Simultaneous Study of Brownian and NÃ©el Relaxation Phenomena in

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Simultaneous Study of Brownian and Néel Relaxation Phenomena in Ferrofluids by Mö ssbauer Spectroscopy J. Landers,*,† S. Salamon,† H. Remmer,‡ F. Ludwig,‡ and H. Wende† †

Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany ‡ Institute of Electrical Measurement and Fundamental Electrical Engineering, TU Braunschweig, Hans-Sommer-Str. 66, 38106 Braunschweig, Germany ABSTRACT: We demonstrate the ability of Mössbauer spectroscopy to simultaneously investigate Brownian motion and Néel relaxation in ferrofluidic samples. For this purpose, Mössbauer spectra of coated iron oxide nanoparticles with core diameters of 6.0−26.4 nm dissolved in 70 vol % glycerol solution were recorded in the temperature range of 234−287 K and compared to low-temperature spectra without Brownian motion. By comparison to theory, we were able to determine the particle coating thickness and the dynamic viscosity of the fluid from the broadening of the absorption lines (Brownian motion), as well as the state of Néel relaxation. Results from Mössbauer spectroscopy were crosschecked by AC-susceptometry at several temperatures for Brownian motion and in the high-frequency regime (100 Hz−1 MHz) for Néel relaxation. KEYWORDS: Ferrofluids, magnetic nanoparticles, Brownian motion, superparamagnetism, Mössbauer spectroscopy, AC-susceptometry relaxation, an applied magnetic field results in a variation of the energy landscape, decreasing the relaxation frequency.

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errofluids composed of magnetic nanoparticles in a liquid solution became increasingly important for technical and medical applications in the past decade. They are used as contrast agents for MRI, as cooling materials in loudspeaker voice coils, as actuators and damper systems, respectively, and versatile magnetic seals for vacuum systems.1−5 Some of these applications utilize magnetic fields to fix the position of the ferrofluidic component or to tune the viscous properties of the ferrofluid, e.g., damping by chain formation in magnetorheological fluids. Therefore, to optimize such a system for applications, it is essential to know whether the superparamagnetic behavior of the nanoparticles is caused by intrinsic Néel relaxation processes leading to a collective fluctuation of the particles’ spins (superspin) between their easy magnetic anisotropy axes or by Brownian motion canceling the net magnetic moment of the nanoparticles by spatial rotation in the fluid. Depending on the process that is involved, the superparamagnetic properties of the ferrofluid will react differently to changes of the temperature or the magnetic field. While both Néel and Brownian relaxation phenomena are influenced by changes in temperature via the thermal energy, the Néel relaxation frequency is also determined by the anisotropy energy, as approximated by eq 1, which is an intrinsic property of the particle. In contrast to this, the Brownian rotation frequency reacts not only to changes of the thermal energy but mainly to temperature-dependent changes of the fluid’s dynamic viscosity, η, as described by eq 2. On the other hand, the magnetic field dependence for Brownian motion is dictated by the torque acting on the particle, proportional to its magnetic moment, whereas for Néel © XXXX American Chemical Society

fNeeĺ =

⎛ K V⎞ 1 exp⎜ − eff ⎟ 2πτ0 ⎝ kBT ⎠

fBrown =

(1)

kBT 8π 2ηRH 3

(2)

Here, f Brown and f Néel are the Brownian rotation frequency and the Néel relaxation frequency, respectively; η is the fluid’s dynamic viscosity, RH the average hydrodynamic radius of the particles, τ0 a relaxation prefactor of 10−9−10−13 s,6 Keff the particles effective magnetic anisotropy, and V the average magnetic volume of the nanoparticles. Néel relaxation is the dominating process in particles below ca. 20 nm when taking typical values for the anisotropy constant of magnetite, room temperature, and deionized water as a medium. Larger particles are magnetically blocked in terms of Néel relaxation and display “superparamagnetic” behavior only because of their rotation in the fluid medium. Effects of magnetic relaxation in ferrofluids or, more generally, in soft matter can be studied by several existing methods, such as magnetorelaxometry (MRX),7−10 ACsusceptometry (ACS),11,12 etc., but most of them lack the ability to investigate both relaxation processes simultaneously. Received: October 30, 2015 Revised: December 4, 2015

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DOI: 10.1021/acs.nanolett.5b04409 Nano Lett. XXXX, XXX, XXX−XXX

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Nano Letters ACS, for example, is a well-proven and often utilized method, which displays superparamagnetic properties by a frequencydependent magnetic susceptibility signal following the Debye relation.13 Both particle rotation by Brownian motion and Néel relaxation of the particle’s superspin result in a canceled net magnetic moment of the ferrofluid. Due to this, only the total (added up) relaxation frequency of the net magnetic moment can be accessed by magnetic measurement methods. Often, f Brown and f Néel differ by several magnitudes; therefore, only the dominating (faster) relaxation process can be observed and evaluated, whose relaxation frequency is in this case nearly identical to the total relaxation frequency.14,15 An independent determination of hydrodynamic particle size and particle magnetic moment from AC-susceptometry measurements on suspensions can be carried out via the magnetic field dependence of the Brownian time constant by recording ACS spectra for different background field values.10 In contrast, Mössbauer spectroscopy is able to examine both relaxation phenomena because they have different effects on the observable spectrum, as explained in more detail below. Mössbauer spectroscopy was successfully used before to obtain the dynamic viscosity of fluids16,17 and is one of the most prominent techniques for studying Néel relaxation in magnetic nanoparticles,18,19 but to the best of our knowledge, to date there is no literature report dealing with the simultaneous study of both phenomena. Experimental Section. Three types of iron oxide nanoparticles (IONPs) with average particle sizes of 6.0 nm (sample S), 14.8 nm (sample M), and 26.4 nm (sample L), coated with a monolayer of amphiphilic polymer and oleic acid (nominal coating thickness ca. 4 nm) and dissolved in 70 vol % glycerol solution (concentration 10 mg iron per ml), were purchased from Ocean NanoTech (SHP-05, SHP-15, and SHP-25). Size and shape of the nanoparticles were studied by transmission electron microscopy (TEM; Philips Tecnai F20). As shown in Figure 1, the particles display a spherical shape and sharp size distribution (ΔD/D ≲ 0.1) as summarized in Table 1. The ferrofluids were magnetically precharacterized by DC and AC superconducting quantum interference device magnetometry (Quantum Design MPMS-5S). The zero-field-cooled/ field-cooled magnetization (mZFC / mFC) measured at 10 mT displays Néel relaxation behavior with a mZFC-maximum at about 40 K for the 6 nm particles (sample S); therefore, the onset of Brownian motion at higher temperatures causes no visible effect because the sample already is superparamagnetic (Figure 2). Particles of about 15 and 26 nm (samples M and L, respectively) exhibit a discontinuity at about 200 K, where the acceleration of Brownian motion due to the decrease in dynamic viscosity leads to superparamagnetic behavior of the particle contribution, which remained blocked in terms of Néel relaxation up to this temperature. A small peak in the magnetization of sample L marks the Verwey transition temperature at ∼110 K, verifying the magnetite (Fe3O4) phase.20 The decrease in mFC observable below 200 K can presumably be attributed to effects of interparticle magnetic dipole interaction, which is enhanced compared to the other ferrofluids because of the larger magnetic moment per particle in sample L.21,22 Measurements of the AC-susceptibility (ACS) of sample L were performed at temperatures between 245 and 310 K and frequencies between 0.1 Hz and 1.5 kHz using an AC magnetic field amplitude of μ0H = 0.4 mT. Room-temperature ACS

Figure 1. TEM images of samples S, M, and L and corresponding core diameter (D) distributions. The inset shows a particle of sample L in 5× magnification to illustrate the particle coating.

Table 1. Size Distribution Parameters Obtained from TEM sample

D (nm)

ΔD (nm)

S M L

6.0 14.8 26.4

0.5 1.6 1.8

Figure 2. ZFC-FC-magnetization at 10 mT of samples S, M, and L normalized to mFC(5 K). The 6 nm particles display superparamagnetic behavior by Néel relaxation, while larger particles become completely superparamagnetic at the onset of sufficient Brownian motion at ca. 200 K.

measurements up to 1 MHz were conducted with an excitation field amplitude of 95 μT utilizing a custom-built setup described in detail in ref 12. B


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Figure 3. Mössbauer spectra of samples S, M, and L recorded at 234−262 K. Low-temperature reference spectra of the ferrofluidic samples measured in a bath cryostat without Brownian motion are shown for comparison on top. Subspectra corresponding to iron on tetrahedral (green) and octahedral (blue) sites are shown as examples for sample L at 150 K. Dashed lines are inserted in the spectrum of sample M at 180 K to visualize the asymmetric line shape caused by beginning Néel relaxation, exemplarily (inner shoulders are marked by arrows).

splitting of the sextet. Because this decrease affects smaller particles more strongly, the distribution in particle diameter leads to asymmetric line shapes with distinct inner shoulders. In contrast to this, Brownian motion leads to a Doppler shift in the nuclear γ-ray absorption spectrum of the 57Fe iron nuclei embedded in the magnetic nanoparticles. Because of the distribution in velocity and direction of the diffusive particle movement, instead of an energy shift, we observe a broadening of the absorption lines. This can be described by eq 3 in the simple approximation of translational Brownian motion16,23 where ΔΓ is the line broadening, E0 the γ-ray energy, and ℏ the reduced Planck constant.

Mössbauer spectra were recorded in transmission geometry in zero external field and constant acceleration mode using a 57 Co source (Rh-matrix). To perform the measurements at various temperatures between 234 and 287 K, a custom-built Peltier setup for liquid samples was utilized (a detailed description can be found in ref 23). Results and Discussion. While ZFC-FC magnetization measurements as shown above allow a general characterization of relaxation properties, it is difficult to obtain direct information on the relaxation frequency. Also, to study Néel relaxation, Brownian motion must be suppressed by freezing the liquid, which can possibly damage the particle coating and lead to increased agglomeration after remelting the sample. The alternative, more complex method of freeze-drying can reduce this effect but cannot completely eradicate it. A method which provides information on the characteristics of both relaxation phenomena without altering the sample behavior would be desirable. Néel relaxation processes, which are fluctuations of the particle superspin between its easy magnetic directions, are canceling the Zeeman-splitting term of the intrinsic hyperfine magnetic field, Bhf. In Mössbauer spectroscopy, this leads to the observation of a superparamagnetic doublet spectrum at sufficiently high relaxation frequencies above the blocking temperature (compared to the nuclear Larmor frequency, here approximately ωLarmor ≈ 2 × 108 s−1). At lower temperatures, effects of Néel relaxation can still be observed due to thermal excitation of the particle magnetic moment. While still too weak to cause a spin-flip, it leads to a reduction in the hyperfine

ΔΓ =

E02kB T 3ℏπc 2 RHη

(3)

Mössbauer spectra of sample S, M, and L are shown in Figure 3, measured at temperatures in the range of 234 K − 262 K. Up to ∼240 K, the broadening of the absorption lines by Brownian motion is relatively small; therefore, we can observe a similar line width as compared to the spectra of the solidified samples shown in the top row as a reference. While the largest particles are magnetically blocked near ambient temperature in terms of Néel relaxation, as can be seen by the spectrum’s sextet structure, sample M displays beginning relaxation effects, leading to a non-Lorentzian line shape with pronounced inner shoulders, as marked by arrows in Figure 3. Sample S is in a transition state near the superparamagnetic doublet, corresponding to a high relaxation frequency close to C


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Nano Letters (2πτ0)−1. These observations are in agreement with magnetic characterization by ZFC-FC magnetization, although one has to consider that Mö ssbauer spectroscopy exhibits blocking temperatures higher than those of standard magnetometry techniques, because of the smaller characteristic time window of about 1/ωLarmor ∼ 5 × 10−9 s compared to ∼1−10 s for magnetometry.24 Mössbauer spectra of sample L are reproduced using two subspectra corresponding to tetrahedral and octahedral lattice sites in magnetite, shown exemplarily for the spectrum at 150 K. Due to larger intrinsic line widths in sample M, these cannot be resolved and are therefore reproduced using a single sextet of larger line width. To reproduce effects of Néel relaxation of samples M and L (like the inner shoulders marked in Figure 3), a many-state relaxation model based on the theory by Jones and Srivastava is applied,24,25 which allows the approximation of the effective anisotropy Keff of sample M to about 10 kJ m−3 from spectra shown in Figure 3. Recording spectra over a wider range of temperatures including the blocking temperature would allow a more precise evaluation of Keff.24,26 The doubletlike transition state of sample S is reproduced by a broadened doublet. Additionally, for all three samples, the total line width (full width at half-maximum) Γ = ΔΓ + Γ0 is varied according to the increasing line broadening ΔΓ by Brownian motion, while “static” line widths Γ0 without effects of Brownian motion were extracted from spectra at cryogenic temperatures (150−180 K), as shown on top of Figure 3. To precisely determine ΔΓ at temperatures of 245 K − 275 K where the line width is comparable to the sextet splitting and the sextet structure becomes obscured by the superposition of the broadened absorption lines, parameters defining the line positions, i.e., isomer shift and hyperfine magnetic field, were extrapolated from low-temperature spectra. We observe a considerable increase of the line width upon rising temperature, which is most pronounced for the smallest particles, as can be seen in Figure 4. In the temperature range of

η0 is a constant, EA the activation energy per mole, and R the molar gas constant.

⎛E ⎞ η = η0 exp⎜ A ⎟ ⎝ RT ⎠

(4)

Values of the line broadening for all three samples were described in Figure 4 by eqs 3 and 4 using an identical exponential slope with an offset in amplitude of 1.58 (S:M) and 1.36 (M:L). Considering that ΔΓ is proportional to RH−1 according to eq 3, one can calculate the coating thickness, x, from the ratio of hydrodynamic radii (RH = RC + x) using the average particle core radii, RC, as obtained from TEM. Good agreement to the above-mentioned ratios in line broadening can be obtained for a coating thickness of ∼5.5 nm, which is close to the nominal value of about 4 nm provided by the manufacturer. Results from Mössbauer spectroscopy were crosschecked by AC-susceptometry. Figure 5a shows data in the high-frequency

Figure 5. Normalized magnetic AC-susceptibility showing relaxation behavior dominated by (beginning) Néel relaxation in the highfrequency regime for samples S and M at room temperature (a) and by Brownian rotation in sample L (b).

Figure 4. Line broadening, ΔΓ, of the Mössbauer absorption line versus inverse temperature. Data sets were fitted assuming the validity of the Andrade equation (eq 4) within the small displayed temperature interval with identical exponential slopes for samples S, M, and L.

regime of about 100 Hz to 1 MHz for samples S and M. In agreement with the nearly superparamagnetic state observed by Mössbauer spectroscopy, indicating a high relaxation frequency, we do not observe any relaxation processes in the measured frequency range for sample S. The magnetic susceptibility of sample M can be described by the Debye relation and a distribution of Néel relaxation frequencies using eq 1, the average core diameter D = 14.8 nm, and the standard deviation ΔD = 1.6 nm of the core size distribution. This approach yields

234−275 K, spectra exhibit a line broadening ΔΓ of ∼0.2 up to 20 mm/s. Spectra measured at higher temperature with higher line widths, resulting in larger error bars, were not considered. The increase in line broadening upon rising temperature given by eq 3 corresponds to the decay in dynamic viscosity, η, as described, for example, by the Andrade equation (eq 4), where D


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to a small temperature dependence in Γ0, which may also cause an additional uncertainty in ΔΓ. Conclusion. Three types of coated iron oxide nanoparticles dispersed in 70 vol % water−glycerol solution were studied using standard magnetometry, AC-susceptometry, and Mössbauer spectroscopy. The former two methods allowed a general magnetic characterization of the samples, showing the dominating Brownian motion for sample L (26.4 nm) and Néel relaxation approximated to f Néel ≈ 10 MHz for sample M (14.8 nm). For sample S (6.0 nm), f Néel was too high to be quantified. However, both relaxation phenomena were simultaneously observed in Mössbauer measurements performed in the temperature range of 234−287 K. Néel relaxation states and parameters correlated to Brownian motion, i.e., coating thickness and solvent’s dynamic viscosity, were directly estimated from Mössbauer spectra of all samples. This proves Mössbauer spectroscopy to be a powerful technique capable of simultaneously investigating Brownian and Néel relaxation phenomena in ferrofluids.

an effective magnetic anisotropy of about 14(1) kJ/m3, using τ0 ≈ 2 × 10−11 s. Using these parameters and the Debye relation for extrapolation, we obtain a maximum of χ″ at about 10 MHz, which is consistent with beginning relaxation effects, e.g., distinct inner shoulders, observed in Mössbauer spectra of this sample. Because effects of Néel relaxation dominate in samples S and M (f Néel ≫ f Brown), information about the solvent’s viscous properties, as they were calculated from Mössbauer absorption line broadening, cannot be obtained by ACsusceptometry without applying a DC magnetic field to suppress Néel relaxation, which would also influence the Brownian motion. Unlike samples S and M, 26 nm particles in sample L display relaxation behavior which is dominated by Brownian motion. Therefore, its magnetic susceptibility was measured in the temperature range of 245−310 K to compare results from Mössbauer spectroscopy with values of the dynamic viscosity calculated from the Brownian rotation frequencies, f Brown, as given by the maximum position of χ″. We observe an exponential increase of f Brown from 3 to 800 Hz upon rising temperature. The solvent’s dynamic viscosity was calculated using eq 2 for the rotation frequency and compared with values determined from the Mössbauer line broadening, ΔΓ, of all three samples. As shown in Figure 6, results of AC-

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Professor Werner Keune for helpful discussions and Ulrich von Hörsten for his expert technical assistance. This work was supported by the DFG (SPP1681, WE2623/7-1, and LU800/4-1) and by Stiftung Mercator (MERCUR).

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REFERENCES

(1) Kim, E. H.; Lee, H. S.; Kwak, B. K.; Kim, B.-K. J. Magn. Magn. Mater. 2005, 289, 328−330. (2) Raj, K.; Moskowitz, R. J. Magn. Magn. Mater. 1990, 85, 233−245. (3) Pérez-Castillejos, R.; Plaza, J. A.; Esteve, J.; Losantos, P.; Acero, M. C.; Cané, C.; Serra-Mestres, F. Sens. Actuators, A 2000, 84, 176− 180. (4) Wang, D. H.; Liao, W. H. Smart Mater. Struct. 2011, 20, 023001. (5) Moskowitz, R. ASLE Trans. 1975, 18, 135−143. (6) Mørup, S.; Hansen, M. F.; Frandsen, C. Comprehensive Nanoscience and Technology 2011, 1, 437−491. (7) Chantrell, R. W.; Hoon, S. R.; Tanner, B. K. J. Magn. Magn. Mater. 1983, 38, 133−141. (8) Labarta, A.; Iglesias, O.; Balcells, L.; Badia, F. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 48, 10240. (9) Eberbeck, D.; Wiekhorst, F.; Steinhoff, U.; Trahms, L. J. Phys.: Condens. Matter 2006, 18, S2829−S2846. (10) Ludwig, F.; Mäuselein, S.; Heim, E.; Schilling, M. Rev. Sci. Instrum. 2005, 76, 106102. (11) Fannin, P. C.; Scaife, B. K. P.; Charles, S. W. J. Magn. Magn. Mater. 1988, 72, 95−108. (12) Ludwig, F.; Guillaume, A.; Schilling, M.; Frickel, N.; Schmidt, A. M. J. Appl. Phys. 2010, 108, 033918. (13) Shliomis, M. I.; Raikher, Yu. L. IEEE Trans. Magn. 1980, 16, 237−250. (14) Rosensweig, R. E. J. Magn. Magn. Mater. 2002, 252, 370−374. (15) Hergt, R.; Hiergeist, R.; Zeisberger, M.; Glöckl, G.; Weitschies, W.; Ramirez, L. P.; Hilger, I.; Kaiser, W. A. J. Magn. Magn. Mater. 2004, 280, 358−368. (16) Bonchev, T.; Aidemirski, P.; Mandzhukov, I.; Nedyalkova, N.; Skorchev, B.; Strigachev, A. Sov. Phys. JETP 1966, 23, 42−46. (17) Fornal, P.; Stanek, J. Acta Phys. Pol., A 2008, 114, 1667−1673.

Figure 6. Dynamic viscosity, η, calculated from the rotation frequency of sample L (from AC-susceptometry data indicated as L(AC)) and from the line broadening, ΔΓ, observable in the Mössbauer spectra of samples S, M, and L using a coating thickness of 5.5 nm.

susceptometry and Mössbauer spectroscopy are comparable in the range of 245−275 K and similar to the literature value of 132 mPas at 0 °C for the macroscopic viscosity at 75 wt % (∼70 vol %) glycerol solution.27 Now spanning a wider temperature range than Mössbauer data alone, one observes a clear deviation in dynamic viscosity from ideal Arrhenius behavior. Similar behavior has been reported earlier in the literature and could be reproduced by the Vogel−Fulcher− Tammann−Hesse equation for viscosities in the region above the glass temperature.28 At lower temperatures one observes a slightly deviating slope in η(T) determined by Mössbauer spectroscopy relative to data from AC-susceptometry, which could be caused by a small difference between the nominal temperature and the actual sample temperature. This deviation was checked to be smaller than 2 at 240 K. In the case of sample S, the undergoing transition to the superparamagnetic doublet with rising T leads E


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Nano Letters (18) Dormann, J. L.; D’Orazio, F.; Lucari, F.; Tronc, E.; Prené, P.; Jolivet, J. P.; Fiorani, D.; Cherkaoui, R.; Noguès, M. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 53, 14291−14297. (19) Madsen, M. B.; Mørup, S.; Costa, T. V. V; Knudsen, J. M.; Olsen, M. Nature 1986, 321, 501−503. (20) Verwey, E. J. W. Nature 1939, 144, 327−328. (21) Mamiya, H.; Nakatani, I.; Furubayashi, T. Phys. Rev. Lett. 1998, 80, 177−180. (22) Wen, T.; Liang, W.; Krishnan, K. M. J. Appl. Phys. 2010, 107, 09B501. (23) Landers, J.; Roeder, L.; Salamon, S.; Schmidt, A. M.; Wende, H. J. Phys. Chem. C 2015, 119, 20642−20648. (24) Landers, J.; Stromberg, F.; Darbandi, M.; Schöppner, C.; Keune, W.; Wende, H. J. Phys.: Condens. Matter 2015, 27, 026002. (25) Jones, D. H.; Srivastava, K. K. P. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 34, 7542−7548. (26) van Lierop, J.; Ryan, D. H. Phys. Rev. B: Condens. Matter Mater. Phys. 2001, 63, 064406. (27) Segur, J. B.; Oberstar, H. E. Ind. Eng. Chem. 1951, 43, 2117− 2120. (28) Schröter, K.; Donth, E. J. Chem. Phys. 2000, 113, 9101−9108.

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Simultaneous Study of Brownian and NÃ©el Relaxation Phenomena in

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