Magnetic and electric effects in magnetorheological suspensions based on silicone oil and polypyrrole nanotubes decorated with magnetite nanoparticles

Results in Physics 61 (2024) 107768 Available online 18 May 2024 2211-3797/© 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/bync/4.0/). Magnetic and electric effects in magnetorheological suspensions based on silicone oil and polypyrrole nanotubes decorated with magnetite nanoparticles Eugen Mircea Anitas a , b , Andrei Munteanu c , Michal Sedlacik c , d , * , 1 , Ioan Bica e , Lenka Munteanu c , Jaroslav Stejskal c a Horia Hulubei National Institute for R&D in Physics and Nuclear Engineering, Reactorului 30, RO-077125 M˘ agurele, Romania b Joint Institute for Nuclear Research, Joliot Curie 6, 141980 Dubna, Moscow Region, Russia 2 c Centre of Polymer Systems, Tomas Bata University in Zlín, Tr. T. Bati 5678, 76001 Zlín, Czech Republic d Department of Production Engineering, Faculty of Technology, Tomas Bata University in Zlín, Vavreckova 275, 760 01 Zlín, Czech Republic e West University of Timișoara, 4 V. Pˆ arvan Ave., Timișoara 300223, Timiș County, Romania ARTICLE INFO Keywords: Magnetorheological suspensions Polypyrrole nanotubes Magnetite nanoparticles Relative dielectric permittivity Dielectric loss factor Active magnetic composites ABSTRACT In this work, two magnetorheological suspensions composed of polypyrrole nanorods decorated with magnetite nanoparticles and suspended in silicone oil were studied as electrical devices. The electrical devices (EDs) were fabricated in a unique cell using nanotubes with different magnetic and electric properties which can be tailored during synthesis. The electrical effects of the suspensions were studied under static electric and magnetic fields and were superimposed on a medium-frequency electric field. The electrical resistance Rp and the quality factor Qp at the terminals of EDs were extracted and analysed. Additionally, the equivalent electrical capacitances Cp were obtained through a well-established theory and then compared for each ED. Through the electrical and magnetic dipolar approximation model, it was illustrated that the electrical effect induced in a suspension can be three times higher depending on the amount of the magnetite. Thus, by tuning the synthesis parameters, it is possible to obtain EDs with well-defined and unique properties. Introduction Magnetorheological suspensions (MRSs) are colloidal intelligent materials consisting of magnetic microparticles which are dispersed in a non-magnetic carrier [1–4]. Under the influence of an external magnetic field, a magnetic phase is formed containing column-like aggregates which are oriented along the magnetic field lines [5,6]. In turn, this leads to a fast and reversible change of the material’s mechanical and electrical properties, including magnetorheological [7,8], magnetoresistive [9] or magneto-dielectric (MDE) behaviour [10,11]. Numerous applications in various fields take advantage of the mentioned effects. The magnetorheological effect is mainly used in shock absorbers and mechanical vibrations [12–16], or in magnetically controllable clutches [17,18]. The MDE effect is a phenomenon in which the electrical capacitance or the relative dielectric permittivity are changed in the presence of a magnetic field. Well-known materials with good MDE properties are MRSs based on silicone oil (SO) and carbonyl iron (CI) microparticles [9] or MRSs absorbed by cotton fabrics [10], for which the relative dielectric permittivity and the dielectric loss factor can be tuned by an external magnetic field. Several types of magnetic particles are generally used for applications. However, when mixed in a solution such magnetic particles tend to sediment due to the high density mismatch [19]. A good solution would be to use rod or tube-like particles [20]. Their high free volume leads to high entropic repulsions which improves the stability of the solution. For tube-like magnetic particles especially, the literature is extremely limited [21]. For that reason, tube-like particles were selected. However, as mentioned above, good electric properties are also * Corresponding author at: Centre of Polymer Systems, Tomas Bata University in Zlín, Tr. T. Bati 5678, 76001 Zlín, Czech Republic. E-mail addresses: [email protected] (E.M. Anitas), [email protected] (A. Munteanu), [email protected] (M. Sedlacik), [email protected] (I. Bica), [email protected] (L. Munteanu), [email protected] (J. Stejskal). 1 ORCID: 0000-0003-3918-5084. 2 International Intergovernmental Organization. Contents lists available at ScienceDirect Results in Physics journal homepage: www.elsevier.com/locate/rinp https://doi.org/10.1016/j.rinp.2024.107768 Received 23 April 2024; Accepted 15 May 2024 Results in Physics 61 (2024) 107768 2 needed. Thus in this work, magnetic and conductive nanotubes are investigated as MDEs. Another benefit of polypyrrole is its use in medical and environmental applications [22]. Environmentally friendly and low-cost MRSs have already been investigated. As an example, magnetically active membranes, consisting of honey, carbonyl iron, and silver microparticles, can be used for various biomedical applications since they allow a remote and magnetically induced release of the bioactive components [23]. For the case of electrical devices based on MRS with honey, the response occurs only upon the application of an external magnetic field. However, here by using PPMY particles, we expect that the response of the electrical device to occur both for external magnetic and electric fields something that other MDEs are lacking. The aim of this work is twofold. Firstly, to show that it is possible for MRS based on SO and polypyrrole nanotubes decorated with magnetite nanoparticles to induce electro-magnetodielectric and electromagnetoconductive effects, by using a medium-frequency electric field superimposed on static electric and magnetic fields. Secondly, to investigate which type of particles are responsible for these effects. To this aim, polypyrrole/magnetite (PPMY) nanoparticles were synthesised in two forms; PPMY6 and PPMY2.5 in accordance to the procedure described in Ref. [24]. Two MRSs, denoted MRS 1 and MRS 2 were prepared by using the same volume fractions of nanoparticles (PPYM6, and PPYM2.5, in the respective order), and SO. By using a measuring cell with a diameter of 20 mm and a height of 2 mm, two electrical devices (ED 1 and ED 2 ) are manufactured. The electrical resistance R p and the quality factor Q p are measured at the terminals of the devices. Following, equivalent electrical capacitance C p of each device is extracted from the obtained data. Further, C p and R p are used to determine the magneto-dielectric, magneto-electroconductive (MCE), as well as electro-magnetodielectric and electromagnetoconductive effects in the obtained suspensions. It is shown that the electro-magnetodielectric effects, and respectively the electromagnetoconductive effects of MRS 1 are up to about three times higher as compared to MRS 2 . Experiment Materials The following materials were used for fabrication of MRSs; silicone oil (SO, MS 100 type produced by Silicone Commerciale SpA, Italy). The density of SO is ρ SO =0.98 g cm −3 and the kinematic viscosity is ν =100 cSt at 25 ◦C. The relative dielectric permittivity at the frequency f =100 kHz and the same temperature is ε r =2.8. This type of SO can be used in a wide range of temperatures, from −55 ◦C up to 220 ◦C. For the magnetic nanoparticles, a two-step synthesis was performed to obtain two kinds of nanotubes. The codenames of PPMY6 and PPMY2.5 were selected to emphasize the molar ratio of FeCl 3 ⋅6H 2 O over pyrrole which was used to make each type of nanotubes. A detailed description of the synthesis is provided in our previous work Ref. [24]. The morphology of the nanoparticles was studied by scanning electron microscope (SEM) NOVA NanoSEM 450 (FEI, The Netherlands) and shown in Fig. 1. As can be seen, the tube-like shape was confirmed for both types of particles and the higher molar ratio of FeCl 3 ⋅6H 2 O resulted in increased amount of magnetite covering the polypyrrole tubes (Fig. 1a) [24]. Regarding the size of both particles, the tubes appear to be approximately around 1–3 μ m in length and diameter in a nanometer range. In magnetorheological fluids based on iron oxide nanorods, the larger the size of the nanorods resulted in a higher performance of the fluids [25]. The PPMY6 and PPMY2.5 nanoparticles, having remanent electrical polarization, form millimetric-size agglomerates with different morphology and a high degree of polydispersity, as shown in Fig. 2. In order to decrease the polydispersity degree, the agglomerates have been partially redispersed using a friction bowl with pestle, for about 15 min per sample. The obtained particles P 1 and P 2 (Fig. 3a and 3b) have smaller sizes: the average diameter of P 1 is 12.55 μ m and a standard deviation of 4.37 μ m, and the average diameter of P 2 is 13.60 μ m and a standard deviation of 4.14 μ m, obtained by a fit with a lognormal distribution, as shown in Fig. 3c and 3d. By measuring the volumes and masses of P1 and P 2 , the densities ρ 1 =0.32 g cm −3 , and ρ 2 =0.27 g cm −3 respectively were extracted. The suspensions MRS 1 and MRS 2 were prepared by manual mixing of 1.5 cm 3 of SO and 1.5 cm 3 of P 1 , and respectively P 2 microparticles, for about 10 min, in a 25 mL Berzelius glass. The magnetization curves of the PPMY6 and PPMY2.5 nanoparticles have been obtained by a vibrating-sample magnetometer (VSM, Model 7407, USA) with the intensity of the magnetic field ranging from –796 to +796 kA m −1 at room temperature. The results are shown in Fig. 4. As can be seen in Fig. 4a, PPMY6 show superior magnetization MSP, exceeding 61 A m 2 kg −1 , in comparison to their counterpart which Fig. 1. The morphology of PPMY6 (a) and PPMY2.5 (b) evaluated by SEM. Fig. 2. The morphology of PPMY6 microparticles, obtained using a digital microscope. PPMY2.5 have a similar morphology. E.M. Anitas et al. Results in Physics 61 (2024) 107768 3 peaked at 31 A m 2 kg −1 . This indicates that especially PPMY6 particles are promising also for magnetorheological suspensions [24]. It is known that between the saturation magnetization MSP of the particles and the saturation magnetization MMRS of the suspensions, the following relationship holds: μ 0MMRS =ΦP μ 0MSP, [21], where μ 0 is the magnetic constant of the vacuum and ΦP is the volume fraction of the particles. Since the volume fractions of particles P 1 and P 2 in their respective suspensions are 50 %, then by using the above relation together with the magnetization curves of the particles form Fig. 4a, one obtains in Fig. 4b the magnetization curves of MRS 1 and MRS 2 . Note that when compared to the pure particles, it is apparent that in suspension form, the overall magnetization is significantly lower, due to decreased concentration of the magnetic nanoparticles, which are responsible for the magnetic response. Fabrication of electrical devices The materials used for the manufacture of the devices are: •A copper foil with electroconductive adhesive (FCua) in the form of a roll (Fig. 5a), was purchased from Fruugo (UK). The length of the copper foil is 20 m, the width is 20 mm and thickness is 0.05 mm. The adhesive side is covered with a paper layer with a thickness of 0.5 mm. •A surgical tape (ST), Durapore 3 M type, was obtained from Help Net (Fig. 5b, pos. 1) in the form of a roll. The length of the tape is 9.5 m, the width is 50 mm and the thickness is 0.2 mm. The outer side of ST is non-adhesive (Fig. 5b, pos. 1), while the inner side is adhesive (Fig. 5b, pos. 2). •A crystal protection film (F), was purchased from Office Direct (Romania), in A4 format. The thickness of the foil is 0.12 mm. Fig. 3. Microparticles P 1 (a), and P 2 (b) visualized in transmission mode, by using OPTIKA microscope (made in Italy). The corresponding histograms of the equivalent diameters (blue bars) and the fit with a lognormal distribution function (black curve) for P 1 (c) and P 2 (d). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 4. The relative magnetization σ function of the intensity H of the magnetic field, for: a) particles PPMY6 and PPMY2.5; b) suspensions MRS1 and MRS2. E.M. Anitas et al. Results in Physics 61 (2024) 107768 4 •A self-adhesive pad (Ba), purchased from Carboy with a diameter of 40 mm and thickness of 2 mm (Fig. 5c). The pad is made from natural rubber and can support a weight of up to 700 N. The EDs were manufactured according to the following steps: 1. Two pieces with dimensions 45 mm ×40 mm were cut from the ST band and the F coil. The adhesive side of ST was placed on the foil F by pressing. 2. The copper foil was placed on the non-adhesive side of the assembly made during step 1 by pressing until the surface area of ST was covered. As a result, the components of the measuring cell MC (Fig. 6a) were completed. 3. A hole with a diameter of 20 mm was made with a steel drill in the pad from Fig. 5(c). This part was placed with the adhesive side on the copper side of the assembly obtained during step 2 (Fig. 6b). As such, the second component of the measuring cell MC (Fig. 6b) is made. 4. The suspensions were then poured on the copper side, as shown in Fig. 7a. Following, the electrical device ED 1 with MRS 1 , and the device ED 2 with MRS 2 were completed by electrically insulating the copper sides through the ST using heating. Fig. 7b show the final configuration of the obtained ED. Experimental setup The overall configuration of the experimental installation is shown in Fig. 8 (pos 6). The setup was used to study the magnetic suspensions in a medium-frequency electric field superimposed on a static magnetic field and uniform mechanical tension forces. The installation consists of an electromagnet, a direct current source (DCS), RXN-3020D type from HAOXIN (China), an RLC bridge Br, E720 type (Belarus), a gaussmeter Gs, DX-102 type from Dexing Magnets (China), a hall probe h, and a force application unit for the deformation of the device. The displacement unit is made of non-magnetic elements, and it consists of a shaft passing through the magnetic pole of the electromagnet and is mechanically coupled with a disk and a plate. The mass marked with a value of 800 g (Fig. 8) on the plate, is a lead disk. The ED and the probe h of the gaussmeter are fixed between the poles of the electromagnet utilizing a non-magnetic disk. The working frequency f of the Br bridge is 10 kHz. The static magnetic field has magnetic flux density values B with a maximum of 420 mT, adjustable in steps of 30 mT. At the beginning, and during the measurements, the values of B were set within the limits of ±2 %. The intensity E inside the EDs can be tuned in steps of 2 kV dc m −1 up to a maximum value of 20 kV dc m −1 by adjusting the voltage on the bridge. Using the Br bridge, the parallel electrical resistance R p and the quality factor Q p of EDs are measured during the application of the magnetic field or the intensity of a static electric field. During the measurements, the impedance at the terminals of the RLC meter is fixed at 100 kΩ. Experimental results, theoretical model and discussions The effect of magnetic field B ∕= 0,E=0 The EDs are inserted one by one between the magnetic poles of the electromagnet. The resistance R p and the quality factor Q p of EDs are measured for magnetic flux density in the range 0 ≤B (mT) ≤420, periodically increased by steps of 30 mT in the absence of the static electric field. The recorded values are shown in Fig. 9. Let us consider that nanoparticles P 1 and P 2 are monodisperse-like and uniformly distributed in the SO matrix (Fig. 10a). In the presence of a magnetic field, they become magnetic dipoles oriented along the magnetic field lines in the form of parallel and equidistant chains (Fig. 10b). Then, two identical and neighbouring magnetic dipoles form an electrical microcapacitor electrically connected in parallel with an electrical microresistor. Through the values of R p and Q p , the equivalent electrical capacitance C p is calculated using the following well-known formula: Fig. 5. (a) Copper foil (pos. 1). Paper band on the side with electroconductive adhesive. (b) Surgical tape roll (pos. 1). The adhesive side of the tape (pos. 2). (c) Natural rubber pad. Fig. 6. The components of the measuring cell MC. (a) Copper foil. (b) Natural rubber ring on top of the copper foil. E.M. Anitas et al. Results in Physics 61 (2024) 107768 5 Cp=Qp 2 π fRp ,(1) Using the parameters mentioned in the experimental setup the abovementioned formula can be rewritten: Cp(pF) ≃ 16Qp Rp(MΩ),(2) By using the variations R p =R p (B) ED from Fig. 9a, and Q p =Q p (B) ED from Fig. 9b, the variation of the capacitance can be deducted with the magnetic flux density, i.e. C p =C p (B) ED , as shown in Fig. 11a. The results in Figs. 9a and 11a suggest that EDs are real capacitors, whose equivalent electrical scheme consists of a resistor and a capacitor connected in parallel. In addition, R p and Q p decreases, and respectively increases with B, leading to an increase of the electrical conductivity. Using the volume fractions of the magnetizable nanoparticles (representing the percentage of magnetizable particles in the MRS), from Ref. [26] it can be shown that the expressions for C p and R p can be written as: Cp=∊0∊ʹ MRS S h0(1−2.25ΦSB2 μ 0kd ),(3) and Rp=h0 S σ 0(1−2.25ΦSB2 μ 0kd ),(4) respectively. Here, ∊0 is the vacuum dielectric constant, ∊ʹ MRS the relative Fig. 7. (a) Subassembly with MRSs. (b) The end configuration of ED. 1 – copper foil, 2 – natural rubber ring with a diameter of 20 mm and thickness of 2 mm, 3 – ST band with non-adhesive surface, 4 – MRSs. Fig. 8. Experimental setup (overall configuration): 1 – magnetic core, 2 – coil, 3 – non-magnetic spindle, 4 – non-magnetic plate, 5 – non-magnetic disk, 6 – non-magnetic marked mass, N and S – magnetic poles, ED – electrical device, Br – RLC bridge, Gs – gaussmeter, h – hall probe, DCS – continuous current source, Oz – coordinate axis, B – magnetic flux density vector, F – force vector, I – intensity of electric current. Fig. 9. Variation of the electrical resistance R p (a) and of the quality factor Q p (b) with the magnetic flux density B for ED 1 (black colour) and ED 2 (red colour). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) E.M. Anitas et al. Results in Physics 61 (2024) 107768 6 dielectric permittivity of the suspensions, S represents the common surface area between the copper foil and MRS, h0 refers to the thickness of MRS, Φ the volume fraction of nanoparticles inside MRS, μ 0 stands for the vacuum magnetic constant, k the deformability constant of the magnetic dipoles chain, d refers to the equivalent diameter of the magnetic dipoles, and equal to that of particles, and σ 0 is the electrical conductivity of MRS in the absence of the magnetic field. Equations (3) and (4) show that the values of C p and R p are highly dependent on the magnetic flux density, in agreement with the experimental data from Fig. 9a and 11a. However, for the same values of the nanoparticles volume fractions, and for the same values of B, the values of R p (Fig. 9a), and respectively of C p (Fig. 11a) are different. According to the model given by Eqs. (3) and (4), the observed effect is due to the values of average diameters of the particles from MRS, and due to the values of the deformability constants of the magnetic dipole chains. In particular, an increase of either the average diameter or of the deformability constant leads to a less pronounced decrease of C p and R p with B. To quantify the contribution induced by the diameters of magnetic dipoles and by the deformability constant of the chains they form, we introduce the magneto-deformation effect: α B≡2.25ΦSB2 μ 0kd ,(5) which describes the ratio between the deformation magnetic force of the magnetic dipole chains and the resistance force opposed by these chains. Therefore, by using Eqs. (4) and (5), α B can be rewritten as: α B=1−Rp Rp0 ,(6) where Rp0 ≡h0 S σ 0 is the resistance in the absence of the magnetic field. By introducing in Eq. (6) the variation of resistance with magnetic flux density from Fig. 9a, variation of α B with magnetic flux density is obtained, i.e. α B= α B(B), as shown in Fig. 11b. The results show that α B for P 1 particles is significantly higher when compared to P 2 particles. In particular, for B≥300 mT, α B is about two times larger for P 1 microparticles, in agreement with the model of the magnetic dipole approximation and confirmed by the results obtained in [23,26,27]. The quantification of the type of nanoparticles on the behaviour of the capacitance and resistance is addressed by using the MDE and MCE effects, defined by: MDE(%) ≡ (Cp Cp0 −1)×100,(7) and respectively by: MCE(%) ≡ (Rp0 Rp −1)×100.(8) Thus, using the data from the capacitance and resistance from Fig. 9a, and 11a respectively, from the Eqs. (7) and (8), the variation of MDE and MCE are obtained, as shown in Fig. 12a, and respectively 12b. The Fig. 10. Distribution of particles P i (i =1,2) in silicone oil (model) in the absence of a magnetic field (a), and respectively in the presence of a magnetic field (b). Here, B is the magnetic field density vector, m i is the magnetic moment vector of particle P i (i =1, 2), Oz is the coordinate axis, h0 and hB are the distances between the copper plates (Cu) in the presence, and respectively in the absence of the magnetic field. Fig. 11. Variation of the electrical capacitance C p (a) and of the dimensionless quantity α B (b) with the magnetic flux density B for ED 1 (black colour) and ED 2 (red colour). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) E.M. Anitas et al. Results in Physics 61 (2024) 107768 7 results indicate that the type of particles used can significantly influence the MRSs MDE and MCE. In particular, for B>0, the contribution of the P 1 nanoparticles is higher if compared to P 2 nanoparticles, for both MDE and MCE. This is due to the different structure and stoichiometric composition of P 1 and P 2 . The observed effects resulted from the magnetization of the two types of particles (see Fig. 4b), as they are responsible for the occurrence of different magnetic forces, and thus for different magnetodeformations of the magnetic dipole chains in MRSs [24,27]. As a result of the interaction between the magnetic dipole chains, for P 1 particles, the resistance (Fig. 9a) and capacitance (Fig. 11a) induce the maximum at B≃340 mT in MDE (Fig. 12a) and MCE (Fig. 12b). Through their proximity and the agglomeration process, the number of columns with electric microcapacitors and microresistors decreases. This leads to a decrease of resistance R p and capacitance C p , therefore changing the behaviour of MDE and MCE for MRS 1 sample. The effect of electric fieldB=0,E∕= 0 The quantities R p and Q p are measured as a function of the intensity E of a static electric field, and in the absence of magnetic field. Using the electric field, the samples were scanned from 0 to 20 kV m −1 , in intervals of 2 kV m −1 . The results are presented in Fig. 13a, and 13b respectively showing that EDs are equivalent, from an electrical point of view, to a resistor connected in parallel to a capacitor. The electric field between the copper foils of EDs is uniformly distributed. As a result, the P i , (i =1, 2) particles obtain electrical charges q, thus becoming electrical dipoles. Within the volumes of MRSs, the quantity of charge can be expressed by [26]: Q=6ΦSq π d2.(9) Similarly to the magnetic dipoles, the electrical dipoles are oriented along the electric field lines, in the form of columns. This formation behaviour is illustrated in Fig. 14. We assume that these columns have equal lengths and are uniformly distributed in the MRS. In an electric field, the length h0 of the columns becomes hE<h0 (as illustrated in Fig. 14). By using the variations R p =R p (B) and Q p =Q p (B) from Fig. 9 in Eq. (2), the variation of capacitance C p =C p (B) can be calculated as demonstrated in Fig. 15a. From the above assumptions and according to the model developed in Ref. [26], the length hE can be calculated as: hE=h0(1−QE h0kE),(10) where kE is the deformability constant of the electric dipole chains. Thus, by knowing hE, we obtain the equivalent electrical capacitance of EDs in static magnetic field, as: Cp=Cp0 1−QE hEkE ,(11) where: Cp0≡∊0∊ʹ MRSS h0(12) Fig. 12. Variation of the MDE (a) and of the MCE (b) with the magnetic flux density B for ED 1 (black colour) and ED 2 (red colour). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 13. Variation of the electrical resistance R p (a) and of the quality factor Q p (b) with the intensity E of a static electric field for ED 1 (black colour) and ED 2 (red colour). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) E.M. Anitas et al. Results in Physics 61 (2024) 107768 8 is the equivalent electrical capacitance of EDs in the absence of the electric field. Similarly, the electrical resistance can be written as: Rp=Rp0(1−QE hEkE),(13) where: Rp0≡h0 σ MRSS(14) is the equivalent electrical resistance of EDs in the absence of electric field. Equations (13) and (14) show that the values of the capacitance and resistance are greatly influenced by the values E of the intensity of the electric field, in agreement with experimental data from Figs. 9a and 11a. However, for the same volume fractions values of the particles, and for the same values of the intensity of the electric field, the values of C p , and R p are varied. According to the model given by Eqs. (13) and (14) the observed effects arise due to the values of the average diameters of the particles, as well as due to the deformability constants of the electrical dipole chains. In order to quantify the contributions of these two factors, we introduce the electro-deformation effect: α E≡QE hEkE ,(15) which describes the ratio between the electrical force of deformations of electrical dipole chains, and the resistance force opposed by the chains. By combining Eqs. (13) and (15), one obtains α E in the form: α E≡1−Rp Rp0 .(16) Then, by using the variation of resistance from Fig. 11a in Eq. (16), the variation α E= α E(E)can be obtained, as shown in Fig. 15b. The results show that for E>0, α E(E)ED1> α E(E)ED2. This effect arises due to the difference in the electrical polarization of particles P 1 and P 2 , at a fixed value of intensity E>0. For the quantification of the contribution of the particles type to the capacitance and resistance, we introduce the relative contribution of the electric field, in the absence of the magnetic field, to the electrical capacitance (ΛC) and to resistance (ΛR), as: ΛC(%) = (Cp Cp0 −1)×100,(17) and respectively: ΛR(%) = (Rp0 Rp −1)×100.(18) Then, by using the variation of the capacitance (Fig. 11a) and of the resistance (Fig. 9a), the variations ΛC=ΛC(E), and ΛR=ΛR(E)are obtained as shown in Fig. 16a and 16b respectively. The results show that ΛC and ΛR have a quasi-linear increase with E, while ΛCMRS1>ΛCMRS2 and ΛRMRS1>ΛRMRS2 for E>0. These effects can be correlated to the different values of the modulus of the electrical polarization vector, and the electrical conductivities of particles P 1 and P 2 [26] due to the accumulation of electrical charges in the volume of MRS and due to the electro and magneto-deformations of the column dipoles. In turn, this leads to an increase of the electrical conductivity and capacitance. The combined effect of the electric and magnetic fieldsB∕= 0,E∕= 0 The EDs are introduced in a static electric field superimposed over a static magnetic field and an electric field of frequency f=10 kHz with an effective value of u=1Vef . The intensity of the static electric field is Fig. 14. Distribution of particles P i (i =1, 2) in silicone oil (model) in the presence of a static electric field. Here, E is the electric field intensity vector, μ I (i =1, 2) is the electric moment, Oz is the coordinate axis, and hE is the distances between the copper plates (Cu) in the presence, of the electric field. For the configuration without electric field, see Fig. 10a. Fig. 15. Variation of the electrical capacitance C p (a) and the quantity α E (b) with the intensity E of a static electric field for ED 1 (black colour) and ED 2 (red colour). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) E.M. Anitas et al. Results in Physics 61 (2024) 107768 9 steadily increased from 0 to 20kV m−1 in steps of 2 kVm−1. The static magnetic field is also altered within the range of 0 and 0.4 T in steps of 100 mT. R p and Q p are measured during the application of the electric and magnetic fields. The obtained values for ED 1 and ED 2 are presented in Figs. 17 and 18, respectively. The results show that for both devices R p (and Q p ) decrease with increasing values of the electric field in agreement with Eq. (13). When the electric field is fixed, R p and Q p decrease with increasing values of the magnetic field. Thus, R p and Q p are greatly influenced by the static electric and magnetic fields superimposed on a medium-frequency electric field. Using the data from Figs. 17 and 18 in Eq. (2) the capacitances of ED 1 and ED 2 can be obtained, as shown in Fig. 19a, and b. The results show that for fixed values of magnetic field, the capacitance has a quasi-linear increase with the electric field, in agreement with Eq. (11). Similarly, considering the fixed values of electric field, the capacitance increases significantly with increasing magnetic field, in agreement with Eq. (3). However, for fixed values of magnetic field the contribution of P 1 particles to the capacitance is two times larger when compared to P 2 particles. The effect is due to the high magnetic and electric polarization of P 1 particles compared to P 2 particles. The quantification of the contribution of these fields, to the values of the relative dielectric permittivity of MRSs is examined by introducing the electro-magnetodielectric effect βC, defined as: βC(%) = (Cp(E)B Cp(E)B=0 −1)×100,(19) where Cp(E)B is the capacitance when E∕= 0 and B∕= 0, and Cp(E)B=0 is the capacitance when E∕= 0 and B=0 T. By using the variation of the capacitance from Fig. 19, the variation of the electro-magnetodielectric effect can be evaluated, as shown in Fig. 20. The results show that for fixed values of field, the βC increases for higher values of the magnetic field. Increasing both fields, leads to the agglomeration of dipole columns [26], which in turn results to a change of the shape of functions βC=βC(E). The quantification of the contribution of the static electric and magnetic fields superimposed on the medium-frequency electric field, to the electrical conductivities of MRSs is performed by introducing the electro-magnetoconductive quantity βR, defined as: βR(%) = (Rp(E)B=0 Rp(E)B −1)×100,(20) where Rp(E)B=0 is the resistance when E∕= 0 and B=0 mT, and Rp(E)B is the resistance when E∕= 0 and B∕= 0. Thus, by using the variation of resistances form Figs. 17 and 18, it is possible to obtain the variation of the electro-magnetoconductive effects, as depicted in Fig. 21. The dependence of the electrical conductivity on the electric field superimposed on the magnetic is also clearly observed. Due to the interactions between column dipoles, the effect of dipole columns agglomeration is much more pronounced for MRS 1 as compared to MRS 2 , for high values of B. Conclusions In this work, two suspensions with considerable magnetorheological properties are manufactured. Silicone oil was utilised as a liquid carrier Fig. 16. Variation of Λ C (a) and ΛR (b) with the intensity E of a static electric field for MRS 1 (black colour) and MRS 2 (red colour). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Fig. 17. Variation of the electrical resistance R p (a) and of the quality factor Q p (b) with the intensity E of a static electric field for ED 1 , at fixed values of magnetic flux density B. E.M. Anitas et al.