8
361
9.0)< 10 -5
220
330
0.62
165
13.6
361
3.8X 10 -5
216
328
0.70
189
15.5
358
1.4)< I0 -5
328
0.95
259
22.7
358
3.3 X 10 -7
326
1.40
375
35.5
358
2.0X 10 8
325
0.80
209
19.9
371
6.1 X 10 - 6
0.78
203
19.3
371
9 . 9 × 10 - 6
0.60
156
13.8
371
5.1X 10 5
')
a) Solvents used for the preparation of PEO-based electrolytes. 6) Plasticizing phase consisting of grafted PEO-PMMA copolymer obtained by hot rolling of both components at 453 K. Ea = activation energy of conduction process; Sa = migration entropy of charge carriers In ao= logarithm of the pre-exponential factor calculated from the Arrhenius equation To = characteristic temperature calculated from the Meyer-Neldel relation; aRT = room temperature ionic conductivity of the studied samples Tg=glass transition temperature; Tm = melting temperature of the crystalline electrolyte phase.
1068
I4/~ Wieczorek / Polymer solid electrolyte tn~olSK/cm] In ~o[SK;cm]
z, ~,
/
36
(b)
6
,/
(a)
/ 40
30
// //'
3O
Q
20
o
c~'
14,
'90
2O
I
0i7
i
1.0
1.3
~
,
1.5 E ~ [ ~ , ;
,
1.0
ll.4
12
i
1.6 E~[~V]
Fig. 1. Plots of log conductivity pre-exponential factor against activation energy for: (a) PEO-PMMA-LiCIO4; (b) PEO-PMMA-Nal blend-based polymeric electrolytes of various blend compositions. The concentration of alkali metal salts is equal to 10 tool% with respect 1o the ethylene oxide molecular unit concentration.
(b)
i m~oISK
c~l
35
(a)
40
'°~ ........ o
tgg [s/cm]
3C
-66 o o
-5.0
o
30
o
o
-7,0
o
o
20 o
o
o
o
o o
o
20
o
-6.(]
o
14 1'0
3•
o
50' [ °'°wt "m~.tM~t
10 '
3'0
-7.6
50 ' [°'o wt P~4 MAI "
3'0
10 '
5 0.
°.'owt . pMMA; .
10 . S,
i Eo [ ~
340
o
300
So
.
50 °,o~qP & A}
30
J,K
iJ;Kt
:,t
1.6
360
13
300 1.C x
o
o
o
1.0 0.7
¢7 10 '
310
200 50' {eewt PMMA] ~
ll0
x
"x
310
510 [e/ewt PM MA]
o o 110
220
3;
50:%
.....
10
3'0
5101°/° wt P MMA]
Fig. 2. Composition dependence of: ionic conductivity at 293 K, log conductivity pre-exponential factor, activation energy, activation entropy for: (a) PEO-PMMA-LiC104; (b) PEO-PMMA-Nal blend-based polymeric electrolytes. The concentration of alkali metal salts is equal to 10 tool% with respect to the ethylene oxide molecular unit concentration.
W.. Wieczorek / Polymer solid electrolyte In ~[.gf( I¢ m ]
1069 tn ~ o l S K / c m l
/
44 4C
o/
36
30
/
20
/ /
/
20
,°,j
10
/
i
0.7
110
L
1.3
116 E.l,v]
Fig, 3. Plots of log conductivity pre-exponentialfactor against activation energyfor (PEOjoNaI-10 wt% of 0-A1203 polymer electrolytes of various grain sizes, of ceramic powder. l Log ~[S-cm-,] -3 "
A
oe D o •
-4
o•
o
o" •
-5 .6
o o
D fl
-6
o t~
&
-7
A A
2~
'
~o
'
3'.2
'
3:,.
IKxJ-
lOOO/T
Fig. 4. Changes of ionic conductivity versus reciprocal temperature for (PEO)~0NaI-10 wt% of 0-A1203 polymer electrolytes of various grain sizes of ceramic powder: ( © ) grain size 2 pm, conductivity measured two weeks after preparation of electrolyte; ( • ) grain size 2 lam, conductivity measured four weeks after preparation of electrolyte; ( [ ] ) grain size 4 lain, conductivity measured two weeks after preparation of electrolyte; (/x ) grain sizes 7 ~tm, conductivity measured two weeks after preparation of electrolyte.
As can be seen from table 1, the activation energy and migration entropy change drastically with increasing grain size of 0-A1203 powder used. Assuming these facts, one can stress that above the melting point of pure PEO, the properties of the amorphous phase previously present in the electrolytes are still
1.0 1.3 E, [evl O5 Fig. 5. Plots of log conductivity pre-exponential factor against activation energy for: (a) (©) PEO-PMMA-LiCIO4 blend-based electrolytes (PMMA of various tacticity); (b) ( × ) PEO-LiC104 electrolyte containing various amounts of plasticizing phase prepared by hot rolling of PEO-PMMA blend.
affected (in the case of great 0-A1203 additives) by inorganic fillers. Hence thermal activation is required to equalize the chemical potentials of the ions in the primary amorphous phase and the secondary (formed after melting of crystalline PEO). Fig. 5 presents a comparison of the functions of In ao versus Ea for blend-based electrolytes containing syndio and atactic PMMA (curve a) with those calculated for PEO-isotactic PMMA blend-based electrolytes. As was previously shown for PEO-APMMA (atactic PMMA) systems, the values of TD are close to the melting point of the crystalline PEO phase. The same is valid also for PEO-SPMMA (syndiotactic PMMA)-LiC104 systems. However, the activation energies and migration entropies in these electrolytes are smaller than in their APMMA analogues. In comparison to the above-described systems, the values of To calculated for PEOIPMMA (isotactic PMMA) blend-based electrolytes are higher and equal to 361 K. As is evident from table 1, these electrolytes are characterized by the highest value of room-temperature ionic conductivity and the lowest activation energy and migration entropy from all systems included in table 1. Moreover, the values of Tg found for these systems from DSC investigations are comparable with these characteristics of pure PEO in spite of the fact that ad-
1o 7 o
14~ Wieczorek / Polymer solid electroh'te
dition of a salt usually increases the stiffness of the polymer hosts. Assuming these observations, it seems to be clear that the properties of the amorphous phase of P E O - I P M M A - L i C I O 4 electrolytes are different from that characteristic of the PEO phase. In addition, they are also profitable for fast ionic transport. It can be assumed then that the a m o r p h o u s phase formed after melting o f PEO is not so flexible as the initial a m o r p h o u s blend phase and hence the temperature at which the free-energy of ions existing in the systems studied becomes the same is higher than 7",,7. Similar observations were made for P E O - L i C104 electrolytes (curve c in fig. 5) containing a plasticizing P E O - P M M A phase formed during hot rolling o f both polymers at 180°C. The product of this operation was a d d e d to the PEO-LiC104 electrolytes, Also in this case TD was about 2 5 - 3 0 K higher than the melting point of pure crystalline PEO, evidencing the facilitating structure o f the amorphous blend phase.
5. Conclusions It was shown that for various blend-based and composite p o l y m e r solid electrolytes the temperature dependence of the ionic conductivity satisfies the Arrhenius law. The function o f the pre-exponential factor a0 against the activation energies can be described in the terms o f the M e y e r - N e l d e l equation. The validity of the M e y e r - N e l d e l rule implied that both the migration entropy and activation energy of the conduction process played a crucial role on the conductivity of the studied systems. Other parameters, and particularly the concentration o f mobile species, seemed to be of less importance. It should be emphasized that the highest values of r o o m - t e m p e r a t u r e conductivity were found for samples characterized by the lowest entropy o f ion migration and low activation energy, ca. 0.4-0.6 eV. The value of 7"D calculated from the M e y e r - N e l d e l law was attributed to the t e m p e r a t u r e at which almost all ions present in the system were free to move. For the pristine P E O - a l k a l i metal electrolytes, TD is equal to
the melting point of pure crystalline PEO. The same is also true for blend-based and composite systems in which addition of the second c o m p o n e n t does not modify the properties of the a m o r p h o u s phase leading only to changes of crystallinity o f the studied electrolytes. For the systems containing modified (e.g. much more stiff or flexible a m o r p h o u s phase than PEO) TD usually differs from the melting point o f pure crystalline PEO. In general, high values o f 7"f~ and low entropy of ion migration and low activation energy were evidence o f fast ion transport in the studied polymeric electrolytes.
Acknowledgements l would like to thank Prof. Wactaw Jakubowski who as the referee of my Ph.D. Thesis brought the M e y e r - N e l d e l rule to my attention. I would like to thank Dr. Katarzyna Such for making available the results o f her Ph.D. work. This work was financially supported by the H e a d m a s t e r of the Warsaw University of Technology according to the 5 0 3 / 1 6 4 / 2 2 0 / 1 research programme. The author wishes to thank the Batory Foundation for a travel Scholarship which enabled him to attend the SSI-8 Meeting and present the above work.
References [ 1] D.P. Almond and A.R. West, Solid State lonics 18/! 9 ( 1986 ) 1105. [2] D.P. Almond and A.R. West, Solid State lonics 23 (1987) 27. [3] J. Garbarczyk, P. Kurek, J. Nowifiski and W. Jakubowski, Solid State lonics 36 (1989) 239. [4] A.S. Nowick, W-K. Lee and H. Jain, Solid State Ionics 2830 (1988) 89. [5] G.J. Dienes, J. Appl. Phys. 21 (1950) 1189. [ 6 ] W. Wieczorek, K. Such, J. Ptocharski and J. Przytuski, Proc. 2nd Intern. Syrup. on Polymeric Electrolytes (Siena, 1989) ed. B. Scrosati (Elsevier Sequoia, Lausanne, 1990) pp. 339346. [ 7 ] J. Ptocharski, W. Wieczorek, J. Przytuski and K. Such, Appl. Phys. A 49 (1989) 55.