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

Resul s in Physics 61 (2024) 107768 A ailable online 18 May 2024 2211-3797/© 2024 The Au ho (s). Published by Else ie B.V. This is an open access a icle unde he CC BY-NC license (h p://c ea i ecommons.o g/licenses/by- nc/4.0/). Magne ic and elec ic e ec s in magne o heological suspensions based on silicone oil and polypy ole nano ubes deco a ed wi h magne i e nanopa icles Eugen Mi cea Ani as a , b , And ei Mun eanu c , Michal Sedlacik c , d , * , 1 , Ioan Bica e , Lenka Mun eanu c , Ja osla S ejskal c a Ho ia Hulubei Na ional Ins i u e o R&D in Physics and Nuclea Enginee ing, Reac o ului 30, RO-077125 M˘ agu ele, Romania b Join Ins i u e o Nuclea Resea ch, Jolio Cu ie 6, 141980 Dubna, Moscow Region, Russia 2 c Cen e o Polyme Sys ems, Tomas Ba a Uni e si y in Zlín, T . T. Ba i 5678, 76001 Zlín, Czech Republic d Depa men o P oduc ion Enginee ing, Facul y o Technology, Tomas Ba a Uni e si y in Zlín, Va ecko a 275, 760 01 Zlín, Czech Republic e Wes Uni e si y o Timișoa a, 4 V. Pˆ a an A e., Timișoa a 300223, Timiș Coun y, Romania ARTICLE INFO Keywo ds: Magne o heological suspensions Polypy ole nano ubes Magne i e nanopa icles Rela i e dielec ic pe mi i i y Dielec ic loss ac o Ac i e magne ic composi es ABSTRACT In his wo k, wo magne o heological suspensions composed o polypy ole nano ods deco a ed wi h magne i e nanopa icles and suspended in silicone oil we e s udied as elec ical de ices. The elec ical de ices (EDs) we e ab ica ed in a unique cell using nano ubes wi h di e en magne ic and elec ic p ope ies which can be ailo ed du ing syn hesis. The elec ical e ec s o he suspensions we e s udied unde s a ic elec ic and magne ic ields and we e supe imposed on a medium- equency elec ic ield. The elec ical esis ance Rp and he quali y ac o Qp a he e minals o EDs we e ex ac ed and analysed. Addi ionally, he equi alen elec ical capaci ances Cp we e ob ained h ough a well-es ablished heo y and hen compa ed o each ED. Th ough he elec ical and magne ic dipola app oxima ion model, i was illus a ed ha he elec ical e ec induced in a suspension can be h ee imes highe depending on he amoun o he magne i e. Thus, by uning he syn hesis pa ame e s, i is possible o ob ain EDs wi h well-de ined and unique p ope ies. In oduc ion Magne o heological suspensions (MRSs) a e colloidal in elligen ma e ials consis ing o magne ic mic opa icles which a e dispe sed in a non-magne ic ca ie [1–4]. Unde he in luence o an ex e nal magne ic ield, a magne ic phase is o med con aining column-like agg ega es which a e o ien ed along he magne ic ield lines [5,6]. In u n, his leads o a as and e e sible change o he ma e ial’s mechanical and elec ical p ope ies, including magne o heological [7,8], magne o- esis i e [9] o magne o-dielec ic (MDE) beha iou [10,11]. Nume ous applica ions in a ious ields ake ad an age o he men ioned e ec s. The magne o heological e ec is mainly used in shock abso be s and mechanical ib a ions [12–16], o in magne ically con ollable clu ches [17,18]. The MDE e ec is a phenomenon in which he elec ical capaci ance o he ela i e dielec ic pe mi i i y a e changed in he p esence o a magne ic ield. Well-known ma e ials wi h good MDE p ope ies a e MRSs based on silicone oil (SO) and ca bonyl i on (CI) mic opa icles [9] o MRSs abso bed by co on ab ics [10], o which he ela i e dielec ic pe mi i i y and he dielec ic loss ac o can be uned by an ex e nal magne ic ield. Se e al ypes o magne ic pa icles a e gene ally used o applica- ions. Howe e , when mixed in a solu ion such magne ic pa icles end o sedimen due o he high densi y misma ch [19]. A good solu ion would be o use od o ube-like pa icles [20]. Thei high ee olume leads o high en opic epulsions which imp o es he s abili y o he solu ion. Fo ube-like magne ic pa icles especially, he li e a u e is ex emely limi ed [21]. Fo ha eason, ube-like pa icles we e selec ed. Howe e , as men ioned abo e, good elec ic p ope ies a e also * Co esponding au ho a : Cen e o Polyme Sys ems, Tomas Ba a Uni e si y in Zlín, T . T. Ba i 5678, 76001 Zlín, Czech Republic. E-mail add esses: [email p o ec ed] (E.M. Ani as), [email p o ec ed] (A. Mun eanu), [email p o ec ed] (M. Sedlacik), [email p o ec ed] (I. Bica), [email p o ec ed] (L. Mun eanu), [email p o ec ed] (J. S ejskal). 1 ORCID: 0000-0003-3918-5084. 2 In e na ional In e go e nmen al O ganiza ion. Con en s lis s a ailable a ScienceDi ec Resul s in Physics jou nal homepage: www.else ie .com/loca e/ inp h ps://doi.o g/10.1016/j. inp.2024.107768 Recei ed 23 Ap il 2024; Accep ed 15 May 2024 Resul s in Physics 61 (2024) 107768 2 needed. Thus in his wo k, magne ic and conduc i e nano ubes a e in es iga ed as MDEs. Ano he bene i o polypy ole is i s use in medical and en i on- men al applica ions [22]. En i onmen ally iendly and low-cos MRSs ha e al eady been in es iga ed. As an example, magne ically ac i e memb anes, consis ing o honey, ca bonyl i on, and sil e mic opa i- cles, can be used o a ious biomedical applica ions since hey allow a emo e and magne ically induced elease o he bioac i e componen s [23]. Fo he case o elec ical de ices based on MRS wi h honey, he esponse occu s only upon he applica ion o an ex e nal magne ic ield. Howe e , he e by using PPMY pa icles, we expec ha he esponse o he elec ical de ice o occu bo h o ex e nal magne ic and elec ic ields some hing ha o he MDEs a e lacking. The aim o his wo k is wo old. Fi s ly, o show ha i is possible o MRS based on SO and polypy ole nano ubes deco a ed wi h magne i e nanopa icles o induce elec o-magne odielec ic and elec o- magne oconduc i e e ec s, by using a medium- equency elec ic ield supe imposed on s a ic elec ic and magne ic ields. Secondly, o in es iga e which ype o pa icles a e esponsible o hese e ec s. To his aim, polypy ole/magne i e (PPMY) nanopa icles we e syn hesised in wo o ms; PPMY6 and PPMY2.5 in acco dance o he p ocedu e desc ibed in Re . [24]. Two MRSs, deno ed MRS 1 and MRS 2 we e p e- pa ed by using he same olume ac ions o nanopa icles (PPYM6, and PPYM2.5, in he espec i e o de ), and SO. By using a measu ing cell wi h a diame e o 20 mm and a heigh o 2 mm, wo elec ical de ices (ED 1 and ED 2 ) a e manu ac u ed. The elec ical esis ance R p and he quali y ac o Q p a e measu ed a he e minals o he de ices. Following, equi alen elec ical capaci ance C p o each de ice is ex ac ed om he ob ained da a. Fu he , C p and R p a e used o de e mine he magne o-dielec ic, magne o-elec o- conduc i e (MCE), as well as elec o-magne odielec ic and elec o- magne oconduc i e e ec s in he ob ained suspensions. I is shown ha he elec o-magne odielec ic e ec s, and espec i ely he elec o- magne oconduc i e e ec s o MRS 1 a e up o abou h ee imes highe as compa ed o MRS 2 . Expe imen Ma e ials The ollowing ma e ials we e used o ab ica ion o MRSs; silicone oil (SO, MS 100 ype p oduced by Silicone Comme ciale SpA, I aly). The densi y o SO is ρ SO =0.98 g cm −3 and he kinema ic iscosi y is ν =100 cS a 25 ◦C. The ela i e dielec ic pe mi i i y a he equency =100 kHz and he same empe a u e is ε =2.8. This ype o SO can be used in a wide ange o empe a u es, om −55 ◦C up o 220 ◦C. Fo he magne ic nanopa icles, a wo-s ep syn hesis was pe o med o ob ain wo kinds o nano ubes. The codenames o PPMY6 and PPMY2.5 we e selec ed o emphasize he mola a io o FeCl 3 ⋅6H 2 O o e py ole which was used o make each ype o nano ubes. A de ailed desc ip ion o he syn hesis is p o ided in ou p e ious wo k Re . [24]. The mo phology o he nanopa icles was s udied by scanning elec- on mic oscope (SEM) NOVA NanoSEM 450 (FEI, The Ne he lands) and shown in Fig. 1. As can be seen, he ube-like shape was con i med o bo h ypes o pa icles and he highe mola a io o FeCl 3 ⋅6H 2 O esul ed in inc eased amoun o magne i e co e ing he polypy ole ubes (Fig. 1a) [24]. Rega ding he size o bo h pa icles, he ubes appea o be app oxima ely a ound 1–3 μ m in leng h and diame e in a nanome e ange. In magne o heological luids based on i on oxide nano ods, he la ge he size o he nano ods esul ed in a highe pe o mance o he luids [25]. The PPMY6 and PPMY2.5 nanopa icles, ha ing emanen elec ical pola iza ion, o m millime ic-size agglome a es wi h di e en mo phology and a high deg ee o polydispe si y, as shown in Fig. 2. In o de o dec ease he polydispe si y deg ee, he agglome a es ha e been pa ially edispe sed using a ic ion bowl wi h pes le, o abou 15 min pe sample. The ob ained pa icles P 1 and P 2 (Fig. 3a and 3b) ha e smalle sizes: he a e age diame e o P 1 is 12.55 μ m and a s anda d de ia ion o 4.37 μ m, and he a e age diame e o P 2 is 13.60 μ m and a s anda d de ia ion o 4.14 μ m, ob ained by a i wi h a logno mal dis ibu ion, as shown in Fig. 3c and 3d. By measu ing he olumes and masses o P1 and P 2 , he densi ies ρ 1 =0.32 g cm −3 , and ρ 2 =0.27 g cm −3 espec i ely we e ex ac ed. The suspensions MRS 1 and MRS 2 we e p epa ed by manual mixing o 1.5 cm 3 o SO and 1.5 cm 3 o P 1 , and espec i ely P 2 mic o- pa icles, o abou 10 min, in a 25 mL Be zelius glass. The magne iza ion cu es o he PPMY6 and PPMY2.5 nanopa icles ha e been ob ained by a ib a ing-sample magne ome e (VSM, Model 7407, USA) wi h he in ensi y o he magne ic ield anging om –796 o +796 kA m −1 a oom empe a u e. The esul s a e shown in Fig. 4. As can be seen in Fig. 4a, PPMY6 show supe io magne iza ion MSP, exceeding 61 A m 2 kg −1 , in compa ison o hei coun e pa which Fig. 1. The mo phology o PPMY6 (a) and PPMY2.5 (b) e alua ed by SEM. Fig. 2. The mo phology o PPMY6 mic opa icles, ob ained using a digi al mic oscope. PPMY2.5 ha e a simila mo phology. E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 3 peaked a 31 A m 2 kg −1 . This indica es ha especially PPMY6 pa icles a e p omising also o magne o heological suspensions [24]. I is known ha be ween he sa u a ion magne iza ion MSP o he pa icles and he sa u a ion magne iza ion MMRS o he suspensions, he ollowing ela ionship holds: μ 0MMRS =ΦP μ 0MSP, [21], whe e μ 0 is he magne ic cons an o he acuum and ΦP is he olume ac ion o he pa icles. Since he olume ac ions o pa icles P 1 and P 2 in hei espec i e suspensions a e 50 %, hen by using he abo e ela ion oge he wi h he magne iza ion cu es o he pa icles o m Fig. 4a, one ob ains in Fig. 4b he magne iza ion cu es o MRS 1 and MRS 2 . No e ha when compa ed o he pu e pa icles, i is appa en ha in suspension o m, he o e all magne iza ion is signi ican ly lowe , due o dec eased concen a ion o he magne ic nanopa icles, which a e esponsible o he magne ic esponse. Fab ica ion o elec ical de ices The ma e ials used o he manu ac u e o he de ices a e: •A coppe oil wi h elec oconduc i e adhesi e (FCua) in he o m o a oll (Fig. 5a), was pu chased om F uugo (UK). The leng h o he coppe oil is 20 m, he wid h is 20 mm and hickness is 0.05 mm. The adhesi e side is co e ed wi h a pape laye wi h a hickness o 0.5 mm. •A su gical ape (ST), Du apo e 3 M ype, was ob ained om Help Ne (Fig. 5b, pos. 1) in he o m o a oll. The leng h o he ape is 9.5 m, he wid h is 50 mm and he hickness is 0.2 mm. The ou e side o ST is non-adhesi e (Fig. 5b, pos. 1), while he inne side is adhesi e (Fig. 5b, pos. 2). •A c ys al p o ec ion ilm (F), was pu chased om O ice Di ec (Romania), in A4 o ma . The hickness o he oil is 0.12 mm. Fig. 3. Mic opa icles P 1 (a), and P 2 (b) isualized in ansmission mode, by using OPTIKA mic oscope (made in I aly). The co esponding his og ams o he equi alen diame e s (blue ba s) and he i wi h a logno mal dis ibu ion unc ion (black cu e) o P 1 (c) and P 2 (d). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) Fig. 4. The ela i e magne iza ion σ unc ion o he in ensi y H o he magne ic ield, o : a) pa icles PPMY6 and PPMY2.5; b) suspensions MRS1 and MRS2. E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 4 •A sel -adhesi e pad (Ba), pu chased om Ca boy wi h a diame e o 40 mm and hickness o 2 mm (Fig. 5c). The pad is made om na u al ubbe and can suppo a weigh o up o 700 N. The EDs we e manu ac u ed acco ding o he ollowing s eps: 1. Two pieces wi h dimensions 45 mm ×40 mm we e cu om he ST band and he F coil. The adhesi e side o ST was placed on he oil F by p essing. 2. The coppe oil was placed on he non-adhesi e side o he assembly made du ing s ep 1 by p essing un il he su ace a ea o ST was co e ed. As a esul , he componen s o he measu ing cell MC (Fig. 6a) we e comple ed. 3. A hole wi h a diame e o 20 mm was made wi h a s eel d ill in he pad om Fig. 5(c). This pa was placed wi h he adhesi e side on he coppe side o he assembly ob ained du ing s ep 2 (Fig. 6b). As such, he second componen o he measu ing cell MC (Fig. 6b) is made. 4. The suspensions we e hen pou ed on he coppe side, as shown in Fig. 7a. Following, he elec ical de ice ED 1 wi h MRS 1 , and he de ice ED 2 wi h MRS 2 we e comple ed by elec ically insula ing he coppe sides h ough he ST using hea ing. Fig. 7b show he inal con igu a ion o he ob ained ED. Expe imen al se up The o e all con igu a ion o he expe imen al ins alla ion is shown in Fig. 8 (pos 6). The se up was used o s udy he magne ic suspensions in a medium- equency elec ic ield supe imposed on a s a ic magne ic ield and uni o m mechanical ension o ces. The ins alla ion consis s o an elec omagne , a di ec cu en sou ce (DCS), RXN-3020D ype om HAOXIN (China), an RLC b idge B , E720 ype (Bela us), a gaussme e Gs, DX-102 ype om Dexing Magne s (China), a hall p obe h, and a o ce applica ion uni o he de o ma ion o he de ice. The displace- men uni is made o non-magne ic elemen s, and i consis s o a sha passing h ough he magne ic pole o he elec omagne and is mechanically coupled wi h a disk and a pla e. The mass ma ked wi h a alue o 800 g (Fig. 8) on he pla e, is a lead disk. The ED and he p obe h o he gaussme e a e ixed be ween he poles o he elec omagne u ilizing a non-magne ic disk. The wo king equency o he B b idge is 10 kHz. The s a ic magne ic ield has magne ic lux densi y alues B wi h a maximum o 420 mT, adjus able in s eps o 30 mT. A he beginning, and du ing he measu emen s, he alues o B we e se wi hin he limi s o ±2 %. The in ensi y E inside he EDs can be uned in s eps o 2 kV dc m −1 up o a maximum alue o 20 kV dc m −1 by adjus ing he ol age on he b idge. Using he B b idge, he pa allel elec ical esis ance R p and he quali y ac o Q p o EDs a e measu ed du ing he applica ion o he magne ic ield o he in ensi y o a s a ic elec ic ield. Du ing he measu emen s, he impedance a he e minals o he RLC me e is ixed a 100 kΩ. Expe imen al esul s, heo e ical model and discussions The e ec o magne ic ield B ∕= 0,E=0 The EDs a e inse ed one by one be ween he magne ic poles o he elec omagne . The esis ance R p and he quali y ac o Q p o EDs a e measu ed o magne ic lux densi y in he ange 0 ≤B (mT) ≤420, pe iodically inc eased by s eps o 30 mT in he absence o he s a ic elec ic ield. The eco ded alues a e shown in Fig. 9. Le us conside ha nanopa icles P 1 and P 2 a e monodispe se-like and uni o mly dis ibu ed in he SO ma ix (Fig. 10a). In he p esence o a magne ic ield, hey become magne ic dipoles o ien ed along he magne ic ield lines in he o m o pa allel and equidis an chains (Fig. 10b). Then, wo iden ical and neighbou ing magne ic dipoles o m an elec ical mic ocapaci o elec ically connec ed in pa allel wi h an elec ical mic o esis o . Th ough he alues o R p and Q p , he equi alen elec ical capaci- ance C p is calcula ed using he ollowing well-known o mula: Fig. 5. (a) Coppe oil (pos. 1). Pape band on he side wi h elec oconduc i e adhesi e. (b) Su gical ape oll (pos. 1). The adhesi e side o he ape (pos. 2). (c) Na u al ubbe pad. Fig. 6. The componen s o he measu ing cell MC. (a) Coppe oil. (b) Na u al ubbe ing on op o he coppe oil. E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 5 Cp=Qp 2 π Rp ,(1) Using he pa ame e s men ioned in he expe imen al se up he abo e- men ioned o mula can be ew i en: Cp(pF) ≃ 16Qp Rp(MΩ),(2) By using he a ia ions R p =R p (B) ED om Fig. 9a, and Q p =Q p (B) ED om Fig. 9b, he a ia ion o he capaci ance can be deduc ed wi h he magne ic lux densi y, i.e. C p =C p (B) ED , as shown in Fig. 11a. The e- sul s in Figs. 9a and 11a sugges ha EDs a e eal capaci o s, whose equi alen elec ical scheme consis s o a esis o and a capaci o con- nec ed in pa allel. In addi ion, R p and Q p dec eases, and espec i ely inc eases wi h B, leading o an inc ease o he elec ical conduc i i y. Using he olume ac ions o he magne izable nanopa icles ( ep- esen ing he pe cen age o magne izable pa icles in he MRS), om Re . [26] i can be shown ha he exp essions o C p and R p can be w i en 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) espec i ely. He e, ∊0 is he acuum dielec ic cons an , ∊ʹ MRS he ela i e Fig. 7. (a) Subassembly wi h MRSs. (b) The end con igu a ion o ED. 1 – coppe oil, 2 – na u al ubbe ing wi h a diame e o 20 mm and hickness o 2 mm, 3 – ST band wi h non-adhesi e su ace, 4 – MRSs. Fig. 8. Expe imen al se up (o e all con igu a ion): 1 – magne ic co e, 2 – coil, 3 – non-magne ic spindle, 4 – non-magne ic pla e, 5 – non-magne ic disk, 6 – non-magne ic ma ked mass, N and S – magne ic poles, ED – elec ical de ice, B – RLC b idge, Gs – gaussme e , h – hall p obe, DCS – con inuous cu en sou ce, Oz – coo dina e axis, B – magne ic lux densi y ec o , F – o ce ec o , I – in ensi y o elec ic cu en . Fig. 9. Va ia ion o he elec ical esis ance R p (a) and o he quali y ac o Q p (b) wi h he magne ic lux densi y B o ED 1 (black colou ) and ED 2 ( ed colou ). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 6 dielec ic pe mi i i y o he suspensions, S ep esen s he common su ace a ea be ween he coppe oil and MRS, h0 e e s o he hickness o MRS, Φ he olume ac ion o nanopa icles inside MRS, μ 0 s ands o he acuum magne ic cons an , k he de o mabili y cons an o he magne ic dipoles chain, d e e s o he equi alen diame e o he magne ic dipoles, and equal o ha o pa icles, and σ 0 is he elec ical conduc i i y o MRS in he absence o he magne ic ield. Equa ions (3) and (4) show ha he alues o C p and R p a e highly dependen on he magne ic lux densi y, in ag eemen wi h he expe i- men al da a om Fig. 9a and 11a. Howe e , o he same alues o he nanopa icles olume ac ions, and o he same alues o B, he alues o R p (Fig. 9a), and espec i ely o C p (Fig. 11a) a e di e en . Acco ding o he model gi en by Eqs. (3) and (4), he obse ed e ec is due o he alues o a e age diame e s o he pa icles om MRS, and due o he alues o he de o mabili y cons an s o he magne ic dipole chains. In pa icula , an inc ease o ei he he a e age diame e o o he de o mabili y cons an leads o a less p onounced dec ease o C p and R p wi h B. To quan i y he con ibu ion induced by he diame e s o magne ic dipoles and by he de o mabili y cons an o he chains hey o m, we in oduce he magne o-de o ma ion e ec : α B≡2.25ΦSB2 μ 0kd ,(5) which desc ibes he a io be ween he de o ma ion magne ic o ce o he magne ic dipole chains and he esis ance o ce opposed by hese chains. The e o e, by using Eqs. (4) and (5), α B can be ew i en as: α B=1−Rp Rp0 ,(6) whe e Rp0 ≡h0 S σ 0 is he esis ance in he absence o he magne ic ield. By in oducing in Eq. (6) he a ia ion o esis ance wi h magne ic lux densi y om Fig. 9a, a ia ion o α B wi h magne ic lux densi y is ob ained, i.e. α B= α B(B), as shown in Fig. 11b. The esul s show ha α B o P 1 pa icles is signi ican ly highe when compa ed o P 2 pa icles. In pa icula , o B≥300 mT, α B is abou wo imes la ge o P 1 mic o- pa icles, in ag eemen wi h he model o he magne ic dipole app oxi- ma ion and con i med by he esul s ob ained in [23,26,27]. The quan i ica ion o he ype o nanopa icles on he beha iou o he capaci ance and esis ance is add essed by using he MDE and MCE e ec s, de ined by: MDE(%) ≡ (Cp Cp0 −1)×100,(7) and espec i ely by: MCE(%) ≡ (Rp0 Rp −1)×100.(8) Thus, using he da a om he capaci ance and esis ance om Fig. 9a, and 11a espec i ely, om he Eqs. (7) and (8), he a ia ion o MDE and MCE a e ob ained, as shown in Fig. 12a, and espec i ely 12b. The Fig. 10. Dis ibu ion o pa icles P i (i =1,2) in silicone oil (model) in he absence o a magne ic ield (a), and espec i ely in he p esence o a magne ic ield (b). He e, B is he magne ic ield densi y ec o , m i is he magne ic momen ec o o pa icle P i (i =1, 2), Oz is he coo dina e axis, h0 and hB a e he dis ances be ween he coppe pla es (Cu) in he p esence, and espec i ely in he absence o he magne ic ield. Fig. 11. Va ia ion o he elec ical capaci ance C p (a) and o he dimensionless quan i y α B (b) wi h he magne ic lux densi y B o ED 1 (black colou ) and ED 2 ( ed colou ). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 7 esul s indica e ha he ype o pa icles used can signi ican ly in luence he MRSs MDE and MCE. In pa icula , o B>0, he con ibu ion o he P 1 nanopa icles is highe i compa ed o P 2 nanopa icles, o bo h MDE and MCE. This is due o he di e en s uc u e and s oichiome ic composi ion o P 1 and P 2 . The obse ed e ec s esul ed om he magne iza ion o he wo ypes o pa icles (see Fig. 4b), as hey a e esponsible o he occu ence o di e en magne ic o ces, and hus o di e en magne o- de o ma ions o he magne ic dipole chains in MRSs [24,27]. As a esul o he in e ac ion be ween he magne ic dipole chains, o P 1 pa icles, he esis ance (Fig. 9a) and capaci ance (Fig. 11a) induce he maximum a B≃340 mT in MDE (Fig. 12a) and MCE (Fig. 12b). Th ough hei p oximi y and he agglome a ion p ocess, he numbe o columns wi h elec ic mic ocapaci o s and mic o esis o s dec eases. This leads o a dec ease o esis ance R p and capaci ance C p , he e o e changing he beha iou o MDE and MCE o MRS 1 sample. The e ec o elec ic ieldB=0,E∕= 0 The quan i ies R p and Q p a e measu ed as a unc ion o he in ensi y E o a s a ic elec ic ield, and in he absence o magne ic ield. Using he elec ic ield, he samples we e scanned om 0 o 20 kV m −1 , in in e als o 2 kV m −1 . The esul s a e p esen ed in Fig. 13a, and 13b espec i ely showing ha EDs a e equi alen , om an elec ical poin o iew, o a esis o connec ed in pa allel o a capaci o . The elec ic ield be ween he coppe oils o EDs is uni o mly dis ibu ed. As a esul , he P i , (i =1, 2) pa icles ob ain elec ical cha ges q, hus becoming elec ical dipoles. Wi hin he olumes o MRSs, he quan i y o cha ge can be exp essed by [26]: Q=6ΦSq π d2.(9) Simila ly o he magne ic dipoles, he elec ical dipoles a e o ien ed along he elec ic ield lines, in he o m o columns. This o ma ion beha iou is illus a ed in Fig. 14. We assume ha hese columns ha e equal leng hs and a e uni o mly dis ibu ed in he MRS. In an elec ic ield, he leng h h0 o he columns becomes hE<h0 (as illus a ed in Fig. 14). By using he a ia ions R p =R p (B) and Q p =Q p (B) om Fig. 9 in Eq. (2), he a ia ion o capaci ance C p =C p (B) can be calcula ed as demons a ed in Fig. 15a. F om he abo e assump ions and acco ding o he model de eloped in Re . [26], he leng h hE can be calcula ed as: hE=h0(1−QE h0kE),(10) whe e kE is he de o mabili y cons an o he elec ic dipole chains. Thus, by knowing hE, we ob ain he equi alen elec ical capaci ance o EDs in s a ic magne ic ield, as: Cp=Cp0 1−QE hEkE ,(11) whe e: Cp0≡∊0∊ʹ MRSS h0(12) Fig. 12. Va ia ion o he MDE (a) and o he MCE (b) wi h he magne ic lux densi y B o ED 1 (black colou ) and ED 2 ( ed colou ). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) Fig. 13. Va ia ion o he elec ical esis ance R p (a) and o he quali y ac o Q p (b) wi h he in ensi y E o a s a ic elec ic ield o ED 1 (black colou ) and ED 2 ( ed colou ). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 8 is he equi alen elec ical capaci ance o EDs in he absence o he elec ic ield. Simila ly, he elec ical esis ance can be w i en as: Rp=Rp0(1−QE hEkE),(13) whe e: Rp0≡h0 σ MRSS(14) is he equi alen elec ical esis ance o EDs in he absence o elec ic ield. Equa ions (13) and (14) show ha he alues o he capaci ance and esis ance a e g ea ly in luenced by he alues E o he in ensi y o he elec ic ield, in ag eemen wi h expe imen al da a om Figs. 9a and 11a. Howe e , o he same olume ac ions alues o he pa icles, and o he same alues o he in ensi y o he elec ic ield, he alues o C p , and R p a e a ied. Acco ding o he model gi en by Eqs. (13) and (14) he obse ed e ec s a ise due o he alues o he a e age diame e s o he pa icles, as well as due o he de o mabili y cons an s o he elec- ical dipole chains. In o de o quan i y he con ibu ions o hese wo ac o s, we in oduce he elec o-de o ma ion e ec : α E≡QE hEkE ,(15) which desc ibes he a io be ween he elec ical o ce o de o ma ions o elec ical dipole chains, and he esis ance o ce opposed by he chains. By combining Eqs. (13) and (15), one ob ains α E in he o m: α E≡1−Rp Rp0 .(16) Then, by using he a ia ion o esis ance om Fig. 11a in Eq. (16), he a ia ion α E= α E(E)can be ob ained, as shown in Fig. 15b. The esul s show ha o E>0, α E(E)ED1> α E(E)ED2. This e ec a ises due o he di e ence in he elec ical pola iza ion o pa icles P 1 and P 2 , a a ixed alue o in ensi y E>0. Fo he quan i ica ion o he con ibu ion o he pa icles ype o he capaci ance and esis ance, we in oduce he ela i e con ibu ion o he elec ic ield, in he absence o he magne ic ield, o he elec ical capaci ance (ΛC) and o esis ance (ΛR), as: ΛC(%) = (Cp Cp0 −1)×100,(17) and espec i ely: ΛR(%) = (Rp0 Rp −1)×100.(18) Then, by using he a ia ion o he capaci ance (Fig. 11a) and o he esis ance (Fig. 9a), he a ia ions ΛC=ΛC(E), and ΛR=ΛR(E)a e ob ained as shown in Fig. 16a and 16b espec i ely. The esul s show ha ΛC and ΛR ha e a quasi-linea inc ease wi h E, while ΛCMRS1>ΛCMRS2 and ΛRMRS1>ΛRMRS2 o E>0. These e ec s can be co ela ed o he di e en alues o he modulus o he elec ical pola iza ion ec o , and he elec ical conduc i i ies o pa icles P 1 and P 2 [26] due o he accumula ion o elec ical cha ges in he olume o MRS and due o he elec o and magne o-de o ma ions o he column dipoles. In u n, his leads o an inc ease o he elec ical conduc i i y and capaci ance. The combined e ec o he elec ic and magne ic ieldsB∕= 0,E∕= 0 The EDs a e in oduced in a s a ic elec ic ield supe imposed o e a s a ic magne ic ield and an elec ic ield o equency =10 kHz wi h an e ec i e alue o u=1Ve . The in ensi y o he s a ic elec ic ield is Fig. 14. Dis ibu ion o pa icles P i (i =1, 2) in silicone oil (model) in he p esence o a s a ic elec ic ield. He e, E is he elec ic ield in ensi y ec o , μ I (i =1, 2) is he elec ic momen , Oz is he coo dina e axis, and hE is he dis- ances be ween he coppe pla es (Cu) in he p esence, o he elec ic ield. Fo he con igu a ion wi hou elec ic ield, see Fig. 10a. Fig. 15. Va ia ion o he elec ical capaci ance C p (a) and he quan i y α E (b) wi h he in ensi y E o a s a ic elec ic ield o ED 1 (black colou ) and ED 2 ( ed colou ). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) E.M. Ani as e al. Resul s in Physics 61 (2024) 107768 9 s eadily inc eased om 0 o 20kV m−1 in s eps o 2 kVm−1. The s a ic magne ic ield is also al e ed wi hin he ange o 0 and 0.4 T in s eps o 100 mT. R p and Q p a e measu ed du ing he applica ion o he elec ic and magne ic ields. The ob ained alues o ED 1 and ED 2 a e p esen ed in Figs. 17 and 18, espec i ely. The esul s show ha o bo h de ices R p (and Q p ) dec ease wi h inc easing alues o he elec ic ield in ag ee- men wi h Eq. (13). When he elec ic ield is ixed, R p and Q p dec ease wi h inc easing alues o he magne ic ield. Thus, R p and Q p a e g ea ly in luenced by he s a ic elec ic and magne ic ields supe imposed on a medium- equency elec ic ield. Using he da a om Figs. 17 and 18 in Eq. (2) he capaci ances o ED 1 and ED 2 can be ob ained, as shown in Fig. 19a, and b. The esul s show ha o ixed alues o magne ic ield, he capaci- ance has a quasi-linea inc ease wi h he elec ic ield, in ag eemen wi h Eq. (11). Simila ly, conside ing he ixed alues o elec ic ield, he capaci ance inc eases signi ican ly wi h inc easing magne ic ield, in ag eemen wi h Eq. (3). Howe e , o ixed alues o magne ic ield he con ibu ion o P 1 pa icles o he capaci ance is wo imes la ge when compa ed o P 2 pa icles. The e ec is due o he high magne ic and elec ic pola iza ion o P 1 pa icles compa ed o P 2 pa icles. The quan i ica ion o he con ibu ion o hese ields, o he alues o he ela i e dielec ic pe mi i i y o MRSs is examined by in oducing he elec o-magne odielec ic e ec βC, de ined as: βC(%) = (Cp(E)B Cp(E)B=0 −1)×100,(19) whe e Cp(E)B is he capaci ance when E∕= 0 and B∕= 0, and Cp(E)B=0 is he capaci ance when E∕= 0 and B=0 T. By using he a ia ion o he capaci ance om Fig. 19, he a ia ion o he elec o-magne odielec ic e ec can be e alua ed, as shown in Fig. 20. The esul s show ha o ixed alues o ield, he βC inc eases o highe alues o he magne ic ield. Inc easing bo h ields, leads o he agglome a ion o dipole col- umns [26], which in u n esul s o a change o he shape o unc ions βC=βC(E). The quan i ica ion o he con ibu ion o he s a ic elec ic and magne ic ields supe imposed on he medium- equency elec ic ield, o he elec ical conduc i i ies o MRSs is pe o med by in oducing he elec o-magne oconduc i e quan i y βR, de ined as: βR(%) = (Rp(E)B=0 Rp(E)B −1)×100,(20) whe e Rp(E)B=0 is he esis ance when E∕= 0 and B=0 mT, and Rp(E)B is he esis ance when E∕= 0 and B∕= 0. Thus, by using he a ia ion o esis ances o m Figs. 17 and 18, i is possible o ob ain he a ia ion o he elec o-magne oconduc i e e ec s, as depic ed in Fig. 21. The dependence o he elec ical conduc i i y on he elec ic ield supe - imposed on he magne ic is also clea ly obse ed. Due o he in e ac ions be ween column dipoles, he e ec o dipole columns agglome a ion is much mo e p onounced o MRS 1 as compa ed o MRS 2 , o high alues o B. Conclusions In his wo k, wo suspensions wi h conside able magne o heological p ope ies a e manu ac u ed. Silicone oil was u ilised as a liquid ca ie Fig. 16. Va ia ion o Λ C (a) and ΛR (b) wi h he in ensi y E o a s a ic elec ic ield o MRS 1 (black colou ) and MRS 2 ( ed colou ). (Fo in e p e a ion o he e e ences o colou in his igu e legend, he eade is e e ed o he web e sion o his a icle.) Fig. 17. Va ia ion o he elec ical esis ance R p (a) and o he quali y ac o Q p (b) wi h he in ensi y E o a s a ic elec ic ield o ED 1 , a ixed alues o magne ic lux densi y B. E.M. Ani as e al.