13188
J. Phys. Chem. B 2007, 111, 13188-13193
Plasticized Single-Ion Polymer Conductors: Conductivity, Local and Segmental Dynamics, and Interaction Parameters Robert J. Klein† and James Runt* Department of Materials Science and Engineering and the Materials Research Institute, The PennsylVania State UniVersity, UniVersity Park, PennsylVania 16802 ReceiVed: July 14, 2007; In Final Form: September 11, 2007
This paper considers high-quality conductivity data for plasticized ionomers in the context of polymer local and segmental processes. Dielectric spectroscopy was conducted on a neat PEO-based ionomer and six mixtures containing 6 wt % plasticizer with a wide range of dielectric constants. Conductivity increased dramatically but remained Vogel Fulcher Tamman (VFT)-like for all plasticized ionomers, indicating that the mechanism of ion transport was unchanged. Relaxation times of the polymer local β and segmental R processes were analyzed for the plasticized ionomers, providing activation energies and relaxation strengths for the β process and VFT fitting parameters for the R process. The glass transition temperature Tg of the mixtures was found to be the critical characteristic governing conductivity, based on four criteria: VFT-like behavior of conductivity, decrease in the conductivity-segmental coupling index upon the addition of plasticizer, statistical insignificance of solvent quality (dielectric constant, donor number, and viscosity) on conductivity, and the creation of a conductivity master curve as a function of Tg-normalized temperature.
1. Introduction So-called “gel” polymer electrolytes (GPEs) are essential components of the Li-ion batteries that support a sizable portion of today’s mobile technology. GPEs act as membranes for Li+ transport and are composed of a high-dielectric constant solvent, a porous polymer matrix, and a Li-based salt.1-4 The solvent and polymer are chosen so that the solvent interacts more strongly with the salt than the polymer, with the polymer acting to provide mechanical reinforcement, as solvent-sheathed ions travel across the membrane.2 Replacing the transport membrane by solid polymer electrolytes (SPEs), which contain only polymer and salt, would result in major advantages, provided that SPE conductivities can approach those of the gels.3 These advantages include the prevention of solvent leaks and reduced flammability, mechanical instability, and dendrite formation.1 As of yet, the chemistries available for SPEs do not provide sufficiently high conductivity, and as an intermediate step, plasticized polymer electrolytes (PPEs) with low solvent fraction are of interest. By understanding the 3-fold interactions occurring in model PPEss solvent-polymer, polymer-salt, and solvent-saltsthe design parameters for a mechanically durable, high-conductivity PPE can be established. Only in a few cases has the quantitative relationship between solvent interaction parameters and ionic conductivity been investigated for polymer electrolytes. Kim and Oh,5 working with GPEs and high solvent fractions, considered donor number (DN) and dielectric constant (), concluding from infrared spectroscopy data that DN, over a limited range, correlates with an increase in infrared absorbance bands that measure free ion fraction. Kumar and Sekhon investigated the effect of DN and on ion conductivity in three systems: highly plasticized poly* To whom correspondence should be addressed. † Present address: Organic Materials Department, Sandia National Laboratories, Albuquerque, NM.
(ethylene oxide) (PEO) containing ammonium fluoride salt,6 nonaqueous solvents with salicylic acid,7 and poly(methyl methacrylate) with added solvents and lithium triflate salt.8 However, only three solvents were examined in the three studies and conclusions as to the influence of and DN were mixed. For PPEs with low plasticizer fraction, the ion transport mechanism is no longer as straightforward as in GPEs with high solvent fractions, because the former system is phase-mixed whereas the latter is phase-separated. In commercialized GPEs, ions are understood to move surrounded by a thick sheath of solvent within the porous polymer, and conductivities can therefore approach those of salts in solvents alone.1 Concepts such as the decoupling index,9 which relates the structural relaxation time of the polymer to the characteristic hopping time of ions involved in conductivity, and ion dynamics on a local scale10,11 are relevant to evaluation of low-solvent-fraction PPEs. With this background in mind, the present study considers data on conductivity, local polymer dynamics and segmental dynamics in PPEs composed of a dipolar solvent and an ionomer. The dielectric behavior of a neat poly(ethylene glycol)based ionomer will be contrasted with plasticized forms that contain 6 wt % of six miscible solvents: propylene carbonate (PC), dioctyl phthalate (DOP), dimethyl sulfoxide (DMSO), N,N-dimethylformamide (DMF), ethylene glycol (EG), and triethylamine (TEA). 2. Experimental Method The ionomer under consideration was synthesized by condensation polymerization, as discussed in previous publications.12,13 It consists of a repeating structure of 13 consecutive units of ethylene oxide (molecular weight of ∼600) separated by a 5-sulfoisophthalate unit (Figure 1). The ionomer is a singleion conductor, since anions are covalently bound to the chains. The total ion concentration of the neat ionomer was determined by atomic absorption (and stoichiometric calculations) to be
10.1021/jp075517c CCC: $37.00 © 2007 American Chemical Society Published on Web 10/31/2007
Plasticized Single-Ion Polymer Conductors
J. Phys. Chem. B, Vol. 111, No. 46, 2007 13189
Figure 1. Repeat unit chemical structure of the single-ion polymer electrolyte under investigation.
Figure 3. Isothermal σ′(f) spectra for the neat ionomer, from 0 to 70 °C every 10 °C. Fits represent the CTRW approximation (eq 2).
for 5 min to encourage mixing, squeezing the electrodes to the correct thickness, and sealing the sample in a dry container overnight to attain equilibrium. Dielectric measurements of the neat sample were found to be very repeatable, but variation in the fraction of added solvent, 6 ( 1%, increased the experimental error slightly. It was confirmed, by comparison with samples containing 1-6 wt % water, that the samples under examination were effectively dry; this confirmation is necessary because the dielectric behavior of this ionomer is strongly affected by the presence of water. Conductivities σ0 were obtained from the dielectric loss15
′′ ) (σ0/ωvac)n
Figure 2. Chemical structures of the solvents used to plasticize the ionomer.
relatively low, ∼6 × 1020 cations/cm3 (for comparison, P(EO)4: LiClO4 contains 5 × 1022 cations/cm3). Small molecules were purchased: anhydrous dimethyl sulfoxide (DMSO; 99.8%, Alfa Aesar), anhydrous N,N-dimethylformamide (DMF; 99.8%, Sigma-Aldrich), triethylamine (TEA; 99%, Sigma-Aldrich), dioctyl phthalate (DOP; 99%, SigmaAldrich), anhydrous ethylene glycol (EG; 99.8%, SigmaAldrich), and propylene carbonate (PC; 99%, Sigma-Aldrich). EG was refluxed for 48 h and dried over molecular sieves for 48 h to increase the purity. EG, DOP, and PC were dried at 110 °C for 1 h prior to use to remove water. The chemical structure of small molecules under consideration are displayed in Figure 2. It would have been advantageous to reflux all solvents to increase the purity, but the negligible effect of impurities follows from considering the following: (1) impurities are most likely constituted by very hard Lewis acid-base salts such as NaCl and KCl, which have no measurable solubility in PEO-based polymers14 due to the high binding energy of the salt; (2) as-provided solvents contain less than 0.01 wt % salt, which a simple calculation indicates impurities to be present at a concentration of ∼6 × 1016 ion pairs/cm3, or 2 impurity ions per 10000 Li+; and (3) the conductivity of the more highly purified system, +EG, has one of the highest conductivities. Dielectric (impedance) spectra were collected isothermally using a Novocontrol GmbH Concept 40 broadband dielectric spectrometer in the frequency range 10-2 to 107 Hz. Temperatures were controlled to within 0.2 °C. Electrodes consisted of polished aluminum circular plates. Samples for dielectric spectroscopy were prepared by carefully drying the polymers and spacers on the electrodes in a vacuum oven at 70 °C for at least 8 h, loosely sandwiching the polymer, solvent, and a Teflon spacer between two electrodes, ultrasonicating the sealed sample
(1)
where radial frequency is related to frequency by ω ) 2πf, vac is the vacuum permittivity, and fitting was done with the six points in ′′(f) that maximized n. dc conductivity is only physically defined for n ) 1, but in real samples, 0.3 < n e 1.0, depending on the pathway tortuosity experienced by ions during diffusion.16 For the samples under consideration, n > 0.95 for T > Tg + 10 K. The existence of only one Tg for all samples, as measured by both differential scanning calorimetry and dielectric spectroscopy, indicate complete miscibility. Polymer-solvent miscibility was also confirmed by the visual appearance of mixtures: all mixtures remained optically clear in the presence of less than 25% solvent. 3. Results and Discussion 3.1. Dielectric Spectra and Fitting. There are three portions of the dielectric temperature-frequency spectra that provide information on conductivity, local polymer dynamics, and segmental polymer dynamics. These portions are respectively displayed, for the neat ionomer, in Figures 3-5. The real part of conductivity, σ′, was obtained from the dielectric loss as σ′ ) ω0′′. Spectra for the plasticized ionomers appear similar and are fit using the same methods. Conductivity is fit in σ′(f) by the continuous-time-random walk (CTRW) approximation17
σ′(f) )
σ0ωτσ arctan(ωτσ) 1 2 ln (1 + ω2τσ2) + arctan2(ωτσ) 4
(2)
where τσ is the characteristic conduction time constant, or the time to overcome the largest energetic barrier to ion conduction, and σ0 is the plateau or “dc” conductivity.
13190 J. Phys. Chem. B, Vol. 111, No. 46, 2007
Klein and Runt
Figure 6. Arrhenius plot of τ for the local β process, the segmental R process, and conductivity of the neat ionomer. Figure 4. Isothermal ′′(f) spectra for the neat ionomer, from -120 to -50 °C every 10 °C. Fits represent the HN model (eq 3).
Figure 7. Plateau conductivity σ0 against inverse temperature for the neat ionomer and six plasticized forms. Higher temperature data for the plasticized forms is abridged due to small molecule evaporation.
Figure 5. Isothermal ′′(f) spectra for the neat ionomer, from 0 to 50 °C every 10 °C. Fits represent the HN model together with a power law representing the high-frequency edge of electrode polarization.
Relaxations of the local or segmental type are fit with the Havriliak-Negami (HN) model:18
[
′′HN(ω) ) Im U +
]
∆ (1 + (iωτ)a)b
(3)
where U is the unrelaxed (high-frequency) dielectric constant, ∆ ) R - U is the relaxation strength, R is the relaxed (lowfrequency) dielectric constant, τ is the time constant, and a and b are respectively the symmetric and asymmetric broadening parameters. At low temperatures (Figure 4), β relaxations can be fit with a simple HN function, but at higher temperatures, conductivity overwhelms the R relaxation. When a conduction-free numerical KK transformation is used,19 the R relaxation is obtained after deconvolution from the loss arising from electrode polarization (EP), as seen in Figure 5. The characteristic times of the three phenomena can be directly compared in an Arrhenius plot (Figure 6). The β process of the neat ionomer appears at much lower temperatures and shorter times than the other two, whereas conduction and segmental dynamics nearly overlap. At least in the neat ionomer, therefore, ion motion is intimately dependent on segmental dynamics and the glass transition (Tg) of the polymer (as discussed by Zhang et al.,11 among others). This dependence is also strongly evidenced by the curved form of τσ(1/T), which
indicates Vogel-Fulcher-Tammann (VFT)-like behavior. The general VFT relation is written
τ(T) ) τ∞ exp
(
B T - T0
)
(4)
where τ∞ is the relaxation time in the high-temperature limit, B is a constant, and T0 is the Vogel temperature. The segmental dynamics of polymers above Tg often follow VFT scaling, and although conductivity should not follow a strict VFT form (see Klein et al.13), VFT-like behavior of the conductivity indicates coupling with segmental dynamics. (The viscoelastic modes responsible for VFT-like curvature include both the cooperative segmental mode and the normal mode,20 the motion of the chain along its entire length.) 3.2. Analysis of Plasticized Ionomers. The most functional parameter identifying any conducting system is of course the dc conductivity σ0. Figure 7 depicts σ0 for the neat ionomer and the plasticized forms under consideration. As described above, the neat ionomer displays marked VFT-like behavior (σ0 and τσ are always proportional, linked by the BartonNakajima-Namikawa relation17). The temperature dependence of conductivity of the plasticized ionomers remains curved in all cases, which signifies that ion motion is governed by segmental motion even with the addition of the dipolar small molecules, at least at the low solvent concentration used in the present study. The higher temperature σ0 data for the plasticized ionomers is unfortunately abridged due to evaporation of the small molecules. 3.2.1. Local β Process. The small molecules are effective in increasing σ0(T), in the order DMF < DOP < TEA ≈ PC
