Yes, it is theoretically and practically possible to have high permittivity and high conductivity simultaneously in a material. However, it's a complex relationship and depends heavily on the specific material and frequency of operation. Here's a breakdown of why and how:

Why it's possible:

• Different Mechanisms: Permittivity (ε) and conductivity (σ) are related to the material's response to an electric field, but they arise from different physical mechanisms:

• Permittivity: Represents the ability of a material to store electrical energy when an electric field is applied. It's related to the polarization of the material, which can be due to electronic, ionic, or orientational polarization.

• Conductivity: Represents the ability of a material to conduct electric current. It's related to the movement of free charge carriers (electrons or ions) in response to an electric field.

• Material Structure and Composition: Certain materials possess structures or compositions that allow for both high polarization and high free charge carrier concentration.

How it's achieved:

• Doped Semiconductors: Semiconductors with high doping concentrations can exhibit both high permittivity and high conductivity. The doping increases the number of free charge carriers (conductivity), while the semiconductor material itself can have a relatively high intrinsic permittivity. However, this often comes with a trade-off as very high doping can sometimes reduce the permittivity.

• Perovskite Materials: Some perovskite materials exhibit ferroelectric behavior (high permittivity) and, with appropriate doping or defects, can also be made conductive.

• Composites: Combining a high-permittivity material with a conductive material in a composite structure can achieve the desired properties. The challenge is to engineer the composite to ensure good connectivity and maintain the desired permittivity.

• Conductive Polymers: While most polymers are insulators, some polymers can be made conductive through doping or by incorporating conductive fillers. These conductive polymers can also exhibit a relatively high permittivity, especially at lower frequencies.

• Metamaterials: Engineered materials with artificial structures can be designed to exhibit both high permittivity and high conductivity at specific frequencies. However, metamaterials are often lossy and can be challenging to fabricate.

We can tune acrylic polymers by adding metal oxides or conductive materials like Griffin barium Titanate is also another option theoretically one should have to increase interfacial polarization