Polymer Science, Ser. A, Vol. 45, No. 8, 2003, pp. 785–794. Translated from Vysokomolekulyarnye Soedineniya, Ser. A, Vol. 45, No. 8, 2003, pp. 1314–1325. Original Russian Text Copyright © 2003 by Burmistr, Shilov, Sukhoi, Pissis, Polizos. English Translation Copyright © 2003 by MAIK “Nauka /Interperiodica” (Russia).
STRUCTURE AND PROPERTIES
Dielectric Relaxation and Ionic Conductivity of Oxyethylene–Alkylaromatic Polyionenes M. V. Burmistr*, V. V. Shilov**, K. M. Sukhoi*1, P. Pissis***, and G. Polizos*** * Ukrainian State University of Chemical Technology, pr. Gagarina 8, Dnepropetrovsk, 49005 Ukraine ** Institute of Macromolecular Chemistry, National Academy of Sciences of Ukraine, Khar’kovskoe sh. 48, Kiev, 02160 Ukraine *** Department of Physics, National Technical University of Athens, Zografou Campus, Athens, 15780 Greece Received April 1, 2002; Revised Manuscript Received April 1, 2003
Abstract—Oxyethylene–alkylaromatic polyionenes were studied in the 10–2 to 106 Hz frequency range and in the –120 to +80°C temperature range using dielectric spectroscopy. Dielectric spectra at low temperatures displayed dipole polarization relaxation due to a local motion of polymer chains, whereas the contribution of electric conduction prevailed at elevated temperatures. Plots of the direct-current conductivity against the reciprocal temperature followed the Arrhenius law with an activation energy of 1–1.5 eV, which is not typical of polymeric electrolytes and indicates that the conductivity is thermally activated. The high conductivity of the polymers at í íg is due to their structure, which resembles the structure of an inorganic glass with ionic sites dissolved in an ordered matrix.
based on the notation of radicals located between
INTRODUCTION The first syntheses of ionene polymers were accomplished in the 1930s [1]. As they possess a set of practically important properties, aqueous solutions of polyionenes show promise for technical use [2]. Studies on certain characteristics of these polymers suggested their structural ordering at the supramolecular level [3–7]. Polyionenes also have high ionic conductivity characteristics, approaching those of the best polymeric electrolytes [8–14]. Note that polyionenes, which are actually polymeric quaternary ammonium salts, possess many properties of these salts. Due to their high electrochemical activity, they are used as a basis for manufacturing a vast family of polymeric electrolytes employed in the design of promising electrochemical devices for electric energy storage, electrical double layer capacitors (supercapacitors) [15, 16]. Therefore, the necessity appeared of making a detailed investigation into a comparatively new class of such systems, alkylaromatic polyionenes containing ether fragments. In this work, we studied polyionenes containing poly(ethylene oxide) and alkylaromatic fragments in the main chain (Table 1): (I) I-2OE-Ph, (II) I-3OE-Ph, and (III) I-6OE-Ph (the coding of the polymers is 1 E-mail:
[email protected]
CH3 Hal– + H2C N CH2
groups).
CH3
EXPERIMENTAL The synthesis and main characteristics of polyionenes are described in [17]. The experimental study of dielectric relaxation was performed in the frequency range 10–2–106 Hz using a Schlumberger FRA SI 1260 dielectric spectrometer with a Chelsea Dielectric Interface buffer amplifier. The samples were placed between blocking brass electrodes in a parallel-plate capacitor cell (Novocontrol) integrated into a Quatro Cryosystem cryostat (Novocontrol). The measurements were conducted in the 80 to –140°C temperature range in a thermostat controlled accurate to within ~0.1°C. All the experiments were conducted in a nitrogen atmosphere in the varying-capacitance mode of the sample-containing capacitor. The samples were first heated to the highest measurement temperature. Then, the temperature was lowered in 10°C steps to obtain the corresponding isothermal capacitance vs. frequency curves. Before recording each curve, the samples were held at the maximum temperature of the experiment for 30 min.
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Table 1. Structure and physicochemical characteristics of polyionenes with the general formula CH3 CH3 Cl– Cl– + + N CH2 R1 H2C N CH2 R2 CH2 CH3
CH3
Polyionene
I
n
R2
R1
CH2 O CH2
II
CH2 O CH2
III
CH2 O CH2
Tg , °C
ηg*, dl/g (c = 0.1 g/dl)
57
4.82
40
2.56
18
0.98
2
3
6
* Measured in water at 25°C.
The simultaneous use of the dielectric spectrometers and Chelsea Dielectric Interface buffer amplifier ruled out the possibility of surface conduction. Detailed descriptions of the setup and experimental procedure are given in [18–20]. To treat the experimental results on the dielectric properties, we used four different approaches employed in data processing in dielectric spectroscopy: analysis of the complex permittivity ε* [21, 22], complex impedance Z* [23, 24], complex electric modulus å* [25, 26], and complex conductivity σ* [21, 22]. Thus, it became possible to separate and identify the contributions of various relaxation processes and conductionrelated processes, as well as to analyze the dielectric spectra of polymeric materials, both true dielectrics and “dielectric conductors” (the latter are characterized by high levels of ionic or electronic conduction). RESULTS AND DISCUSSION Complex Permittivity Ion-conducting dielectrics, including polyionenes, are characterized by a superposition of the contributions of dipole relaxation and conduction on the ε'( f ) and ε''( f ) isotherms (Fig. 1). The superposition of these two processes is reflected in a sharp increase in ε' and ε'' with decreasing frequency and increasing temperature and in a maximum manifested on the ε''( f ) curves at low temperatures. Heating shifts this maximum toward higher frequencies. The contributions of conduction and dipole relaxation were separated using the formula [14] '' ( f ) + ε rel '' ( f ) . ε'' ( f ) = ε cond
(1)
Studies of the dielectric properties of polyionenes have shown that the conductivity term is approximated by a single power function with unsatisfactory accuracy; hence, it was necessary to use a superposition of two power functions [14]. Our investigations confirmed this conclusion: S1
S2
'' ( f ) = K 1 ( 2πf ) + K 2 ( 2πf ) . ε cond
(2)
The resulting calculated parameters ä1, K2, S1 , and S2 are listed in Table 2. The contribution of dielectric relaxation to the total function ε''( f ) was analyzed using the Havriliak– Negami formula [27] ∆ε '' ( f ) = Im ---------------------------------------- , ε rel f (1 – α) β 1 + i ---- f 0
(3)
where ∆ε is the relaxation force equal to the difference between the low- and high-frequency ε' values of the relaxation process; f0 is the relaxation frequency; and the α and β parameters determine the width and asymmetry of the relaxation maximum, respectively. The parameters of Eq. (3) are listed in Table 2. Table 2 demonstrates that the ä1 and ä2 values, in contrast to S1 and S2 , significantly change with temperature. As the length of the oxyethylene fragment increases, the ä1 and ä2 values, which determine the conductivity level, decrease. This agrees with the fact that ε' and ε'' increase more steeply as the length of the ethylene oxide fragment decreases (Table 2), thus indiPOLYMER SCIENCE
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rectly indicating a higher conductivity of polyionenes with shorter oxyethylene fragments. Figure 2 shows the ε''( f ) plots illustrating the contributions of the conduction and dipole relaxation for polymer I. The curves are calculated according to Eqs. (1)–(3). As is seen from Table 2, the α and β parameters, in contrast to parameters of the power functions, are not temperature-dependent; however, their invariance with respect to changes in the molecular structure of the polymers is especially interesting. Figure 3 shows the plots of the logarithmic dipole relaxation frequency fε'' vs. reciprocal temperature for polymers I–III. The rectilinear character of the plotted lines indicates that these processes obey the Arrhenius law. The activation energies of the relaxation process are given in Table 3. Analyzing the frequency dependences of the real and imaginary parts of permittivity for the polyionene series of interest, one can note that very high ε' and ε'' values at high temperatures and low frequencies are typical of ion-conducting systems [18, 23]. As is known, such high ε' values in the case of conducting dielectrics may be due to charge buildup at the sample– electrode interface, the so-called space charge polarization [28]. Accordingly, high ε'' values at low frequencies are observed for the free motion of charges in the material and are associated with conductivity relaxation [29]. The dipole relaxation, which is manifested by the presence of a maximum on the ε''( f ) curves at low temperatures, may be associated with a local motion of the polymer chain. For example, the relaxation at 1 Hz takes place at a temperature of about –110°C, which is in agreement with the results obtained by some
1 2 3 4 5 6 7 8 9
(a) 10 3
10 2
10 1 ε'' 10 6
(b)
10 4 10 2 10 0
10 0
10 2
10 4
787
10 6 f, Hz
Fig. 1. Isotherms representing the (a) permittivity and (b) dielectric losses vs. frequency for polymer I. T = (1) 60, (2) 40, (3) 20, (4) 0, (5) –20, (6) –40, (7) –60, (8) –80, and (9) –100°C. ε'' 1.0
fε'', Hz 10 5 1 2
0.6
1 2 3
10 3 0.2 10 1 10 0
10 2
10 4
10 6 f, Hz
Fig. 2. Separation of the conductivity and dipole relaxation contributions in polymer I. The points correspond to experimental data, and the solid and dashed lines represent the contributions of the conductivity and dipole relaxation, respectively. T = (1) −40 and (2) –60°C. POLYMER SCIENCE
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4.5
5.0 5.5 (10 3/T), K–1
Fig. 3. Arrhenius plots of the frequency maxima of ε'' for polymers (1) I, (2) II, and (3) III. 2003
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BURMISTR et al. Z'', Ω 10 12
anism of the dipole relaxation process. This indicates that the local motion of polymer chains is a thermally activated process. In similar studies of aliphatic polyionenes, Kremer et al. [14] also observed such a process with an activation energy of about 0.5 eV, which is consistent with our results.
1 2 3 4 5 6 7 8
10 10 10 8
Complex Impedance
10 6
10 0
10 2
10 4
An alternative way of representing dielectric relaxation data is to use the pair of functions Z'( f ) and Z''( f ) instead of the above pair ε'( f ) and ε''( f ). The use of the complex impedance allows direct determination of the bulk resistance [23, 35, 36]. Figure 4 shows the isotherms of the imaginary part Z'' of complex impedance vs. frequency for polymer III. It is seen that these plots contain a maximum, which shifts toward lower frequencies as the temperature '' , decreases; at the same time, the maximum value Z max which determines the conductivity, increases. In the '' of the maxima polyionene series, the height Z max increases with the length of the oxyethylene spacers (polymers I–III), indicating a decrease in the bulk conductivity. The contributions of the dipole relaxation observed at high frequencies are very small compared to the conductivity effects. Figure 5 shows the Z* plots in the complex plane (Nyquist diagrams) for polymer I; to depict all the isotherms in the same figure, the Z' and Z'' values are multiplied by the coefficients given in the figure caption.
10 6 f, Hz
Fig. 4. Isotherms representing the imaginary part Z'' of the complex impedance vs. frequency for polymer III. T = (1) 60, (2) 40, (3) 20, (4) 0, (5) –20, (6) −40, (7) –60, and (8) –100°C.
researchers for PEO at the same frequency [30, 31]. Relaxation of this kind has been observed for polyurethanes [32], polyamides, and other carbon-chain polymers [32–34]. A notable fact is that the activation energies of the local motion of the polymer chain are equal for polyionenes with different molecular structures. This indicates that the nature of this motion is identical and invariant to the concentration of ionic sites. Another specific feature of the oxyethylene–alkylaromatic polyionenes in question is the Arrhenius mech-
Table 2. Parameters of the power functions describing the conductivity contribution and parameters of the Havriliak– Negami equation, which describes the contribution of the dipole relaxation in the dielectric loss isotherms for polyionenes of the oxyethylene–alkylaromatic series (α = 0.65, β = 1, and S2 = 0.95) Polyionene
T, °C
∆ε
K1
S1
K2
I
–20
12000
1.23
9.3
0.4
187.0
–40
1000
0.57
0.9
0.2
5.7
–60
32
0.56
0.35
0.2
0.18
0.54
0.11
0.2
0.02
–80 II
1.4
0
15265
3.5
0.4
682.0
–20
2000
2.8
5.81
0.4
21.7
–40
166
2.3
1.20
0.4
0.6
–60
10
2.1
0.17
0.4
0.07
1.9
0.01
0.4
0.017
–80 III
f0 , Hz
0.36
22.1
0
28180
2.5
30.4
0.4
340.3
–20
3000
2.0
3.9
0.4
5.0
–40
250
1.9
0.68
0.4
0.01
–60
13
1.7
0.05
0.4
0.006
1.6
0.005
0.4
0.001
–80
0.4
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The isotherms of the Z''(Z') plots for temperatures from +60 to –20°C are close to semicircles, have deviations in the low-frequency region, and shift upward as the temperature decreases. The deviations are due to polarization effects and become more marked as the temperature is elevated, and, consequently, the mobility and effective density of charge carriers increase as well.
1 2 3
7.5 × 10 5
4 5 6
5.0 × 10 5 2.5 × 10 5
At temperatures from –40 to –100°C, it is difficult to determine the position of the maximum on the parametric dependences of the complex impedance within the specified frequency range.
5.0 × 10 5
1.0 × 10 6 Z', Ω
Comparing the complex impedance arcs for the polymers in question, one can note that the height and width of the semicircles below room temperature change in the order I < II < III. Hence, the conductivity decreases with the length of the oxyethylene spacers.
Fig. 5. Parametric dependences of the complex impedance for polymer I in the +60 to –40°C temperature range. The Z' and Z'' values are multiplied by coefficients K. T = (1) 60, (2) 40, (3) 20, (4) 0, (5) −20, and (6) –40°C; K = (1) 1, (2) 0.2, (3) 10–2, (4) 5 × 10−4, (5) 2.5 × 10–5, and (6) 10–5.
In studies of polymeric electrolytes, the dc bulk conductivity σd.c is usually determined on the basis of complex impedance arcs. The σd.Ò values excluding the polarization effect were found using extrapolation to the Z' axis; this extrapolation consisted in completing the first half of the semicircle by a symmetrical semicircle. The resulting values are listed in Table 4. An alternative method is to determine σd.Ò from the plateau on the σ'( f ) frequency plots. The σd.Ò values found from the frequency plots of the real part of conductivity (the procedure for determining σd.Ò from the corresponding
dependences is described below) are also listed in Table 4. Analyzing these data, we may conclude that the studied oxyethylene–alkylaromatic polyionenes have a high conductivity. Having the highest concentration of ionic sites, polyionene I exhibits the highest conductivity in the series. Near the glass transition temperature (57°C), it has σd.Ò = 2.7 × 10–6 Ω–1 cm–1. The σd.Ò value
Table 3. Activation energies found from the Arrhenius plots of σd.c, f1,M'', f2,M'', and fε'' Ea (σd.c)
Polyionene eV
Ea (f1, M")
Ea (f2, M")
Ea (fε")
kJ/mol
eV
kJ/mol
eV
kJ/mol
eV
kJ/mol
I
1.02
98
1.04
100
0.63
61
0.65
63
II
1.12
108
1.25
120
0.61
59
0.60
58
III
1.44
139
1.52
146
0.63
61
0.64
62
Table 4. Direct-current conductivities σd.c for polymers I–III found from the σ'(f) and Z* plots σd.c values, Ω–1 cm–1 T, °C
I σ'(f)
II Z*
σ'(f)
Z*
–
–
80
2.5 × 10–5
60
2.7 ×
40
2.3 × 10–7
3.6 × 10–7
8.2 × 10–8
20
1.1 × 10–8
1.5 × 10–8
0
3.8 × 10–10
–20
1.9 × 10–11
–40
4.9 × 10–13
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III
–
– 3.6 × 10–6
1.1 × 10–7
2.4 × 10–7
3.1 × 10–7
2.3 × 10–9
2.8 × 10–9
5.2 × 10–9
7.5 × 10–9
5.9 × 10–10
7.0 × 10–11
9.3 × 10–11
3.2 × 10–11
4.5 × 10–11
2.3 × 10–11
2.2 × 10–12
3.1 × 10–12
6.5 × 10–13
8.5 × 10–13
1.0 × 10–13
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–
10–6
3.0 ×
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–
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M' 0.06
10 6
(a)
(a) 0.04
0.02
1 2 3
1 2 3 4 5 6 7 8 9
10 2
3.0
M'' 0.015
3.5
4.0
4.5 (10 3/T), K–1
f2, M'', Hz
(b)
10 5 (b)
0.010 10 3 0.005 10 1
10 0
10 2
10 4
10 6 f, Hz
Fig. 6. Isotherms representing the imaginary part of the complex electric modulus vs. frequency for polymer I in the (a) high- and (b) low-temperature regions. T = (1) 60, (2) 40, (3) 20, (4) 0, (5) –20, (6) –40, (7) −60, (8) –80, and (9) –100°C.
decreases as the length of the ethylene oxide fragment increases [37, 38]. Complex Electric Modulus Another way of representing the dielectric spectroscopy data is to use the å''( f ) and å'( f ) pair, which is widely practiced when dealing with conducting dielectrics. Within the complex electric modulus, the space charge effects are suppressed and conduction relaxation can be better analyzed. Figure 6 presents the isotherms of the frequency dependence for the imaginary part å'' of the electric modulus of sample I in the high- and low-temperature regions, respectively. The å'' vs. frequency isotherms display (in contrast to ε'') two characteristic maxima with the frequencies f1, M'' and f2, M''; they lie in the regions corresponding to the conductivity contribution in ε''( f ) and to the frequency range of dipole relaxation in ε'', respectively. The first peak is observed at high temperatures in the region of the transition to the dc
4.0
4.5
5.0 5.5 (10 3/T), K–1
Fig. 7. Arrhenius plots of the frequencies f1, M'' and f2, M'' corresponding to the maxima on the M''( f ) curves in the (a) high- and (b) low-temperature regions for polymers (1) I, (2) II, and (3) III.
conductivity σd.Ò , which shifts toward higher frequencies with temperature. The second, smaller, peak is observed at low temperatures and slowly shifts to the right as the temperature is elevated. Comparison of the frequency dependences of å'' for the polyionenes in question shows that the highest values at the first peak are reached for polymer I, which has the shortest ethylene oxide block; as the length of this block increases, the intensity of the maximum decreases. As regards the second maximum, variations in the molecular structure have no effect on its shape or height. The temperature dependences of the frequencies f1, M'' and f2, M'' of the relaxation maxima for polymers I– III are shown in Fig. 7. All these dependences are adequately described by the Arrhenius equation; the activation energies are listed in Table 3. The relaxation process in the high-temperature region is characterized by an activation energy identical to the activation energy of conductivity relaxation POLYMER SCIENCE
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found from the σ'( f ) dependences (Table 3). This fact indicates that the f1, M'' frequencies correspond to the conductivity relaxation. The frequency of the f1, M'' maximum makes it possible to determine the conductivity relaxation time τ = 1/2πf1, M'' , which characterizes the time of ion motion. By representing the experimental data by frequency dependences of the imaginary part of the electric modulus, one can analyze the possible mechanisms responsible for the relaxation processes. For example, by extrapolating the Arrhenius dependence of f1, M'' to 1.46 Hz (the frequency corresponding to the relaxation time τ = 100 s), one can show that the relaxation at this frequency takes place at approximately –60°C. Thus, the conductivity is activated as ethylene oxide fragments are devitrified. It is interesting that, as we pass from polymer I to polymer II, the first and second å'' peaks shift toward lower and higher frequencies, respectively. This implies that an increase in the length of the ethylene oxide block is accompanied by aggregation of the ionic groups into multiplets, and the total amount of free charge carriers in the material decreases as a result. The clustering of ionic groups probably results in a higher activation energy of the conductivity relaxation and, consequently, in a lower conductivity. The most interesting thing here is the Arrhenius mechanism of the conductivity relaxation, which indicates that the ion motion is thermally activated. This is absolutely untypical of most polymeric electrolytes: the corresponding dependences for them are described by the Vogel–Tammann–Fulcher equation, indicating an influence of the free volume on charge transfer processes. The second peak of the M''( f ) curve with f2, M'' at higher frequencies, which gradually shifts to the right with temperature, is due to the local motion of groups in the polymer chain, which is manifested on the ε''( f ) plot as well. This is indicated by the equality of the activation energies calculated according to the plots of f2, M'' and fε'' vs. the reciprocal temperature. Complex Conductivity The relationship between the frequency and the real σ' and imaginary σ'' parts of the complex conductivity of polyionene I is shown in Fig. 8 in logarithmic scale for the entire temperature range examined. For all the polymers in question, the real part of the conductivity displays a behavior typical of solid electrolytes [23]. In the region where ε' and ε'' display a sharp increase in their frequency dependences, the σ'( f ) curves have a plateau corresponding to the dc conductivity σd.Ò [39, 40]. At low temperatures, the frequency dependence of σ' is virtually linear. The slope of the linear portion slightly increases with the length of the ethylene oxide fragment POLYMER SCIENCE
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σ', Ω–1 cm–1 (a) 1×
10 –6
1 × 10 –8 1 2 3 4 5 6 7 8 9
1 × 10 –10 10 –12 10 0 σ'', Ω–1 cm–1 1 × 10 –5
10 2
10 4
10 6 f, Hz
10 4
10 6 f, Hz
(b)
1 × 10 –7 1 × 10 –9 10 –11
10 0
10 2
Fig. 8. Isotherms representing the (a) real and (b) imaginary parts of the complex conductivity vs. frequency for polymer I. T = (1) 60, (2) 40, (3) 20, (4) 0, (5) –20, (6) –40, (7) –60, (8) –80, and (9) −100°C.
and amounts to 0.89, 0.90, and 0.92 for polymers I, II, and III, respectively. From the plateaus in the σ'( f ) plots, one can determine the dc conductivity σd.Ò through extrapolation to the ordinate axis. The σd.Ò values thus obtained are listed in Table 4. Comparing them for the polyionenes in question, one can conclude that polymer I has the highest conductivity in all cases and its value changes within the polymer series as I > II > III. For example, the conductivity at 0°C is equal to 3.8 × 10–10, 7.0 × 10−11, and 3.2 × 10 –11 Ω–1 cm–1 for polymers I, II, and III, respectively. Figure 9 shows σd.Ò for polymers I–III as a function of the reciprocal temperature, found from the plateaus in the σ' vs. frequency plots. The curves for all the polymers are described by the Arrhenius equation with the activation energies as given in Table 3. Thus, the temperature dependences of σd.Ò differ from those of most polymeric electrolytes based on flexible-chain polyethers, for which the Arrhenius
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σd. c, Ω–1 cm–1
σ', Ω–1 cm–1
1 × 10 –4
1 × 10 –5 1 2 3
1 × 10 –8
1 × 10 –9
1 × 10 –13
10 –12 3.0
3.5
4.0
4.5 3 (10 /T), K–1
Fig. 9. Arrhenius plots of the dc conductivity σd.Ò in the 353–233 K range for polymers (1) I, (2) II, and (3) III.
curves are described by the Vogel–Tammann–Fulcher equation. As is seen from Table 3, the activation energy of the process associated with conduction significantly increases with the length of the ethylene oxide fragment. The real part of conductivity is also presented in Fig. 10 in the form of σ' vs. reciprocal temperature plots at various frequencies for polymer I. Two conductivity regions are easily distinguished. At low temperatures, the thermal activation of conductivity is slight but highly dependent on the frequency. When the temperature rises above a certain critical point ícr , the conductivity sharply increases and its dependence on the frequency becomes insignificant. The Arrhenius plot of σd.Ò is also shown in Fig. 10. The critical temperatures of the transition between the two conductivity regions are listed in Table 5. Table 5. Critical temperatures for the dc conductivity σd.c of polymers I–III at various frequencies Tcr , K
f, Hz 0.1 1 10 102 103 104 105 106
I
II
III
217 227 238 250 266 277 285 290
232 238 250 256 263 270 287 291
241 250 256 274 277 280 284 291
1 2 3 4 5 6 7 8 9
3
4
5
6 (10 3/T),
K–1
Fig. 10. Real part of the complex conductivity of polymer I vs. reciprocal temperature at a frequency of (1) 0.1, (2) 1, (3) 10, (4) 102, (5) 103, (6) 104, (7) 105, and (8) 106 Hz; (9) is the Arrhenius plot for σd.Ò .
As is seen from Table 5, the critical temperatures of activation of conduction increase in the I–II–III polymer series at low frequencies and become equal for all these polymers at high frequencies. The critical conduction activation temperatures are an important characteristic specifying the so-called conduction boundaries. However, the important thing here is not the critical temperatures themselves but the rate of their increase with frequency. For example, analyzing the data of Table 5, one can conclude that polymer I has the widest range (73 K) of conduction activation temperatures; further, this width decreases to 59 or 50 K for polymer II or III, respectively. Thus, the polyionene with two ethylene oxide fragments has the highest conductivity, which is activated at lower temperatures compared to other studied polyionenes of the oxyethylene–alkylaromatic series. It is interesting that the activation energies of conductivity relaxation exceed those of the local motion by a factor of 1.5–2.5. In the case of the local motion of polymer chains, the activation energy is the energy required for the motion of some chain fragment. For the relaxation of conductivity, this is the energy needed to transfer an ion from its original position to some other position, including the energy required for the local motion of the chain segments participating in the ion motion [18–20]. In other words, in the case of conductivity relaxation, its activation energy must exceed that of dipole relaxation, as is reflected in the results of this study. Specifics of Ionic Conductivity for Polyionenes It is generally accepted that ion transport in highconductivity polymeric electrolytes (usually solutions of lithium salts in polyether systems), which includes POLYMER SCIENCE
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1 × 10 –8
1 1 × 10 –12
3
2
4.0
4.5
5.0 Tg /T
Fig. 11. Scaling Arrhenius plots for polymers (1) I, (2) II, and (3) III.
segmental motion of the main polymer chain, exists only above the glass transition temperatures Tg [41–43]. For inorganic systems, on the contrary, ionic conductivity in the solid state is a common phenomenon and sometimes reaches 10–2 Ω–1 cm–1 at room temperature [42, 44, 45]. These differences may be discussed using the socalled decoupling index Rτ introduced by Angell [42, 46]. This index reflects the relationship between the conductivity level and the system mobility. According to Angell, the Rτ index at Tg is defined as Rτ = τç/τσ,
(4)
where τç is the relaxation time of a polymer segment in an amorphous region (for the DSC determination of Tg , the τç value is usually assumed to be equal to 100 s) and τσ = ε''ε0 /σd.c is the conductivity relaxation time at Tg (determined from the Arrhenius dependences of f2, M''). Equation (4) reflects the extent of the concordance between the processes of charge motion and segmental movement. For example, Rτ for inorganic glasses usually amounts to 1011 (e.g., silicate glasses) and even reaches 1013–1014 in some superconducting systems [43]. For the overwhelming majority of polymeric electrolytes of the salt-in-polyether type, the Rτ values generally do not exceed unity. The reason for such low valTable 6. Rτ indices for the studied polyionenes Tg, °C
τ1, M' , s
Rτ = τH /τσ
I
57
3 × 10–7
3.3 × 108
II
40
8 × 10–6
1.3 × 107
III
18
1 × 10–4
1.0 × 106
Polyionene
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ues is the ion mobility, which decreases because of ion binding as the system approaches the glass transition temperature [43]. Figure 11 shows the scaling Arrhenius curves (relative to Tg) for polyionenes of the oxyethylene–alkylaromatic series. The decoupling indices calculated according to Eq. (4) for the polyionenes in question are listed in Table 6. The highest values are observed for polymer I, for which σ(íg) 2.7 × 10–6, and Rτ increases with the concentration of the ionic sites. The conductivity of traditional solvent-free polymeric electrolytes [46–53] is usually optimized by intensifying the local motion of polymer segments involved in the ion motion below the glass transition temperature of the polymer and by reducing the tendency toward the formation of ion pairs. However, there is very little published information on the ionic conductivity in polymers below their glass transition temperatures [14, 54–56]. The polyionenes synthesized in this work display a high conductivity at temperatures much lower than Tg . For the earlier studied classical polymeric electrolytes based on polyether matrices, a number of methods have been developed for enhancing the conductivity by reducing the glass transition temperature of the polyether segments and by introducing additional ion-solvating groups [49–53]. The systems in question contain comparatively rigid chains with a low (compared to polyether chains) mobility. Thus, the high level of ionic conductivity does not depend on the mobility of chains and is determined by a mechanism other than the one characteristic of traditional polymeric electrolytes. Most likely, it is associated with the presence of ordered ionic sublattices, which have been postulated for such systems [13, 14]. REFERENCES 1. Meyer, W.H., Polymer Electrolytes II, MacCallum, J.R. and Vincent, C.A., Eds., London: Elsevier, 1989. 2. Lipatov, Yu.S., Burmistr, M.V., and Privalko, V.P., Dokl. Akad. Nauk SSSR, 1991, vol. 318, no. 3, p. 632. 3. Feng, D., Wilkes, G.L., Lee, B., and McGrath, J.E., Polymer, 1992, vol. 33, no. 3, p. 526. 4. Leir, C.M. and Stark., J.E., J. Appl. Polym. Sci., 1989, vol. 38, no. 8, p. 1535. 5. Dominguez, L., Enkelman, V., Meyer, W.H., and Wegner, G., Polymer, 1989, vol. 30, p. 2030. 6. Dominguez, L. and Meyer, W.H., Solid State Ionics, 1988, vols. 28–38, p. 941. 7. Dominguez, L., Meyer, W.H., and Wegner, G., Makromol. Chem., Rapid Commun., 1987, vol. 8, p. 151. 8. Cheng, P., Subramanyam, S., and Blumstein, A., Polym. Prepr. (Am. Chem. Soc., Div. Polym. Chem.), 1992, vol. 33, no. 2, p. 339. 9. Zhang, S. and Sha, Q., Solid State Ionics, 1993, vol. 59, p. 179.
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Vol. 45
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2003
