59th Annual Report on Research 2014

            A principal goal of our research has been the development of a better theoretical understanding of the ways in which electrical energy can be stored in a polymer dielectric within a capacitor.   The driving force for the work reported here is that it should be possible to optimize the  stored energy by designing the most efficient polymer structure.  To achieve this end requires a compromise between two conflicting criteria.  In some materials, the molecules carry large permanent dipole moments, and thus interact strongly with applied fields, but polarize too easily to be able to store significant elastic energy in the distorted bonds of the molecular chain.  They also suffer from having a large internal friction that leads to heat-generating losses on charging and discharging.  On the other hand, some different materials are stiff enough to resist any large distortion of molecular bonds, and thus have very low dielectric losses, but show too weak a polarization to be able to store significant energy.   Somewhere between these two extremes lies the optimum material that we seek to identify.  

            In our work we have introduced a simple model, and have examined how the various parameters of the model influence the amount  of energy that can be stored.  It was possible to clarify an important fact about how energy is stored in a polymer chain exposed to an electric field, namely that it resides in the potential energy due to the distortion of the molecular conformation.   We have explored a detailed model in which a crystalline polymer consists of an array of parallel chains held perpendicular to an applied electric field.  Permanent electric dipoles of fixed magnitude are associated with some of the individual monomers.  We then suppose that each chain in this array is free to rotate about its axis without steric hindrance.  As one example, this might be considered as an approximate representation of a copolymer of polyvinylidene fluoride (PVDF) with some larger monomers, such as those with a chlorine substitution, that would keep the chains some distance form each other.  We assumed the chains to be sparsely cross-linked in a way that prevented rotation at the linking site.  Our idealized model is then one in which chain segments of N + 1 monomers, each carrying a dipole moment, are pinned at their ends.  The moments are initially parallel, and at an angle to the direction along which the electric field is to be applied.  The potential energy is due to the N elastic springs, each of spring constant K, that act between adjacent monomers in the system.

            Because our calculation was undertaken for point dipoles, it was necessary to verify that taking into consideration the actual finite size of the molecular dipoles did not significantly alter the results.  A simulation was accordingly performed, the results of which showed that the average electric field on a monomer was largely unaltered when each monomer of the PVDF was treated as a point dipole instead of a realistically sized molecule.   We also investigated the instability that occurs whenever the molecular polarizability is sufficiently large to cause spontaneous polarization in the absence of a field.  In this situation, the polarization changes discontinuously from positive to negative as the field is reduced from positive values through zero to negative values.  The stored energy is correspondingly reduced.  The final results of our analysis showed that, for the particular numerical values chosen in our model, chain segments for which N was equal to or greater than eight exhibited a negative apparent susceptibility at low fields.  This unphysical behavior cannot occur, and so the polarization must change discontinuously, from the positive value found as the applied field approaches zero from above, to the negative of this quantity as the field is further lowered through zero.

            The property of most interest, namely the energy density, was evaluated for various N as a function of the maximum field E_b that can be applied without breakdown of the sample.   For N = 2, the energy increased only slowly with E_b.  As the number of monomers N per pinning site was increased, it was observed that the curvature with which the energy grows also increased, but the field at which the energy density started to saturate decreased.  The optimum value of N thus decreases with increasing breakdown field.

            Our overall conclusion in this study of the nature of energy storage in polymer dielectrics has been that the stored energy resides largely in the potential energy of distortion of molecular bonds, and that for a model of a polymer dielectric containing permanent electric dipoles, the energy stored in these bond distortions becomes small if the length of segment of chain that is free to rotate is either very large or very small. We have also identified the strong influence of the Clausius-Mossotti instability, which can reduce the stored energy by an order of magnitude, and which is strongly dependent on the length of the unpinned chain segments. Our conclusion is that great attention must be paid to the density of cross links in a polymer dielectric consisting of polar monomers if the stored energy density is to be optimized.