The Pennsylvania State University The Graduate School DIELECTRIC PROPERTIES OF CONDUCTIVE IONOMERS A Thesis in Materials Science and Engineering by Robert James Klein c 2007 Robert James Klein Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2007 The thesis of Robert James Klein was reviewed and approved∗ by the following: James Runt Professor of Polymer Science Associate Head for Graduate Studies of the Department of Materials Science and Engineering Thesis Advisor, Chair of Committee Ralph H. Colby Professor of Materials Science and Engineering Ronald Hedden Assistant Professor of Materials Science and Engineering Janna K. Maranas Associate Professor of Chemical Engineering and Materials Science and Engineering Gary L. Messing Distinguished Professor of Ceramic Science and Engineering Head of the Department of Materials Science and Engineering ∗Signatures are on file in the Graduate School. Abstract Ion and polymer dynamics of ion-containing polymers were investigated, with the majority of results obtained from application of a physical model of electrode polarization (EP) to dielectric spectroscopy data. The physical model of MacDon- ald, further developed by Coelho, was extended for application to tan δ (the ratio of dielectric loss to dielectric constant) as a function of frequency. The validity of this approach was confirmed by plotting the characteristic EP time as a function of thickness and comparing the actual and predicted unrelaxed dielectric constant for a poly(ethylene oxide) (PEO) -based ionomer neutralized by lithium, sodium, and cesium. Results were obtained for ion mobility and mobile ion concentration for a neat PEO-based ionomer, two (methoxyethoxy-ethoxy phosphazene) (MEEP) -based ionomers, two MEEP-based salt-doped polymers, sulfonated polystyrene (SPS) neutralized by sodium with a high sulfonation fraction, and SPS neutralized by zinc with a low sulfonation fraction. Additionally, the conductivity parameters of six plasticized forms of a neat PEO-based ionomer were characterized, but the method apparently failed to correctly evaluate bulk ionic behavior. In all cases except the SPS ionomers ion mobility follows a Vogel-Fulcher-Tammann (VFT) temperature dependence. In all cases, mobile ion concentration follows an Arrhe- nius temperature dependence. Fitting parameters from these two relationships yielded direct information about the state of ionic diffusion and ion pairing in each system. Combination of these two functionalities predicts a relationship for conductivity that is significantly different than the VFT relation typically used in iii the literature to fit conductivity. The most outstanding result was the extremely small fraction of ions found to be mobile. For ionomers it can be concluded that the primary reason for low conductivities arises from the low fraction of mobile ions. The local and segmental dynamics of the neat and plasticized PEO-based ionomer were also studied in comparison to conductivity, with the conclusion that the glass transition temperature (a manifestation of the segmental segments) is the primary property governing conduction behavior in single-phase ionomers. Con- sideration of the solvent quality parameters yielded a similar result, that the plas- ticization effect on the glass transition is far stronger than the dielectric constant, donor number, or viscosity of the solvents. iv Table of Contents List of Figures ix List of Tables xvii Acknowledgments xix Chapter 1 Introduction 1 1.1 Motivation . 1 1.2 Historical development of polymer electrolytes for ion transport 2 1.3 Purpose and organization of this study . 5 Chapter 2 Dielectric Spectroscopy of Polymers: Theory and Analytical Methods 9 2.1 Basics of Dielectric Spectroscopy . 9 2.2 Theories Relating Macroscopic Measurements to Microscopic Quantities . 14 2.3 Theory Linking Polymer Dynamics and Dielectric Spectroscopy 17 2.3.1 Dynamical Theories . 17 2.3.2 Glass Transition Theories . 18 2.4 Transformations of Dielectric Permittivity . 19 2.5 Fitting Relations . 21 v 2.5.1 Relaxations . 21 2.5.2 Conductivity . 23 2.6 Classification of Relaxations . 25 2.7 Scaling Analysis . 27 2.8 Electrical Analogs . 27 Chapter 3 Electrode Polarization Theory 32 3.1 Introduction . 32 3.2 History . 34 3.3 Background Theory . 35 3.4 Pivotal Relationships . 42 3.5 Fitting EP in tan δ ......................... 43 3.6 Temperature Dependence of Free Ion Concentration, Mobility, and Conductivity . 45 Chapter 4 Modeling Electrode Polarization in Dielectric Spectroscopy: Ion Mobility and Mobile Ion Concentration of Single-Ion Polymer Electrolytes 47 4.1 Introduction . 47 4.2 Fitting Routine . 49 4.3 Experimental . 49 4.4 Results and Discussion . 51 4.4.1 Model Verification . 51 4.4.2 Data Analysis . 55 4.4.3 Discussion . 61 4.5 Summary . 64 Chapter 5 Dielectric Behavior of Plasticized Ionomers: Conductivity, Local and Segmental Dynamics, Plasticizer Interaction Parameters, Ion Mobility and Mobile Ion Concentration 65 5.1 Introduction . 65 5.2 Experimental Method . 67 5.3 Polymer Dynamics and Solvent Interaction Parameters: Results and Discussion . 70 5.3.1 Dielectric spectra and fitting . 70 5.3.2 Analysis of plasticized ionomers . 75 5.3.2.1 Local β process . 76 vi 5.3.2.2 Segmental α process . 79 5.3.3 Discussion . 80 5.4 Conductivity Parameters from EP: Results and Discussion . 84 5.5 Summary . 90 Chapter 6 Counterion Effects on Ion Mobility and Mobile Ion Concentration of Tailored, Salted Polyphosphazenes and Polyphosphazene Ionomers 92 6.1 Introduction . 92 6.2 Experimental Method . 94 6.3 Results and Discussion . 96 6.3.1 Results and Analysis . 96 6.3.2 Discussion . 103 6.4 Summary . 105 Chapter 7 Comparison of Conductivity Parameters Evaluated from Electrode Polarization for Various Ionomers 107 7.1 Introduction . 107 7.2 Experimental . 109 7.3 Results and Discussion . 110 7.4 Summary . 120 Chapter 8 Summary and Suggestions for Future Work 121 8.1 Summary . 121 8.2 Future Work . 123 Appendix A Discrepancies Between Various PEO−Li+ Ionomer Samples and the Apparent Transition in Mobile Ion Concentration 127 A.1 Review of Results . 127 Appendix B Plasticized Ionomer Data 137 B.1 Dielectric Constant, Loss, and tan δ . 137 B.2 Full Temperature Range of Conductivity, Ion Mobility, and Mobile Ion Concentration . 144 B.3 Influence of n on the Evaluation of Conductivity . 147 vii Appendix C Mathematicar Programs for Data Processing 150 C.1 Splicing and Fitting tan δ for EP . 150 C.2 Kramers-Kronig Transform . 153 C.3 Splicing Dielectric Data . 156 C.4 Fitting ε00 with Debye Function and Two Conductivities . 158 C.5 Fitting the Real Part of Conductivity with the CTRW Approx- imation . 163 Bibliography 167 viii List of Figures 1.1 The functional relationships concerning ion motion in polymer electrolytes, simulating the structure of this thesis. Numbers indicate chapters that are attached to particular concepts. 7 2.1 Three classification types of polymers containing dipoles: type-A, with dipoles parallel to the backbone (e.g., poly(cis- 1,4-isoprene)); type-B, with dipoles rigidly perpendicular to the backbone (e.g., poly(vinyl-chloride)); and type-C, with dipoles flexibly attached to the backbone (e.g., poly(methyl methacrylate)). Adapted from [1, 2]. 10 2.2 Various types of dipolar motions, represented schematically: (a) local crankshaft main-chain rotation, as in poly(ethylene oxide); (b) local side-chain rotation, as in poly(methyl-methacrylate); (c) local rattling within a generic free-volume cage; (d) coopera- tive segmental motion, as in poly(ethylene oxide), which extends over a domain of chains; and (e) normal mode, which extends over the entire chain length, as in poly(cis-1,4-isoprene). 10 ix 2.3 Schematic illustration of the dipolar transition from a mobile to immobile state under an ac field. At high temperatures and long switching times of the field, dipoles are free to move with the field. As the temperature decreases or the switching time decreases, the ions no longer have sufficient energy to remain in phase with the field. At some intermediate time, the time constant of the process is equal to the switching time and the correlation function is maximized. 11 0 00 2.4 Appearance of ε (f) and ε (f) for a Debye relaxation. εR is the low-frequency, or relaxed, dielectric constant, and εU is the high-frequency, or unrelaxed, dielectric constant. The value of ε00 at its maximum is half the relaxation strength. The dotted curve indicates the shift in the dielectric loss due to increased temperature. 12 2.5 Schematic of the effect of a dielectric material on the charge Q stored by a capacitor. The dielectric constant of the material increases the charge stored by a factor equal to the dielectric permittivity ε............................. 13 2.6 Cavity model used to construct physical representation of a sin- gle dipole moving with an electric field. The cavity and distribu- tion of charges on the inside of the cavity, which neutralize the dipole, are constructed such that the bulk electric field lines are unaffected by the presence of the cavity. Adapted from [3]. 16 2.7 Illustration of particles embedded in a matrix that will give rise to an MWS relaxation. The conductivities σ and dielectric con- stants ε of the matrix and inclusion phases must be significantly different in order to create an ionic or electronic charge build-up at the interfaces. 26 2.8 τmax (T ) for the α and β processes in a hypothetical polymer. The merging of the β process into the α process at higher temper- atures physically represents the unifying of local and cooperative motion. 28 2.9 An illustration of the simplest combinations of a resistor and ca- pacitor, along with the impedance behavior shown to the right of the electrical analog. R and C are the magnitudes of the re- sistor’s resistance and capacitor’s capacitance, respectively. The lines in the impedance plots are derived from the locus of points evaluated at different radial frequencies ω.