- Email: [email protected]
Mechanical behavior of polymeric electrolytes in the glassy and rubber-like regions
Solid State Communications, Vol. 67, No. 5, pp. 561-564, 1988. Printed in Great Britain.
0038-1098/88 $3.00 + .00 Pergamon Press plc
M E C H A N I C A L BEHAVIOR OF P O L Y M E R I C E L E C T R O L Y T E S IN T H E GLASSY A N D RUBBER-LIKE REGIONS A. Bartolotta and G. Di Marco Ist. di Tecniche Spettroscopiche del C.N.R., 1-98166 Contrada Papardo, Messina, Italy E. Bonetti Dip. di Fisica "A. Righi", Universit~i degli Studi di Bologna and G.N.S.M. del C.N.R., 1-48126 Bologna, Italy and G. Carini Ist. di Fisica Gen., Universith degli Studi di Messina and G.N.S.M. del C.N.R. 1-98166 Contrada Papardo, Messina, Italy
(Received 11 January 1988 by R. Fieschi) The mechanical characteristics (resonant frequency and internal friction) have been measured as a function of temperature in the 100-320 K range for polyethyleneoxide-NaSCN polymeric electrolytes. The mechanical behaviors reveals the presence of a low temperature 7-relaxation, little influenced by the addition of sodium thyocianate and of an ~,-relaxation, arising from the segmental motions typical of the glass-rubber like transition region. Moreover, in the temperature region between the 7 and ~-relaxation, a loss further peak is found. Some information concerning its microscopic origin is obtained by following its behavior as a function of the NaSCN content and comparing the results with the known structure of these polymeric complexes. are characterized by a very high mobility of the ions
1. I N T R O D U C T I O N IN T H E last few years a growing amount of effort has been devoted to polymeric electrolytes, mostly for their technological applications as solid electrochemical devices [1, 2]. These systems are polymer-salt solid solutions, commonly characterized by a relatively high ionic conductivity at room-temperature (10 -6 f~ ~cm 1). These materials are different from other solid electrolytes, such as the superionic glasses, where the mobile ions are highly decoupled from a rigid host matrix, in that in these materials the ionic motion is connected to the movements of the surrounding structure (coupled motion). In this respect it has now been ascertained that in a polymer-electrolyte solution high chain flexibility of the polymeric solvent is necessary not only to promote the ion transport but also for the initial formation of the complex. As a consequence, it is important to understand how the dynamics of the polymeric structure could assist the ionic motion. Now the polyethyleneoxide (PEO)-NaSCN systems are semicrystalline polymers and it seems that only amorphous regions 561
[3]. We present here an analysis of the resonant frequency and internal friction behavior as a function of temperature in PEO-NaSCN complexes in order to study the microscopic motions of the structural units present in them. 2. E X P E R I M E N T A L P R O C E D U R E The materials were prepared by dissolving appropriate amounts of PEO (M.W. 600000) and NaSCN (reagent grade) in methanol, in order to obtain complexes of the desired stoichiometry. The compositions of the mixtures are given by specifying the respective molar fractions. The samples were obtained by evaporating the solvent in air at about 40°C for 48 h and then dried under vacuum at the same temperature for two or three days. Furthermore an appropriate compression was used to obtain rods with size useful for mechanical measurements (about 30 × 10 × 0.3mm). The internal friction and the resonant frequency
562
Vol. o/, No. 5
M E C H A N I C A L B E H A V I O R OF P O L Y M E R I C E L E C T R O L Y T E S
were measured in the 200-280 Hz range by a vibrating reed Bordoni-type apparatus [4], using electrostatic excitation and detection of the vibrations by frequency modulation. The surface of the polymeric sample were made electrically conducted by a gold metal coating. Measurement were carried out under 10 ~torr vacuum in the whole temperature range (100-320 K). The temperature was measured by a copperconstantan thermocouple and was controlled to within 0 . 1 K in the whole range by an home-made apparatus.
g
~00._
N
c
-~ ~0 ~ ~ F 1 20 I
•6eoe
oe°e°e~ °°°e°°°°ee°°°°°e°°ee[ 150
20O T(K)
I
250
50O ~L2
,i 00 300
Fig. 2. Temperature behavior of the resonant frequency and the internal friction in (PEO)0.89(NaSCN)0.11 •
3. R E S U L T S A N D D I S C U S S I O N In Fig. 1 is shown the temperature behavior of the internal friction in the pure PEO and in the (PEO)0 s2 (NaSCN)0.js. The temperature behavior of the resonant frequency (connected to the dynamic modulus) and of the internal friction in the sample with the lowest N a S C N content are reported in Fig. 2. The following features are evident: 1. A broad peak at ~ 175 K, whose temperature location shows a very little variation with the N a S C N content. A slight inflexion in the resonant frequency curve is correspondently visible, see Fig. 2. As previously emphasized in dielectric relaxation measurements [5], this peak arises from the 7-relaxation, typical of the polymeric structures. 2. A peak at about 230 K in the pure PEO, which emerges from a "background", fastly increasing with the temperature. It is connected to the glass-rubber transition (a~-relaxation) of the amorphous part of the polymer [5] and it shifts at higher temperatures with the N a S C N content, 270 K for X = 0.11 and 295 K for X = 0.18. The reason for these assignments will be more clear in the following. 3. A peak at about 260 K, whose height decreases
i00I I0-3
],~0-3
quite strongly with the salt content, while its temperature location seems to be constant. Now we discuss separately the cited contributions to the internal friction spectra, in order to clarify the underlying mechanisms and the possible microscopic origin. The 7-relaxation has been extensively studied in pure PEO by electrical [5], mechanical [6] and thermally stimulated depolarization current (TSDC) [7] techniques and also in some complexes PEO-alkali metal salt by dielectric relaxation [5] and TSDC measurements [7]. It appears to be thermally activated and unexplainable in terms of a single relaxation time. In order to carry out a quantitative interpretation of the corresponding peak in our data we assume the existence of a distribution of relaxation times due to random deviation in the local arrangement of the system. Since in a thermally activated process the relaxation time is defined by an activation energy E and a characteristic time %, z = %exp(E/kT), a z-distribution corresponds to a distribution of E and ~0. Assuming a single value for %, the >distribution can be related to and E-distribution P(E), which was taken as Gaussian for the randomness of the studied systems (the pure PEO and their complexes are semicrystalline). In this case a useful form for the internal friction is [8]
O{ a
g
_
z~ O~a A
x
2Eo ~oz(E) 1 + co2z2(E)
dE.
JJ (1)
A
'5"c 2G~_
Fo o.,.-7
100
150
•
• • • • . j • • •
[ 200 T(K)
] 250
I 300
Fig. I. Temperature behavior of the internal friction in (PEO)j_ ,(NaSCN)~ polymers: A, X = 0; O, X = 0.18.
In the equation (1) co is the angular frequency, T the temperature and A a parameter which is related to the number of relaxing "particles" and to the coupling between the mechanical stress and the system; E,, and E0 are the most probable value and the width of the distribution. In order to apply the equation (1) to our experimental data for the 7-relaxation, we suppose
Vol. 67, No. 5
M E C H A N I C A L BEHAVIOR OF P O L Y M E R I C E L E C T R O L Y T E S
Table 1. Values of the parameters A, E,., Eo and zofor the )'-relaxation in (PEO)I_x(NaSCN)x. The values of the glass transition temperature TG are taken from [3] X
[A] (105eV-' K)
Em E0 (eV) ( e V )
It0] (10-'3s)
TG (K)
0.0 0.11 0.18
[1.4] [0.72] [0.83]
0.33 0.32 0.34
[2.5] [1.23] [1.6]
213 262 292
0.034 0.046 0.039
that the frequency of our probe is constant (the resonant frequency shift in the ),-relaxation region is almost constant, e.g. 0.48-0.41 Khz). Moreover to evaluate only the contribution of the )'-relaxation to the internal friction we subtract a "background", which is weakly dependent upon temperature, and which corresponds to the flat behaviour of Q- J observed at lowest temperatures. The least-squares fit of the data by a Minuit C E R N minimum search program furnishes values of the parameters Era, Eo, Zo and A, which are reported in Table 1. A typical fit of the )'-relaxation loss, for the sample with X = 0.18, is shown by a continuous line in Fig. 3 and the agreement between the experimental and theoretical behavior confirms the goodness of the approach. The value of Em for the pure PEO is close to that obtained by the shift of the peak temperature with the frequency in dielectric relaxation measurements [5]. The values of the fit parameters do not show a definite behaviour as a function of the NaSCN content and particulary the values of the Em clearly indicate that the )'-relaxation is little influenced by the presence of sodium thiocyanate. This circumstance seems to support the actual hypothesis on the structural modifications of the PEO polymeric network, when an alkali metal salt is added. In fact it is supposed [1, 9] that the mobile cations are located within the tunnel of the helicoidal-shaped polymeric chains,
Ixl~3 L
c~ :r
I
~00
~50
2oo T (K)
r
250
Fig. 3. Comparison between the experimental data, concerning the )'-relaxation loss, and the theoretical fit with a distribution of activation energies (continous line) for the (PEO)0.82(NaSCN)0., 8 sample.
563
being the tunnel radius 1.5-1.8 A [10]. It follows that cations with a ionic radius smaller than the tunnel radius, as sodium ions, should not appreciably modify the chain structure. As a consequence local motions of some parts of the chains, as segments or chain-end hydroxyl groups (two among the possible microscopic origins of the ),-relaxation in the pure PEO [11, 12]) will be relatively unaffected. A quantitative analysis of loss peaks at higher temperatures is very difficult both because of overlap and the presence of a dissipation "background" strongly increasing with the temperature above 250 K. This "background" is due to other dissipative mechanisms and, at present, its contribution is not calculable. However a tentative identification of the remaining peaks can be carried out. In pure PEO the peak at 230 K is due to the ~-relaxation associated with the glass-rubber like transition region [5, 6]. This relaxation is related to the increase of the molecular segment mobility, connected with the fast change in the flexibility of the polymeric chains, typical of this region. The addition of sodium thiocyanate gives rise to the formation of amorphous regions of P E O - N a S C N mixtures and the glass transition temperature TGshifts to higher temperatures with an increase in the NaSCN content [3]. The values of T~ for these samples, as measured by DSC technique with an heating rate of 40°C m i n - ' , are inserted in Table 1. There is a good agreement between the temperature of the calorimetric results and the peaks, labelled by ~t~, which as a consequence, are related to the glass transition of the polymeric complexes. This assignment is also confirmed by the sharp bending shown from the resonant frequency in the same temperature region (see Fig. 2), which is clearly connected to a gradual softening of the system. The origin of the peak at ~ 263 K (third point of our introductive Table) is less clear. In the pure PEO it was impossible to reveal it, because a very high dissipation prevented us to obtain reliable data in this temperature region. However TSDC measurements [7] in the pure PEO reveaed at ~ 170 K a peak, labelled by the authors ct,., which should shift up to a temperature of 260K in our frequency range. The c£-relaxation was tentatively attributed to defects present in the crystalline phae of PEO. Recent experiments [3] support the presence of crystalline PEO in our systems and we like to follow that hypothesis for still other reasons: 1. The temperature of the peak does not change with the salt content, indicating that the relaxation mechanism is not influenced from an energetic point of view.
564
MECHANICAL BEHAVIOR OF POLYMERIC ELECTROLYTES
2. On the other hand the peak height decreases appreciably as salt concentration increases, showing a corresponding decrease in the number of relaxing particles. Consequently, the results are consistent with assigning the relaxation process to some local motion present in the PEO crystalline regions which decrease with the NaSCN content. An appropriate extension of these measurements to a wider range of concentrations and also to other PEO-metal salt complexes would be useful in order to clarify this relaxation mechanism further.
3. 4. 5. 6. 7. 8. 9.
REFERENCES 1.
2.
M.B. Armand, J.M. Chabagno & M.J. Duclot, Fast Ion Transport in Solids, p. 131, (Edited by P. Vashishta), Mundy, Shenoy, North Holland, (1979). C.A. Angell, Solid State Ionics 18-19, 72 (1986).
10. 11. 12.
Vol. 67, ~q6.5
Y.L. Lee & B. Crist, J. Appl. Phys. 60, 2683 (1986). P.G. Bordoni, M. Nuovo & L. Verdini, Nuovo Cim. 20, 667 (1961). J.J. Fontanella, M.C. Wintersgill & J.P. Calame, Solid State Ionics 8, 333-339 (1983); J. Polymer Sci.: Polymer Phys. Ed. 23, 113 (1985). N.K. Kalfoglou, J. Polymer Sci.: Polymer Phys. Ed. 20, 1259 (1982). J.P. Calame, J.J. Fontanella, M.C. Wintersgill & C.G. Andeen, J. Appl. Phys. 58, 2811 (1985). G. Carini, M. Cutroni, M. Federico, G. Galli & G. Tripodo, Phys. Rev. B30, 7219 (1984). J.M. Parker, P.V. Wright & C.C. Lee, Polymer 22, 1305 (1981). B.L. Papke, M.A. R a t n e r & D.F. Shriver, J. Electrochem. Soc. 129, 1694 (1982). P. Hedvig, Dielectric Spectroscopy of Polymers, Hilger, Bristol, England, (1977). T. Suzuki & T. Kotaka, Macromolecules 13, 1495 (1980).
0038-1098/88 $3.00 + .00 Pergamon Press plc
M E C H A N I C A L BEHAVIOR OF P O L Y M E R I C E L E C T R O L Y T E S IN T H E GLASSY A N D RUBBER-LIKE REGIONS A. Bartolotta and G. Di Marco Ist. di Tecniche Spettroscopiche del C.N.R., 1-98166 Contrada Papardo, Messina, Italy E. Bonetti Dip. di Fisica "A. Righi", Universit~i degli Studi di Bologna and G.N.S.M. del C.N.R., 1-48126 Bologna, Italy and G. Carini Ist. di Fisica Gen., Universith degli Studi di Messina and G.N.S.M. del C.N.R. 1-98166 Contrada Papardo, Messina, Italy
(Received 11 January 1988 by R. Fieschi) The mechanical characteristics (resonant frequency and internal friction) have been measured as a function of temperature in the 100-320 K range for polyethyleneoxide-NaSCN polymeric electrolytes. The mechanical behaviors reveals the presence of a low temperature 7-relaxation, little influenced by the addition of sodium thyocianate and of an ~,-relaxation, arising from the segmental motions typical of the glass-rubber like transition region. Moreover, in the temperature region between the 7 and ~-relaxation, a loss further peak is found. Some information concerning its microscopic origin is obtained by following its behavior as a function of the NaSCN content and comparing the results with the known structure of these polymeric complexes. are characterized by a very high mobility of the ions
1. I N T R O D U C T I O N IN T H E last few years a growing amount of effort has been devoted to polymeric electrolytes, mostly for their technological applications as solid electrochemical devices [1, 2]. These systems are polymer-salt solid solutions, commonly characterized by a relatively high ionic conductivity at room-temperature (10 -6 f~ ~cm 1). These materials are different from other solid electrolytes, such as the superionic glasses, where the mobile ions are highly decoupled from a rigid host matrix, in that in these materials the ionic motion is connected to the movements of the surrounding structure (coupled motion). In this respect it has now been ascertained that in a polymer-electrolyte solution high chain flexibility of the polymeric solvent is necessary not only to promote the ion transport but also for the initial formation of the complex. As a consequence, it is important to understand how the dynamics of the polymeric structure could assist the ionic motion. Now the polyethyleneoxide (PEO)-NaSCN systems are semicrystalline polymers and it seems that only amorphous regions 561
[3]. We present here an analysis of the resonant frequency and internal friction behavior as a function of temperature in PEO-NaSCN complexes in order to study the microscopic motions of the structural units present in them. 2. E X P E R I M E N T A L P R O C E D U R E The materials were prepared by dissolving appropriate amounts of PEO (M.W. 600000) and NaSCN (reagent grade) in methanol, in order to obtain complexes of the desired stoichiometry. The compositions of the mixtures are given by specifying the respective molar fractions. The samples were obtained by evaporating the solvent in air at about 40°C for 48 h and then dried under vacuum at the same temperature for two or three days. Furthermore an appropriate compression was used to obtain rods with size useful for mechanical measurements (about 30 × 10 × 0.3mm). The internal friction and the resonant frequency
562
Vol. o/, No. 5
M E C H A N I C A L B E H A V I O R OF P O L Y M E R I C E L E C T R O L Y T E S
were measured in the 200-280 Hz range by a vibrating reed Bordoni-type apparatus [4], using electrostatic excitation and detection of the vibrations by frequency modulation. The surface of the polymeric sample were made electrically conducted by a gold metal coating. Measurement were carried out under 10 ~torr vacuum in the whole temperature range (100-320 K). The temperature was measured by a copperconstantan thermocouple and was controlled to within 0 . 1 K in the whole range by an home-made apparatus.
g
~00._
N
c
-~ ~0 ~ ~ F 1 20 I
•6eoe
oe°e°e~ °°°e°°°°ee°°°°°e°°ee[ 150
20O T(K)
I
250
50O ~L2
,i 00 300
Fig. 2. Temperature behavior of the resonant frequency and the internal friction in (PEO)0.89(NaSCN)0.11 •
3. R E S U L T S A N D D I S C U S S I O N In Fig. 1 is shown the temperature behavior of the internal friction in the pure PEO and in the (PEO)0 s2 (NaSCN)0.js. The temperature behavior of the resonant frequency (connected to the dynamic modulus) and of the internal friction in the sample with the lowest N a S C N content are reported in Fig. 2. The following features are evident: 1. A broad peak at ~ 175 K, whose temperature location shows a very little variation with the N a S C N content. A slight inflexion in the resonant frequency curve is correspondently visible, see Fig. 2. As previously emphasized in dielectric relaxation measurements [5], this peak arises from the 7-relaxation, typical of the polymeric structures. 2. A peak at about 230 K in the pure PEO, which emerges from a "background", fastly increasing with the temperature. It is connected to the glass-rubber transition (a~-relaxation) of the amorphous part of the polymer [5] and it shifts at higher temperatures with the N a S C N content, 270 K for X = 0.11 and 295 K for X = 0.18. The reason for these assignments will be more clear in the following. 3. A peak at about 260 K, whose height decreases
i00I I0-3
],~0-3
quite strongly with the salt content, while its temperature location seems to be constant. Now we discuss separately the cited contributions to the internal friction spectra, in order to clarify the underlying mechanisms and the possible microscopic origin. The 7-relaxation has been extensively studied in pure PEO by electrical [5], mechanical [6] and thermally stimulated depolarization current (TSDC) [7] techniques and also in some complexes PEO-alkali metal salt by dielectric relaxation [5] and TSDC measurements [7]. It appears to be thermally activated and unexplainable in terms of a single relaxation time. In order to carry out a quantitative interpretation of the corresponding peak in our data we assume the existence of a distribution of relaxation times due to random deviation in the local arrangement of the system. Since in a thermally activated process the relaxation time is defined by an activation energy E and a characteristic time %, z = %exp(E/kT), a z-distribution corresponds to a distribution of E and ~0. Assuming a single value for %, the >distribution can be related to and E-distribution P(E), which was taken as Gaussian for the randomness of the studied systems (the pure PEO and their complexes are semicrystalline). In this case a useful form for the internal friction is [8]
O{ a
g
_
z~ O~a A
x
2Eo ~oz(E) 1 + co2z2(E)
dE.
JJ (1)
A
'5"c 2G~_
Fo o.,.-7
100
150
•
• • • • . j • • •
[ 200 T(K)
] 250
I 300
Fig. I. Temperature behavior of the internal friction in (PEO)j_ ,(NaSCN)~ polymers: A, X = 0; O, X = 0.18.
In the equation (1) co is the angular frequency, T the temperature and A a parameter which is related to the number of relaxing "particles" and to the coupling between the mechanical stress and the system; E,, and E0 are the most probable value and the width of the distribution. In order to apply the equation (1) to our experimental data for the 7-relaxation, we suppose
Vol. 67, No. 5
M E C H A N I C A L BEHAVIOR OF P O L Y M E R I C E L E C T R O L Y T E S
Table 1. Values of the parameters A, E,., Eo and zofor the )'-relaxation in (PEO)I_x(NaSCN)x. The values of the glass transition temperature TG are taken from [3] X
[A] (105eV-' K)
Em E0 (eV) ( e V )
It0] (10-'3s)
TG (K)
0.0 0.11 0.18
[1.4] [0.72] [0.83]
0.33 0.32 0.34
[2.5] [1.23] [1.6]
213 262 292
0.034 0.046 0.039
that the frequency of our probe is constant (the resonant frequency shift in the ),-relaxation region is almost constant, e.g. 0.48-0.41 Khz). Moreover to evaluate only the contribution of the )'-relaxation to the internal friction we subtract a "background", which is weakly dependent upon temperature, and which corresponds to the flat behaviour of Q- J observed at lowest temperatures. The least-squares fit of the data by a Minuit C E R N minimum search program furnishes values of the parameters Era, Eo, Zo and A, which are reported in Table 1. A typical fit of the )'-relaxation loss, for the sample with X = 0.18, is shown by a continuous line in Fig. 3 and the agreement between the experimental and theoretical behavior confirms the goodness of the approach. The value of Em for the pure PEO is close to that obtained by the shift of the peak temperature with the frequency in dielectric relaxation measurements [5]. The values of the fit parameters do not show a definite behaviour as a function of the NaSCN content and particulary the values of the Em clearly indicate that the )'-relaxation is little influenced by the presence of sodium thiocyanate. This circumstance seems to support the actual hypothesis on the structural modifications of the PEO polymeric network, when an alkali metal salt is added. In fact it is supposed [1, 9] that the mobile cations are located within the tunnel of the helicoidal-shaped polymeric chains,
Ixl~3 L
c~ :r
I
~00
~50
2oo T (K)
r
250
Fig. 3. Comparison between the experimental data, concerning the )'-relaxation loss, and the theoretical fit with a distribution of activation energies (continous line) for the (PEO)0.82(NaSCN)0., 8 sample.
563
being the tunnel radius 1.5-1.8 A [10]. It follows that cations with a ionic radius smaller than the tunnel radius, as sodium ions, should not appreciably modify the chain structure. As a consequence local motions of some parts of the chains, as segments or chain-end hydroxyl groups (two among the possible microscopic origins of the ),-relaxation in the pure PEO [11, 12]) will be relatively unaffected. A quantitative analysis of loss peaks at higher temperatures is very difficult both because of overlap and the presence of a dissipation "background" strongly increasing with the temperature above 250 K. This "background" is due to other dissipative mechanisms and, at present, its contribution is not calculable. However a tentative identification of the remaining peaks can be carried out. In pure PEO the peak at 230 K is due to the ~-relaxation associated with the glass-rubber like transition region [5, 6]. This relaxation is related to the increase of the molecular segment mobility, connected with the fast change in the flexibility of the polymeric chains, typical of this region. The addition of sodium thiocyanate gives rise to the formation of amorphous regions of P E O - N a S C N mixtures and the glass transition temperature TGshifts to higher temperatures with an increase in the NaSCN content [3]. The values of T~ for these samples, as measured by DSC technique with an heating rate of 40°C m i n - ' , are inserted in Table 1. There is a good agreement between the temperature of the calorimetric results and the peaks, labelled by ~t~, which as a consequence, are related to the glass transition of the polymeric complexes. This assignment is also confirmed by the sharp bending shown from the resonant frequency in the same temperature region (see Fig. 2), which is clearly connected to a gradual softening of the system. The origin of the peak at ~ 263 K (third point of our introductive Table) is less clear. In the pure PEO it was impossible to reveal it, because a very high dissipation prevented us to obtain reliable data in this temperature region. However TSDC measurements [7] in the pure PEO reveaed at ~ 170 K a peak, labelled by the authors ct,., which should shift up to a temperature of 260K in our frequency range. The c£-relaxation was tentatively attributed to defects present in the crystalline phae of PEO. Recent experiments [3] support the presence of crystalline PEO in our systems and we like to follow that hypothesis for still other reasons: 1. The temperature of the peak does not change with the salt content, indicating that the relaxation mechanism is not influenced from an energetic point of view.
564
MECHANICAL BEHAVIOR OF POLYMERIC ELECTROLYTES
2. On the other hand the peak height decreases appreciably as salt concentration increases, showing a corresponding decrease in the number of relaxing particles. Consequently, the results are consistent with assigning the relaxation process to some local motion present in the PEO crystalline regions which decrease with the NaSCN content. An appropriate extension of these measurements to a wider range of concentrations and also to other PEO-metal salt complexes would be useful in order to clarify this relaxation mechanism further.
3. 4. 5. 6. 7. 8. 9.
REFERENCES 1.
2.
M.B. Armand, J.M. Chabagno & M.J. Duclot, Fast Ion Transport in Solids, p. 131, (Edited by P. Vashishta), Mundy, Shenoy, North Holland, (1979). C.A. Angell, Solid State Ionics 18-19, 72 (1986).
10. 11. 12.
Vol. 67, ~q6.5
Y.L. Lee & B. Crist, J. Appl. Phys. 60, 2683 (1986). P.G. Bordoni, M. Nuovo & L. Verdini, Nuovo Cim. 20, 667 (1961). J.J. Fontanella, M.C. Wintersgill & J.P. Calame, Solid State Ionics 8, 333-339 (1983); J. Polymer Sci.: Polymer Phys. Ed. 23, 113 (1985). N.K. Kalfoglou, J. Polymer Sci.: Polymer Phys. Ed. 20, 1259 (1982). J.P. Calame, J.J. Fontanella, M.C. Wintersgill & C.G. Andeen, J. Appl. Phys. 58, 2811 (1985). G. Carini, M. Cutroni, M. Federico, G. Galli & G. Tripodo, Phys. Rev. B30, 7219 (1984). J.M. Parker, P.V. Wright & C.C. Lee, Polymer 22, 1305 (1981). B.L. Papke, M.A. R a t n e r & D.F. Shriver, J. Electrochem. Soc. 129, 1694 (1982). P. Hedvig, Dielectric Spectroscopy of Polymers, Hilger, Bristol, England, (1977). T. Suzuki & T. Kotaka, Macromolecules 13, 1495 (1980).