15142
J. Phys. Chem. 1995,99, 15142-15152
Conductivity and Morphological Studies of TPU-N&CF3S03 Polymeric Electrolytes J. van Heumen, W. Wieczorek, M. Siekierski? and J. R. Stevens* Department of Physics, University of Guelph, NIG 2W1, Guelph, Ontario, Canada Received: March 8, 1995; In Final Form: August IO, 1995@
NH4CF3SO3 has been used to dope thermoplastic polyurethane (TPU) with soft segments (SS) of poly(tetramethy1ene glycol) (PTMG) and poly(propy1ene glycol) (PPG), each having a SS molecular weight (M,)= 1000 g/mol. The PTMG-based TPU was examined at salt cqncentrations from 0.15 to 2.00 mmoYg of TPU at a constant hard segment (HS) concentration of 20%. The PPG-based TPUs of HS concentrations varying from 20% to 50% were doped at a single salt concentration of 0.67 mmoVg of TPU. Although room S/cm), these systems can be used to elucidate the temperature ionic conductivities are low (-1 x relationship between structure and morphology and between structure and ionic conductivity. In the PPGbased TPU/N&CF3S03 system, in which the conductivity follows a VTF form as a function of temperature, S/cm. However, in the F'TMG-based the salt is dissociated and ionic conductivity at 100 "C is -1 x TPU/NH&F3S03 system, in which the conductivity temperature behavior is Arrhenius at low temperatures and VTF at higher temperatures, the salt is 'not completely dissociated, and conductivity at 100 "C is about 1.5 x S/cm. Phenomenological and effective medium theories have been used to fit the experimental conductivity data with good agreement.
Introduction Polymer electrolytes based on polyether matrices are the most intensively studied systems among polymer ionic conductors. This results from the variety of possible applications in ambient temperature electrochemical devices such as batteries, electrochromic windows, sensors and fuel cells2 The high polymer chain flexibility of the polyether matrix and the presence of an electronegative oxygen in the polymer chain having sufficient donor power to complex metal cations are the main advantages of polyethers over other polymeric electrolyte systems. It has been found that fast ionic transport in polyether-based electrolytes is associated with the presence of a flexible, amorphous phase characterized by a low glass transition temperature (Tg).3 Unfortunately, the mechanical stability of amorphous polyether matrices is poor, and polymer electrolytes often creep under the pressures applied in electrochemical devices. Therefore, many research groups search for amorphous, mechanically stable polyether hosts as matrices for polymeric electrolytes.2 This includes the synthesis of polymer blends,' composite polymer electrolytes containing finely dispersed inorganic or organic filler^,^ and polymer networks' prepared by either chemical or physical cross-linking processes. Recently, thermoplastic polyurethanes (TPU) doped with various alkali metal salts have also been studied as matrices for polymeric electrolyte^.^-^ Thermoplastic polyurethanes are condensation polymers characterized by a phase segregated morphology in which the soft phase, containing either polyether or polyester polyols, is reinforced by a hard phase containing an aromatic diisocyanate chain extended with a short chain diol. The TPUs, of current interest in this study, contain a soft phase of either poly(propylene glycol) (PPG) or poly(tetramethy1eneglycol) ( m G ) reinforced by condensation with a hard phase containing methylene bis(pheny1 isocyanate) (MDI) chain extended with 1,4-butanediol (BDO). Relatively little is known about the relation between the structure and morphology of TPUs and between the structure
' On leave from the Department of Chemistry, Warsaw University of
Technology, ul. Noakowskiego 3, 00-664 Warszawa, Poland. * To whom comespondence should be addressed. Abstract published in Aduunce ACS Abstrucrs, September 15, 1995. @
0022-365419512099-15142$09.0010
and conductivity of polymeric electrolytes obtained by the doping of TPUs. Previous investigations have concentrated on using lithium-based ionic salts in the preparation of TPU polymer electrolyte^^-^ which exhibit moderate ambient temperature ionic conductivities and good mechanical properties. It is apparent that it is the soft segment polyether that contributes to the overall conductivity of these ionic composites, but it is unclear what contribution, if any, the hard segment makes to the ionic conductivity in the presence of the dopant. In the present paper we examine the effect that such factors as ionic salt and hard segment concentration have on the conductivity of TPUAVhCF3S03 electrolytes. The temperature and frequency dependence of the conductivity is analyzed by the phenomenological Meyer-Neldel and Almond-West formalisms?-I2 An effective medium theory has also been used to predict the temperature and hard segment concentration dependencies of the conductivity of TPU/NH&F3SO3 electrolytes. On the basis of these calculations some conclusions conceming the relation between the structure and morphology of TPUs and between the structure and ionic conductivity can be drawn.
Conductivity of Polymeric Electrolytes From the point of view of the application of polymeric electrolytes the temperature dependence of the conductivity a(T) is one of the most important properties of polymer ionic conductors. Generally a(r ) curves obtained for polymeric electrolytes have one of the following behaviorial characteristics: 13-16
1. VTF behavior occurs throughout the available temperature range according to eq 1. =
A B T'/2 exp( - k(T - To))
Here a& is the dc ionic conductivity, A is a preexponential factor proportional to the concentration of charge carriers in the electrolyte, B is a pseudoactivation energy for conduction, To is a thermodynamic glass transition temperature which is usually 0 1995 American Chemical Society
J. Phys. Chem., Vol. 99, No. 41, 1995 15143
TPU-NH4CSS03 Polymeric Electrolytes 30-50 K lower than the experimentally measured Tgand k is the Boltzmann ~ o n s t a n t . ' ~ * ' ~ 2. Arrhenius behavior (see eq 2) occurs for low temperatures (usually below the melting point, T,, of any crystalline phase), and VTF behavior only occurs at higher temperature^.'^ ad,
= 0, exp( -E,/kT)
Phenomenological Models According to a random walk theoretical approach,I7 the temperature dependence of a d , follows an Arrhenius type relation. In this phenomenological approach the assumption is made that the ions move independently of each other in the solid polymer electrolyte. Equation 3 is the result of this approach.
The term z(l - c) is the fraction ( 1 - c) of the z nearestneighbor energetically equivalent sites that are empty, c is the fraction of these sites that are occupied, a is the jump distance between energetically equivalent sites, N (=n/c) is the density of energetically equivalent sites, n is the number of charge carriers each with charge q, T is a temperature, and f is a correlation factor. wo is the true hopping attempt frequency or a particular optical mode vibration frequency (-10-l2 s-l) given by a harmonic potential well expression of the form 2 1/2
+
(2)
Here, a, is a preexponential factor and E, is an activation energy for conduction. 3. Arrhenius behavior occurs throughout the available temperature range, with two different activation energies: a higher one at temperatures between the Tg and the Tm of the crystalline polymer phase(s) and a lower one above Tm.15a 4. VTF behavior occurs at temperatures slightly above Tg and Arrhenius behavior at high temperature^.'^^^^^^^ This occurs for electrolytes of extremely low Tg values for which at high temperatures the VTF term (T - To) (see eq 1) becomes almost identical to T i n the Arrhenius equation (see eq 2). 5. There is neither VTF nor Arrhenius behavior.I6 The first three types of behavior are the most common. As will be presented in the following sections, the YlMG-based TPU composite electrolytes display the second type of behavior while the PPG-based TPUs exhibit a VTF behavior over the temperature range covered. The phenomenological models described below attempt to analyze the temperature and frequency dependence of the ionic conductivity of these multiphase systems.
wo = (Em/2ma )
+
Here Sa = (S, S,) is a total activation entropy for conduction, and Ea = E, E,. Equation 5 is related to ionic conductivity in solid electrolytes and is of the same form as eq 2 if
wp = we exp( -Em/kT)
(3 (3(3
c, exp - exp - - c, exp -
(4)
ce is the effective number of charge carriers, and E, and S, are respectively the activation energy and activation entropy for charge carrier creation. Substitution of eq 4 into eq 3 yields eq 5.
(6)
(7)
where we is the effective hopping attempt frequency and is given by we = w, exp(Sm/k)
(74
Therefore, using eqs 2 and 7 and comparing values of E, and Em, we will be able to discuss whether the conductivity in a system with Arrhenius behavior depends mostly on charge carrier mobility (E, % E m ) or whether charge carrier creation also contributes to the total conductivity. To perform these calculations, a method of determining ad, and wp at each experimental temperature has to be developed. After empirically analyzing the data for various materials in which conduction is mainly due to charge hopping, JonscherI8 proposed that the frequency dependence of electrical conductivity is given by
where w (= 2nf) is the angular ac frequency, nl and n2 are empirical constants of the material, and wc is a characteristic frequency. For materials which show a frequency-independent region of conductivity such as TPU-based electrolytes, nl = 0, n2 = n, and a(@)= (w,
+ w,
l-n
w n ) = Kewc
+ Kewc1-"wn
(8a)
where Ke is a constant of proportionality. Almond and W e ~ t ~have , ' ~developed a formalism based on the applicability of Jonscher's universal power law'2s18for the description of the frequency dependence of the conductivity of solid ionic conductors. For these purposes eq 8a is utilized in the following form. U(W)
c (1 - c)
Nq2a2zc$ 6kT
Kt is the theoretical cation and anion charge carrier concentration term. The random walk approach also gives the following expression for up,the hopping frequency.I7
(3a)
Here m is the effective mass of each charge carrier, and E m and S, are respectively the activation energy and activation entropy for ion migration. Equation 3 also contains a charge carrier creation term (c(1 - c)) which for some solid electrolytes, for relatively low c values,I7 is temperature dependent according to eq 4.
where Kt =
a, = K p 0 e x p k )
= ad,
+ Awn
(9)
Here A and n are the temperature-dependent material parameters, and n is limited to 0 < n < 1. The authors identified the characteristic frequency wc with the hopping frequency wp (see eq 7). Under these conditions it can be demonstrated that, for w = oc= up,u(w) = 2adc where (sdc = K,wPlo (see eqs 8a and 9). Therefore, by substituting u(wp) = 20dc into eq 9, Almond and West developed a method to separately calculate the carrier hopping rate wp from eq 10 and the experimental charge carrier concentration term K , from eq 11:
15144 J. Phys. Chem., Vol. 99, No. 41, 1995
van Heumen et al.
Therefore, the total concentration of mobile ions can be expressed as eq 12.
KJK, = % of mobile ions
(12)
The values of ffdc and up(eqs 9 and 10) determined from the analysis of the ac conductivity behavior of TPU-based electrolytes are later used to calculate the Ea and Em values from eqs 2 and 7. The proposed formalism has been successfully used to describe the mobility and charge carrier concentration for various crystalline, glassy, and polymeric solid ionic conductors.'0.'1,'9-21In the present paper the conductivities of several TPU-based electrolytes will be analyzed according to the formalism described above in the temperature range where the conductivity satisfies eq 2. On the other hand, rewriting the prefactor a, of eq 2 (see eq 6), we obtain
In a,= Salk
+ In K p 0
(13)
For many materials Sa and Ea are related by the following empirical equation,
This equation was originally used by Dienes to describe the atomic diffusion in metals.22 For metals TD represents the melting point, but for fast ionic conductors this temperature usually corresponds to the order-disorder transitions in the electrolyte. A method for the calculation of To, for the temperature region in which the electrolytes obey the Arrhenius equation, can be obtained by combining eqs 13 and 14.
where a = l/kT and /3 = In Ktw,. Note that since both a and /3 are constant, Kt is constant independent of temperature (see eq 6). Equation 15 has been recently usedg to describe the correlation between preexponential factors and activation energies calculated from eq 2 for various solid ionic conductors.
Effective Medium Theory TPU-based electrolytes can be treated as media consisting of two phases, each of which contributes to the ionic conductivity. Therefore, it seems reasonable to apply an effective medium theory (EMT) to describe the changes in ionic conductivity of the TPU/NH&F3SOs system as a function of the hard segment (HS) concentration and temperature. For the TPU's in this investigation it has been assumed that the HS phase is embedded in a soft segment ( S S ) matrix to produce a space-filling random mixture of two components. It has also been assumed that the HS polymer phase has spherical symmetry. Under these assumptions each polymer phase in the heterogeneous material is symmetrically embedded in a self consistent effective medium with the same effective conductivity o* as the bulk electrolyte. Our description is thus given in terms of the complex conductivity of this inhomogeneous dielectric material considered to possess macroscopic uniformity. The general self-consistent equation for a multiphase material is23
wi(a,- a*) =O (d - l)o*
+
Here d is a dimensionality parameter equal to 3 for spherical HS aggregates, ui are the dc conductivities of the particular polymer phases participating in ionic transport, and w ;is the volume fraction of each phase ( i = 1, 2). Equation 16 will be
TABLE 1: GPC data for PPG-Based TPUs % HS io3M , (g/mol) 103M" (g/moi) 20 228 90 30 110 42 34 40 94 50 110 18
M,M, 2.5
2.6 2.1
6.3
used in the EMT calculations of the ionic conductivity of the TPU/N€hCF3S03 system.
Experimental Section PTMG-Based TPUs. The PTMG-based TPU is a commercial TPU (ESTANE 5714, BF Goodrich Co.) having a hard segment concentration of 20 mass % and composition of MDI and BDO having a Mw and (Mn) of respectively 149 000 and 32 000 g/mol and a polydispersity of 4.7. The polymer was doped with WCF3SO3 concentrations ranging from 0.15 to 2.00 mmoYg of TPU. PPG-Based TPUs. PPG-based TPUs were prepared by the bulk polymerization method. Prior to the polymerization, the active hydroxyl compounds (1,Cbutanediol (Aldrich) and PPG (Poly G-55- 112 (Oh))) were preblended in the proportions necessary to achieve the desired HS concentration. The preblend was then dried over 4A molecular sieves. The MDI (ICI) was stored as a liquid at 80 "C and used as received. The stannous octoate (Aldrich) was used as received. In the absence of solvent, the PPG and 1,4-butanediol were stirred while heated to a reaction temperature of 110 "C in the presence of 0.04 g of stannous octoate (per 180 g polymerization). In a separate vessel the MDI was equilibrated at 110 "C. The reactants were quickly combined and vigorously mixed for a reaction time of 2 min, at which point the material was transferred to a Teflon-coated vessel and allowed to cool. The reaction was brought to completion in an 80 "C oven for 24 h. To ensure a homogeneous material, the polymers were coarsely ground in a rotary grinder followed by extrusion in a Brabender twin screw extruder with a strand die attachment. The strands were then chopped into '/g in. pellets using a strand pelletizer. The solvent tetrahydrofuran (THF, Fisher) was dried over molecular sieves while the dopant m C F 3 S 0 3 was dried for 24 h at 110 "C and reduced pressure Torr). TPU-salt complexes were prepared by dissolving both the N&CF3S03 and TPU in THF at 10 mass %. The solution was cast onto Teflon plates, and the solvent was removed under a reduced pressure of Torr for 24 h at 110 "C. For FTIR analysis, samples were prepared in a similar manner from a 5 mass % solution in THF. The solutions were cast directly on NaCl plates, and the solvent was evaporated under reduced pressure at 110 "C for 24 h. Only a single NhCF3S03 concentration of 0.67 mmoVg of TPU was used for the PPG-based TPUs. Gel Permeation Chromatography (GPC). GPC measurements on the PPG-based TPUs were carried out on a Waters GPC ,equipped with a Waters 410 DRI detector. The system was operated with 2 PL-gel columns of mixed-diameter 5 p m porosity at 25 "C with THF as the eluent. Polystyrene (Polymer Laboratories) was used in order to generate the universal calibration. To ensure homogeneity of the polymer solutions, 5 g of TPU was diluted to a 10 mass % solution in THF and stirred for 24 h. The 10 mass % solution was then further diluted to 0.15 mass % in THF. From this final solution an injection volume of 100 p L was used. Table 1 presents the number-average (&) and weight-avera_ge (fiw) molecular weights as well as the polydispersity ( k w / M n ) for the TPUs of the various hard segment concentrations. All samples were relatively similar in polydispersity except for the
J. Phys. Chem., Vol. 99, No. 41, 1995 15145
TPU-NhCF3S03 Polymeric Electrolytes
TABLE 2: Effect of Hard Segment Concentration and [N&CF3S03] on the Tgof the PPG 1000 Based TPUs T, ("C)
sampleb PPG TPU, 20% HS TPU, 30% HS TPU, 40% HS TPU, 50% HS ~~
a
before salt
after salt"
-69
-59 6
~
-16 -15 -12 -4
10 13 24
AT, ("C) 10 22 25 25 28
'i
J
[N&CF3S03] = 0.67 mmovg of TPU. Prepared from PPG 1OOO.
TABLE 3: DSC Data for N&CF3S03-Doped TPU for PTMG T. solution solution (mmoVg of TPU) T, ("C) (mmoVg of TPU) TE("C) 0.0 -50 0.48 -46 0.67 -46 0.15 -49 -48 0.32
50% HS sample, which has a polydispersity of 6.3. This broad polydispersity is a function of the low fin observed. This indicates the presence of a large number of smaller, possibly oligomeric, chains. Due to the fact that polymerization was conducted in the bulk, this polydispersity may be a result of premature phase separation during the polymerization which is characterized by an opacity not observed in the TPUs containing 40% HS or less. Differential Scanning Calorimetry (DSC). DSC data were obtained between - 110 "C and +200 "C using a DuPont TA 29 10 scanning calorimeter with a low temperature measuring head and liquid nitrogen-cooled heating element. Approximately 15 mg of polymer electrolyte sample was loaded into the aluminum pans and then cooled at 10 " C h i n to -1 10 "C, where it was equilibrated prior to beginning the temperature sweep at 10 " C h i n to 200 "C. Conductivity Measurements. Ionic conductivity was determined using the complex impedance method in the temperature range -20 to +110 "C. The samples were sandwiched between two stainless steel blocking electrodes and placed in a temperature-controlled fumace. The impedance measurements were carried out on a computer-interfaced HP 4192A impedance analyzer over the frequency range 5 Hz to 13 MHz. Peak-topeak voltage used for impedance measurements was equal to 1 V. FT-IR. Fourier transform infrared spectroscopy (FT-IR) utilized a computer-interfaced Nicolet FT-IRSystem 4.4 instrument with a wavenumber resolution of 2 cm-I. The TPU thinfilm electrolytes were analyzed between two NaCl plates. Results and Discussion DSC of PPG-Based TPUs. As a means to measure the effectiveness of the NhCF3S03 complex formation with the TPU SS, it is necessary to examine the T, of the SS phase. Table 2 indicates the changes occumng in the SS Tg before and after m C F 3 S O 3 addition to the PPG-based TPU electrolyte. It is evident from the data that the preparation of a TPU containing a low HS concentration, such as 20% HS, has a significant effect on the SS T, compared with the Tg of the PPG alone. Considering the short soft segment molecular weight (1000 g/mol), a high degree of phase intermixing is anticipated, resulting in an increased Tg of the SS. HS concentrations between 20 and 40 mass % do not significantly raise the SS Tg;at 50 mass % HS an additional 8 "C increase in the SS T . is observed. With the addition of NbCF3S03 there is a further increase in the Tg of the SS. This Tg increase has been shown
wavenumben ("I)
Figure 1. Relative IR absorbance versus frequency for the frequency region 1060-1000 cm-' for TPUs based on PPG and PTMG at 20% HS measured at 25 "C. (a) 2.00 mmoUg of TPU (PTMG), (b) 1.2 mmol/g of TPU (PTMG), (c) 0.67 mmoVg of TPU (PTMG), (d) 0.67 mmoVg of TPU (PPG), (e) 0.31 mmoVg of TPU (PTMG), and (0 undoped PTMG-based TPU. before8 to be due to the formation of transient ionic cross-links between the cation, in this case N&+, and the electron-rich ether oxygens. An increase of -10 "C in Tgresults from the addition of NbCF3SO3 to the PPG polymer; this is contrasted in the TPU electrolytes where, on the average, a AT 25 "C increase in T, for a 10 mass % increase in HS concentration is observed. The decreased chain mobility within the soft segment domain not only is the result of ionic cross-link formation between ether oxygens but also may be due to an additional mechanism which is causing an enhanced increase in the SS Tg greater than that observed for the PPG/NHdCF3SO3 complex alone. With the salt addition an increasing amount of HS is believed to be phase intermixing with the SS, resulting in decreased chain mobility and an increase in the in the SS Tg. DSC of PTMG-Based TPUs. The PTMG-based TPUs have been examined initially for changes in the Tg of the SS as a function of salt concentration. As seen in Table 3, the soft segment is largely unaffected by NH&F3SO3 addition up to 0.67 mmoVg of TPU. This suggests that the ionic salt is only loosely coupled to the polymer host; ions are not tightly coupled to the segmental motions of the PTh4G segments. This is in contrast to the PPG-based TPU (see Table 2 ) where the soft segment Tgis strongly affected by the addition of NhCF3S03 (salt concentration 0.67 mmoVg of TPU). FT-IR. Ionic transport in polymeric electrolytes is governed, in large part, by the ability of the polymer host to solvate the dopant salt. Poor solvation of the salt leads to the formation of both contact ion pairs and higher order aggregates and is observed as a reduction in the overall ionic conductivity of the polymer electrolyte. The formation of these contact ion pairs (m+CF3SO3-) and higher order aggregates causes a perturbation of the bonds of the triflate anion as observed in both IR and R a m a ~ *For ~ MCF3S03(M = Li, Na, K) systems only the SO3 stretch frequencies are affected as observed by a shift to higher frequencies for the Y ( S O ~ ) , .The ~ ~ IR , ~ region ~ of 1060-1000 cm-I, which contains the Y(so3)sat 1031 cm-' for the "free anion", was examined for the higher frequency species: contact ion pairs and higher order aggregates. In Figure 1 (25 "C) curves a-c and e refer to the salt-doped PTMGbased TPU, curve d refers to the PPG-based TPU doped at 0.67 mmoVg of TPU, and curve f refers to the undoped F'TMG-based TPU. Figure 1 illustrates three IR-active bands. The v(SO& band associated with the "free" solvated anion (CF3S03-) is observed at about 1031 cm-I. Note that a feature at 1033 cm-'
15146 J. Phys. Chem., Vol. 99, No. 41, 1995
can be separated out at the highest salt concentration of 1.99 mmoYg of TPU where a precipitate is observed in the PTMGbased TPU electrolyte. The second band is observed at 1018 cm-' and is the CH "in-plane" bending mode of the hard segment aromatic rings and is unaffected by the addition of salt. The third band is a broad feature at 1048 cm-' which, up to 1.2 mmoYg of TPU of NH4CF3SO3, increases in band area as determined by a deconvolution using a Galactic Grams 386 software package. The band at 1048 cm-' is associated with the addition of salt as can be seen by comparing the spectra curves a-c, and e with the spectrum for the undoped PTMGbased TPU (curve 0. For the highest concentration, the intensity of the 1048 cm-' band decreases as the 1033 cm-' vibration is observed. The band at 1031 cm-' in Figure 1 also broadens up to 1.2 mmoVg of TPU with increase in salt concentration as is expected due to an increase in ion pairing with increase in concentration.24~25 Although, the 1048 cm-' vibration is associated with the salt, we find it difficult to assign it to the v(SO3), vibration. We believe that a frequency shift of the V ( S O ~CF3S03)~ anion to 1048 cm-' is unlikely due to the demonstrated weak interaction of the N h f cation with the anion. In later discussion we will assume that the 1048 cm-' vibration is associated in some way with higher order ionic aggregates. We believe that at low salt concentrations ions from N&CF3SO3 are loosely coupled to the polymer, while at the highest salt concentrations the NH4CF3S03 precipitates from the polymer matrix as observed upon visual inspection of the 1.99 mmoYg of TPU electrolyte. Varetti et al.27have observed the IR Y ( S O ~in) ~powder and single crystal for NH4CF3S03 at 1035 cm-I. This evidence may explain our observed overlapping ~ ( S 0 3 band ) ~ at 1033 cm-' in the sample of the highest salt concentration where "salting out" effects28would be observed. The PPG-based TPU electrolytes exhibit quite different salt effects in the 1000- 1060 cm-' IR region. Figure Id illustrates that at room temperature (25 "C) the NH4CF3S03 is fully solvated as seen by only a single band at 1031 cm-' for a PPGbased TPU of 20% HS. All PPG-based TPUs of varying HS concentration examined in this IR region exhibited a single band at 1031 cm-I. Conductivity. PTMG-Based TPU Electrolytes. The conductivity isotherms for the PTMG-based TPU electrolytes are shown in Figure 2 for various NhCF3S03 concentrations at 25 "C (298 K), 50 "C (323 K), and 100 "C (373 K). The TPU electrolytes were seen to be weakly concentration dependent with ambient temperature conductivities slightly higher than S/cm, the same conductivity range as for the pristine PEObased electrolytes. Furthermore, the ionic conductivity was found to increase to approximately 10-7-10-6 S/cm at higher temperatures (100 "C (373 K)). The observed conductivities measured at the highest temperature (100 "C (373 K)) are scattered. This scatter is believed to be significant given that the error in measurement is approximately the size of the actual data points in Figure 2. The relevance of the change in conductivity with salt concentration is discussed below. At approximately 0.48 mmoYg of TPU a small minimum was found for all temperatures examined. Such an effect is not uncommon, given the observed presence of significant ionic aggregates (see Figure 1). It has been proposed that the electrolyte permittivity may actually rise with increasing salt concentration due to the increase in polarizability caused by the presence of ion pairs and higher order aggregate^.',^^,^^ The effect of an increase in permittivity is to increase the ionic dissociation constants at high salt concentrations, resulting in a
van Heumen et al. -6 I
V
e
!-I v
M
-1
0
O
O
O
O
O
0
25OC 50's
v
-10 0 . 0
0.5
100
c
1 .o
1.5 [NH4CF3S03] mmol/gTPU
2.0
Figure 2. Conductivity isotherms at 25 "C (298 K), 50 "C (323 K), and 100 "C (373 K) plotted versus NHXF3S.03 concentration (mmol/g of TPU) for a PTMG-based TPU with 20% HS.
TABLE 4: Permittivity (E') Calculated for PTMG-Based TPUs Doped with Various N&CF3S03 Concentrations e'( 1 MHz)"
T ("C) 25
50
100 a
0.32 mmoVg of TPU 2.42 2.81 2.69
All values of
6'
0.48 mmoVg of TPU
2.26 2.80 2.21
0.67 mmoVg of TPU 3.20 4.12 4.71
were calculated using eq 20 at 1 MHz
partial "redissociation" of the associated species, and is observed as an increase in the ionic conductivity. The real part of the permittivity has been calculated for the present TPU electrolytes, and values of E' are presented in Table 4. Corresponding to the rise in conductivity observed in Figure 2 at 0.67 mmoYg of V U , a concomitant rise in the permittivity is also found at the same N&CF3SO, concentration. Hence, a redissociation process of the associated species in the TPU is proposed for the observed minimum at 0.48 mmoYg of TPU. At 100 "C (373 K), the conductivity is found to reach a maximum at approximately 0.67 mmoYg of TPU, which is followed by a significant decrease in conductivity at higher salt concentrations. It has been shown previouslyz8in systems where the polymer host exhibits poor solvating ability that a "salting out" effect is observed at higher temperatures, also resulting in a decreased conductivity. As a precipitate or ionic aggregate, the salt is no longer a source of the ionic species necessary for conduction; thus, the overall charge carrier concentration is decreased in the electrolyte, resulting in the observed decrease in conductivity. Figure 3 presents the temperature-dependent conductivity for the FTh4G-based TPU/NH4CF3S03 electrolytes of salt concentrations between 0.15 and 0.67 mmol/g of TPU. It can be seen that the ambient temperature conductivities for samples of low salt concentration are slightly higher than those obtained for systems of high m C F 3 S 0 3 concentration. The conductivity plots for all salt-doped TPUs appear to overlap in the temperature range 45-60 "C (318-333 K) and cannot be connected with any transitions observed by DSC studies. The inflection is likely due to an order-disorder transition of the ionic aggregates found only in the PTMG-based TPU electrolytes and
TPU-NfiCF3S03 -6
[NH,CF3S03] 'mmolygTPU
0
0
o UNDOPED
,'"
- fik . -.,"io v
-7.
J. Phys. Chem., Vol. 99, No. 41, 1995 15147
Polymeric Electrolytes
v v
0.15 0.31 0.48
o
0.67
0
8
1
-.--
.v 0 V
o. 0 0
'0
0 0
I
-10
0
2.4
v
. O 0
I
0
1
-11
.
.ov
0
2.6
2.8
3.0
3.2
3.4
3.6
I 3.8
1000 K/T
Figure 3. Ionic conductivity for N&CF,SO3-doped PTMG-based TPU electrolytes of 20% HS versus inverse temperature. -2
0 -0XHS
1
-4
-
h
I
f
-6
m
\ v
TABLE 5: VTF Parameters for PPG-Based TPU/ N&CF3S03 Electrolytes; Samples of Different HS Concentrations HS conc A (vol %) (S cm-I) Blk (K) To (K) T, (K) 0 0.27 474 210 214 20 0.15 786 250 279 30 0.10 926 232 282 40 0.03 992 236 286 50 0.03 1115 235 297
-10
- 1 2-
2.5
3.0
3.5
4.0
4.5
5.0
1000 K / T
Figure 4. Conductivity versus reciprocal temperature for PPG-based TPU/N&CF3SO3 electrolytes. Samples of different HS concentration (denoted in vol %). The concentration of N&CF$303 is equal to 0.67 mmoYg of TPU. will be discussed further below. This behavior has also been observed for ethylene ionomers3' where an inflection in the conductivity plots was assigned to the order-disorder transition of the ionic aggregates. A similar transition was not observed in the conductivity plots of the PPG-based TPUs in which ionic aggregates were not observed (Figure Id). PPG-Based TPU Electrolytes. Figure 4 shows the changes in the conductivity versus reciprocal temperature for PPG-1000/ NhCF3S03 and for the PPG-based TPU/NH&F3S03 electrolytes containing various HS concentrations. The conductivity observed for all TPU-based electrolytes is significantly lower than that of the PPG 1000/NH4CF3S03 electrolyte over the entire temperature range studied. I n addition, an increase in the HS content serves to further decrease the conductivity of the electrolytes. The empirical VTF model (eq 1) has been fit to the conductivity data of these PPG-based TPU electrolytes, and these fits are shown as solid lines in Figure 4. The values for the VTF parameters, obtained by nonlinear least-squares fitting of the experimental data, are summarized in Table 5. The pseudo activation energy parameter B increases with an increase in the HS concentration whereas the preexponential factor A decreases. The A and B values obtained for the PPG
1.24 1.12 1.08 1.03 1.03
1000-based electrolyte are quite different from those determined for the PPG-based TPU electrolytes. The To value calculated for the PPG 1000/NH&F3S03 electrolyte is close to that of the Tg measured by DSC, while To values obtained for PPG-based TPU electrolytes are within the range Tg - 65 K < To < Tg 30 K, and the difference between Tg and To increases with an increase in the HS concentration. As can be seen from Figure 4, the experimental points deviate from the VTF curve at temperatures slightly above the S S Tg's. The Tc/Tgratio (where Tcis a temperature at which experimental points begin to deviate from the VTF curve) decreases with an increase in the HS concentration (see Table 5 ) . This indicates that below the critical temperature Tc the conductivity mechanism changes from a VTF type in which the conductivity is coupled to the segmental motion of the polymer to a thermally activated Arrhenius process in which conduction occurs by activated hopping. As stated above, the conductivity of these PPG-based TPU electrolytes is decreasing with an increase in the volume fraction of HS. As the HS concentration is increased, further intermixing of the hard and soft phases is anticipated, resulting in an increase in the Tgof the S S . Furthermore, the addition of NH&F3SO3 serves to form transient cross-links primarily between the cation and the ether oxygens of the SS. This will also cause a decrease in the S S flexibility and is observed as an increase in the S S T,. Since ionic conduction is coupled to the segmental motion of the polymer host, any decrease in chain flexibility results in a decrease in the mobility of the charge carriers. The final contributing factor in the observed loss in conductivity is the loss of electron acceptor sites. Any increase in HS concentration, would also serve to reduce the S S concentration; with a corresponding loss in the number of ether oxygens. This is supported by the VTF data (Table 5) which illustrate a decrease in the value of the preexponential factor A and an increase in the pseudo activation energy B with increasing HS concentration. Given that the VTF factor A is proportional to the charge carrier concentration, this would suggest a loss in the number of oxygen acceptor sites which are largely responsible for charge carrier formation. The increase in B can be interpreted as an increase in the energy required for charge carrier migration. This would be observed as a decrease in the ionic conductivity of the TPU. Comparison of PPG- and PTMG-Based TPU Electrolytes. At room temperature, the conductivities of the PPG-based TPU and PTMG-based TPUs are relatively similar at the same salt concentration, but at elevated temperatures (100 "C) the conductivity is at least 2 orders of magnitude higher for PPGbased TPUs than for the equivalent salt concentration in the PTMG-based TPU. As observed by FT-IR, this is due to the difference in concentration of "free" ions in the prepared TPU electrolytes. For example see Figure lc,d, where at the same salt and HS concentration the PPG-based TPU exhibits a higher concentration of "free" anions than the PTMG-based TPU. This is the result of an increase in ether oxygen content for a SS of PPG (16 per lOOOM,) compared with only 13 per lOOOM, for a S S of PTMG, but may also be due to the larger distance between ether oxygens for the S S of the PTMG. This increased
m+
I - 8 3
TJT,
van Heumen et al.
15148 J. Phys. Chem., Vol. 99, No. 41, 1995
24OC 54OC v 94OC 0
4
W
3
4
5
6
7
8
Log (w/Hz)
Figure 5. Ac conductivity versus the logarithm of the angular frequency in Hz of a PTMG-based TPU doped with 0.85 mmoVg of TPU/N&CF=,SO3 at 24 "C (297 K), 54 "C (327 K), and 94 "C (367 K). The solid lines are a fit of eq 9 to the data.
distance between ether oxygens may act as a physical barrier to charge migration. Conductivity Models (Arrhenius). The ac conductivity behavior of the FTMG-based electrolytes studied is analyzed according to eqs 8- 11. Figure 5 shows the frequency dependence of conductivity obtained for a sample containing 0.85 "01 of NbCFsS03/g of TPU. The curves consist of two regions: a low-frequency plateau (0dc region) and a high-frequency rise (the dielectric region). From the plateau region the a&of the electrolyte can be calculated by a nonlinear least-squares fitting of the experimental data to eq 9. The high-frequency part corresponds to dielectric phenomena occurring in electrolytes and can be described by the same eq 9. The results of these calculations are summarized in Table 6 and shown as the solid lines in Figure 5. For most of the electrolytes studied (except the sample doped with 0.48 mmol of NH&F3S03/g of TPU), the activation energy for charge carrier creation is less than the experimental error and thus is assumed to be negligible (see Table 6). This indicates that the mobility of the charge carriers has a dominant effect on conductivity. The higher Ec value obtained for the sample containing 0.48 mmol of NH&F3S03/g of TPU is consistent with data presented in Table 4 where the lowest permittivity of those investigated is observed. This is indicative of poor solvation of the dopant salt by the polymer host, resulting in the creation of nonconductive aggregates. The frequency exponent n (see eq 9) was found to be weakly temperature dependent and close to 1 for all of the PTMGbased TPU systems studied. This implies that our electrolytes behave as almost ideal capacitors at high frequencies. Table 6 also shows that the number of mobile charge species does not exceed 10% except for the sample of the lowest salt concentration. Figure 6 shows the temperature dependence of the fraction of mobile charge carriers (as calculated on the basis of eq 12). Only for the sample of the lowest salt concentration does the number of mobile charge carriers increase at approximately 330 K. For all the other electrolytes the fraction of mobile species remains almost constant over the temperature range studied. Figure 3 illustrates the temperature-dependent conductivity for most of the PTMG-based TPUs studied. At temperatures
below the temperature range between 50 and 60 "C (323 and 333 K) the conductivity is best described by an Arrhenius empirical model. Above this temperature, however, VTF temperature dependence for conductivity is observed. This behavior is not observed for samples with significant aggregation as in the sample containing 0.48 mmol of NH&F3S03/g of TPU. The conductivity curves intersect in the range 50-60 "C (323333 K), which may suggest changes in the conductive mechanism in this temperature range due to the presence of an orderdisorder transition. Assuming that the fraction of mobile anions and cations is weakly dependent on the salt concentration (as shown in Figure 6 for the temperature range below 60 "C (333 K)), eq 15 can be applied to describe the relation between the total activation energy for conduction and the conductivity preexponential factor (as calculated from eq 2) in the temperature range where the temperature dependence of conductivity obeys the Arrhenius equation. Figure 7 illustrates the linear dependence between In uo and Ea for all the samples studied. The characteristic order-disorder temperature TD (eq 15) is equal to 53 "C (326 K) (see Figure 3), which is believed to be associated with the order-disorder transition3' of ionic aggregates in FTMG-based TPUs and is not observed in PPGbased "Us. EMT Calculations. Dc Conductivity. EMT calculations have been performed using eq 16 for the PPG-based TPU electrolytes. It has been assumed that the conductivity of the nonconducting HS phase (02) is temperature independent and very low S/cm) in comparison to the conductivity of the SS phase. It is assumed that the temperature dependence of the conductivity for the doped S S PPG phase (al) follows the VTF type equation (eq 1). Indirect support for this assumption is obtained from Figure 4. It has also been assumed that the S S phase has been modified by the formation of crosslinks due to the presence of hydrogen bonding between HS and SS phases. Therefore, the mobility of the S S phase in the PPGbased TPU electrolytes is lower than for the PPG electrolyte itself. (See the T, data in Table 2). Furthermore, the To included in the VTF equation (eq 1) should be a function of the hard segment concentration. Hence, the experimentally measured Tg for PPG-based TPU electrolytes can be approximated by the following semiempirical equation:
+
T,(SS) = KO K,V
+ K2V2
(17)
Here KO,K I ,and K2 are empirical constants, and Vis the volume fraction of the hard segment where the specific gravity of the HS has been approximated as unity. The values KO, K I , and K2 have been calculated on the basis of a nonlinear least-squares fitting of the right side of eq 17 to plots of the T, of the S S (see Table 2) versus V. On the basis of this fitting, the following equation describing the effect of the HS concentration on the Tgof the SS in the PPG-based TPU/NhCF3S03 system can be written.
T,(SS) = 216
+ 351V - 397V2
(18)
As can be seen from eq 18, KOcorresponds to the glass transition temperature of the pristine PPG (1000)flrJH4CF3S03 system. The best fitting for the temperature dependence of the conductivity was obtained when To = T g ( S S )- 50, where the T,(SS) was calculated on the basis of eq 18. The values for the pseudoactivation energy (B/k) and preexponential factor (A) used for the calculations of u1 are respectively 1000 K and 0.1 S/cm K.-0.5 These are typical values obtained for the TPU/NH4CF3SO3 electrolytes as seen in Table 5. The conductivities u1 and u2 are introduced into the self-consistent EMT equation (eq 16),
J. Phys. Chem., Vol. 99, No. 41, 1995 15149
TPU-NhCF3S03 Polymeric Electrolytes
TABLE 6: PTMG-Based TPU-N&CFJSO~Electrolytes and Their Thermodynamic Properties [NH4CSSO31 (mmoYg of TPU)
E, (kJ/mol)
E,,, (kJ/mol)
E, (Hlmol)
nb
u at RT (S/cm) 9.5 x 10-11 4.4 10-9
KJK, (%Yb
[ions]
0.0 40.7 53.5 f 4.0 2.2 0.9-1.0 7-26 1.34 0.15 55.7 i 2.9 46.2 f 2.4 0.5 0.9- 1.O 1.6 x 3-6.5 1.76 0.31 46.7 f 3.6 54.6 f 3.1 15.8 0.9-1.0 6.8 x 1-4 1.92 0.48 70.4 f 2.9 52.9 f 1.8 4.0 0.80-0.95 1.3 x 3-7 3.26 0.67 56.9 f 3.0 23.1 f 3.7 7.6 0.8-0.95 1.7 x 3-4 3.63 0.85 30.7 f 0.2 20.6 f 4.5 0.9 0.85-1.0 2.0 x 10-8 2.5-4 7.16 1.99 21.5 f 2.9 a K, has been calculated from eq 6 with the following parameters: c = 0.5, z = l , f = 1, a is the jump distance between nearest ether oxygens in the soft polyether phase, and N is calculated based on the stoichiometry of each composition. Ranges for these terms are determined from the temperature range of the conductivity experiment (-10 to +110 "C).
(1 - V)(a,- a*) (TI 2a*
+
0.48 mmol/g 0 . 6 7 mmol/g 0.85 mmol/g
3
0
n
0 . 300
275
325
350
375
T/K
Figure 6. KJK, versus temperature in kelvin for PTMG-based TPU of 20% HS containing NH4CF3SO3 concentrations ranging from 0.15 to 1.99 mmol/g of TPU.
- Line of best fit o experimental data
/
/
/
/ /
/
"/
/
I
0
-in 0.1
0.2
0.3
0.4
0.5
E./eV
Figure 7. Natural logarithm of the preexponential factor (ao) in ( S K cm-I) versus the total activation energy in eV. Data are fit to eq 15 to
determine TD. from which the final conductivity (T* of the PPG-based TPU/ N&CF3S03 is calculated. For these purposes eq 16 can be rewritten in the following form (eq 19)
+
V(a, - a*) a2+2a* = O
(19)
Here (TI is calculated according to eq 1 with To = Tg- 50, and Tg is calculated according to eq 18 for different HS volume fractions (V). Figure 8 illustrates the room temperature (25 "C) conductivity versus the HS volume fraction. The solid lines indicate the conductivity as determined by the EMT model for the PPGbased TPU/NH4CF3S03 electrolytes. The applied model correctly predicts the drop in conductivity in the PPG-based TPU/ NhCF3SO3 system in comparison with the PPG(1000)/ NH4CF3S03 electrolyte. Figures 9, a and b, shows the temperature-dependent conductivity for samples containing 20 and 50 mass % (or vol %) of HS, and again the solid lines indicate the conductivity determined by the EMT model. For the sample containing 20 vol % of HS the theoretical curve follows the experimental points quite well up to temperatures around 80 "C (353 K). Above this temperature the experimentally measured data are slightly above the theoretical curve. This is probably due to the participation of hard segments in the conductivity due to an increase in HS mobility above its Tg.32 This contribution to the conductivity from the HS is not predicted by the present model. For the electrolyte containing 50 vol % of HS theoretical and experimental data are in good agreement at temperatures above 30 "C (303 K), while at lower temperatures, close to the Tg(SS)of the electrolyte, conductivities deviate from the VTF plot. In this temperature region, the polymer segmental motion is drastically reduced, and since ion mobility is coupled to the segmental motion of the polymer host, ionic conductivity is also significantly reduced. Ac Conductivity. The ac behavior of the PPG-based TPU/ NH4CF3S03 electrolytes has also been examined. For ac conduction behavior the conductivity parameters 01and 0 2 in eq 19 have been replaced by the frequency-dependent complex conductance parameters.
Here ai(w) represents the complex conductance of a particular phase, (Ti& is the direct current conductivity for this phase, ~i is the dielectric constant of the ith phase, and w is the frequency applied. The frequency dependence of the conductivity calculated for the PPG-based TPU/N&CF3SO3 electrolyte (50 vol % HS) at three different temperatures is compared with the experimental data in Figure 10. The model data, shown as solid lines, fit much better to experimental data at 53 "C (326 K) (Figure lob) and 103 "C (376 K) (Figure 1Oc) than at the lowest temperature 33 "C (306 K) (Figure loa). The disagreement between the experimental and theoretical data is particulary evident at high frequencies (above lo7 Hz) (see Figure 10a,b). At 103 "C (376
15150 J. Phys. Chem., Vol. 99, No. 41, 1995
van Heumen et al. 1 e-003
\
0 -experiment theory
T=306K -experimental d a t a theory
le-005
t
7 le-006
-
2 le-007
-
le-008
1
Figure 8. Comparison of the room temperature (T = 25 "C (298 K)) conductivity data calculated on the basis of the EMT model (eq 19) with experimentally measured for PPG-based TPUNKCF3SO3 elec-
1 e-003
trolytes.
le-004
1
-
-6
le-004
--
h
I
5 cn
2
5 cn
-8
m
-0
-12 I 0.0
0.1
0.2 0.3 0.4 volume f r a c t i o n of HS
__ ): .
1
,"/
8
I 0.5
-4
T=326K C -experimental theory data
1 e-005
-6
I
!I $
-8
v
W
1 e-009
le-010
-10
1 e-003
-12 2.5
3.0
3.5
T=376K
4.0
1 OOOK/T
le-004 1 e-005
-
-6
!I
m
1
-experimental d a t a theory
I
E !A
\
d
1
- __
-8
-2 v
e-008
3
e-009
M
-10
e-010
0
2
4
6
8
10
log
-12 2.5
3.5
3.0
4.0
1 DODK /T
Figure 9. Comparison of the temperature dependence of conductivity for data calculated on the basis of the EMT model (eq 19) with experimentally data measured for PPG-based TPU/N&CF3S03 electrolytes: (a, top) sample containing 20 vol % HS; (b, bottom) sample containing 50 vol % HS. K) the effect of the electrode-electrolyte interactions is observed at frequencies below approximately 104 Hz, which is not described by the EMT model. The disagreement between experiment and the EMT model observed in the high-frequency region is due to the nonideal dielectric behavior of the PPGbased TPU electrolytes. The experimental data and EMT model have been analyzed
Figure 10. Comparison of the frequency dependence of conductivity for data calculated on the basis of the EMT model (eq 20) with data experimentally measured for PPG-based TPU/NH4CF,S03 electrolyte containing 50 vol % HS.
according to the Almond-West formalism using eqs 9- 11. The results of this analysis are included in Table 7, where the experimental data are shown in part a and data obtained from the EMT model are shown in part b. The model data analysis show constant values of the materials parameters A and n (see eq 9), which implies that the electrolyte should behave like an ideal capacitor in the high frequency range. The analysis of the experimental data, however, do not c o n f i i this assumption. The A parameter (see Table 7a) is obviously temperature dependent. The n parameter equals 1 at temperatures lower than 53 "C (326 K), while for higher temperatures n varied
TPU-NH&F3SO3
J. Phys. Chem., Vol. 99, No. 41, 1995 15151
Polymeric Electrolytes
TABLE 7: Comparison of the ac Conductivity Parameters Calculated on the Basis of eqs 9-11 Using Experimental Data and Model Data Calculated on the Basis of Effective Medium Theory (Ea 20)" T(K) ud,(S cm-I) A (S cm-l) n op(Hz) K, (S s) (a) Experimental Data 266 1 10-11 2.8 10-15 1.00 3.6 x 103 2.8 x 10-15 275 1 10-11 2.9 10-15 1.00 3.5 x 103 2.9 x 10-15 286 2.5 x lo-" 3.7 x 1.00 6.6 x lo3 3.8 x 296 5.7 10-11 5.3 10-15 1.00 1.1 io4 5.2 x 10-15 306 3.2 x 6.8 x 1.00 4.6 x 104 6.9 x 316 2.5 10-9 9.8 10-15 1.00 2.6 x 105 9.8 x 10-15 326 9.1 x 1.9 x 0.98 6.4 x lo5 1.4 x 9.7 x 0.90 1.5 x lo6 2.3 x 335 3.5 x 0.95 4.6 x lo6 2.1 x 4.6 x 347 9.8 x 0.93 6.6 x lo6 3.1 x 9.5 x 356 2.1 x 364 4.5 10-7 1.3 10-13 0.93 1.1 x 107 4.1 x 10-14 376 7.2 x 7.2 x 0.98 1.4 x lo7 5.1 x 387 1.2 10-6 7.2 10-14 1.00 1.7 x 107 7.1 x 10-14 (b) Model Data 1.00 6.6 x 10' 4.8 x 266 3.2 x lo-'* 4.9 x 1.00 6.6 x 10' 4.8 x 275 3.2 x lo-'* 4.9 x 286 3.3 io-l* 4.9 10-14 1.00 6.7 x 107 4.9 x 10-14 1.00 2.4 x lo2 5.0 x 296 1.2 x lo-" 4.9 x 306 2.1 10-10 4.9 10-14 1.00 4.3 x 103 4.9 x 10-14 316 1.7 10-9 4.9 x 10-14 1.00 3.6 x io4 4.7 x 10-14 326 8.7 10-9 4.9 10-14 1.00 1.8 x 105 4.8 x 10-14 4.9 x 10-14 1.00 5.6 x 105 5.0 x 10-14 335 2.8 10-8 347 9.0 10-8 4.9 10-14 1.00 1.8 x io6 5.0 x 10-14 356 2.0 10-7 4.9 x 10-14 1.00 4.0 x io6 5.0 x 10-14 364 3.5 10-7 4.9 10-14 1.00 7.1 x i o 6 4.9 x 10-14 376 7.2 x 10-7 4.9 x 10-14 1.00 1.5 x 107 4.8 x 10-14 387 1.2 10-6 4.9 10-14 1.00 2.6 x 107 4.6 x 10-14 a Experimental data and EMT calculations for PPG-based TPUl NH4CF3S03electrolytes. Samples containing 50 vol% of HS.
between 0.9 and 1.0. The values of the dc conductivity (c&) estimated for the experimental and EMT model are in good agreement at temperatures higher than the Tgfor the PPG-based TPU/N&CF3S03 electrolyte (Tg= 24 "C (297 K), see Table 2). Therefore, further differences between the hopping frequency and Ke parameter obtained for the EMT model and experimental data are a result of differences in the behavior of the A and n parameters. The temperature variation of A is neither predicted by our model nor assumed in the original Almond-West approach; this is probably the reason for the disagreement between model and experimental data. The nonideal behavior of the PPG-based TPU electrolytes results from interactions between hard and soft segments possibly occurring at the phase boundaries. The effect of the electrodeelectrolyte interactions which are not assumed in the EMT model (based upon a bulk continuum approach) is another source of error. Generally, it can be assumed that our model fits the experimental data reasonably well at temperatures higher than 47 "C (320 K) and particularly in the frequency range associated with phenomena occurring in the bulk electrolyte. Figure 11 presents a comparison between the low frequency (1 kHz) dielectric constants, as a function of HS concentration, calculated on the basis of the impedance experiments with those calculated on the basis of the ac EMT calculations. A decrease in the dielectric constant with an increase in the HS concentration is observed and suggests a decreasing amount of polarizable component within the TPU. It is also evident that the model is able to successfully predict such a drop in the dielectric constant with increasing volume fraction of HS.
Conclusions N&CF3S03 has been used to dope TPUs of different soft segment types. The salt is completely dissociated in the TPU
I
10, 0 -experiment
-theory 0
- 6 I Y
0
I 0.1
0.2
0.3
0.4
0.5
0.6
volume froction o f HS
Figure 11. Comparison of the room temperature (T = 25 "C (298 K)) low-frequency dielectric constant for data calculated on the basis of the EMT model (eq 20) with data experimentally measured for PPGbased TPU/NH&F3SO3 electrolytes (samples of various HS concentration).
with the PPG 1000 soft segment whereas in the TPU with the PTMG 1000 soft segment the salt only partially dissociates, leaving cation-anion aggregates. This is reflected in the ionic conductivity, which is approximately the same for these two systems at room temperature (1 x lo-* S/cm (25 "C)) but for the PPG-based TPU/NH4CF3S03 system is an acceptable 1 x S/cm at 100 "C about 1.5 orders of magnitude better than that for the PTMG-based TPU/NH4CF3SO3 system. In the PPGbased TPU system conductivity decreases with increase in hard segment concentration, and the dc ionic conductivity follows the VTF form. In the PTMG-based TPU system Arrhenius behavior is observed at low temperatures and VTF at higher temperatures. The introduction of salt into the PPG-based TPU system results in a large change in the Tg;this is not observed in the PTMG-based TPU system. It is concluded that the introduction of salt into the PPG-based TPU system promotes phase intermixing. Furthermore, on the basis of both DSC and FTIR data, it can also be concluded that the PPG S S has a greater solvating ability for NbCF3S03 than does FTMG. Phenomenologicalconductivity models applied to the PTMGbased TPU/NbCF3SO3 complex indicate that the ionic conductivity is a function of charge carrier mobility and only slightly dependent upon the concentration of charge carriers. The linear dependence of lna, versus Ea confirms that charge carrier concentration has a minor effect on conductivity. The phenomenological theory predicts an order-disorder transition at about 53 "C, which is suggested to be the transition temperature related to the order-disorder transition of the ionic aggregates formed only in the PTMG-based TPU and signifies a change in the conductivity mechanism from Arrhenius, below 53 "C, to VTF, above 53 "C. Conductivity data from the PPG-based TPU/NbCF3S03 complex have been fitted to the EMT model. The EMT model can be used to predict ac and dc conductivity behavior as a function of hard segment concentration and temperature in TPU electrolytes.
Acknowledgment. This work was financially supported by the BF Goodrich Co. J.v.H. thanks the Ontario Centre for Materials Research, and W. W. to thanks the NATO Research Office and NSERC Canada for an International Fellowship. We also thank Ms. Cathy Cliver for the molecular weight distribution determinations of the TPUs.
15152 J. Phys. Chem., Vol. 99, No. 41, 1995
References and Notes (1) See for instance: Polymer Electrolyte Reviews-1 and Polymer Electrolyte Reviews-2; MacCallum, J. R., Vincent, C. A,, Eds.; Elsevier: London, 1987 and 1989. Bruce, P. G.; Vincent, C. A. J. Chem. Soc., Faraday Trans. 1993, 89, 3187. (2) Scrosati, B. Applications of Electroactive Polymers; Chapman and Hall: London, 1993. (3) Berthier, C.; Gorecki, W.; Minier, M.; Armand, M. B.; Chabagno, J. M.; Rigaud, P. Solid State Ionics 1983, 11, 91. (4) Wieczorek, W.; Such, K.: Florjahczyk, Z.; Stevens, J. R. J. Phys. Chem. 1994, 98, 6840. (5) Seki, M.; Sato, K. Makromol. Chem. 1992, 193, 2971. (6) McLennaghan, A. W.; Hooper, A,: Pethrick, R. A. Eur. Polym. J. 1989, 25, 1297. (7) Watanabe, M.: Sanui, K.; Ogata, N. Macromolecules 1986,19, 815. (8) van Heumen. J. D.; Stevens, J. R. Macromolecules 1995,28,4268. (9) Almond, D. P.; West, A. R. SolidState Ionics 1986, 18-19, 1105. (10) Almond, D. P.; West, A. R. Solid State Ionics 1987, 23, 27. (11) Jain, H.; Mundy, J. N. J. Non-Cryst. Solids 1987, 91, 315. (12) Jonscher, A. K. In Dielectric Reluxation in Solids; Chelsea Dielectric Press: London, 1983. (13) (a) Watanabe, M.; Nagano, S.; Sanui, K.; Ogata, N. Solid State Ionics 1986, 18&19, 338. (b) Chung, H. S.; Such, K. S.; Wieczorek, W.: Stevens, J. R. J. Polym. Sci., Polym. Phys. Ed. 1994, 32, 2733. (14) Ratner, M. A. In Polymer Electrolyte Reviews-I; MacCallum, J. R., Vincent, C. A., Eds.; Elsevier: London, 1987; Chapter 7, p 173. (15) (a) Ratner, M. A,; Shriver, D. F. Chem. Rev. 1988, 80, 109. (b) Kobayashi, N.; Uchiyama, M.; Shigehara, K.; Tsuchida, E. J. Phys. Chem. 1985, 89, 987. (16) Reitman, E. A,; Kaplan, M. L.; Cava, R. J. Solid State Ionics 1985, 17, 67.
van Heumen et al. (17) Goodenough, J. B.; Shukla, A. K. In Solid Stare Ionic Devices; Chowdari, B. V. R., Radhakrishna, S., Eds.; World Scientific: Singapore, 1988, pp 573-604. Goodenough, J. B. Proc. R. SOC.London A 1984,393, 215. (18) Jonscher, A. K. Phys. Thin Films 1980, 11, 231. (19) Almond, D. P.; Duncan, G. K.; West, A. R. Solid State Ionics 1983, 8, 159. (20) Almond, D. P., West, A. R. Solid State Ionics 1983, 9-10, 277. (21) Such, K.; Stevens, J. R.; Wieczorek, W.; Siekierski, M.; Flojahczyk, Z . J. Polym. Sci., Polym Phys. Ed. 1994, 32, 2221. (22) Dienes, G. J. J. Appl. Phys. 1950, 21, 1189. (23) Nan, C. W. Prog. Mater. Sci. 1993, 37, 1. (24) Ferry, A,; Jaccobson, P.; Stevens, J. R. Manuscript in preparation. (25) Schantz, S.; Torell, L. M.; Stevens, J. R. J. Chem. Phys. 1991, 94, 6862. (26) Bemson, A.; Lindgren, L. Solid State Ionics, 1993, 60, 37. (27) Varetti, E. L.; Femandez, E. L.: Ben Altabef, A. Spectrochim. Acta. 1991, 47A. 1767. (28) Wintersgill, M. C.; Fontanella, J. J.; Greenbaum, S. G.; Teeters, D.: Frech, R. Solid State Ionics, 1986, 18/19, 271. (29) Cavell, E. A. S.; Knight, P. C. Z. Phys. Chem. (Munich) 1968, 57, 3. (30) Albinsson, I.; Mellander, B.-E.: Stevens, J. R. Solid State Ionics 1993, 60, 63. (31) Kutsumizu, S.; Hashimoto, Y.: Sakaida, Y.; Hara, H.; Tachino, H.; Hirasawa, E.; Yano, S. Macromolecules 1994, 27, 5457. (32) Petrovic, Z. S.; Javni, I. J. Polym. Sci., Polym. Phys. Ed. 1989,27, 545 JP9506550
