Skip to content
BY-NC-ND 4.0 license Open Access Published online by De Gruyter December 3, 2020

Dielectric behaviour of magnetic hybrid materials

Gareth J. Monkman, Dirk Sindersberger, Nina Prem, Andreas Diermeier and Tamara Szecsey
From the journal Physical Sciences Reviews

Abstract

The objectives of this work include the analysis of electrical and magnetic properties of magneto-elastic hybrid materials with the intention of developing new techniques for sensor and actuator applications. This includes the investigation of dielectric properties at both low and high frequencies. The behaviour of capacitors whose dielectrics comprise magnetic hybrid materials is well known. Such interfacial magnetocapacitance can be varied according to magnetic content, magnetic flux density and the relative permittivity of the polymer matrix together with other dielectric content. The basic function of trapping electrical charges in polymers (electrets) is also established technology. However, the combination of magnetoactive polymers and electrets has led to the first electromagnetic device capable of adhering to almost any material, whether magnetically susceptible or not. During the course of this research, in addition to dielectrics, electrically conductive polymers based on (PDMS) matrices were developed in order to vary the electrical properties of the material in a targeted manner. In order to ensure repeatable results, this demanded new fabrication techniques hitherto unavailable. The 3D printing of silicones is far from being a mature technology and much pioneering work was necessary before extending the usual 3 d.o.f. to include orientation about and diffusion of particles in these three axes, thus leading to the concept of 6D printing. In 6D printing, the application of a magnetic field can be used during the curing process to control the particulate distribution and thus the spatial filler particle density as desired. Most of the devices (sensors and actuators) produced by such methods contain levels of carbonyl iron powder (CIP) embedded magnetic filler of up to 70 wt%. Contrary to this, a hitherto neglected research area, namely magnetoactive polymers (MAPs) having significantly lower magnetic particle concentrations (1 to 3 wt% CIP) were also investigated. With filler concentrations lower than 3 wt%, structures are formed which are completely absent at higher filler levels. CIP concentrations in the range of 1wt% demonstrate the formation of toroidal structures. Further development of coherent rings with a compact order results as filler concentrations increase towards 2 wt%. Above 3 wt% the structure eventually disintegrates to the usual random order found in traditional MAP with higher CIP content. Structured samples containing 1%–3 wt% CIP were investigated with the aid of X-ray tomography where solitary ring structures can be observed and eventually the formation of capillary doubles. Over wavelengths ranging from 1 to 25 µm, spectroscopic analysis of thin film MAP samples containing 2 wt% CIP revealed measurable magnetic-field-dependent changes in IR absorption at a wavenumber 2350 (λ = 4.255 µm). This was found to be due to the diamagnetic susceptibility of atmospheric carbon dioxide (CO2). Consequently, the first potential application for sparse matrix MAPs was found.

1 Introduction

Magnetoactive polymers (MAPs) are elastomeric composites comprising micrometre-sized ferromagnetic or paramagnetic particles distributed within a mechanically compliant, nonmagnetic matrix [1]. Their mechanical [2], [3], [4] and electrical [5], [, 6] properties have been extensively investigated, though research into the behaviour of small quantities or even single filler particles is still in its infancy [7].

The project commenced with investigations into the effects of an applied magnetic field on the dielectric properties of MAPs. It rapidly became clear that although the electrical capacitance of an MAP could be changed by the influence of an external magnetic field, this was clearly attributable to interfacial capacitive effects caused by changes in the inter-particle distance between discrete magnetic content rather than any changes in dielectric permittivity.

Much of the basic theory and measurements concerning interfacial magnetocapacitance have been thoroughly investigated [5], although it is often (incorrectly) called magneto-dielectric effect [8], [9], [10], [11].

Whilst embedded within an elastomer, movement of the magnetic particles is highly restricted. Because magnetic saturation is likely to be achieved long before the elastic limit of the polymer matrix is reached, magnetically influenced changes in capacitance are relatively small. Nevertheless, a decrease in distance between the particles along the magnetic flux lines, with increasing magnetic field strength, can be measured. However, it should be noted that only a change in capacitance takes place, not a change in the dielectric permittivity of the polymer matrix. This is not a true magnetodielectric effect as the relative permittivity is a function of the polymer material alone, which remains uninfluenced by the magnetic field.

Although magnetocapacitance can exist without multiferroic coupling, the term magnetodielectric refers specifically to single-phase materials having ferroelectric and ferromagnetic or antiferromagnetic order. Alternatives comprise composite materials combining conventional ferroelectrics and ferromagnetics segregated on a nanoscale level [12]. Lawes states categorically: “great care should be taken to separate intrinsic magnetodielectric coupling from interfacial magnetocapacitance” [13]. Consequently, the magnetodielectric effect implies electromagnetic coupling at the atomic, or at least molecular, level where the relative permittivity of the dielectric may change subject to an externally applied magnetic field. At the other end of the mesoscopic scale, where micrometre-sized particles are distributed within a polymer dielectric matrix, changes in capacitance are due purely to rearrangements in the magnetic particle structure or a shift of the magnetic domains within a single particle of sufficient size. The relative permittivity of the dielectric matrix remains constant [14]. Consequently, neither two-phase MAPs [15] nor ferromagnetic–ferroelectric heterostructures employing permanently magnetized hard magnetic materials [16] and ferroelectric content such as magnetoactive electrets [17] can be considered to be magnetodielectrics. Using pulsed magnetic fields, a slight magnetoelectret effect [18] may be observed, but in a MAP, due to the electrical conductivity of the particles, the induced electrical charge rapidly diminishes.

The often used term “dielectric constant” is also incorrect in that εr is a function of frequency (i.e. not a constant). In fact, at very high frequencies (i.e. light) εr = n2 where n is the refractive index. For almost all polymeric materials, this value is considerably lower than that measured at lower frequencies. The correct term for εr is relative permittivity and the absolute permittivity ε is the product of free space permittivity and relative permittivity ε0 εr [19]. For clarity, this (correct) nomenclature is used throughout this work.

The 3D printing of magnetoactive, electroactive or pure silicones and the newly developed 6D printing of MAPs [20] offer many possibilities for the production of suitable prototypes with complex geometries. For the 3D and 6D printing of the aforementioned polymer combinations, a special miniature extruder was developed. This allows the combination of the respective components whilst simultaneously performing degassing of the mixture in order to achieve cavity-free compounds [21].

Printing of a 3D silicone structure is augmented by the addition of magnetic content, which must be achieved prior to curing. Control of the additional 3 degrees of freedom (orientation and diffusion gradient of the particles) is realized by means of an externally applied magnetic field. This results in 6D printing. In addition to magnetic content, MAPs may also be made partly or wholly electrically conducting by the addition of carbon black, graphite [21] or aluminium graphite [22].

As most researchers have hitherto concentrated on maximizing magnetic content, MAPs with lower magnetic concentrations have been an area of neglected interest. During the course of this work, sparsely populated polymer matrices were found to have some very interesting, and often surprising, characteristics. Because of the lack of a true magnetoelectric effect, spectral investigations from infrared to ultraviolet reveal little, if any, magnetic-field-induced changes in transmission. One exception was discovered with MAP containing less than 3 wt% CIP content where the interaction with diamagnetic CO2 was found to result in transmission changes at a wavelength of 4.255 µm [23]. These new and interesting results will be presented and discussed later in this chapter.

2 Sample fabrication and preparation

Addition-curing RTV-2 silicone rubbers [24] may be cross-linked at room temperature and can be used immediately after demoulding. The electrical and mechanical properties of silicone compounds and particularly poly(dimethylsiloxane) (PDMS) are well known [25].

Initially two components A (base material) and B (catalyst with platinum complex) of a RTV-2-silicone, typically SF00 or SF13 (Silikonfabrik), must be combined equally, as illustrated in Figure 1. Cross-linking commences at temperatures above 10 °C. Throughout this work curing was achieved at room temperature (22 °C), though it may be accelerated using higher temperatures (up to 200 °C).

Figure 1: Cross-linking of silicone base and silicone catalyst [26]. 1.) End of polymer chain, 2.) cross-linker, 3.) Pt catalyst.

Figure 1:

Cross-linking of silicone base and silicone catalyst [26]. 1.) End of polymer chain, 2.) cross-linker, 3.) Pt catalyst.

In order to produce cavity-free silicone structures, a miniature extruder was developed, as depicted in Figure 2. This provides cavity-free mixtures suitable for 3D and 6D printing [20], [, 22].

Figure 2: Miniature silicone extruder.

Figure 2:

Miniature silicone extruder.

Following cavity-free mixing, the silicone may be combined with the desired particulate. For MAPs, carbonyl iron particles can be used (CIP SQ from BASF). The CIP used are both mechanically and magnetically soft with diameters between 3.9 and 5 µm. CIP SQ has a pure iron (Fe) content of up to 99.8%. This differs considerably from MAP containing nanoparticles or micro-particles in solution where ionic strength must be considered [27]. In traditional MAPs, the CIP are embedded in a PDMS matrix and make up between 10 and 90 wt% of the mass of the entire mixture [2]. In this work, a much lower CIP concentration is employed, and the PDMS matrix is relatively soft (Shore A 00 or A 13 hardness). Finally, the uncured mixture may be poured into a mould or printed onto a substrate as desired and cavities deliberately added by injection.

A large range of samples were prepared with carbonyl iron (CIP) contents ranging from 1 to 12% by weight. In order to eliminate the possibility of inter-particle magnetism being solely responsible for the structure formation, nickel and silver particle fillers were also used. As similar structures emerged, it could be concluded that this was neither a purely magnetic function nor something exclusively related to iron. Nevertheless, with magnetically susceptible particles, the structure can be influenced by an externally applied magnetic field.

2.1 Magnetization measurements

The magnetization behaviour of similar samples from the same production batch was measured using a SQUID magnetometer (Quantum Design MPMS XL) including MPMS RSO Controller and digital R/G Bridge. Measurements were carried out to the working limits of the measuring system; whereby only portions of the samples produced were analysed in order to remain within the limits of magnetic moments.

The resulting range of permeabilities measured are comparable to those found with magnetorheological fluids where values lie typically between 3 and 7 for magnetizable content in the range of 10–30 wt% [28]. Ferrofluids have much lower permeability, around 1.2 [29], and it is known that magnetoactive elastomers containing nanoparticles exhibit only very limited magnetoactive effects [17].

The relative permeabilities measured are not the permeabilities of individual iron particles. The values shown in Figure 3 represent the bulk permeabilities of the material samples. This shows that even at only 1 wt% CIP content, the permeability is not proportionally lower than that with 12 wt%.

Figure 3: Magnetic permeability of SF13 samples containing 1, 7 and 12 wt% CIP.

Figure 3:

Magnetic permeability of SF13 samples containing 1, 7 and 12 wt% CIP.

2.2 Interfacial magnetocapacitance

In an electrorheological or magnetorheological fluid, the particles may freely rotate and translate [30]. This is not the case in an MAP where the elastic matrix limits such movement.

Figure 4 shows the influence of an externally applied magnetic field on the effective electrical capacitance of an MAP. Here Cn represents the increase in capacitance for the MAP subjected to an external magnetic field compared to that without a magnetic field and that measured while the MAP is subjected to an external magnetic field.

Figure 4: Capacitance as a function of applied magnetic flux density.

Figure 4:

Capacitance as a function of applied magnetic flux density.

As may be observed from Figure 4, the electrical capacitance increases with rising magnetic flux density. The slight decrease about the zero point where the two plots cross is where the magnetic field changes from assisting fields (N-S) to opposing fields (N-N or S-S). For the purposes of interfacial magnetocapacitance, the use of PDMS as a matrix has now been largely superseded by boron-organo-silicon oxide polymers [31].

2.3 Internal toroidal structural formation

During vacuum evacuation, bubbles rise to the surface before being released. With very sparse filler particle concentrations, particles tend to gather on the boundary layers of ascending cavities [32]. A similar effect, previously intended for the attachment of lower-density talcum particles, has been documented [33] as has the self-assembly of particles into ring structures in two-phase fluids [34].

The hydrodynamic interaction of the higher-viscosity polymer tends to hinder the ascent of the heavier particles under the influence of gravitational acceleration causing them to lag behind the basic flow field [35]. The addition of the filler following mixing of the silicone components suggests that incipient cross-linking aids in stripping the ring from the bubble. Due to the velocity of cavity ascent, rather than a homogeneous distribution of particles over the spherical surface, a circumferential collection and subsequent ring (Torus) formation are created, as shown in Figure 5a.

Figure 5: X-ray tomography of toroidal formations in SF13 with a) 1 wt% and b) 2 wt% CIP.

Figure 5:

X-ray tomography of toroidal formations in SF13 with a) 1 wt% and b) 2 wt% CIP.

The point at which the filler particle ring surrounding the rising cavity breaks free depends on the rate of ascent. The diameter of the toroid being a function of bubble dimension depends on the surface tension of the polymer, the mixing strategy and the degree of cross-linking at the point of release. In Figure 5a, for 1 wt% CIP samples, average toroidal diameters of 80–90 µm resulted.

Cavity ascent is subject to purely laminar flow as the Reynolds factor {1} is far too low for turbulence to develop, thus maintaining a stable geometry.

(1)Re=VρLμ

Reynolds factor is a function of flow rate v, medium density ρ, the characteristic length L and dynamic viscosity µ. For an 80 µm diameter bubble rising at a velocity of 0.1 m/s through a medium with a dynamic viscosity of µ = 1500 mPa/s at 23° (the polymer prior to curing), then expression {1} yields a maximum Reynolds number much lower than 1, thus guaranteeing laminar flow [36].

Expression {2} gives the volume of the torus formed,

(2)Vr=2π2Rα2

where R is the radius of the torus and α the radius of its tubular cross section. However, cavities do not always rise vertically but can also rise at an angle to the vertical, thus forming regular ring layers [32].

As long as the bubbles are so spaced that they do not make contact with one another, then depending on the flow regime, the rising bubble will collect particles in a volume represented by an oblique cylinder with radius R and height h, the volume for which is given in {3}.

(3)Vc=0hπR2dx=πR2h

Dividing {2} by {3} gives the volume fraction ϕ in expression {4}

(4)ϕ=2πα2R2

Clearly, the particulate material has an influence on the resulting ring dimensions. When for 1 wt% nickel or silver filler particles are used, ring diameters with an average value of about 24 µm are formed. For 1 wt% CIP, the median diameter is about 80 µm. Inserting a mean toroidal radius of R = 40 µm and a cylinder height h = 100 µm, for particles of average radius r = 2.5 µm in expression {4} reveals a volume fraction for a ring of single particles of 2.45%. However, the density of iron is 7.86 kg/m3 and that of silicone around 0.96 kg/m3 [37]. Consequently, the mass fraction is 8.2 times lower or 0.3%. This represents the absolute minimum particle mass faction required before torus production can commence and assumes that all free particles within VC (3) are gathered by the rising cavity. At the other end of the scale, it is logical to assume that there must be a maximum mass concentration for which toroid production is possible.

2.4 Capillary doublet formation

Increasing the CIP concentration towards 2 wt% results in a growth in toroid diameter until contiguation takes place as shown in Figure 5b. At this point the ring diameters were found to be around 130 μm. The enlargement of the outer diameter of the toroid caused by a higher weight percentage of filler material, in this case 2 and 3 wt%, can also be observed for nickel. This can be easily explained by the fact that the bubbles expand slightly as the weight of the collected particles causes them to be shed towards the interface between two connecting cavities.

This leads to axially symmetrical CIP containing volumes, known as capillary doublets [32], [, 38], which are formed at the interface between two rings in contact. This effect can be seen in the X-ray tomograph of Figure 6.

Figure 6: X-ray tomography showing capillary doublets at slightly above 2 wt%.

Figure 6:

X-ray tomography showing capillary doublets at slightly above 2 wt%.

The nucleation and growth of capillary bridges, formed in colloidal crystals during the liquid phase separation process, are described step by step by Cheng and Wang [34]. The formation of capillary doublet structures is schematically illustrated in Figure 7. This is a familiar geometry in electronic engineering [39].

Figure 7: Formation of concave capillary doublets through bubble contiguation.

Figure 7:

Formation of concave capillary doublets through bubble contiguation.

There are many mathematical derivations for the volume of a capillary bridge. Between two spheres they are catenoidal, but the upper and lower surfaces can be concave or convex, as shown in Figure 8. Expression {5} appears frequently as the basis of the relationship between capillary width and volume [40], [, 41]. Applying a somewhat simplified analysis to the model illustrated in Figure 7 reveals some approximate but interesting results.

(5)d=s2(1+2VπRs21)
Figure 8: A single isolated carbonyl iron powder (CIP) capillary doublet after curing.

Figure 8:

A single isolated carbonyl iron powder (CIP) capillary doublet after curing.

Transposing expression {5} for volume V gives {6}:

(6)V=πRs22((2ds+1)21)

Taking approximate measurements from Figures 5 and 8 and inserting values for d ≈ s ≈ 15 µm and R ≈ 35 µm in {6} yields a volume Vb of 9.896 × 10–14 m3.

Assuming the formation of capillary bridges between all neighbouring cavities, the entire volume from which the particles are collected can be roughly modelled as the cylindrical volume given by {3}. Using the values extracted from Figure 8, the resulting cylindrical volume Vc of 5.03 × 10–13 m3 can be calculated. The quotient between Vb and Vc represents the volume fraction in the capillary bridge, in this case ca. 19.67%. However, as previously mentioned, the density of carbonyl iron is 7.86 kg/m3 and that of silicone around 0.96 kg/m3. Consequently, the weight percentage is only 2.4%.

Given the observed onset of capillary doublet formation at 1.5 wt% which reaches a fully developed condition at around 2 and 3 wt% being the limit, the earlier calculated value is not unrealistic.

As higher CIP (>3 wt%) concentrations are reached, these structures then disappear with the usual random distribution of agglomerated particles within the polymer matrix shown in Figure 9 remaining. A similar situation also exists where the percentage of nickel or silver exceeds a threshold of about 3 wt%. The absence of any visible structure is typical for the usual high CIP concentration MAP, in which an arbitrary distribution of filler particles in spatially separated aggregates prevails.

2.5 Spectral analysis

The dielectric properties of MAP at high frequencies are important to the design of modern sensory elements associated with applications such as instrumentation, telecommunications and soft robotics. However, most current research has concentrated on lower frequency ranges [42] with a few investigations at microwave levels [43].

Optical properties concerning MAP surface structures have been investigated [44], [45] as has X-ray scattering [46]. Consequently, spectroscopy at wavelengths shorter than 1 µm has not been considered during this work.

The transmission/absorption behaviour of PDMS alone (without magnetic filler) in the infrared spectrum is well known [47]. MAPs have occasionally been the subject of spectroscopic analysis, usually on a secondary basis in order to verify other findings [48], [, 49]. The more usual MAP compounds containing higher ferromagnetic or paramagnetic content (40–80 wt%) have previously been subjected to IR spectral investigation but without decisive results with regard to the influence of an applied magnetic field [3], [, 50].

In transmission spectroscopy, the effective path length of the infrared radiation passing through the sample is determined by both the thickness and orientation of the sample to the directional plane of the IR beam [51]. Figure 10 shows the FTIR spectrum of PDMS sans CIP which is in agreement with other findings [52]. Spectra of samples containing 7, 12, 17, 23 and 35 wt% CIP reveal no changes in individual wavelengths but merely a shift of the entire spectrum due to opacity variations. Other findings concerning FTIR spectra of polyurethane-based magnetorheological polymers with considerably higher CIP content reveal similar results [3].

Figure 9: X-ray tomography showing a random distribution of CIP in SF00 3 wt%.

Figure 9:

X-ray tomography showing a random distribution of CIP in SF00 3 wt%.

Nevertheless, Figure 11 reveals a small, but easily observable, difference at a wavelength of 4.255 µm (wavenumber 2350 cm−1) when the sample is subjected to a radial magnetic field. The black curve is the initial condition without magnetic field. The red curve denotes the condition following the application of a magnetic field, and blue represents the relaxation of the MAP immediately following removal of the magnetic field. This difference occurs exclusively for samples containing 2 wt% CIP.

Figure 10: FTIR spectrum, PDMS alone.

Figure 10:

FTIR spectrum, PDMS alone.

The experiments were repeated for the same samples but under the influence of a transverse magnetic field, where the effects were slightly lower but appeared at the same wavelength. In this case the effect commences with samples containing more than 1.5 wt% CIP and reaches a maximum at 2 wt% CIP. However, the effects are apparent at 1.5 wt% only under the influence of the transverse magnetic field.

The difference between IR transmission in the 2 wt% CIP samples, with and without magnetic field, is shown more clearly in the expanded graph of Figure 12 for PDMS with 2 wt% carbonyl iron powder (CIP).

Figure 11: FTIR spectrum, MAP with 2 wt% of CIP in radial magnetic field.

Figure 11:

FTIR spectrum, MAP with 2 wt% of CIP in radial magnetic field.

The intensity changes shown in Figure 11 (expanded in Figure 12) are not large compared to changes generally seen throughout the entire IR spectrum. However, they were found to be observable and repeatable for over 40 samples each containing 2 wt% CIP. As illustrated in Figure 12, these intensity differences are observable only at a wavelength of 4.255 µm. Everywhere else in the spectrum there are only changes in average transmission level over the entire spectrum due to general material opacity.

However, samples containing 1 and 3 wt% CIP are largely unaffected by the influence of either a radial or a transverse magnetic field and merely resemble the characteristics of higher CIP concentration MAP. Clearly, the IR absorption in MAP samples having 2 wt% CIP content shows the greatest magnetic field dependency, while those with 1.5 wt% exhibit changes only in a transverse magnetic field. Although the effects of agglomeration and clustering cannot be entirely ruled out, samples containing 1.0, 2.5 and 3 wt% reveal no measurable influence.

The wave number band 2300–2400 cm−1 is indicative of carbon dioxide absorption, and this effect disappears when the same measurements are made in a pure dry nitrogen atmosphere. However, the amount of CO2 in air is merely 0.04% volume. Nevertheless, CO2 is known to be diamagnetic with a molar magnetic susceptibility of −20.88·10−6 cm3/mol [53] which is greater than that of copper −6.4·10−6 cm3/mol [54]. Nitrogen is also diamagnetic but has a magnetic susceptibility of only −12·10−6 cm3/mol [54], and oxygen is paramagnetic with a magnetic susceptibility of 3335·10−6 cm3/mol [53]. Consequently, it is almost certain that the diamagnetic effects of CO2 are responsible for the change in spectral absorption at this wavelength. Further experiments with 2 wt% MAP containing other diamagnetic materials such as copper instead of CIP revealed no such magnetic-field-induced changes in the IR spectra. Consequently, it can be concluded that the effect results from the interaction between diamagnetic CO2 and the 2 wt% CIP magnetoactive elastomer. From Figures 5 and 6, it should also be noted that 2 wt% is the CIP concentration at which capillary doublets start to occur.

3 Conclusions

During the course of this research project, many developments have been made, which were necessary for the fabrication of test samples in order that repeatable investigations could be performed. The need for 3D printing of silicones led to the enhancement to 6D printing in order to achieve the required particle distribution within MAPs. For small batch production, the development and integration of a miniature extruder with automatic decavitation were necessary. This enabled the consistent production of a large number of test samples on which the remainder of this research was based.

Extensive spectral investigations concerning MAP with low CIP concentrations have been carried out. X-ray tomography has revealed how, with relatively low CIP concentrations, the formation of cavities in MAP causes the development of ring structures during gas evacuation. With increasing CIP concentration inter-cavity capillary doublets are formed which result in clearly measurable magnetic-field-dependent changes in IR absorption at a wavelength of 4.255 µm. This is almost certainly due to interactions between diamagnetic atmospheric CO2 and the capillary doublet structures formed exclusively in MAP with CIP mass fraction between 1.5 and 3 wt%. Although the full effects (also on other diamagnetic gases) remain to be investigated, this inevitably has potential implications for future gas sensor devices.

The ring structures resulting from this research also represent microinductivities which can be fabricated in a targeted manner, thus enabling new applications in the high-frequency radio field. Furthermore, these anisotropic but well-organized structures have many magnetic-field-dependent implications for optical, thermal, acoustic and medical applications. Capillary doublet geometries offer many possibilities for microantennae designs at sub-millimetre wavelengths.

Figure 12: Transmission difference following application and removal of magnetic field.

Figure 12:

Transmission difference following application and removal of magnetic field.


Corresponding author: Gareth J. Monkman, Mechatronics Research Unit, OTH-Regensburg, Regensburg, Germany, E-mail:

Funding source: Deutsche Forschungsgemeinschaft

Award Identifier / Grant number: INST 102/11-1 FUGG

Award Identifier / Grant number: MO 2196/2-1

Acknowledgments

The authors would like to express their thanks to the German Research Federation (DFG) for financial support within the SPP1681 (Grant MO 2196/2-1) research programme and for the micro-computertomograph (Grant INST 102/11-1 FUGG). A special word of thanks to Birgit Striegl for the X-Ray analysis, Helmut Körner (Universität Regensburg) for the SQUID measurements and Manfred Röhrl for assistance with the Raman and FTIR spectroscopy.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The authors would like to express their thanks to the German Research Federation (DFG) for financial support within the SPP1681 (Grant MO 2196/2-1) research programme and for the micro-computertomograph (Grant INST 102/11-1 FUGG).

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

References

1. Odenbach, S. Microstructure and rheology of magnetic hybrid materials. Arch Appl Mech 2016;86:269. https://doi.org/10.1007/s00419-015-1092-6.Search in Google Scholar

2. Li, WH, Zhou, Y, Tian, TF. Viscoelastic properties of MR elastomers under harmonic loading. Rheol Acta 2010;49:733–40. https://doi.org/10.1007/s00397-010-0446-9.Search in Google Scholar

3. Xu, Y, Gong, X, Xuan, S, Zhang, W, Fan, Y. A high-performance magnetorheological material: preparation, characterization and magnetic-mechanic coupling properties. Soft Matter 2011;7:5246. https://doi.org/10.1039/c1sm05301a.Search in Google Scholar

4. Stoll, A, Mayer, M, Monkman, G, Shamonin, M. Evaluation of highly compliant magneto-active elastomers with colossal magnetorheological response. J Appl Polym Sci 2014;131. https://doi.org/10.1002/app.39793.Search in Google Scholar

5. Bica, I. The influence of the magnetic field on the elastic properties of anisotropic magnetorheological elastomers. J Ind Eng Chem 2012;18:1666–1669. https://doi.org/10.1016/j.jiec.2012.03.006.Search in Google Scholar

6. Petcharoen, K, Sirivat, A. Magneto-electro-responsive material based on magnetite nanoparticles/polyurethane composites. Mater Sci Eng 2016;C61:312–23. https://doi.org/10.1016/j.msec.2015.12.014.Search in Google Scholar

7. Metsch, P, Schmidt, H, Sindersberger, D, Kalina, K-A, Brummund, J, Auernhammer, G, et al.. Field-induced interactions in magneto-active elastomers: a comparison of experiments and simulations. Smart Mater Struct 2020.10.1088/1361-665X/ab92dcSearch in Google Scholar

8. Semisalova, AS, Nikolai, S, Perov, G, Stepanov, GV, Kramarenko, EY, Khokhlova, AR. Strong magnetodielectric effects in magnetorheological elastomers. Soft Matter 2013;9:11318. https://doi.org/10.1039/c3sm52523f.Search in Google Scholar

9. Belyaeva, IA, Kramarenko, EY, Shamonin, M. Magnetodielectric effect in magnetoactive elastomers: transient response and hysteresis. Polymer 2017;127:119–28. https://doi.org/10.1016/j.polymer.2017.08.056.Search in Google Scholar

10. Kostrov, SA, Shamonin, M, Stepanov, GV, Kramarenko, EY. Magnetodielectric response of soft magnetoactive elastomers: effects of filler concentration and measurement frequency. Int J Mol Sci 2019. MDPI.10.3390/ijms20092230Search in Google Scholar PubMed PubMed Central

11. Bica, I, Anitas, EM. Magnetodielectric effects in hybrid magnetorheological suspensions based on beekeeping products. J Ind Eng Chem 2019;77:385–92. https://doi.org/10.1016/j.jiec.2019.05.002.Search in Google Scholar

12. Catalan, G. Magnetodielectric effect without multiferroic coupling. Appl Phys Lett 2006;88:102902. https://doi.org/10.1063/1.2177543.Search in Google Scholar

13. Lawes, G, Kimura, T, Varma, CM, Subramanian, MA, Rogado, N, Cava, RJ, et al.. Magnetodielectric effects at magnetic ordering transitions. Prog Solid State Chem 2009;37:40–54. https://doi.org/10.1016/j.progsolidstchem.2009.08.001.Search in Google Scholar

14. Guo, F, Du, C-b, Li, R-p. Viscoelastic parameter model of magnetorheological elastomers based on Abel Dashpot. Adv Mech Eng 2014.10.1155/2014/629386Search in Google Scholar

15. Varga, Z, Filipcsei, G, Zrínyi, M. Smart composites with controlled anisotropy. Polymer 2005;46:7779–87. https://doi.org/10.1016/j.polymer.2005.03.102.Search in Google Scholar

16. Böse, H, Hesler, A, Monkman, G. Magnetorheologische Kompositmaterialien mit hartmagnetischen Partikeln, Verfahren zu deren Herstellung sowie deren Verwendung. Deutsche Patent DE 10 2007 028 663 A1. Priority: 21.06.2007. European Patent EP 2 160 741 B1 Granted: 17.08.2011.Search in Google Scholar

17. Monkman, GJ, Sindersberger, D, Diermeier, A, Prem, N. The magnetoactive electret. Smart Mater Struct 2017.10.1088/1361-665X/aa738fSearch in Google Scholar

18. Bhatnagar, CS. The magnetoelectret. Indian J Pure Appl Phys 1964;2:331–2.Search in Google Scholar

19. IEEE Std 211. IEEE standard definitions of terms for radio wave propagation; 1997. Reaffirmed 2003 – INSPEC Accession Number: 6010439.Search in Google Scholar

20. Sindersberger, D, Diermeier, A, Prem, N, Monkman, GJ. Printing of hybrid magneto active polymers with 6 degrees of freedom. Mater Today Commun 2018.10.1016/j.mtcomm.2018.02.032Search in Google Scholar

21. Prem, N, Chavez Vega, J, Böhm, V, Sindersberger, D, Monkman, GJ, Zimmermann, K. Properties of polydimethylsiloxane and magnetoactive polymers with electro conductive particles. Macromol Chem Phys 2018.10.1002/macp.201800222Search in Google Scholar

22. Prem, N, Sindersberger, D, Monkman, GJ. Mini-extruder for 3D magnetoactive polymer printing. Adv Mater Sci Eng 2019a. Hindawi.10.1155/2019/8715718Search in Google Scholar

23. Prem, N, Sindersberger, D, Monkman, GJ. Infrared spectral analysis of low concentration magnetoactive polymers. J Appl Polym Sci 2019b.10.1002/app.48366Search in Google Scholar

24. Wacker gmbh. Processing Rt V-2 silicone rubbers. München: Hg. v. Wacker GmbH. Wacker Chemie; 2009.Search in Google Scholar

25. Kuo, ACM. Poly(dimethylsiloxane) – polymer data handbook. Oxford: Oxford University Press; 1999.Search in Google Scholar

26. Domininghaus, H, Elsner, P, Eyerer, P, Hirth, T. Kunststoffe: Eigenschaften und Anwendungen. Berlin, Heidelberg: Springer; 2012. VDI-Buch.10.1007/978-3-642-16173-5Search in Google Scholar

27. Nguyen, N-V, Wu, J-S, Jen, C-P. Effects of ionic strength in the medium on sample preconcentration utilizing nano-interstices between self-assembled monolayers of gold nanoparticles. BioChip J 2018;12:317–25. https://doi.org/10.1007/s13206-018-2402-1.Search in Google Scholar

28. Simon, TM, Reitich, F, Jolly, MR, Ito, K, Banks, HT. The effective magnetic properties of magnetorheological fluids. Math Comput Model 2001;33:273–84. https://doi.org/10.1016/s0895-7177(00)00244-2.Search in Google Scholar

29. Mayer, D, Polcar, P. A novel approach to measurement of permeability of magnetic fluids. Przeglad Elektrotechniczny 2012. 0033-2097. R. 88 NR 7b.Search in Google Scholar

30. Block, H, Kelly, JP. Electrorheology. J Phys D Appl Phys 2000;21:1661. 11. https://doi.org/10.1088/0022-3727/21/12/001.Search in Google Scholar

31. Monkman, GJ, Striegl, B, Prem, N, Sindersberger, D. Electrical properties of magnetoactive Boron-organo-silicon oxide polymers. Macromol Chem Phys 2020.10.1002/macp.201900342Search in Google Scholar

32. Sindersberger, D, Prem, N, Monkman, GJ. Structure formation in low concentration magnetoactive polymers. AIP Adv 2019;9:035322. https://doi.org/10.1063/1.5079997.Search in Google Scholar

33. Beaussart, A, Parkinson, L, Mierczynska-Vasilev, A, Ralston, J, Beattie, DA. Effect of adsorbed polymers on bubble-particle attachment. Langmuir 2009;25:13290–4. American Chemical Society. https://doi.org/10.1021/la903145h.Search in Google Scholar

34. Cheng, T-L, Wang, YU. Shape-anisotropic particles at curved fluid interfaces and role of Laplace pressure: a computational study. J Colloid Interface Sci 2013;402:267–78. https://doi.org/10.1016/j.jcis.2013.03.047.Search in Google Scholar

35. Mileva, E. Solid particle in the boundary layer of a rising bubble. Colloid Polym Sci 1990;268:375–83. https://doi.org/10.1007/bf01411680.Search in Google Scholar

36. Millett, PC, Wang, YU. Diffuse interface field approach to modeling and simulation of self-assembly of charged colloidal particles of various shapes and sizes. Acta Mater 2009;57:3101–9.10.1016/j.actamat.2009.03.016Search in Google Scholar

37. Roberts, C, Graham, A, Nemer, M, Phinney, L, Garcia, R, Stirrup, E. Physical properties of low-molecular weight polydimethylsiloxane fluids. Sandia Report SAND2017-1242. Sandia National Laboratories; 2017.10.2172/1343365Search in Google Scholar

38. Soulié, F, El Youssoufi, MS, Cherblanc, F, Saix, C. Capillary cohesive local force: modelling and experiment. In: Peigney, M, editor Towards optimal bounds on the recoverable strains in polycrystalline shape memory alloys; 2012.10.1007/978-3-642-24638-8_17Search in Google Scholar

39. Gromit. Electronics for dogs. Sparkford, Somerset: Haynes; 2010.Search in Google Scholar

40. Gladkyy, A, Schwarze, R. Comparison of different capillary bridge models for application in the discrete element method – soft condensed matter. Cornell University; 2014.10.1007/s10035-014-0527-zSearch in Google Scholar

41. Gabrieli, F, Lambert, P, Cola, S, Calvetti, F. Micromechanical modelling of erosion due to evaporation in a partially wet granular slope. Int J Numer Anal Meth Geomech 2011;36:918–43. https://doi.org/10.1002/nag.1038.Search in Google Scholar

42. Balasoiu, M., Bica, I. Composite magnetorheological elastomers as dielectrics for plane capacitors: effects of magnetic field intensity. Results Phys 2016;6:199–202. Elsevier. https://doi.org/10.1016/j.rinp.2016.04.006.Search in Google Scholar

43. Kuznetsova, IE, Kolesov, VV, Zaitsev, BD, Fionov, AS, Shihabudinov, AM, Stepanov, GV, et al.. Electrophysical and acoustic properties of magnetic elastomers structured by an external magnetic field. Bull Russ Acad Sci Phys 2017.10.3103/S1062873817080184Search in Google Scholar

44. Forster, E, M Mayer, R Rabindranath, H Böse, G Schlunck, GJ Monkman, und M Shamonin. Patterning of ultrasoft, agglutinative magnetorheological elastomers. J Appl Polym Sci 2013;128:2508–15. https://doi.org/10.1002/app.38500.Search in Google Scholar

45. Nadasi, H, May, K, Eremin, A, Stannarius, R. Magnetoresponsive dispersions of anisometric pigment particles and gels; 2016. DFG SPP1681 Tagung, Benediktbeuern.Search in Google Scholar

46. Schatte, S, Seliger, J, Prevost, S, Gradzielski, M. Magnetic nanocubes in worm-like micellar gels; 2016. DFG SPP1681 Tagung, Benediktbeuern.Search in Google Scholar

47. Hamciuc, C, Hamciuc, E, Okrasa, L. Silica/polyimide-polydimet hylsiloxane hybrid films. Thermal and electrical properties. Macromol Res 2011;19:250–60. https://doi.org/10.1007/s13233-011-0311-4.Search in Google Scholar

48. Fuchs, A, S Joko, G Faramarz, C Mert Bahadir, Y Liu. Surface polymerization of iron particles for magnetorheological elastomers. J Appl Polym Sci 2010;117:934–42. https://doi.org/10.1002/app.31533.Search in Google Scholar

49. A Garcia-Márquez, D Arnaud, H Benoît, G Daniel, B-C Sylvie, D Bertrand. Iron oxide nanoparticle-containing main-chain liquid crystalline elastomer: towards soft magnetoactive networks. J Mater Chem 2011;21:8994. https://doi.org/10.1039/c1jm11381j.Search in Google Scholar

50. Wei, B, Gong, X, Jiang, W. Influence of polyurethane properties on mechanical performances of magnetorheological elastomers. J Appl Polym Sci 2009.10.1002/app.31474Search in Google Scholar

51. Griffiths, P, De Haseth, JA. Fourier transform infrared spectrometry. Hoboken, NJ: Wiley-Interscience; 2007. 0471194042.10.1002/047010631XSearch in Google Scholar

52. Lambert, J, Biele, C, Marsmann, HC. Strukturaufklärung in der organischen Chemie, vol 2. München: Pearson; 2012. 9783868941463. Auflage.Search in Google Scholar

53. Havens, GG. The magnetic susceptibilities of some common gases. Phys Rev 1933;43:992. https://doi.org/10.1103/physrev.43.992.Search in Google Scholar

54. Martienssen, W. Numerical data and functional relationships in science and technology – diamagnetic susceptibility – new Landolt-Börnstein series II/16. Heidelberg: Springer; 1986.Search in Google Scholar

Published Online: 2020-12-03

© 2020 Gareth J. Monkman et al., published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Scroll Up Arrow