Elsevier

Journal of Non-Crystalline Solids

Volume 406, 15 December 2014, Pages 11-21
Journal of Non-Crystalline Solids

A molecular interpretation of Maxwell–Wagner–Sillars processes

https://doi.org/10.1016/j.jnoncrysol.2014.09.035Get rights and content

Highlights

  • Associated, non-covalently bound dipoles relax upon discharge which causes MWS process.

  • MWS relaxation is activated at non-phonon timescales.

  • Effective dipole moment has an exponential temperature dependence.

  • MWS relaxation varies based on insulator properties.

Abstract

Broadband Dielectric Relaxation Spectroscopy was used to molecularly interpret Maxwell–Wagner–Sillars (MWS) relaxation processes, termed a ζ process, in a heterogeneous laminate configuration with different insulators. The ζ process is due to associated non-covalently bound dipoles that assist in charge migration where the role of the insulator is to allow subsequent discharge away from the material of interest in order for relaxation to occur. The temperature dependent dynamics were characterized in terms of the relaxation time, effective dipole moment and relative molecular associations which were extrapolated from fits of the Havriliak–Negami (HN) equation. The dynamics of the anomalous relaxation process showed a dependence on the properties of the insulator. The ζ process was activated at non phonon timescales. The effective dipole moment of the ζ process phenomenologically had an exponential dependence on temperature and a frictional resistance parameter was introduced. The relative molecular associations through inter and intra cluster interactions depended on characteristics of the insulator and material.

Introduction

Material characterization studies utilizing Broadband Dielectric Relaxation Spectroscopy (DRS) often manifest in electrode polarization which has a pronounced effect on the low frequency and high temperature regimes of the dielectric spectrum. Electrode polarization occurs when charge gets blocked at the surface of the electrode while under the force of the electric field. Charge transport, especially in relation to dipole orientation, presents a scientific challenge that has broad technological implications. From a practical standpoint, electrode polarization is an undesired phenomenon because it diminishes the long term stability of dielectrics through a strong dispersion.

The use of insulating materials to reduce the effects of conductivity may introduce a relaxation process in the composite which is not observed when the insulator is absent. Relaxation processes unique to heterogeneous systems, when compared to the dynamics of the constituents, are often referred to as Maxwell–Wagner–Sillars (MWS) interfacial processes [1], [2], [3]. Since the dielectric is rendered heterogeneous by the presence of the insulator it is challenging to present a molecular mechanism that is related to the material in question. It is called an interfacial process because there is speculation that the polarization occurs at the interface of the constituents. Electrode polarization therefore falls under the category of a MWS interfacial process. The relaxation of this anomalous process is difficult to discern from a dipolar relaxation. MWS processes are typically modeled as an average of the dynamics of the constituents in the composite material with respect to their volumetric ratios. However, models based on the average properties of the constituents are not complete in their description because they do not give insight into the molecular aspects of the process. In the case of using muscovite mica as an insulating material, it was found that these models lack predictive capabilities over a wide frequency range and the proper model had to be attained through trial and error [4].

Heterogeneous systems have been used in industrial and research efforts to circumvent issues in technical applications of a lone material and to take advantage of the properties of all entities in the system. For example, insulating layers are typically used to avoid direct charge injection from an electrode. In display technology where nematic liquid crystals – whose conduction is mostly of ionic origin – are employed, an insulating layer is deposited as protection from direct charge injection. Here it will be said that the role of the insulator is to allow an effective discharge to and from the material without charge build-up in the material. In this manner charge does not accumulate at the interface of the material and electrode.

In research, the elimination of electrode polarization in order to reveal any underlying relaxation processes at low frequency and high temperature is desired especially if a moderately to highly conducting fluid is being studied. Wubbenhorst and van Turnhout [5] developed an analytical method for the removal of electrode polarization by taking advantage of the Kramers–Kronig transform [6] for the complex permittivity, ε*. This method approximates the loss spectrum, ε″, by taking the derivative of the real permittivity spectrum, ε′, since it is lesser affected by electrode polarization. The ion sweeping method [7] has been used to remove ions from a material in order to reduce the conductivity in the dielectric spectrum. Ion exchange membranes [8] are also employed to remove ions from a material and have been known to increase the effective resistance of a sample by limiting charge injection from the electrodes. By shielding the electrode with an insulator [9], [10], [11], [12], [13], [14], [15] the frequency independent conductivity is also reduced.

The focus here shall be on the latter method because of the potential significance in understanding the molecular effect of an insulator on the dynamics of a molecule. In a system with freely rotating dipoles, a relaxation process will ensue where the dynamics has a monotonic temperature dependence. If this same system were placed in the presence of an insulator, an additional relaxation process may occur that also has monotonic temperature dependent dynamics. It is posited that the relaxation of this process is also dipolar in nature. The dipole is produced from associative properties caused by electric forces from unsaturated or secondary valences that arise from local dipoles within the molecule, molecular dipoles or van der Waal's forces. Separating the forces due to unsaturated or secondary valences from those exerted by the electric moment of the molecule is not the focus of this study. It may be conceived that these forces come into play when the molecules form compounds by the sharing of electrons or hydrogen nuclei between their structures. The Grotthuss mechanism [16], [17] can be used to explain the role of charge in the anomalous relaxation process.

Cooperative processes where the motion of correlated protons take place is a closely interrelated microscopic mechanism that can bring about a macroscopic property [18], [19]. The condition under which a proton may traverse a dielectric is that it has to be coupled to a donor group and an acceptor group. A hydrogen bonded system may be symbolized as R1δ   Hδ +⋯⋯R2δ  where R1δ  and R2δ  are respectively the donor and acceptor groups. Each hydrogen bond thus has an electrical moment. In a system where hydrogen bonds are oriented in a singular direction the moments add up to a macroscopic moment; likewise if the hydrogen bonds are oriented in opposing directions the moments cancel. A distinction should be made between compounds able to act as either a donor or acceptor of a single hydrogen bond, forming a multimer of limited size, and compounds able to act as donor and acceptor of multiple hydrogen bonds such that a three dimensional and extensive network is formed.

The dielectric polarization of hydrogen bonded molecules should depend very strongly on their physical structure. At transitions, especially at the glass-rubber transition, in order to obtain large scale mobility of the chains, hydrogen bonds must be broken. The situation becomes complicated when the change in length of the hydrogen bonded chains as a function of temperature is considered, but is ratified once the effect of conformational change is regarded. Due to the variable nature of the hydrogen bond, its role in the electrical properties of matter is very important. In liquids, the variability of the hydrogen bond is obvious as it is constantly broken and reformed. Hydrogen bonds may occur as chains, rings and extensive networks in solids and the energy difference amongst configurations may be so small that they fluctuate spontaneously. However, in cases where the configurations have different polarizations an electric field may influence the molecular structure to a large extent.

The strength of the hydrogen bond depends on the local geometry as well as the type and strength of the interaction between donor and acceptor groups of the proton. The strength of this local interaction is strong enough to determine the structure of many molecules ranging from small molecules such as water to macromolecules such as proteins. When the molecules form an extended network over the entire liquid the dielectric relaxation process is structural in which irregularities to the structure play an important role. Bjerrum [20] realized that if a hydrogen bonded system was capable of discharging a proton at the end of its path then depolarization results. Recall that charge gets blocked at the interface of an electrode thus the relaxation process due to charge migration will not occur in typical DRS experiments. The relaxation of imidazole upon discharge is used to demonstrate the concept in Fig. 1 which was adapted from Kawada [21]. The role of the insulator should therefore not be understated.

Proton migration can be facilitated by glasses [22]. Relegating the role of the insulator to a bath for protonic discharge to allow depolarization is a slight notion that requires careful investigation. Insulators such as muscovite mica have ion exchange capabilities but not all insulators possess this property. If the resultant relaxation process facilitated by the presence of the insulator is due to non-covalent interactions amongst a network of dipolar groups that involve charge transfer (such as a hydrogen bond), then the technique of incorporating insulating materials in a dielectric can be instrumental in decoupling polarization phenomena due to free and bound charge. This manuscript will aim to interpret the MWS relaxation process as being due to an effective discharge that allows the reorientation of associated dipoles that facilitate charge migration.

Section snippets

Materials & methods

Grade V-4 muscovite mica of dimensions 12 mm diameter and 0.15 mm thickness was purchased from Structure Probe Incorporated (West Chester, PA). Glycerol was purchased from Life Technologies, Gibco BRl Division (Grand Island, NY). Phenyl salicylate (salol) was purchased from MP Biomedicals (Solon, OH). Imidazole, polymethylhydrosiloxane (PMHS), triethoxymethylsilane (TEMS), 4′-pentyl-4-biphenyl-carbonitrile (5CB) and poly(3,3′,4,4′-benzophenonetetracarboxylic

Results and discussion

In order to characterize the MWS relaxation process, considerations were first made of the dynamics of the insulator and probe molecules separately so as to establish a basis of comparison. p(ODTES-co-TEMS) (Fig. 2(b)) had the lowest permittivity of the insulators and showed evidence of a strained loss process at high frequencies that was beyond the measurement range of the instrument. The strained process is due to the crystalline structure of p(ODTES-co-TEMS) because it is now a glass that

Conclusion

The dynamics of charge transfer, termed a ζ process –a coupled dipolar process manifested through the relaxation of a network of associated dipoles – was characterized using a heterogeneous laminate configuration in DRS with different insulators. The temperature dependence of this anomalous relaxation process was examined through the relaxation time, effective dipole moment and relative molecular associations. Molecular interpretations of the dielectric relaxation strength and shape parameters

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