Introduction to Dielectric Materials
Dielectric materials comprise a class of non-metallic electrical insulating materials, including therefore a broad variety of polymeric materials. They are defined as possessing an inherent/permanent or induced electric dipole, whereby the molecular or crystalline structure of the material exhibits a division between positive and negative electrical charges. This special property makes dielectric materials particularly useful in the context of electrical capacitor applications. Here, the dipole-electric field interactions play a crucial role in defining the overall electrical energy and charge storage qualities of such capacitor devices.
Most dielectric materials available today consist typically in either ceramics (e.g. glass, porcelain, titanates, steatite, and mica) or polymers. Their qualities as electrical insulators have found them a broad range of industrial and commercial applications, in addition to capacitors, such as in the electrical insulation of wires and power lines/cables, in switch bases, in light receptacles, and in a variety of other semiconductor devices. Polymers, in particular, are now becoming more and more common as dielectrics in modern technological devices. This is largely a result of their easier processing, flexibility, manufacturing customisability, and better resistance to chemicals and other forms of environmental damage, compared to inorganic alternatives.
Capacitors and their Capacitance
Capacitors are electrical devices typically consisting of two parallel conducting metallic plates, across which a voltage difference is applied. This leads to the accumulation of positive charges on one plate, and of negative ones on the other plate. This in turn generates a uniform and unidirectional electrical field in between the two plates, oriented from the positive to the negative charge direction. Capacitors are typically used for storing electrical energy and electrical charge in this way. Their storage capacity is defined in terms of a property known as the Capacitance C, measured in the units of Farads (F).
The relative permittivity, also known as dielectric constant, ε r of the dielectric medium filling the space in between the two plates can increase such capacitance values. This highlights the importance of such dielectric materials for providing enhanced charge-storing capacity and performance in the design of capacitor devices. The relative permittivity of a material in essence defines its ability to become polarized in response to an applied electric field. Therefore, the greater the relative permittivity of that material, the greater will be its polarization under a given electric field, and the better the dielectric material will thus be in terms of its overall performances for such applications.
The values of ε r for some common dielectrics, including for a selection of polymer materials, are presented in the table below (reproduced from Ref. ). This table also includes values for the dielectric strength of the various materials. This quantity represents the maximum electric field magnitude that the material can support, before undergoing breakdown and failure. Air, with a dielectric constant of just 1.02, is considered the reference dielectric.
Dielectric Constants and Strengths for Some Dielectric Materials
It can be deduced from the above table that inorganic/ceramic materials generally tend to have higher dielectric constants, and therefore be more performant in dielectric applications, than organic polymeric materials. Such inorganic compositions in fact inherently tend to contain ions and polar groups, which contribute positively to their dielectric qualities by providing the required electric dipoles. However, as mentioned in the introduction, polymers provide numerous other advantages, in particular in relation to their easier synthesizability and lower, more manageable processing temperatures.
The phenomenon of polarization is given rise by the natural alignment effect of the electric dipoles present within the dielectric material, along the direction of the externally-applied electrical field in which the material itself is immersed. There are essentially three main modes of polarization within a dielectric material:
- Electronic polarization – slight displacement of electron cloud with respect to their corresponding nuclei. This results in a separation of positive and negative electric charges, and the corresponding molecules thus behave like an electric dipole.
- Ionic polarization – displacement of atomic positions within an ionic crystal lattice, as a result of these atoms having a net charge. Anions and cations thus move in opposite directions.
- Orientational polarization – only applicable to polar molecules containing a permanent electric dipole, in which there is a tendency for such permanent dipoles to align with the applied electric field, thus giving a net polarization in that same direction.
The total polarization of a dielectric material is then given by the sum of the above individual contributions. Some of these contributions may be negligible or absent altogether in certain materials, such as covalent solids obviously not including any ionic polarization.
Finally, it is also worth mentioning how the dielectric constant of a material can be affected by an oscillating electric field with a time-dependant orientation, as opposed to the static fields considered so far in this document. In fact, in many practical situations, capacitors and other electric devices that make use of dielectrics are subjected to such alternating currents (AC). In general, with each reversal of the electric field’s direction, the dipoles will every time try to reorient themselves along the field, taking some finite amount of response time in so doing. This response and re-orientation time depends on the polarization type (electronic, ionic or orientational), and the inverse quantity to such time interval is referred to as the relaxation frequency. If the frequency of the oscillating applied electric field exceeds such relaxation frequency, those particular types of dipoles will be unable to make a constructive contribution to the overall dielectric constant of the material. These frequency-dependent contributions for the afore-mentioned three main types of polarization are represented in the diagram below (reproduced from Ref. ):
Variation of dielectric constant with frequency of an alternating electric field.
Electronic, ionic, and orientation polarization contributions to the dielectric constant are indicated.
In general, to minimize electrical energy losses, it is preferable to use dielectrics in which the various relaxation frequencies are markedly distant from the value of the applied electric field frequency.
Polymers as Dielectric Materials
Polymers are today gaining prominence as dielectric materials, mainly thanks to being lightweight, cheap, and easy to process and manufacture. The figure below (reproduced from Ref. ) illustrates some of the most commonly-employed polymer compositions within the realm of thin-film capacitors:
Structures of some common polymers for thin-film capacitors. 
Polymeric materials can be both polar, e.g. PMMA, PVC and Nylon, and non-polar, e.g. PTFE and many other fluoropolymers. This depends on the overall chain geometry and on whether the dipole moments of their constituent units reinforce or cancel each other. As a result of the presence of such permanent polar moments, the polymer’s dielectric properties can be significantly impacted. For example, in the case of the PTFE polymer composition, the large dipole moments of the -CF 2- units at each alternating carbon backbone cancel each other, since they point in opposite directions. Hence, the net dipole moment of the whole polymer chain is effectively zero, yielding a non-polar structure with a relatively low dielectric constant of 2.1. On the other hand, PVC has parallel dipole moments, producing a net strengthening of the overall moment of the polymer structure and thus a higher dielectric constant of 4.5.
Certain group structures and elements within the polymer chains exhibit a high polarizability, such as aromatic rings, sulphur, iodine and bromine atoms. Their presence is therefore likely to increase the dielectric constant of the corresponding parent material. In the context of aromatic rings, the π bonding electrons around such rings are loosely bound compared to direct sigma bonds, and consequently get polarized straightforwardly. With regards to large atoms such as bromine and iodine, the surrounding electron cloud is similarly also loosely bound to the nucleus, due to its relatively large size and large separation distance of the outermost electrons. An opposite example would be the fluorine atom, which has instead much more tightly-packed electrons due to its small atomic radius, and therefore low polarizability.
Polymer dielectrics with both low and high dielectric constants have a wide range of applications in the electronics industry. A low dielectric constant makes the material suitable essentially for electrical insulation applications. For example, this can be useful for insulating signal-carrying conductors and communication cables from each other, for fast signal propagation, and as interlayer dielectric to reduce the resistance-capacitance (RC) time delays, crosstalk and power dissipation. In addition, such dielectrics are often used in dense multi-layered integrated circuit boards, in which they act to prevent coupling and stray capacitance between adjacent metal lines, which could otherwise affect negatively the device performance. On the other hand, high dielectric constant polymer materials are employed as polarizable media within capacitor devices, as discussed previously, but also for facilitating the propagation or reflection of electromagnetic waves, and in other devices such as piezoelectric transducers, dielectric amplifiers or rectifiers, and memory elements in semiconductor circuits.
Computational Design and Discovery of Polymer Dielectrics
The search for new polymer structures and compositions for dielectric applications has benefitted tremendously from the advent of modern computational and data-driven methods. Computationally-assisted materials design and discovery can in fact save large amounts of time and money compared to a direct experimental screening of all potential candidates, including therefore both the synthesis and testing steps.
When one is aiming to discover new and advanced polymer dielectrics for energy storage capacitor applications, DFT can be particularly useful to predict from first principles, or ab-initio, two crucial properties of all polymer materials, the dielectric constant and the bandgap. Knowledge of these two properties can in fact pave the way for defining initial screening criteria for capacitor dielectrics. Subsequently, the various promising candidate structures can be identified for ensuing experimental synthesis and characterization.
Within the world of DFT, Density Functional Perturbation Theory (DFPT), such as implemented by the DFT code Quantum ESPRESSO, is an effective technique for estimating the dielectric constants of materials, by simulating the response of the sample to an applied electric field. The bandgap, on the other hand, can be computed accurately, as part of the general electronic structure properties of the material, using the hybrid Heyd–Scuseria–Ernzerhof (HSE06) electronic exchange-correlation functional. This functional rectifies the bandgap underestimation typically obtained with standard DFT. Dielectric constants and bandgaps computed using DFPT and the HSE06 functional, respectively, have consistently been found to be in very good agreement with experimentally-measured values.
The dielectric properties of polymers also can be investigated via Classical Molecular Dynamics (MD) techniques. MD is a computational technique by which the atomic trajectories of a system of numerous particles are generated by numerical time integration of Newton's classical equations of motion, within a given statistical ensemble. Classical MD codes such as LAMMPS and GROMACS have in fact proven to be effective in determining both the molecular structures and physical/chemical properties of polymer-based materials. This depends of course on a judicious choice for the interatomic potential, otherwise known as force field, governing the conduct of atomic motion and interactions during MD simulations.
GROMACS, for example, directly includes the feature to calculate the frequency-dependent dielectric constant of materials from the autocorrelation function of the total dipole moment. Similar functionalities also exist in the LAMMPS code, where the user can for example compute the temperature-dependent dielectric constant of a certain polymeric structure following an initial thermalization of the sample. In general, thermal effects can significantly impact the value of the dielectric constant. The thermal motion of the polymer chains, which increases with rising temperature, can in fact hamper the orientation and alignment process of the polar groups along the direction of the applied electric field, especially when such field is rapidly alternating. Hence, starting from ambient temperatures, we expect the dielectric constant of polymers to decrease in value with increasing temperature. Conversely, at very low temperatures we also predict the dielectric constants to be lowered, as a result of atomic chain motion becoming practically frozen and dipole alignment being thus made difficult.
: “Materials Science and Engineering” (10th edition). William D. Callister, David G. Rethwisch. Wiley, 2020
: “Polymeric Dielectric Materials”. Zulkifli Ahmad. IntechOpen publication, 2012 (http://dx.doi.org/10.5772/50638)
: “Polymer Dielectrics for Capacitor Application”, from Kirk-Othmer Encyclopedia of Chemical Technology. Wiley, 2017 (http://ramprasad.mse.gatech.edu/wp-content/uploads/2018/03/172.pdf)
: “Dielectric Properties of Polymers”, from the Polymer Properties Database (https://polymerdatabase.com/polymer%20physics/Permitivity.html)
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