4148
J. Phys. Chem. 1994,98, 4148-4154
Conductivity and Dielectric Constant of PPO and PPO-Based Solid Electrolytes from Dc to 6 GHz Andrew L. Tipton, Mark C. Lonergan,' Mark A. Ratner, and Duward F. Shriver Department of Chemistry and Materials Research Center, Northwestern University, 21 45 Sheridan Road, Evanston, Illinois 60208-31 13 Thomas T. Y. Wong' and Keli Han Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, Illinois 60616 Received: October I I , 1993; In Final Form: January 4, 1994"
The conductivity and dielectric response of poly(propy1ene oxide) (PPO) and the polymeric solid electrolytes (PPO)gNH&F3SO3, (PPO)lbNaI, (PPO)loNaI, and (PP0)gNaI were studied in the frequency range from d c to 6 GHz and the temperature range from 173 to 323 K with the objective of elucidating the dynamic factors that affect ion transport in polyether electrolytes. The temperature dependencies of the primary a-relaxation of PPO and the dc electrical conductivity of the salt complexes are consistent with this relaxation playing a key role in ionic conduction in polymer electrolytes. For the salt complexes, the a-relaxation appears to be shifted to lower frequencies relative to pure PPO, and this is attributed to virtual cross-linking. High-frequency room temperature measurements permit for direct comparison of the dielectric properties of (PPO)sNH4CF3SO3 with a supercooled amorphous (PEO)*NH&!F3SO3 complex. A dissimilarity between optical dielectric constants and those measured a t approximately 3 GHz for the salt complexes suggests the presence of a highfrequency ionic relaxation as predicted by the dynamic bond percolation model. The relative influence of segmental mobility and ion-ion interactions on the d c conductivity of polymer salt complexes is discussed.
Introduction
Experimental Section
Polymer electrolytes, solutions of salts dissolved in polar polymers, have attracted great interest in the past 15 years with respect to fundamental understanding of ion transport in polymers and applications in electrochemical devices, such as high-energydensity batteries.'-5 Ion transport in these systems occurs by a liquidlike mechanism that can be roughly described by the dynamic bond percolation theory.69 Studies of the frequency-dependent conductivity and dielectric response in the kilohertz through the gigahertz range have aided the discrimination between detailed mechanisms for inorganic solid electrolytes, and this type of study is similarly informative for polymer electrolytes.*@20 Few studies of polymer electrolytes including the radio and microwave frequency ranges have been rep0rted.2'-*~ Earlier work in this field focused on the salt complexes of poly(ethy1ene oxide) (PEO).25-27 At room temperature, PEO is semicrystalline and forms crystalline phases when complexed with metal salts. Since ion transport principally occurs in the amorphous phase of polymer-salt complexes,28 crystalline regions are unfavorable with regard to high ionic conductivity. In contrast, noncrystalline atactic poly(propy1eneoxide) (PPO) forms single-phase, amorphous complexes. PPO-salt complexes, however, display lower dc conductivities than analogous amorphous PEO-salt complexes. In the present research, a PPOammonium trifluoromethanesulfonate complex, (PPO)sNH4CF3S03,29 was chosen for study because its frequency can be readily compared to the previously published results for a metastable, supercooled, amorphous phase of (PEO)sNH4CF3S03.2' The conductivity and dielectric response of three solutions of NaI dissolved in PPO, PP0,NaI ( n = 8,10, 16), were measured to elucidate the dielectric response of polymer electrolytes as a function of salt concentration.
The polymer-salt complexes were prepared by dissolving PPO and NaI or NH4CF3SO3 in a common solvent, methanol, followed by solvent removal under rough vaccum followed by high vacuum. All samples were handled under an inert atmosphere following preparation to prevent the introduction of moisture and oxygen. PPO (Mw = 12 928, M , = 8080, M,/M, = 1.60 from G.P.C.) was generously supplied by John A. DeRosa of A R C 0 Chemical Co., Newtown Square, PA. Ammonium trifluoromethanesulfonate and sodium iodide were obtained from Aldrich. Three different techniques were used to measure the complex conductivity of the sample. In the frequency range 1-6 GHz, the sample was placed in a coaxial sample holder with a short circuit in direct contact with the back of the sample. The reflection coefficient for the microwave signal at the front surface of the sample is measured by a microwave network analyzer. From the measured data, the complex conductivity can be determined by solving for tr, the complex permittivity, in the equation30
8
Abstract published in Advance ACS Abstracts, March 1, 1994.
t r ' I 2 - tanh(yd) +
+ tanh(yd) = O
(1)
where p is the reflection coefficient, d is the sample thickness, and y = w(-l.cototr)l/2 with and t o the permeability and permittivity of freespace, respectively. The complexconductivity, u, is related to the complex permittivity through the relation u = u' + id' = iweoe, = iweo(e,' - it,") with i being (-1)IP. The sample holder was weighed before and after loading to determine the mass of the sample. The sample thickness was then calculated from the cross-sectional area of the sample holder and thedensity ofthe sample. Thedensityof PPO was determined by measuring the volume of water or heptane displaced by a known mass of PPO. The densities of the salt complexes were determined by filling a container of known volume. For frequencies from 20 to 500 MHz, a similar sample holder was employed, but with the short circuit replaced by a high-
0022-3654/94/2098-4148$04.50/0 @ 1994 American Chemical Society
The Journal of Physical Chemistry. Vol. 98, No. 15, 1994 4149
Conductivity of PPO-Based Solid Electrolytes
TABLE 1: Values Used for Fit of the PPO and 1-Propanol Dielectric Loss Spectra to the Havriliak-Negami Equation PPO 1-propanol ts- c m 2.21 19.5 a
B 7 0 (SI
0.30
0
0.65
1
1.19 X
3.58 X
Qualitatively, ion transport in macromolecular electrolytes is controlled by the viscosity of the solution as suggested by Walden's rule.36 P
io5 io6
i o 7 i o 6 i o 9 i o l o io1'
io12
o / radians s-' Figure 1. Normalized dielectric loss (cT/(cI - em)) as a function of and l-propano13*(0) at room temperature. As frequency for PPO (0) shown by the solid lines, the data for 1-propanol fit well to a simple Debye relaxation whereas that for PPO exhibit a much broader primary loss peak as modeled by the empirical Havriliak-Negami function. The deviation in the PPO spectrum from the Havriliak-Negami fit at low frequencies is due to a weak, secondary relaxation.
impedance Teflon terminator. The impedance presented by this termination was first calibrated and taken into consideration in the final expression for the reflection coefficient at the front surface of the sample. At frequencies lower than 20 MHz the sample was sandwiched between two tantalum electrodes with a Teflon spacer in an airtight cell. The admittance spectra were taken for the full and empty cell using an HP 4192A L F impedance analyzer and a Solartron 1250 frequency response analyzer. The complex permittivity and conductivity were calculated according to3'
I
iweoe/ = d = -(Ill cos 6 - lY,l cos e,) A e;
=1
1 1 +-(lv weo A
sin 8 - lY,l sin e,)
where Y,0, I , and A are the admittance, phase angle, sample length, and area, respectively, and the subscript e refers to the empty cell. The dc conductivity was determined by complex impedance analysis of data collected over the frequency range 5 Hz to 13 MHz. The glass transition temperatures were measured by differential scanning calorimetry (DSC) using a Perkin-Elmer DSC-7. Samples were loaded under an inert atmosphere into hermetically sealed pans. Glass transitions were measured at three heating rates (5, 10, and 20 K/min), and the T, for the sample was determined by extrapolating to a zero heating rate the onset point of the transition curve. Refractive index measurements were performed at room temperature on a Bausch and Lomb Abbe refractometer.
Results and Discussion The room temperature dielectric losses as a function of frequency for PPO and, for comparison, 1-propanol32 are shown in Figure 1. Amorphous PPO shows two relaxations in the frequency range covered. At low frequencies, a weak secondary relaxation (a'relaxation) is observed that shows some dependence on molecular weight and is believed to arise from motions of the entire polymer chain.33-35 The high-frequency peak (a-relaxation) is the primary feature of the spectrum. The characteristic frequency of this relaxation is generally molecular weight independent. It is attributed to the micro-Brownian motion of the polymer33-35 and correlates with charge transport in polymer electrolytes.
OE
l/s
(3)
where p is the mobility and q is the viscosity. Typically, this rule is written in terms of the bulk viscosity which is molecular weight dependent. The conductivity of polymer-salt complexes, however, does not generally depend on molecular weight; hence, Walden's rule in its usual form does not hold.37 Ion transport in polymer electrolytes is dependent on the "microviscosity", which represents the constrained motions of short segments of polymer chains. The onset of these motions occurs around the glass transition, and they give rise to the a-relaxation in the dielectric spectrum of PPO. Accordingly, our studies have focused on this feature of the dielectric relaxation spectrum. The dielectric loss data for the a-relaxation of PPO was fit to the imaginary part of the empirical Havriliak-Negam?* function: (4) where w = 21rJ a describes the width of the relaxation time distribution (0 < a < l ) , 0 describes the skewness of thedispersion (0 < /3 < l), €0 and t, are the static and limiting high-frequency dielectric constants, and TO is the average relaxation time. The best least-squares fit of eq 4 to the room temperature data is shown in Figure 1. For comparison, the data for 1-propanol were fit to a simple Debye relaxation (a = 0, (3 = 1 in eq 4). The values used for these fits are listed in Table 1. The broad peak for PPO represents a wide distribution of relaxation times. The connectivity of the polymer chain in which no dipole can move independentlymaybe responsible for thisdistribution. In contrast, the dielectric loss spectrum of 1-propanol displays a much sharper relaxation peak than that of PPO. This Debye behavior is consistent with weakly interacting dipoles.39 Figure 2a shows the frequency-dependent dielectric loss of PPO at several temperatures along with the corresponding Havriliak-Negami fits. The temperature dependence of the characteristic frequency, 00 = 1/TO,extracted from the HavriliakNegami fits is shown in Figure 2b. These data are in good agreement with previous work. For example, Yano et al.40*41 demonstrated that the VTF equation in the form wmax = (6.28 X 1012 rad/s) exp(-1139 K/(T - 167 K)) fit their data as well as that of Williams42 and that of Baur and Stockmayer.33 This equation also provides a good representation of our temperaturedependent data. Fontanella and co-workersI1J2 have pointed out the similar temperature and pressure dependencies of the peak frequency of the a-relaxation in PPO and the conductivity of PPO-salt complexes.43 The temperature-dependent comparisons were based on fits to the empirical VTF equation:
AT)= A T I / ~exp[--1 T -B To where A , B, and TOare fitting parameters, and f(r ) is either the characteristic frequency of the a-relaxation or the dc conductivity of the salt complexes. Equation 5 can be derived from considerations of configurational entr0py~~8~5 or free v0lume,4~.~~ and TOis empirically related to the glass transition temperature, T,,
Tipton et al.
4150 The Journal of Physical Chemisfry, Vol. 98, No. 15, 1994 , , "".'I
i-1
,
, ,
'"."'i
.''-''1
' ,
I
'1''"1
1
1 0 q 1
,
1o5
1o4
106
10'
0
260
108
280
v '
300
11
(PPO),Nal 2
320
340
1
360
temperature I K
w I radians s-'
Figure 3. Temperature-dependentdc conductivity of (PPO)sNH&FsSO3 ( O ) , (PPO)l6NaI (0),(PP0)loNaI (A),and (PP0)sNaI (V)and
corresponding two-parameter VTF fits (solid lines). Best fit VTF parameters are shown in Table 2.
3"
103
102 1
0
220
240
1
260
1
280
300
temperature I K Figure 2. (a) Frequency-dependent dielectric loss of PPO at several temperatures: 227 (0),234 (0),242 (A),and 250 K (V). The solid lines represent the best fitsto the Havriliak-Negami equation. (b) Temperature dependence and VTF fit (solid line) of 00 for PPO. Best fit VTF parameters are shown in Table 2.
typically being 35-45 deg lower. In the work of Fontanella e? al., fits to the conductivity and dielectric data yielded values of the pseudoactivation parameter B within 10% of each other, suggesting a strong relation between the polymer motions that give rise to the a-relaxation and conductivity in polymer-salt complexes.Il Our data allow this comparison to be made over similar ranges of T - TOand with salt complexes of varying concentration and composition. The temperature-dependent dc conductivities of the various salt complexes studied are shown in Figure 3. In fitting these data and the dielectric data for the a-relaxation of PPO to the VTF equation, we reduced the number of variable parameters by determining TOvia the empirical relation To = Tg- c. (See Table 2 for a listing of glass transition temperatures.) The parameter c was estimated by the average difference between TOdetermined from an initial three-parameter VTF fit of these data and T,. (Results of this three-parameter fit are shown in Table 2 as 4 , B3, and TO.)Theconductivity and dielectric relaxation data were then refit fixing TO= Tg- 42 K. The resulting VTF parameters, A2 and B2, are listed in Table 2, and the fits to the experimental data are shown in Figures 2B and 3. As can be seen, the resulting values of Bz are similar for the dielectric relaxation data on PPO and for the conductivity measurements on the various PPO-salt complexes. The agreement with Bz for the dielectric data on PPO is best for the most dilute electrolytestudied, namely, PPOI6NaI. As the salt content is increased, a greater disparity is observed. Comparison of the various complexes of PPO suggests that this disparity is not a simple function of the degree of perturbation, as measured by Tg,
to the chain dynamics of the pure host polymer. Due to the nature of these fits, however, detailed conclusions beyond the qualitative observation that the a and ion-conduction processes exhibit similar temperature dependencies would be speculation. The comparison of the temperature-dependent a-relaxation for PPO and the conductivity data for PPO-salt complexes performed by Fontanella et al. yielded better agreement than observed here. These workers reported B = 1030 K for the dielectrical data on the a-relaxation of PPO as compared to B = 1000,952, and 986 K for the electrical conductivity data of PPOsLiCF3S03, PPOsLiC104, and PPOsLiI, respectively.*I Nonetheless, the correspondence between our measurements for these two quantities is still rather striking as emphasized in Figure 4, which plots the conductivity of PPOI6NaI (right ordinate) and wo for the glass transition relaxation of PPO (left ordinate) as a function of T TB' In Figure 5,theconductivity diffusion coefficient, D,,calculated via the Nernst-Einstein equation
D, = k,Ta/nq2
(6)
where kb is the Boltzmann constant, n is the carrier density, and q is the carrier charge, is plotted as a function of T - Tg. In our application of eq 6, carriers are always defined as single ions, and hence the carrier density is equal to the ion density. Figure 5 represents an attempt to normalize the conductivity data on the various salt complexes with respect to differences in carrier concentration (plotting D,)and host segmental mobility (using T - Tg as the abscissa). The latter normalization is required since the introduction of salt raises T, due to the formation of virtual cros~-links.~8 The use of a scaled temperature to correct for this effect, T - Tg,is based on the assumption that, for a given temperature above Tg(or above TO),the polymer host dynamics will be similar for a particular polymer and its corresponding salt complexes. Within the free volume m 0 d e 1 , this ~ ~ ~corresponds ~ to making a constant free volume comparison of D,. The D, of the PP0,NaI (n = 8, 10, 16) salt complexes is a strongly decreasing function of salt concentration as evidenced by the room temperature D,of PP016NaI being over 3 orders of magnitudegreater than that of PPOgNaI. (The room temperature D,for each salt complex is indicated by a solid symbol in Figure 5). In Figure 5,however, this ordering is reversed with the most concentrated sample exhibiting the highest D, at a given value of T - T,. If the rescaling in Figure 5 correctly accounts for differences in host segmental mobility, any remaining variation in D, is due to the effects of ion-ion interactions on the conductivity. A complicating factor in this analysis is that the
The Journal of Physical Chemistry, Vol. 98, No. 15, 1994 4151
Conductivity of PPO-Based Solid Electrolytes
TABLE 2
Physical Properties and VTF Fitting Parameters’ for PPO, (PP0)8NH&O$F% and (PP0)DaI
P (g/mL) nd
TB (K) A,b
Ba (K)
To (K) A2‘ B2 (K)
PPO
PPOl6NaI
PPOloNaI
PPOsNaI
PPOsNH,CF,SO,
0.97i= 0.02 1.450 203 5.92x 1014 1500 156 2.23 x 1014 1320
1.16f 0.07 1.493 243 2.42 1160 206 5.21 1300
1.13 i= 0.05 1.495 270 4.48 1100 230 5.87 1138
1.27 & 0.07 1.467 287 3.63 993 245 4.06 1010
1.19 f 0.03 1.452 248 11.77 1450 188 2.45 1060
a A3, B3, and TOare the results of a threeparameter VTF fit to the data, whereas A2 and B2 are the result of a two-parameter fit with TO= T, 42 K. In units of rad K1/2 s-l for PPO and S K1/2cm-I for the salt complexes.
6” 1 o3
40
20
60
100
80
T-T, I K Figure 4. wo (left ordinate) for the a-relaxation of PPO (+) as a function of rescaled temperature, T - T,,and the conductivity (right ordinate), u, as a function of T - T, for (PPO)l6NaI (0). Notice the similar temperature dependencies of the dielectric data for PPO and the conductivitydata for the salt complex; this is indicative of the correlation between ion transport in polymer electrolytes and the polymeric motions associated with the a-relaxation. 1 0-7
0 0
l1 0o -9 l
0
O
I
(PPO),NH,CF,SO, A
v
Iv
1 0 . ~ ~v 1A
(PPO),Nal
f i
10-15
0
20
40
60
80
100
120
it is difficult to assess the magnitude of the variation in D,( T TB)due to differences in absolute temperature ( T varies up to about 15% at a given value of T - TBfor the salt complexes studied), Figure 5 is still suggestive that ion-ion interactions increasingly reduce the conductivity as the salt concentration is lowered. Several studies of the concentration dependence of D, for polymer-salt complexes have been performed.4s51 Although these measurements cannot directly distinguish between effects of Coulomb interactions and changes in the host segmental mobility, they do provide some insight into the role of ion-ion interactions with regard to D,. Typically, these results suggest D , is, at very low salt content, a decreasing function of concentration. As the salt concentration is increased further, however, D, begins to increase until a maximum is reached and then decreases again. The initial drop a t low salt content has been attributed principally to Coulombic effects since changes in TB,and hence the host’s segmental mobility, are negligible in this concentration range. Specifically, this reduction has been attributed to ion pair formation. At higher concentrations, the increase in D, has been explained in terms of the formation of higher charged aggregates, ion shuttling between aggregates, or screening effects as the electrolyte becomes better described as a concentrated Coulomb fluid. It is important tonote that invoking the formationof discrete ion clusters, especially in the higher concentration regime, is not required to explain thevariation of D , with concentration. Rather, more short-lived interactions may be at work. Finally, the maximum arises from the increasing effect of virtual cross-linking on the host’s segmental mobility. The NaI salt complexes of PPO studied here fall into this latter region where the concentration dependence of D , is principally determined by host dynamics rather than Coulomb forces. Renormalizing thedata as in Figure 5 , however, essentially removes the differences due to changes in polymer segmental mobility and carrier density so only the effects of ion interactions remain. From the above discussion, D, ( T TB)would not then be expected to exhibit a maximum but rather to continue increasing with concentration. Indeed, this is what is observed in Figure 5 . The effects of Coulomb forces on the conductivity can be separated into two types as embodied by a more general form of the Nernst-Einstein equation:
T-T, I K Figure 5. Conductivity diffusion coefficient, D,,of (PPO)sNH&F3SOa (O),(PP0)16NaI(O), (PP0)loNaI (A),and (PP0)gNaI (V)asa function of rescaled temperature T- Ts The room temperature D d of each of the complexes are indicated by solid symbols. This constant free volume comparison of D, implies that Coulomb interactions reduce D,the most in the least concentrated sample studied.
absolute temperature at which D , was measured for the various salt complexes at a given value of T - TBdiffers. Therefore, the ordering of D , at any vlaue of T - TBdepends on both the concentration and temperature dependence of Coulomb interaction effects. Nonetheless, if diffusion was strictly controlled by segmental mobility, as modeled by the VTFequation, D, would primarily depend on T - T,, which is clearly not thecase. Although
ts = nq2D,/k,THR
(7)
where Dsis the self-diffusion coefficient (generally taken as an average for systems containing charge carriers with differing mobilities), which is proportional to the mean-squared displacement of an ion over a unit time interval, and HR(=D,/D,) is a correlation factor known as the Haven ratio. For systems containing mobile ions of opposite charge, Coulomb interactions generally reduce conductivity relative to the noninteracting case through diminishedvalues of D,and through thecorrelated motion of particles with opposite charge as indicated by H R > 1.52 In the above discussion, no distinction between these two were made. Self-diffusion measurements, however, allow for these two processes to be separated and for H R to be evaluated.
4152
The Journal of Physical Chemistry, Vol. 98, No. 15, 1994
Tipton et al.
10'
w'
1 oo
10' I
1b5
106
107
'
' '"*'''I
io8
''.''''I
109
* ' J
' """'I
1010
o / radians s-' Figure 6. Dielectric loss as a function of frequency for (PP0)sNHdCF3SOp (o),(PP0)IsNaI (0),(PP0)loNaI (A),(PP0)sNaI (V),and
PPO (+) at rmm temperature. The salt complexes' responses are dominated by a dc conduction loss. The a-relaxation clearly visible in PPO is not apparent in the salt complexes. Presumably, it is shifted to lower frequencies in the salt complexes due to virtual cross-linking.
Boden et al.53 have performed self-diffusion measurements on molten PEO salt complexes using pulsed field gradient NMR. Their workshows that at high salt concentrations theself-diffusion coefficient and the diffusion coefficient derived from the conductivity via the Nernst-Einstein equation are in good agreement (HR= l), suggestive of weak correlations between anions and cations. As the salt concentration is lowered, however, the increasing deviations between the self-diffusion and conductivity diffusion coefficients suggest increased correlation between carriers (HR> l), consistent with the observed concentration dependence of D,( T - T g ) .The variation of HRwith concentration observed by Boden et al., however, is smaller than the order of magnitude difference in D,( T - TB)for the PPO-salt complexes studied here. This suggests that the Coulomb interactions between ions not only effect HRbut also play a role in determining D,. It is noted, however, that D,still appears to be principally governed by segmental mobility considerations with ion-ion interactions playing a secondary role. This is evident from comparison of the difference in the room temperature values of D, and those at a given value of T - Tg for the PP0,NaI salt complexes (Figure
5). Figure 5 can also be used to interpret the observed differences between the NH4CF3SO3 and NaI complexes. Although the room temperature conductivity of (PPO)sNH4CF3S03 is nearly 2 orders of magnitude greater than (PP0)8NaI, a much smaller difference is observed between these two salt complexes in this rescaled format. This suggests that the conductivity of these two salt complexes differs primarily due to the relative strengths of NH4CF3S03 and NaI as virtual cross-linking agents with differences in ion-ion interactions playing a more minor role. The frequency-dependent dielectric losses of PPO and the PPOsalt complexes at room temperature are shown in Figure 6 . No appreciable relaxation peaks for the salt complexes are observed. Notably, the a-relaxation is clearly not present in the same frequency range as observed for the pure polymer. Due to the effect of ions on the polymer's dynamics, this relaxation has been shown to shift to lower frequencies upon the addition of salt.13~2~ Assuming that the VTF parameters A2 and Bz for the cy-relaxation in the salt complexes are similar to those observed for pure PPO, an estimate of the location of this feature can be made via the VTF equation using TOderived from the appropriate Tg(c = 42 K). For PP016Na1, this procedure predicts the a-relaxation to occur a t approximately 2 MHz under ambient conditions. As can be seen from Figure 6 , the conductivity loss at this frequency dominates the response resulting in the cy-relaxation being hidden.
105
io6
10'
io8
lo9
iol0
10"
o / radians s-' Figure 7. Real part of the frequency-dependent conductivity for (PPO)8NH.+CF3SOp(O), (PP0)16NaI (0),(PP0)loNaI (A),(PP0)sNaI (v),and PPO (+) at room temperature. Notice the larger rise in d(w) with frequency for PPO relative to the salt complexes. This is attributed to more rapid dipolar reorientation in the pure host polymer than in the salt complexes where virtual cross-linking inhibits rotational mobility. The shift in this relaxation should be the least in PP016NaI since it has the lowest Tg. For the other samples, the larger shfit in the a-relaxation again results in it being hidden by the conductivity loss. In principle, it is possible to resolve the "dipolar" contribution, ed", to e," via subtraction of the dc conductivity loss according to e[
= E," - (udc/wtO)
(8)
This relation yields the purely dipolar contribution only when the ionic response is simply that of a frequency-independent dc conduction process. Often, however, more complicated behavior is expected. When applied to the description of the dielectric response of polymer-salt complexes, the dynamically disordered hopping (DDH) model predicts, in addition to a simple Udc/(OtO) contribution, another ionic component to the dielectric The subtraction suggested by eq 8, however, was unsuccessful in resolving any additional features. Figure 7 shows the real part of the room temperaturefrequencydependent conductivity, d(w), for PPO and the salt complexes investigated. At low frequencies, the d ( w ) values of the polymersalt complexes gradually approach their dc values while that of PPO decreases sharply as is expected for an insulator. The increase of d ( w ) with frequency for the salt complexes is in part due to the dipolar processes (for PPO this is mainly the a-relaxation), which could not be clearly resolved in the e," representation. The large increase in d ( w ) for PPO to values higher than that of the salt complexes is consistent with the faster dipolar reorientation in the pure host material. This can be rationalized by considering a simple Debye process. For such a relaxation, the real part of the limiting high-frequency conductivity is given by eo(c, - c , ) / T , where T is the relaxation time constant. Thus, for the dipolar component, the shorter the relaxation time, the greater the real part of the limiting high-frequency conductivity. Due to virtual cross-linking, the segmental motion of the host is significantly retarded on complex formation. As a result, the observed increase in d ( w ) due to the dipolar contribution is much less in the PPO-salt complexes than in PPO. Figure 8 compares d ( w ) at room temperature for our measurements on (PPO)gNH4CF$O3 and those of Ansari et ~ 1 . for ~ ' a metastable amorphous sample of (PE0)8NH&FsSO3. Theoverall frequency dependence is similar for both salt complexes with the room temperature dc conductivity of amorphous ( P E O ) B N H ~ C F ~ (udC S O ~= 1.3 X S/cm)21 being an order
The Journal of Physical Chemistry, Vol. 98, No. 15, 1994 4153
Conductivity of PPO-Based Solid Electrolytes
10 9 8
7 6
w‘ 5 4
3 10-7
io4 io5 io6
10’
IO*
io9
1o’O
ioll
io5
io7
io6
w / radians s-‘ Figure 8. Comparison of the real part of the frequency-dependent conductivity for amorphous (PE0)sNH4CF3SO3( 4 ) and (PPO)8NH4CF3SO3 ( 0 ) at room temperature.
of magnitudegreater than that of (PP0)8NH4CF3S03(a& = 9.4 X lo-’ S/cm). Although it is difficult todraw direct conclusions about the relative rate of segmental mobility in these two complexes, the dc conductivities suggest that it is faster in the amorphous PEO-salt complex. Dielectric measurements on partially crystalline PEO samples resolve a relaxation analogous to the a-relaxation observed in PPO (typically termed the /3-relaxation in PEO). This relaxation occurs at 0.1 GHz in PPO at room temperature as compared to PEO, where it occurs around 1 G H Z . ~ Although ~ ~ ~ ’ the effect of the crystalline regions of PEO on the dynamics of the amorphous regions is u n ~ e r t a i n , these ~~-~~ measurements suggest that the micro-Brownian motion of polymer segments is faster in amorphous PEO than in PPO. The slower segmental mobility of PPO relative to PEO is likely caused by the rotational hindrance introduced upon replacing a hydrogen with a bulkier methyl group. The rotational barrier around the C2-C3 bond of n-pentane(1) (4.2 k c a l / m ~ l ) for , ~ ~example, is approximately 0.6 kcal/mol lower than that of the C2-C3 bond of 2-methylpentane(l) (4.8 kcal/mol).60 If the effect of NH4CF3S03 on polymer dynamics is similar in both PPO and amorphous PEO, these results suggest that segmental mobility should be more rapid in the PEO-salt complex than in the PPO complex, which is consistent with the observed differences in their (Td& The real part of the dielectric constant of PPO and the PPOsalt complexes is shown as a function of frequency in Figure 9. The dielectric constant decreases with increasing frequency as the space charge and dipolar components of the polarizability are relaxed out. For PPO, both the primary a and secondary a’ relaxations are visible. Fits of the real part of the HavriliakNegami function to the a-relaxation yielded a value oft, = 2.09. With regard to the salt complexes, c,l(w) becomes dominated by the space charge polarizability as the frequency is lowered. As a result, the divergence of t,l(w) as the frequency is lowered is strongest for the most conductive complex. At higher frequencies, each of the t,l(w) for the PPO-salt complexes appears to approach a limiting high-frequency value, E,. The PP0,NaI samples approach a similar high-frequency value, e, = 3.3, while the PPOsNH4CF3S03 sample approaches a somewhat higher value (e, = 4.0). Table 2 shows the refractive indexes, nd, for PPO and the salt complexes. Comparison of the optical dielectric constant, nd2, with the values oft, for the various samples suggests the presence of an additional contribution to e,(w) for the PPO-salt complexes notpresentinPPO(t,-ndz= 1.1 for (PPO),NaI, 1.9for(PPO)sNH4CF3S03, and -0.01 for PPO). In the DDH model, a contribution to t,(w) is expected to arise from the polarization of ions in finite regions of space as they “wait” for a renewal event
io8
io9
1olo
10‘’
w / radians s-’ Figure 9. e; as a function of frequency for (PPO)8NH,CF,SO, ( O ) , (PP0)16NaI (0),(PP0)loNaI (A), (PPO)sNaI (V), and PPO (+) at room temperature. Both the a and a’relaxations are visible in the PPO spectrum, whereas the salt complexes’ responses are dominated by the space-charge polarizability. Tg(PPO)
l
.
,
r Tg
Tg (PP0,NH,CF3S0,)
o
i
(PP0,Nal)
3
+ o v
U
PPO (PPO)8NH,CF,S0,
i
10.5 160
200
(PPO),Nal
240
280
320
temperature / K Figure 10. Temperature-dependent d at 3 GHz for (PPO)8NH&F3SO3 ( O ) , (PP0)sNaI (v),and PPO (+). The lines are present only as a guide to the eye. The glass transition temperatures are marked by arrows. Notice that the inflection points in the conductivity curves correlate with the glass transition temperatures. The increase in segmental mobility that occurs at the glass transition is presumably responsible for the inflection points.
to occur. This process is predicted to be at frequencies much higher than the time scale for renewal, and hence, it is likely to occur a t frequencies greater than the cu-rela~ation.~~.55 The difference between nd2 and e , may be indirect evidence for its existence. Figure 10 shows the real part of the conductivity of PPO, (PPO)8NH4CF3S03,and (PP0)gNaI at 3 GHz as a function of temperature. No hysteresis was observed ‘in the heating and cooling curves. Inflection points correlate with the glass transition temperatures (Table 2). Presumably, theonset of local segmental motion of the polymer t h a t occurs at Tgis responsible for the more rapid increase in a’(3 GHz) above Tg. Summary
Studies of the dielectric response of PPO and salt complexes of PPO with NH4CF3SO3 and NaI were performed. These measurements provide further insight into the detailed mechanism by which ion transport occurs in polymer electrolytes. Some key observations are summarized below:
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The Journal of Physical Chemistry,Vol. 98,No. 15, 1994
1. The characteristic frequency of the a-relaxation for PPO yields a good fit to the VTF equation over 6 decades of response. Good fits of the VTF equation to the temperature-dependent dc conductivity are also observed. These fits yield similar values of the pseudoactivation parameters, B, for the a-relaxation of PPO and for the dc conductivity of the salt complexes, although the agreement is not as good as observed by other workers.11 This correspondence offers further evidence for the intimate role played by the segmental mobility of the polymer host, specifically of the a-process, in governing ion transport in polymer-salt complexes. 2. The a-relaxation for the salt complexes studied were not observed in the dielectric loss spectrum due to a large dc conductivity loss. The retardation of segmental motion caused by ionic cross-linking, however, is evident when the data are presented in terms of the real part of the frequency-dependent conductivity. 3. Comparison of the conductivity diffusion coefficient, D,, for the salt complexes as a function of rescaled temperature T - T, p,rovides insight into the role of ion-ion interactions in governing ion transport. For the salt complexes studied, these interactions appear to play an important but secondary role to the host dynamics in determining the observed dc conductivity. Furthermore, concentration-dependent studies on PP0,NaI (n = 16, 10, 8) suggest that ion-ion interactions, at least in this range of concentrations, become less important with regard to as the salt content increases. This is consistent with conclusions drawn from concentration-dependent self-diffusionS3and conductivity ~tudies.~9-51 4. High-frequency (up to 6 GHz) room temperature measurements of e{ allow for comparison of e, to the optical dielectric constant, nd2. For PPO, em = nd2 = 0 whereas t, - nd2 > 1 for the salt complexes. This difference suggests the presence of a high-frequency relaxation due to some form of ionic polarization. This observation is consistent with predictions of the dynamic bond percolation model where the polarization of ions as they "wait" for a renewal event is expected to give rise to a highfrequency relaxation pr0cess.5~~55
Acknowledgment. This research was sponsored by the Army Research Office Contract DAAL-03-09-G-0044. This work made use of MRL Central Facilities supported by the National Science Foundation, a t the Materials Research Center of Northwestern University, under Award No. DMR-9120521. We are grateful to A. Nitzan, S.D. Druger, G. M. Kloster, and N. Bonanos for helpful discussions. References and Notes ( I ) MacCallum, J. R.; Vincent, C. A. Polymer Electrolyte Reuiews I ; Elsevier: London, 1987. (2) Ratner, M. A.; Shriver, D. F. Chem. Reu. 1988, 88, 109. (3) MacCallum, J. R.; Vincent, C. A. Polymer Electrolyte Reviews 2: Elsevier: London, 1989. (4) Tonge, J. S.;Shriver, D. F. In Polymers for Electronic Applications; Lai, J. H., Ed.; CRC Press: Boca Raton, FL, 1989; p 157. ( 5 ) Gray, F. M. Solid Polymer Electrolytes; VCH: New York, 1991. (6) Druger, S. D.; Nitzan, A.; Ratner, M. A. J. Chem. Phys. 1983, 79, 3133. (7) Druger, S . D.; Ratner, M. A. Phys. Reu. B 1988, 38, 12589. (8) Druger, S. D.; Ratner, M. A. Chem. Phys. Lett. 1988, 151, 434. (9) Ratner, M. A. In Polymer Electrolyte Reviews I ; MacCallum, J. R., Vincent, C. A., Eds.; Elsevier: London, 1987; p 173. (10) Fontanella, J. J.; Wintersgill, M. C.; Calame, J. P.; Andeen, C. G. Solid State tonics 1983,8, 333. (1 1) Fontanella, J. J.; Wintersgill, M. C.; Smith, M. K.; Semancik, J.; Andeen, C. G. J. Appl. Phys. 1986, 60, 2665.
Tipton et al. (12) Fontanella, J. J.; Wintersgill, M. C.; Calame, J. P.; Smith, M. K.; Andeen, C. G. Solid State tonics 1986, 18&19, 253. (13) Fu, Y.; Pathmanathan, K.; Stevens, J. R. J. Chem. Phys. 1991,94, 6323. (14) Wintersgill, M. C.; Fontanella, J. J.; Calame, J. P.; Figueroa, D. R.; Andeen, C. G.Solid State Ionics 1983, I I , 15I. (15) Wintersgill, M. C.; Fontanella, J. J.; Welcher, P. J.; Andeen, C. G. J. Appl. Phys. 1985, 58, 2875. (16) Wintersgill, M. C.; Fontanella, J. J. In Polymer Electrolyte Reviews 2: MacCallum, J. R., Vincent, C. A., Eds.; Elsevier: London, 1989; p 43. (17) Wong, T.; Brodwin, M.; McOmber, J. I.; Shriver, D. F. Solid State Commun. 1980, 35, 591. (18) Wong, T.; Brodwin, M.; Dupon, R. Solid State Ionics 1981, 5, 489. (19) Funke, K. Solid State Ionics 1986, 188~19,183. (20) Vaitkus, R.; Kezionis, A.; Saumlionis, A.; Orliukas, A.; Skritskij, V. Solid State Ionics 1990, 40141, 922. (21) Ansari, S. M.; Brodwin, M.; Stainer, M.; Druger, S. D.; Ratner, M. A.; Shriver, D. F. Solid State Ionics 1985, 17, 101. (22) Wong, T.; Brodwin, M.; Papke, B. L.; Shriver, D. F. Solid State Ionics 1981, 5, 689. (23) Gray, F. M.; Vincent, C. A.; Kent, M. Solid State Ionics 1988,2830, 936. (24) Gray, F. M.; Vincent, C. A.; Kent, M. J. Polym. Sci., Polym. Phys. Ed. 1989, 27, 2011. (25) Fenton, B. E.; Parker, J. M.; Wright, P. V. Polymer 1973, 14, 589. (26) Wright, P. V. Br. Polym. J . 1975, 7 , 319. (27) Armand, M. B.; Chabagno, J. M.; Duclot, M. J. K. In Fast Ion Transport in Solids; Vashishta, P. M., Mundy, J. N., Shenoy, G.K. Eds.; North-Holland: Amsterdam, 1979; p 131. (28) Berthier, C.; Gorecki, W.; Minier, M.; Armand, M. B.; Chabagno, J. M.; Rigaud, P. Solid State Ionics 1983, 11, 9 1. (29) In the nomenclature (RY),MX, n refers to the number of moles of monomer unit, RY, per mole of dissolved salt, MX. (30) Ginzdon, E. L. Microwave Measurement; McGraw-Hill: New York, 1957. (31) Impedance Spectroscopy; Macdonald, J. R., Ed.; John Wiley and Sons: New York, 1987; p 346. (32) Garg, S. IC; Smyth, C. P. J. Phys. Chem. 1965, 69, 1294. (33) Baur, M. E.; Stockmayer, W. H. J. Chem. Phys. 1965, 43, 4319. (34) McCrum, N. G.; Read, B. E.; Williams, G.Anelasticand Dielectric Effects in Polymeric Solids; John Wiley: London, 1967. (35) Ishida, Y. J. Polym. Sei., Part A-2 1969, 7 , 1835. (36) Walden, P. Z . Phys. Chem. (Munich) 1906, 55, 207. (37) Mendolia, M. S.; Farrington, G. C. Chem. Mater. 1993, 5, 174. (38) Havriliak, S.;Negami, S. J. Polym. Sci., Part C 1966, 14, 99. (39) Debye, P. Polar Molecules; Dover: New York, 1929. (40) Yano, S.;Rahalkar, R. R.; Hunter, S. P.; Wang, C. H.; Boyd, R: H. J . Polym. Sci., Polym. Phys. Ed. 1976, 14, 1877. (41) In ref 40, the data were fit to logCf/Hz) = 12.00 - (494.4 K/(T 167 K)). In the text of this article, we have rewritten this in terms of the exponential function for comparison to our fits to eq 5 . (42) Williams, G. Trans. Faraday SOC.1965,61, 1564. (43) In the work of Fontanella and co-workers, the polymer host used was Parel 58 (Hercules, Inc.), a copolymer with propylene oxide as its primary constituent. As with poly(propy1ene oxide), this copolymer is also referred to as PPO in the text of this article. (44) Gibbs, J. H.; DiMarzio, E. A. J. Chem. Phys. 1958, 28, 373. (45) Adam, G.;Gibbs, J. H. J. Chem. Phys. 1965, 43, 139. (46) Cohen, M. H.; Turnbull, D. J. Chem. Phys. 1959, 31, 1164. (47) Grest, G.S.; Cohen, M. H. Phys. Reo. B 1980, 21, 4113. (48) Lemmon, J. P.; Kohnert, R. L.; Lerner, M. M. Macromolecules 1993, 26. 2161. -.,- . (49) MacCallum, J. R.; Tomlin, A. S.; Vincent, C. A. Eur. Polym. J. 1986, 22, 787. (50) Gray, F. M. Solid State Ionics 1990, 40141, 637. (511 Grav. F. M. J. Polvm. Sei.. Polvm. Phvs. Ed. 1991. 29. 1441. (52) Lonkrgan, M. C.; Perram, J. W:; Ratner, M. A.; Shriver, D. F. J . Chem. Phys. 1993, 98, 4937. (53) Boden, N.; Leng, S.A.; Ward, I. M. Solid State Ionics 1991, 45, 261
(54) Druger, S.D.; Ratner, M. A.; Nitzan, A. Solid State Ionics 1986,
188~19,106.
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