r. Ahmadi, h.r. madaah hosseini Department of Materials Science and Engineering, Sharif University of Technology, Tehran, Iran

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1 o u r n l o f. Min. Metll. Sect. B-Metll. 48 () B (0) 8-88 M i n i n g n d M e t l l u r g y A new ApproAch for calculation of relaxation time And magnetic AnIsotropy of ferrofluids containing superparmagnetic nanoparticles r. Ahmdi, h.r. mdh hosseini Deprtment of Mterils Science nd Engineering, Shrif University of Technology, Tehrn, Irn (Received 0 Mrch 0; ccepted 5 August 0) Astrct In this work, new pproch is descried for the clcultion of the relxtion time nd mgnetic nisotropy energy of mgnetic nnoprticles. Ferrofluids contining monodispersed mgnetite nnoprticles were synthesized vi hydrotherml method nd then heted using the 0 ka/m externl AC mgnetic fields in three different frequencies: 0, 50 nd 00 khz. By mesuring the temperture vritions during the ppliction of the mgnetic field, the totl mgnetic time constnt including oth Brownin nd Neel relxtion times cn e clculted. By mesuring the mgnetic core size nd hydrodynmic size of prticles, the mgnetic nisotropy cn e clculted too. Synthesized ferrofluids were chrcterized vi TEM, XRD, VSM nd CS techniques nd the results were used for the mentioned clcultions. Keywords: relxtion time; mgnetic nisotropy; Ferrofluids; mgnetite nnoprticles. Introduction Ferrofluids contining the mgnetic nnoprticles hve wide rnge of iomedicl pplictions such s drug delivery [], Mgnetic Resonnce Imging (MRI) contrst gent [, ] nd mgnetic hyperthermi [4, 5]. The physicl properties of these ferrofluids such s viscosity, prticles mgnetic nisotropy nd het cpcity ply n importnt role in ferrofluid temperture rise used in hyperthermi pplictions. This temperture rise is minly due to three types of power loss including # Corresponding uthor: rehmdy@yhoo.com DOI:0.98/MMB00004A

2 8 R. Ahmdi / MM 48 () B (0) 8-88 hysteresis loss, Brownin loss nd Neel loss. In the cse of superprmgnetic nnoprticles in which hysteresis loss is zero, power loss cn e written s [6]: f 0 0H ( f )...() Where, o is the permeility of free spce, o is mgnetic field dependent term, H nd f re the mplitude nd frequency of the AC field nd is the totl relxtion time: N B...() Where, N nd B re the Neel nd Brownin relxtion times, respectively nd cn e presented s [7]: KV N 0 exp( ) kt B...() V Vh B kbt...(4) Where, 0 is time constnt pproximtely equl to 0 9 sec, K is the prticle mgnetic nisotropy, V is the prticle volume, k B is the Boltzmn constnt, T is the solute temperture, is the ferrofluid crrier viscosity nd V h is the prticle hydrodynmic volume. Assuming tht temperture rise, ΔT, increses liner with power loss,, the reltionship etween temperture rise nd power loss due to the pplied externl mgnetic field cn e written s: T C T...(5) T Where, C is constnt of proportionlity. If mgnetic field frequency f chnges while mounts of other prmeters such s physicl properties of ferrofluid, mgnetic field strength H nd initil ferrofluid temperture T remin constnt, the following equtions cn e written y mesurement of T due to frequency vrition: T T f f...(6) f 0 0H ( f ) f 0 0H ( f ) ( f ) [ ( f ) ] [ ( f ) ] ( f...(7) ) 4 f 4 f According to Eqs. 4, the totl relxtion time,, is independent of pplied ferequency, f, so = nd Eq. 7 cn e simplified s: 4 f 4 f...(8) 4 ( f f ) So, the totl relxtion time cn e clculted vi ΔT mesurement in two different mounts of frequencies. Eqution 8 cn e written s: f...(9) f ln 4 ( ) ln ln So, in the cse of the multi frequency AC mgnetic field, i, s equl to the intercept of the plot A ln 4 ( f of versus f ) B ln. Oviously, the slope of this plot

3 R. Ahmdi / MM 48 () B (0) should e unity. According to Eqs. 4,, is function of some mteril properties nd environmentl conditions nd cn e written s: ( T, K, V, V, )...(0) So, if the mounts of T, V, V h nd re known, K cn e clculted too. On the other hnd, y using this pproch in different vlues of initil ferrofluid temperture, T, mounts of V, V h nd cn e clculted too nd compred with experimentl results. Among numerous methods of synthesizing mgnetic nnoprticles such s co precipittion [8, 9], sol gel [0], therml decomposition [, ] nd hydrotherml [ 5], therml methods such s hydrotherml process led to the formtion of monodispersed prticles with nrrow size distriution. Since clcultion of K vi descried pproch requires nrrow size distriution of prticles, mgnetite nnoprticles were synthesized vi hydrotherml process in this work. Experimentl dt were used ccording to the ove mentioned pproch nd two resonle mounts of nd K ws clculted for two different ferrofluids. It seems tht the descried pproch cn e used in similr cses for the clcultion of nd K for vrious mgnetic nnoprticles.. experimentl procedure.. smple preprtion h Mgnetite nnoprticles were synthesized vi hydrotherml process using FeSO 4.7H O s Fe + source, dimethyl sulfoxide (DMSO) s oxidnt to oxidize to Fe +, tetr methyl mmonium hydroxide (TMAH) s reducing gent nd oleic cid s surfctnt. All chemicl regents were of nlyticl grde nd used s received without further purifiction. The detiled hydrotherml process ws illustrted elsewhere []. Briefly, the reltive mounts of FeSO 4.7H O, DMSO, TMAH nd oleic cid were mgneticlly stirred t 40 o C for 60 minutes under rgon tmosphere. Then, the lck product ws wshed three times with cetone, mgneticlly seprted nd finlly dried in oven nd used for X Ry Diffrction (XRD) nd Virtion Smple Mgnetometer (VSM) chrcteriztions. By chnging the system lklinity, two smples of oleic cid cpped nnoprticles were synthesized (smples A nd A). The reltive molr rtio FeSO4.7HO / DMASO / oleic cid / TMAH ws equl to /0.08/ 0.008/0.00 nd /0.08/0.008/0.00 for smples A nd A, respectively. mg of smples A nd A were dispersed in 0 ml of hexne nd prepred for Trnsmission Electron Microscopy (TEM) nd hoton Correltion Spectroscopy (CS) chrcteriztions. 50 mg of smples A nd A were dispersed in0 ml of hexne to prepre ferrofluids with concentrtion of 5 mg (prticle)/ml (ferrofluids F nd F, respectively). 0.5 ml of the synthesized ferrofluid ws put in therml insultion continer with minimum het trnsfer nd AC mgnetic field ws pplied to it. The temperture vrition versus time ws mesured nd recorded in period of 60 seconds (Fig. ). Fe +

4 84 R. Ahmdi / MM 48 () B (0) 8-88 Fig.. Used setup for mesuring temperture increse due to ppliction of externl AC mgnetic field... Apprtus nd chrcteriztions XRD ptterns were tken y Siemens D5000 X ry diffrctometer using grphitemonochromtized high intensity Cu K α rdition (λ=.5406 A). A EOL TEM EM 00F ws used to determine the verge prticle size nd morphology of the powders on n ccelerting voltge of 00 kv. Beckmn prticle size nlyzer ws employed for hydrodynmic dimeter mesurement vi CS technique. Also, Lkeshore 7470 VSM ws used for mgnetic chrcteriztion. One AC mgnetic field genertor ws used for heting the synthesized ferrofluid t 0 ka/m nd three different mounts of frequency: 0, 50 nd 00 khz. The fier optic temperture sensor (FOTS) system ws employed for exct mesurement of temperture vrition (Fig. ).. results nd discussion TEM imges of smples A nd A re presented in Fig., showing sphericl monodispersed prticles. So, prticle volume 4 cn e clculted from, V where r r Fig.. TEM imges nd prticle size distriution of smples A (, ) nd A (c, d).

5 R. Ahmdi / MM 48 () B (0) is the prticle rdius. Mesuring 00 prticles for ech specimen, the men prticle size ws clculted s.64 nd 8.84 nm for the smples A nd A, respectively. XRD ptterns of smples A nd A re shown in Fig., reveling the inverse spinel structure of these smples, elonging to Fe O 4. The chrcteristic peks for these smples (θ = 0.0, 5.5, 4., 5.48, 56.8 nd 6.77 ) re well mtch with the mgnetite chrcteristic peks (CDS crd: 9 069). VSM digrms of smples A nd A re shown in Fig. 4, verifying the superprmgnetic ehvior of synthesized prticles, so hysteresis loss is zero. Sturtion mgnetiztions re equl to 68. nd 65.4 emu/gr for smples A nd A, respectively. Figure 5 shows the size histogrms of smples A nd A otined from CS mesurement. The men hydrodynmic sizes from these histogrms re equl to 5.8 nd 4. nm for the smples A nd A, respectively. The recent mesurement ws repeted four times for ech smple nd the men results were reported s the men hydrodynmic size. The mounts of temperture increse (ΔT) fter 60 seconds ppliction of the AC mgnetic field to 0.5 ml of the ferrofluids A nd A re listed in tle nd Fig. 6. These mounts re clculted from three Fig.. XRD ptterns of smples A nd A. Fig. 4. VSM digrm of smples A (Ms = 68. emu/gr) nd A (Ms=65.4 emu/gr). Fig. 5. Men hydrodynmic size of ferrofluid ) A nd ) A. The results were otined from CS mesurements performed four times for ech smple.

6 86 R. Ahmdi / MM 48 () B (0) 8-88 mesurements t ech frequency. According to dt listed in tle, the totl mgnetic time constnt of ferrofluids A nd A cn e clculted using Eq.. According to the pproch descried in the introduction section, cn e clculted y plotting A ln 4 ( f f ) versus B ln (Fig. 7). As shown in Fig. 7, curve slopes re close to unity so cn e clculted from the intercepts, ccording to Eq. 9. These intercepts re equl to 7.05 nd Fig. 6. Temperture increse of ferrofluids A nd A versus AC mgnetic field frequency t 0 ka/m (n=). Fig. 7. Digrms showing A f versus for smples ) A nd f ln 4 ( ) B ln ) A. Intercepts re clculted s nd for smples A nd A, respectively. Tle. Temperture increse of ferrofluids A nd A t 0 ka/m nd vrious frequencies Smple D TEM D CS Viscosity ΔT 0kHz ΔT 50kHz ΔT 00kHz (nm) (nm) (c) ( o C) ( o C) ( o C) A A viscosity of ferrofluid crrier (hexne) t 0 o C Tle. Clcultion of A f nd for smples A nd A f ln 4 ( ) B ln smple f (khz) f (khz) ΔT ( o C) ΔT ( o C) A B 4 A A

7 R. Ahmdi / MM 48 () B (0) for smples A nd A, respectively. The detiled clcultions re listed in tle nd vlues re determined s.58 nd.06 μsec for ferroflluids A nd A, respectively. Using the dt tulted in tle, the mgnetic nisotropy, K, cn e clculted from Eqs. 4. Using Eq. 4, vlues of, 0000., sec, k 8. 0, 00 K T K B 4 9 nd Vh ( ) m, led to clculted. of 7.7 μsec for smple A. So, ccording Eq. N 7. sec nd 9 using, s 0 0 sec, k. 8 0, nd V ( 6. 0 ) m, is 8500 clculted s for A. Similr pproch m leds to clculted vlue of 8450 for A. m These results re relile ccording to the literture [6, 7] in which reported K vlues in the rnge of 500 to for mgnetite nd ccording to this fct tht K is size dependent fctor tht increses with prticle size decrese. 4. conclusion B o K T K m In this work, ferrofluids contining monodispersed oleic cid cpped mgnetite nnoprticles were synthesized vi hydrotherml method. By using one clorimetric method, ferrofluids relxtion time nd prticles mgnetic nisotropy were clculted. It seems tht this pproch cn employed for similr clcultions for vrious mgnetic nnoprticles. refrences [] M. Arrueo, R. Fernndez checo, M. R. Irr,. Sntmri, Nnotody, (007). [] D. K. Kim, Y. Zhng,. Kehr, T. Klson, B. Bjelke, M. Muhmmed,. Mgen. Mgen. Mter., 55 (00) 56. [] Y. Wu, C. Wng, L. Wu, T. Yng, X. Zhng, Y. Zhng, The Seventh Chin Kore Symposium On Biomterils nd Nno Biotechnology, Nnjing/Suzhou, Chin, Octoer 9, 009, p. 87. [4] G. Bldi, D. Boncchi, C. Innocenti, G. Lorenzi, C. Sngregorio,. Mgen. Mgen. Mter., (007) 0. [5] R. Xu, H. Yu, Y. Zhng, M. M, Z. Chen, C. Wng, G. Teng,. M, X. Sun, N. Gu, IEEE Trns. Mg., 45 (009) 085. [6] R.E. Rosensweig,. Mgn. Mgn. Mter., 5 (00) 70. [7] M.B. Mntecon, K. O Grdy,. Mgn. Mgn. Mter., 96 (006) 4. [8] V. M. Guilherme,. Corio,. Ruim,. Electronlyticl Chem., 60 (007) 7. [9] R. Y. Hong, T. T. n, Y.. Hn, H. Z. Li,. Ding, S. Hn,. Mgn. Mgn. Mter., 0 (007) [0] S. Lurent, Chem. Rev., 08 (008) 064. [] D. Mity, S. N. Kle, R. K. Ghnekr,. M. Xue,. Ding,. Mgn. Mgn. Mter., (009) 09. []. L. Zhng, R. S. Srivstv, R. D. K. Misr, Lngmuir, (007) 64. [] C. Y. Wng,. M. Hong, G. Chen, Y. Zhng, N. Gu, Chinese Chemicl Letters, (00) 79.

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