A solid electrolyte is a crucial component of any solid state battery. Polymer gel electrolytes have received increasing attention in recent years due to their high ionic conductivity, flexibility, and improved safety. However, a general tradeoff usually exists between the mechanical properties and ionic conductivity in such materials. Molecular ionic composites (MICs) are a new type of rigid polymer gel electrolyte based on ionic liquids (ILs) and a double helical rigid-rod polyamide, poly(2,2′-disulfonyl-4,4′-benzidine terephthalamide) (PBDT). MICs have high ionic conductivity, high thermal and electrochemical stability, and widely tunable and high tensile modulus even at relatively low polymer content. MICs show great promise as solid electrolytes for solid state batteries. This dissertation describes the preparation and characterization of MIC electrolyte membranes. These transparent, flexible, and tough membranes are prepared through a convenient solvent casting process. A large variety of ILs, including both hydrophilic and hydrophobic examples, are suitable to prepare MIC electrolyte membranes by adjusting the solvents used in the casting process. The prepared membranes show a biphasic internal structure consisting of a PBDT-rich “bundle” phase and an IL-rich “puddle” (interconnected fluid) phase. Similar to the bulk MIC ingots prepared previously through an interfacial ion exchange process, the MIC membranes also have high ionic conductivity and tensile modulus at low polymer content. A MIC membrane composed of 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide (Pyr₁₄TFSI), LiTFSI, and PBDT in a mass ratio of 8:1:1 is tested as a solid electrolyte for lithium metal batteries. This electrolyte membrane shows high ionic conductivity and high rigidity. The shear storage modulus of this MIC electrolyte membrane only decreases by 35% when heated to 200 °C from room temperature, suggesting great mechanical stability at high temperatures. The electrolyte membrane is successfully used as solid electrolyte for a Li/LiFePO₄ battery working over a large temperature range from 23 to 150 °C, and the discharge capacity retention of the cell is as high as 99% after 50 cycles at 150 °C. By replacing the IL in the MIC with a charge-neutral liquid, single-ion-conducting polymer gel electrolyte composed of PBDT and polyethylene glycol (PEG) oligomer are obtained. Similar to the MICs, these single-ion-conducting materials also have high Young’s modulus and biphasic internal structures. This study reveals that the counter ion (Li⁺ or Na⁺) of the PBDT has a major effect on both the ionic conductivity and modulus of the materials. Due to the stronger intermolecular interactions, LiPBDT-PEG demonstrates lower ionic conductivity but higher Young’s modulus. This dissertation also evaluates the viability of rigid PBDT as a polymer binder for electrodes. Aqueous solution-processed LiFePO₄ electrodes with only 3 wt% PBDT demonstrate stable cycling over 1000 cycles without obvious capacity decay, and the rate capacity of these aqueous solution-processed electrodes are comparable to the electrodes prepared with conventional poly(vinylidene difluoride) (PVDF) as the binder, suggesting PBDT can serve as a potential electrode binder for commercial applications. / A solid electrolyte is a crucial component of any solid state battery. Polymer gel electrolytes have received increasing attention in recent years due to their high ionic conductivity, flexibility, and improved safety. However, a general tradeoff usually exists between the mechanical properties and ionic conductivity in such materials. Molecular ionic composites (MICs) are a new type of rigid polymer gel electrolyte based on ionic liquids (ILs) and a double helical rigid-rod polyamide, poly(2,2′-disulfonyl-4,4′-benzidine terephthalamide) (PBDT). MICs have high ionic conductivity, high thermal and electrochemical stability, and widely tunable and high tensile modulus even at relatively low polymer content. MICs show great promise as solid electrolytes for solid state batteries. This dissertation describes the preparation and characterization of MIC electrolyte membranes. These transparent, flexible, and tough membranes are prepared through a convenient solvent casting process. A large variety of ILs, including both hydrophilic and hydrophobic examples, are suitable to prepare MIC electrolyte membranes by adjusting the solvents used in the casting process. The prepared membranes show a biphasic internal structure consisting of a PBDT-rich "bundle" phase and an IL-rich "puddle" (interconnected fluid) phase. Similar to the bulk MIC ingots prepared previously through an interfacial ion exchange process, the MIC membranes also have high ionic conductivity and tensile modulus at low polymer content. A MIC membrane composed of 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide (Pyr14TFSI), LiTFSI, and PBDT in a mass ratio of 8:1:1 is tested as a solid electrolyte for lithium metal batteries. This electrolyte membrane shows high ionic conductivity and high rigidity. The shear storage modulus of this MIC electrolyte membrane only decreases by 35% when heated to 200 °C from room temperature, suggesting great mechanical stability at high temperatures. The electrolyte membrane is successfully used as solid electrolyte for a Li/LiFePO4 battery working over a large temperature range from 23 to 150 °C, and the discharge capacity retention of the cell is as high as 99% after 50 cycles at 150 °C. By replacing the IL in the MIC with a charge-neutral liquid, single-ion-conducting polymer gel electrolyte composed of PBDT and polyethylene glycol (PEG) oligomer are obtained. Similar to the MICs, these single-ion-conducting materials also have high Young's modulus and biphasic internal structures. This study reveals that the counter ion (Li+ or Na+) of the PBDT has a major effect on both the ionic conductivity and modulus of the materials. Due to the stronger intermolecular interactions, LiPBDT-PEG demonstrates lower ionic conductivity but higher Young's modulus. This dissertation also evaluates the viability of rigid PBDT as a polymer binder for electrodes. Aqueous solution-processed LiFePO4 electrodes with only 3 wt% PBDT demonstrate stable cycling over 1000 cycles without obvious capacity decay, and the rate capacity of these aqueous solution-processed electrodes are comparable to the electrodes prepared with conventional poly(vinylidene difluoride) (PVDF) as the binder, suggesting PBDT can serve as a potential electrode binder for commercial applications. / Doctor of Philosophy / Solid state batteries are widely considered as the pathway to next-generation high performance batteries. In a solid state lithium battery, the liquid organic carbonate electrolyte is replaced with a solid electrolyte. Polymer gel electrolytes are a type of potential solid electrolyte that have been widely studied in recent decades. This dissertation describes the application of a rigid polymer in preparing polymer gel electrolytes. This highly charged and rigid polymer is a water-soluble polyamide known as PBDT with a double helical structure akin to DNA. Through a modified solvent casting process, a new type of polymer gel electrolyte, known as molecular ionic composite (MIC), is prepared using PBDT and various ionic liquids. Extra salt (which can contain lithium) can also be incorporated into the MIC membrane. This type of new polymer gel electrolyte is rigid with high tensile modulus even at high temperatures and low polymer (PBDT) content. MIC membranes are used as solid electrolytes for lithium metal batteries working over a wide temperature range from 23 to 150 °C. A rigid polymer gel electrolyte can also be obtained by replacing the ionic liquids in MICs with polyethylene glycol. Besides the application in preparing solid electrolytes, PBDT is also evaluated as a polymer binder for aqueous processed electrodes. Preliminary study reveals that PBDT holds great potential for a range of commercial energy storage applications.