Designing tailored combinations of structural units in polymer dielectrics for high-temperature capacitive energy storage

Many mainstream dielectric energy storage technologies in the emergent applications, such as renewable energy, electrified transportations and advanced propulsion systems, are usually required to operate under harsh-temperature conditions. However, excellent capacitive performance and thermal stability tend to be mutually exclusive in the current polymer dielectric materials and applications. Here, we report a strategy to tailor structural units for the design of high-temperature polymer dielectrics. A library of polyimide-derived polymers from diverse combinations of structural units are predicted, and 12 representative polymers are synthesized for direct experimental investigation. This study provides important insights into decisive structural factors necessary to achieve robust and stable dielectrics with high energy storage capabilities at elevated temperature. We also find that the high-temperature insulation performance would experience diminishing marginal utility as the bandgap increases beyond a critical point, which is strongly correlated to the dihedral angle between neighboring planes of conjugation in these polymers. By experimentally testing the optimized and predicted structures, an increased energy storage at temperatures up to 250 °C is observed. We discuss the possibility for this strategy to be generally applied to other polymer dielectrics to achieve further performance enhancement.

where d is the crystal plane spacing, θ is the angle between the incident X-ray and the corresponding crystal plane, λ Is the wavelength of X-ray, and n is the diffraction order. Obviously, the molecular chain spacing of the polymers containing m-benzene shows a significant increase, which is not conducive to the formation of preferred layer packing (PLP) and mixed layer packing (MLP), thus leading to the decrease of Tg. Except for m-benzene structure, other structural units have minor impact on the stacking of molecular chains, indicating that the rigidity of structural units is the main factor affecting the Tg of polymers.

Section 2. High-field insulation and low-field dielectric properties
In order to further understand the conduction mechanism of charge in polymer, we used electrode-limited conduction mechanism and bulk phase-limited conduction mechanism to verify. The most common electrode-limited conduction mechanism in dielectrics at high temperatures is Schottky injection (also known as thermionic emission). The carrier is thermally excited to obtain enough energy to overcome the barrier at the interface, and the process of injection is called Schottky injection.
Schottky injection current density can be expressed by, where A is the Richardson constant, T is the absolute temperature, q is the charge of the carrier, qϕB is the Schottky injection barrier, εr is the relative permittivity of the dielectric material, ε0 is the vacuum dielectric constant, kB is the Boltzmann constant, E is the electric field strength, m0 is the free electron mass, and h is the Planck constant. Equation (1) can be equivalently transformed into, Therefore, for the Schottky injection model, the relationship between ln(J/T 2 ) and E 1/2 is linear. The linear fitting results of ln(J) on E 1/2 can be used to determine whether the Schottky injection is the dominant conduction mechanism. However, it should be noted that the fitting slope is related to the dielectric constant of the material. Even if the fitting degree is high, if the dielectric constant derived from the slope does not match the experimental dielectric constant, it is not in the mechanism of Schottky injection. The intercept of the fitting line of the Schottky diagram is related to the barrier height. At the same temperature, the smaller intercept means the higher Schottky injection barrier.
The conduction mechanism of the bulk phase limitation is Poole-Frenkel (P-F) emission and solid-state hopping conductance. P-F emission refers to the process that electrons captured by traps in the dielectric material are heated and excited into the conduction band to form current. By applying an electric field on the dielectric, the potential energy of electrons can be reduced, thus increasing the probability of electrons being heated and excited. Therefore, P-F emission usually appears at high temperature and high electric field. P-F emission current density can be given as, where μ is the carrier migration rate, NC is the state density of conduction band, qϕT is the trap level (i.e. P-F emission activation energy), and other parameters have the same meanings as those in the Schottky injection current density formula. Equation (4) can be equivalently transformed into, For P-F emission, ln(J/T 2 ) is linear with E 1/2 . The linear fitting results of ln(J/T 2 ) on E 1/2 can be used to determine whether the P-F emission is the dominant conduction mechanism. The determination rule is similar to the Schottky injection. The slope of the fitting line is related to the dielectric constant of the dielectric, and the intercept of the fitting line is related to the trap energy level. P-F emission is similar to Schottky injection, while hopping conduction is similar to tunneling effect. In the hopping conduction, carriers trapped by traps cannot obtain enough energy to be excited into the conduction band, but they can still "jump" between different traps through tunneling effect. The current density generated by hopping conductance can be expressed as, where n is the carrier density, q is the electric charge of the carriers, λ is the average hopping distance, ν Is the attempt-to-escape frequency, Ea is the activation energy of hopping conductance, kB is the Boltzmann constant, T is the absolute temperature, and E is the electric field strength. The hyperbolic sine function can be approximated to an exponential function at high electric field. Thus, the Equation (6) can be transformed into, From the above formula, for the leakage current J generated by the hopping conductance, the relationship between lnJ and E is linear at high electric field.
Generally, when the temperature is fixed, the hyperbolic sine function can be given as, The leakage current density measured under different electric field intensity is fitted to determine whether the dominant conduction mechanism is the hopping conduction. In the formula, the fitting parameter β is a constant related to the hopping distance, which can be used to calculate the hopping distance.
For the sake of a brief discussion of the TSDC theory, only the electrons injected from the electrode will be considered in the following. In case of a continuous trap level distribution with the distribution function, which is spatially uniform deep into the film with a distance l, the induced current in the external circuit during TSC measurement can be calculated as follows 3 , where e is electronic charge quantity，f0 is the initial occupancy of a trap level and is a constant, E is the trap energy (trap depth). en(E,T)=νexp(-Et/kT) is the emission rate of electrons at trap level E and temperature T. k is the Boltzmann constant, d is the thickness of the film and β is the heating rate. ν is commonly called the frequency factor or attempt-to-escape frequency. The usual interpretation of ν is that it represents the number of times per second a bound electron interacts with the lattice phonons.
The normal value expected for ν is therefore the lattice vibration frequency 3 , typically 10 12 -10 14 s −1 . In this paper, ν was assumed to be 10 12 s −1 as suggested by Mott 4 Table S3. Comparison of θ, leakage current density, hopping distance, breakdown strength and Eg of PI-derived polymers with hopping conduction. Hopping distance is obtained from leakage current density of the polymer conforming to hopping conduction (Equation (6)), and a shorter hopping distance corresponds to a deeper trap depth 6   Supplementary Figure S32 The Gasteiger charges distribution of the experimental dielectric polymers in this work. The Gasteiger charges distribution implies that the negative charge has a high concentration near the oxygen atom, while the carbon atom connected to it has a corresponding high concentration of positive charge. Therefore, the oxygen atom with negative potential in the diamine monomer may also become a bridge for electron transfer between adjacent benzene rings, resulting in low trap levels.     Figure S53 Temperature-dependent electric field and discharged energy density of PI-oxo-iso and PEI under the precondition that discharge efficiency is higher than 90%. Considering the difference of glass transition temperature, the maximum test temperature of PEI and PI-oxo-iso is defined as 200 °C and 250 °C, respectively.