Dynamics of Ferrofluids Studied by MÃ¶ssbauer Spectroscopy

Research Article Cite This: ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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In-Field Orientation and Dynamics of Ferrofluids Studied by Mössbauer Spectroscopy Joachim Landers,*,† Soma Salamon,† Hilke Remmer,‡ Frank Ludwig,‡ and Heiko Wende† †

ACS Appl. Mater. Interfaces Downloaded from pubs.acs.org by TULANE UNIV on 01/20/19. For personal use only.

Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg−Essen, Lotharstr. 1, 47057 Duisburg, Germany ‡ Institute for Electrical Measurement Science and Fundamental Electrical Engineering, TU Braunschweig, Hans-Sommer-Straße 66, 38106 Braunschweig, Germany ABSTRACT: By studying the response behavior of ferrofluids of 6−22 nm maghemite nanoparticles in glycerol solution exposed to external magnetic fields, we demonstrate the ability of Mössbauer spectroscopy to access a variety of particle dynamics and static magnetic particle characteristics at the same time, offering an extensive characterization of ferrofluids for in-field applications; field-dependent particle alignment and particle mobility in terms of Brownian motion have been extracted simultaneously from a series of Mössbauer spectra for single-core particles as well as for particle agglomerates. Additionally, information on Néel superspin relaxation and surface spin frustration could be directly inferred from this analysis. Parameters regarding Brownian particle dynamics, as well as Néel-type relaxation behavior, obtained via Mössbauer spectroscopy, have been verified by complementary AC-susceptometry experiments, modulating the AC-field amplitude, and using an extended frequency range of 10−1 to 106 Hz, while field-dependent particle alignment has been cross-checked via magnetometry. KEYWORDS: ferrofluids, magnetic nanoparticles, field-alignment, superparamagnetism, Mössbauer spectroscopy, AC-susceptometry

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INTRODUCTION Magnetic hybrid materials are utilized at an increasing rate in industry and research. For ferrofluids and elastic composites containing magnetic nanoparticles (MNPs), tuning the particle response to external magnetic fields may be considered as one of the most important criteria. This includes the field-induced deformation or positioning of magnetic media1−3 as well as the tunable viscosity in ferrofluids and magnetorheological fluids via the hindrance of rotational particle motion and chain formation4 and remote-controlled heating via AC-magnetic fields in engineering and medical applications.5,6 To develop and optimize ferrofluids, gels, polymers, and other deformable magnetic composites, precise knowledge of the behavior of MNPs under working conditions is essential. These include external magnetic fields of varying amplitudes, directions, or frequencies, exposure to different temperatures, or embedding in media of different viscosities or (visco)-elastic behaviors. Here, we demonstrate Mössbauer spectroscopy to be a suitable method for this purpose, as it provides simultaneous access to static and dynamic characteristics of ferrofluids or magnetic particles in deformable media in general. Although most of the abovementioned characteristics can also be determined via the combination of other (magnetic) experimental techniques, 57Fe-Mössbauer spectroscopy can also be applied in the case of, for example, opaque media, where optical methods are not feasible. On the basis of its © XXXX American Chemical Society

detection mechanism, utilizing the optical Doppler effect, and being sensitive to individual iron spins instead of the net magnetic moment of particles, different magnetic relaxation mechanisms such as Néel superspin relaxation7,8 and Brownian particle motion9,10 as well as field-induced particle alignment will result in clearly distinguishable modifications of the spectral structure, as demonstrated in the following. By probing spin dynamics on the nanosecond timescale, information from Mö ssbauer spectra regarding particle mobility does not reflect the macroscopic properties of composite systems but instead the influence of the local nanostructure on the particle motion, also referred to as nanoviscosity in fluid media.11,12 Thereby, using ferrofluids as simple model systems, we want to demonstrate that the same approach can also be applied for the in-depth characterization of more complex soft magnetic composites and gels, which will be the subject of our future investigations.

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RESULTS AND DISCUSSION Three samples of monodisperse iron oxide nanoparticles (IONPs) capped by oleic acid and an amphiphilic polymer with a shell thickness d of ca. 5 nm, dissolved in 70 vol % Received: September 19, 2018 Accepted: December 24, 2018 Published: December 24, 2018 A

DOI: 10.1021/acsami.8b16356 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces glycerol solution, were purchased from Ocean NanoTech, denominated here as samples S, M, and L. Particles in samples S−L display regular spherical shape and are highly monodisperse; samples S and M have been the subject of our previous studies, with core diameters DC of 6.0 ± 0.5 nm (S) and 14.8 ± 1.6 nm (M), determined via transmission electron microscopy (TEM),13 while TEM images of sample L shown in Figure 1 indicate core sizes of 22.0 ± 1.9 nm.

Figure 2. Imaginary part χ″ of magnetic AC-susceptibility of samples S−L measured at 5−300 K and 0.1−1500 Hz normalized to the maximum value of each individual sample as well as χ′ and χ″ of sample M and L measured in an extended frequency range up to 1 MHz.

Figure 1. TEM image of sample L, showing the core−shell structure of spherical monodisperse particles and the corresponding distribution of particle core diameters (solid line, filled symbols), yielding DC ≈ 22.0 ± 1.9 nm, hydrodynamic diameters with DH ≈ 32 nm (dotted line, open symbols), and an average shell thickness d of ca. 5 nm.

parameter, often reported to be in the range of 10−12 to 10−9 s.14

Mössbauer spectra shown later on are consistent with the expected magnetite/maghemite spinel structure. However, Mössbauer spectroscopy experiments performed at cryogenic temperatures as well as temperature-dependent magnetization curves, showing the Verwey transition as a minor feature, indicated the presence of a magnetite byphase only in particles larger than 15 nm.13 Thereby, we expect the particles to contain primarily maghemite, with a potential minor volume of remaining magnetite material in larger particles (sample L), presumably shielded from further oxidation by a maghemite passivation surface layer. To take this into account, we utilize maghemite parameters to evaluate our results on all ferrofluids in the following. Some particle agglomeration is visible in Figure 1, which could, however, be caused by the preparation of the liquid on the TEM grid. Agglomeration in the ferrofluids, which is known to critically influence performance and shelf-life of liquids containing MNPs, will be discussed later on in detail in terms of AC-susceptometry (ACS) and Mössbauer spectroscopy. To study the general magnetization dynamics of the three ferrofluidic samples, the magnetic AC-susceptibility was measured at 5−300 K in the low-frequency regime. The imaginary part of the susceptibility χ″ is shown in Figure 2, normalized to its maximum value in the studied temperature and frequency range. Relaxation processes allowing magnetic alignment along the current field direction are visible by Debye-type signals corresponding to peaks in χ″. Thereby, streak-like features in the AC-susceptibility mapping reflect the characteristic temperature dependency of the relaxation frequency of the specific processes, namely, Néel-type relaxation and Brownian motion. Relaxation times τN and τB,0 of those processes can be described in first approximation by eqs 1 and 2, respectively, where K is the effective magnetic anisotropy constant, VC is the particle core and VH is the hydrodynamic particle volume, kBT is the thermal energy, η is the dynamic viscosity of the fluid, and τ0 is the relaxation

ji KV zy τN = τ0·expjjj C zzz j kBT z k {

(1)

3ηVH kBT

(2)

τB,0 =

The largest particles (sample L) display a peak signal at temperatures above ca. 220 K, slowly shifting to higher relaxation frequencies upon rising temperature. This represents Brownian particle motion, allowing magnetic relaxation via spatial particle rotation, where the decrease in relaxation time reflects the roughly exponential decrease in the dynamic viscosity η of the fluid.15,16 The peak frequency will be evaluated in more detail in further AC experiments with regards to the hydrodynamic particle diameter (see below). Below its glass-transition temperature TG at ca. 180 K,17,18 the glycerol solution can be considered an amorphous solid, in which no particle motion is possible. The absence of magnetic relaxation below TG in sample L proves magnetically blocked behavior, also in terms of Néel relaxation. On the contrary, sample M displays a much broader peak in magnetic susceptibility because of the exponential dependence of the Néel relaxation time τN on the magnetic anisotropy energy of the particles,19 whereby even highly monodisperse particle ensembles will exhibit a wide range of τN. However, no second streak representing Brownian motion is visible, indicating that for all particles in sample M, Néel-type relaxation is faster than the Brownian mechanism. A similar behavior is visible for sample S, with a considerably lower blocking temperature TB in the range of ca. 30 K, marking the transition from the magnetically blocked state to free fluctuation of the particle magnetic moment, resulting from the lower particle volume compared to sample M with an average TB of ca. 150 K. Taking into account eq 1 as an approximation of τN and the respective core volumes of the particles determined from TEM analysis, B


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ACS Applied Materials & Interfaces the observed peak positions can roughly be converted to effective magnetic anisotropy constants of K ≈ 70 kJ m−3 (sample S) and K ≈ 19 kJ m−3 (sample M). Both are considerably increased relative to the magnetocrystalline anisotropy constant of maghemite in the range of |K1| ≈ 4.7 kJ m−3 because of surface anisotropy contributions21 and comparable to values reported for particles of similar diameter.8,20 In ref 13, a slightly lower anisotropy constant of ca. 14 kJ m−3 was found from measurements at room temperature, where the main part of the relaxation peak feature was outside the attainable frequency range, presumably leading to this minor difference. To gain more detailed information at temperatures common for most ferrofluid applications, ACS measurements were performed in an extended frequency range up to 1 MHz at room temperature to detect signals of both Brownian and Néel origin, as shown in Figure 2 for samples M and L. For sample S, no changes in magnetic susceptibility were observed in the studied frequency range, which was previously explained in terms of fast Néel-type relaxation.13 Medium-sized particles (sample M) display beginning Debye-type behavior close to the megahertz-regime, matching the expectation of relatively slow Néel relaxation for 15 nm IONPs and also comparable measurements shown in ref 13. Particle rotation frequencies of sample L, on the other hand, are not consistent with the anticipated hydrodynamic particle diameter in the range of DH = 2d + DC ≈ 32 nm, with the shell thickness d ≈ 5 nm. Instead, there is a broad peak feature at relatively low frequencies, which, when being reproduced using an extended Debye model, including distributions of core and hydrodynamic particle sizes,22 would yield a broad particle size distribution with DH ≈ 130 nm and a size distribution width of ca. 100 nm. As TEM analysis verified monodisperse particles, the broad distribution of Brownian rotation times points toward particle agglomeration in sample L, which is a natural assumption, as larger particles are more susceptible to agglomeration due to the much stronger dipolar interparticle interaction. We will elaborate on the ability to quantify nanoparticle agglomeration (via susceptometry as well as Mössbauer spectroscopy) in some detail here, as agglomeration of magnetic particles is a known and critical problem in ferrofluids and certain soft matter systems, and the primary factor limiting the shelf-life of such media for applications. Note that the generalized Debye model applied above assumes uncorrelated core and hydrodynamic size distributions. This is definitely not the case for single-core nanoparticles with rather thin shells.20 Agglomerates of single-core nanoparticles can be considered as multicore particles, for which a correlation coefficient ρ = 0.5 is expected.23 Thus, the ACS analysis on sample L was repeated by implementing a bivariate distribution of core and hydrodynamic diameters with ρ = 0.5, resulting in a median hydrodynamic diameter of 77 nm. ACS measurements were also performed for different amplitudes of the AC magnetic field. The measured spectra of the imaginary part of the complex susceptibility are depicted in Figure 3a. They were fitted with the phenomenological Havriliak−Negami model24 for a precise determination of the characteristic peak positions. As expected and known from previous studies,25,26 the characteristic Brownian peak shifts to higher frequencies and its amplitude decreases with increasing field amplitude. The characteristic frequency positions are plotted in Figure 3b as a function of field amplitude.

Figure 3. (a) Imaginary part χ″ of the AC-susceptibility as a function of frequency measured on sample L for different amplitudes of the AC field. (b) Characteristic frequencies obtained from (a) vs AC field amplitude. Red curve: fit with eq 3 between 0.2 and 0.4 mT (τB,0 = 0.032 s, m = 2.34 × 10−17 A m2); blue curve: fit between 2 and 5 mT (τB,0 = 0.193 s, m = 3.52 × 10−16 A m2). (c) Calculated effective magnetic moment vs magnetic field amplitude. (b,c) Error bars are of the size of the symbols.

In ref 27, Yoshida and Enpuku numerically solved the Fokker−Planck equation for Brownian MNPs exposed to a large sinusoidal magnetic field and derived the following empirical equation for the Brownian relaxation time28 τB,0 τB = 1 + 0.126ξ1.72 (3) Here, ξ = mB/(kBT) is the Langevin parameter with the particle magnetic moment m and the applied flux density B. As we demonstrated in refs 25 and 26, this empirical equation is a good approximation to determine the magnetic moment and the zero-field Brownian relaxation time from the field dependence of ACS spectra. Applying eq 3 to fit the data in Figure 3b, thereby using a constant net magnetic moment, did not provide a reasonable result. Neglecting minor effects of distributions of zero-field Brownian relaxation times τB,0 and magnetic moments m (corresponding to the particle size distribution) on the dependence of the peak position on magnetic field amplitude, this means that the effective magnetic moment meff is dependent on the magnetic field. Monte-Carlo simulations for the effective magnetic moment of agglomerated and multicore MNPs including interaction effects were presented by Schaller et al.,29 however, only for small amplitudes of the magnetic field. As can be seen from the fit parameters of Figure C


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Figure 4. Mössbauer spectra of sample L, recorded at 242−263 K in external magnetic fields up to 99 mT parallel to γ-ray propagation (top) and 199 mT in perpendicular geometry (bottom), which are illustrated schematically.

in-field alignment and diffusive motion via Mö ssbauer spectroscopy. Early experiments on ferrofluids following a similar approach were performed by Winkler et al., however, without a detailed characterization of particle orientation.31 Spectra of sample L shown in Figure 4 were recorded at 242− 263 K without an external magnetic field and with varying field amplitudes parallel and perpendicular to the γ-ray propagation direction, respectively. They have been modeled using the “Pi” program package32 and the many-state relaxation model to reproduce minor asymmetries in the lineshape caused by beginning Néel relaxation in sample M and L.8,33 As the subspectra of tetrahedral A- and octahedral B-sites in maghemite exhibit very similar hyperfine magnetic fields BHF close to room temperature,34 only one slightly asymmetric sextet is observable in the spectra, wherefore these have been reproduced using only one subspectrum to minimize the number of free variables. Doing so, at 242 K, we obtain an isomer shift (relative to α-Fe at room temperature) of 0.37 mm/s and BHF ≈ 50.9 T, which are in good agreement with maghemite hyperfine parameters from the literature.34,35 This indicates the absence of a considerable magnetite fraction in the particles, as this would be accompanied by the observation of Fe2+ components, clearly distinguishable from maghemite subspectra because of their higher isomeric shift and lower hyperfine magnetic field.8,35 Upon rising temperature T, the exponential decrease in viscosity η leads to a corresponding increase ΔΓ in linewidth, correlated via the optical Doppler shift to the translational diffusion coefficient DT of the nanoparticles experiencing Brownian motion, as described36 by eq 5.

3b, the effective agglomerate magnetic moment increases upon rising field amplitude. This can be understood as the transition from randomly distributed magnetic moments of the individual particles in the agglomerates, resulting in very limited net magnetic moment, to a more parallel alignment of particle magnetic moments at higher fields. To determine the magnetic field dependence of meff, eq 3 was converted to ÄÅ ÉÑ1/1.72 2 kBT ÅÅÅÅ (2πτB,0fch ) − 1 ÑÑÑÑ ÅÅ ÑÑ meff (B) = ÑÑ B ÅÅÅ 0.126 (4) ÅÇ ÑÖÑ with the characteristic frequency fch. The zero-field Brownian relaxation time was estimated to 0.032 s by extrapolating the data points in Figure 3b to zero-field amplitude. The magnetic field dependence of meff is depicted in Figure 3c. At low field amplitudes, the quadratic dependence of meff on B is allusively discernable, while meff approaches a value of 45 × 10−18 A m2 at high field amplitudes, which is about a factor of 2.8 higher than the zero-field value. According to Schaller et al.29 the effective magnetic moment at nominally zero magnetic field scales with the square of the number of particles N in the agglomerate, while at high fieldsapproaching uniform nanoparticle alignmenta scaling proportional to N is expected. Combining this with the factor of 2.8 between meff at high and zero magnetic fields, N ≈ 8 is found. On the other hand, taking the expected value of the magnetic moment of a single 22 nm nanoparticle of m ≈ 2.0 × 10−18 A m2 (assuming Ms ≈ 350−400 kA/m for maghemite or magnetite/maghemite nanoparticles of similar size20,30) and the value of the effective magnetic moment meff = Nm = 45 × 10−18 A m2 for the agglomerate at high-field amplitudes, N ≈ 22 is found. Neglecting more complex effects like compressibility of the coating material and the inner structure of the agglomerate and just comparing effective particle and agglomerate volumes, an agglomerate of 8 (22) densely packed nanoparticles of DH ≈ 32 nm has a total (hydrodynamic) diameter of 64 (90) nm, in good agreement with the findings from low-field amplitude ACS measurements (77 nm). Now that we have an overview of the relaxation dynamics of the ferrofluid, we perform an in-depth examination of particle

ΔΓ = 2ℏk 2DT ∝

T RHη

(5)

Further valuable information can be inferred from the relative line intensity, reflecting the canting angle between γray propagation direction and spin orientation, therefore being directly dependent on the geometry of the incident γ-ray relative to the magnetic field direction. The relative intensity A23 of line 2 to 3 (and 5 to 4, respectively) is correlated with the canting angle θ as given by eq 6, resulting in A23 = 2, for D


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energy (Figure 6). This is in agreement with the low blocking temperature observed in AC-mappings (Figure 2), while

example, for random spin orientation as expected in ferrofluids in the absence of magnetic fields, while total alignment coaxial to the field direction corresponds to A23 = 0 for γ parallel to H and A23 = 4 for γ perpendicular to H, accordingly. A 23 =

I2 4 sin 2(θ ) = I3 1 + cos2(θ )

(6)

The sensitivity of relative line intensities to magnetic particle orientation will be utilized here to determine the average canting angle, wherefore A23(H) is modeled following the Langevin approach for a (super-) paramagnetic system within a wide range of temperatures and magnetic field amplitudes. Doing so, the particle magnetic moment m can also be derived and later on compared to magnetometry data to verify Mössbauer information on the particle alignment process. For sample L, enhanced particle alignment is displayed via an increased intensity of lines 2 and 5 for perpendicular and decreasing intensity for parallel field geometry. It is worth mentioning that the extraction of A23 from Mössbauer spectra, allowing the study of particle magnetic alignment, and further particle characteristics as demonstrated here, may, however, be hindered by severe line broadening in ferrofluids with much smaller particles or lower viscosity. Spectra of smaller particles (sample M) displayed in Figure 5 are similar in structure to those of sample L, proving the

Figure 6. Mössbauer spectra of sample S, measured in perpendicular field geometry up to 0.5 T. The transition from fast Néel relaxation to a magnetically mostly blocked state is induced by the external magnetic field and visible via the doublet to sextet transition. To consider the complex deformation of particles performing Néel relaxation in the presence of external fields, the spectral shape was reproduced using a hyperfine field sextet distribution, the shape of which was fixed at higher temperatures to estimate dynamic line broadening.

blocked behavior in Mössbauer spectra of sample M can be explained by the shorter time window of Mössbauer spectroscopy compared to that of ACS, leading to much higher blocking temperatures. In the superparamagnetic state, eq 5 is still applicable, as the sextet−doublet transition is caused by Néel-type magnetic relaxation, while the broadening of absorption lines directly corresponds to the Doppler shift of absorbed γ-rays by moving particles, which can be considered as independent processes here. Still, fast Néel relaxation prevents the determination of A23 in sample S at low magnetic fields. Upon rising field amplitude, the Zeeman energy of the particle net magnetic moment in the external field will, however, modify the energy landscape defined by the magnetic anisotropy of the particle, resulting in a dramatic increase in relaxation time and the observation of a sextet, from which the magnetic orientation can again be inferred. To study the field-dependent particle alignment in detail, A23(H) is compared for parallel and perpendicular alignment beginning with sample M in Figure 7. It is evident that a simple Langevin model is insufficient to reproduce the peculiar saturation behavior in A23. Using a more sophisticated approach, we modeled experimental data by superposition of a fraction s of surface atoms, showing no response to external fields due to strong spin frustration, and a second contribution (1 − s) corresponding to the particle core, showing bulk-like properties. Although this is a simple realization of the magnetic structure of particles with moderate surface spin canting, it is a well-established procedure for theoretical models37 and the evaluation of magnetic measurement data.38,39 Results obtained by this model are shown in Figure 7 by dashed lines, yielding very good agreement with experimental line ratios for an alignable (core) particle magnetic moment of 6.8 ± 0.5 × 10−19 A m2 and a fraction s ≈ 13% of canted surface

Figure 5. Mössbauer spectra of sample M, measured in parallel field geometry up to 122 mT. A visible line asymmetry indicates beginning Néel-type relaxation.

magnetically blocked state with TB well above ca. 250 K. In spectra recorded, for example, at 243 K, sufficiently small linewidths allow the observation of asymmetric line shapes, indicating the commencing collapse of the sextet structure caused by beginning Néel relaxation with relaxation times higher than the inverse Larmor precession frequency in the range of 5 ns. Because of the lower hydrodynamic particle diameter compared to sample L, higher linewidths are observed despite the identical fluid viscosity, in agreement with eq 5. To study the particle alignment process in detail, A23(H) will be compared for the ferrofluids later on. Sample S deviates in the spectral structure from the ferrofluids shown above, as the 6 nm particles display a broadened doublet structure caused by fast Néel relaxation due to their smaller core diameter and lower magnetic anisotropy E


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Figure 7. Field dependence of line ratio A23 for sample M for parallel and perpendicular orientation of the magnetic field relative to the γray propagation direction measured at about 240−260 K. The dashed line corresponds to theoretical modeling of A23(H) explained in the text. (a−c) represent low-field random alignment (a), partial magnetic particle alignment (b), and beginning alignment of frustrated surface spins (c), schematically.

Figure 8. Field dependence of line ratio A23 of sample L (symbols) and modeled for sample M in comparison (dashed line) for parallel and perpendicular orientation of the magnetic field relative to the γray propagation direction measured at about 240−260 K. (a−c) represent low-field random alignment (a), partial alignment of the agglomerate net magnetic moment (b), and beginning alignment of individual particle moments out of the direction preferred by magnetic anisotropy (c), schematically.

spins. These values seem reasonable: using a saturation magnetization of MS,300K = 76 emu/g ≈ 400 kA/m for bulk maghemite,40 average particle core volumes of sample M from TEM analysis correspond to 7.6 × 10−19 A m2 particle magnetic moment or 6.6 × 10−19 A m2 considering 13% of spin canting. As illustrated schematically in Figure 7, the trend in A23(H) consists of three regions: (a) widely random orientation at very low fields, (b) alignment of the particle net magnetic moments according to the Langevin equation, and (c) partial alignment of canted surface spins toward the (not measured here) high-field region. A deviant behavior is observed for larger particles in sample L (Figure 8), showing faster alignment in fields up to some mT, whereas a far lower degree in magnetic alignment compared to sample M is observed above ca. 25 mT, which cannot be explained in the model of separately moving core− shell particles. Taking into regard the surprisingly low rotation frequency and the field dependence in particle net magnetic moment determined in ACS experiments, a reasonable assumption would be a change in the orientational behavior due to particle agglomeration, where the much larger net magnetic moment meff of the particle ensemble in an agglomerate drives faster alignment along the field direction below 25 mT. The particles, however, which are assumed to be pinned together in random orientation here, will display an ensemble of nonidentical easy magnetic directions (dotted lines). These represent a second source of magnetic misalignment, necessary to explain the low degree of orientation of sample L, as larger particles are usually expected to exhibit considerably lower spin canting due to the lower fraction of surface atoms.

A comparison to sample S as a third reference system, which could provide further insight into the orientational dynamics of smaller nanoparticles, is, however, not possible, as A23 cannot be determined from the spectra of sample S below a critical minimum field of ca. 0.4 T. Nevertheless, a value of A23 ≈ 3.4 was obtained at 0.5 T, corresponding to a partially aligned state, matching expectations for smaller particles with more pronounced spin canting and far lower net magnetic moment. When comparing A23(H) to M(H) data presented in the following section, one has to keep in mind that A23 gives an absolute measure of alignment, while M(H) is usually normalized to the magnetization at the highest attainable field amplitude, where residual spin canting still decreases the magnetization relative to saturation to a considerable extent. We also extracted information regarding the mobility and hydrodynamic diameter of the particles from Mössbauer spectroscopy, which will be compared to results from ACS. In Figure 9, the line broadening ΔΓ of absorption lines is shown for all three ferrofluids, given as the difference of the total linewidth and the static linewidth extrapolated from measurements at sufficiently low temperatures, where Brownian motion is hindered by reaching ultrahigh viscosities approaching the glass-transition temperature. Experimental values of ΔΓ were modeled here using reference data from ref 41 of 70−80 wt % glycerol solution and the Vogel−Fulcher law, often used to describe the temperature dependence of the viscosity η in glass-forming liquids. Using the so-defined function of η(T), the only free parameter in eq 5 is the hydrodynamic particle radius RH, which allows the determination of the effective particle size from ΔΓ, as it has been F


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to the total line broadening in addition to translational motion, wherefore rotational motion was not regarded in the evaluation of temperature-dependent line broadening described in the previous section. As translational motion should not be directly affected by magnetic fields, a decrease in linewidth matching the trend of particle alignment from A23 may indeed stem from increasingly blocked rotational motion. As this variation in linewidth upon rising fields could not be observed consistently for all samples, it is not shown or discussed in detail. However, this will be subject of a future investigation to obtain insight on an additional type of particle dynamics accessible by Mössbauer spectroscopy, apart from translational Brownian motion, Néel relaxation, and particle alignment. The particle alignment process, as observed in Mössbauer spectroscopy, was cross-checked via static magnetometry measurements. As field-dependent magnetization curves of different ferrofluids are to be compared, we normalized the magnetization curves obtained at 240 K, close to the temperature in the abovementioned Mössbauer experiments, to the saturation magnetization MS, as shown in Figure 10. The

Figure 9. Temperature dependence in Mössbauer line broadening: experimental data (symbols) and calculation (line) based on eq 5 and viscosity data for 70−80 wt % glycerol solution from ref 41.

demonstrated for such fluids in ref 13. As the focus of the ongoing study was to prove the feasibility of simultaneous determination of particle mobility and orientation, the number of temperature points is smaller than that in previous studies13 but still allows a relatively precise determination of DH,MS. As highly concentrated glycerol solutions are relatively hygroscopic, the ferrofluid samples were kept in airtight containers during storage to prevent a change in glycerol concentration. Also, during the extensive timespan of the experimental series, the samples were sealed in airtight PCR tubes for ACS, while Mö ssbauer samples were placed in liquid-proof screwmountable sample holders. Minor changes in glycerol concentration are of course still possible via the absorption of minimal amounts of water vapor from the small air volumes within the sample container. However, the good agreement of literature values of comparable glycerol solutions with the dynamic viscosity of the solution illustrated in Figure 9 and previously in ref 13, determined from ACS as well as Mössbauer data, indicates otherwise, as even a small decrease in the relative glycerol content would result in a considerable decrease in the viscosity of the glycerol solution. A hydrodynamic diameter of ca. 16 ± 2 nm for sample S is in agreement with previous measurements and expectations for 6.0 nm particles and a capping thickness of ca. 5 nm. Also, a value of 33 ± 3 nm in the case of sample M shows minor deviation from theory, considering the core diameter of 14.8 nm, but may indicate minor agglomeration or aging effects. These hydrodynamic diameters can, however, not be directly cross-checked via ACS measurements, as Néel relaxation is the dominant process in sample S and M. Sample L, on the other hand, displays much lower particle mobility, corresponding to an effective diameter of ca. 68 ± 2 nm. On the basis of a core diameter of ca. 22 nm, this is proof of considerable agglomeration effects, which are more likely to take place in ferrofluids containing larger particles due to stronger magnetic dipolar interaction. The value of DH is in reasonable agreement with that determined from ACS spectra (77 nm) by accounting for a correlation between core and hydrodynamic diameters and field-dependent ACS measurements (64−90 nm). An additional finding is a minor decrease in ΔΓ upon rising field, which may reflect the blocked rotational motion described in theory by refs 42 and 43 as a minor contribution

Figure 10. Field-dependent magnetization of samples S−L measured at 240 K, normalized according to the canting angles from Mössbauer spectroscopy as explained in the text, with the inset showing the lowfield region up to 22 mT in magnification.

latter has been estimated for sample M and L by using the average canting angles θ extracted from A23 ratios of spectra recorded in an external magnetic field of 99 mT, yielding θM ≈ 29° and θL ≈ 34°. From the magnetization M given at the same field amplitude and temperature, we can determine the saturation magnetization using M = MS cos(θ), which is a valid approximation in the case of moderate canting angles. We decided to follow this approach, as IONPs of 5−25 nm, as studied here, are prone to surface spin canting, meaning that magnetization values, even recorded at highest attainable magnetic fields, can be considerably lower compared to MS. As particles in sample S are much smaller, they exhibit more pronounced surface spin frustration as well as a lower net magnetic moment. Therefore, the usage of Mössbauer spectra and magnetization data obtained at 5 T (not shown here) was required for the determination of MS following the same method. Although this approach only yields approximate results, the thereby obtained normalized magnetization curves still represent the general magnetization behavior, showing an intersection of M and L magnetization at ca. 25−30 mT, G


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purchased from Ocean NanoTech. Core diameters of sample S and M were taken from ref 13 and determined for sample L using TEM (JEOL 2200FS). Mössbauer spectra of the fluidic samples were recorded at temperatures of ca. 230−270 K, in external magnetic fields using a custom-built sample holder with an integrated Peltier cooling module.12 All measurements were performed in transmission geometry and constant acceleration mode. Magnetic fields were provided by a set of NdFeB ring magnets placed coaxially in front of and behind the cylindrical fluid sample holder, yielding field amplitudes of up to 122 mT parallel to the γ-ray propagation direction. Alternatively, an electromagnet setup (Bruker B-E10) was utilized to apply magnetic fields of up to 0.5 T in perpendicular geometry. ACS experiments were performed using two custom-built setups, combining measurements in the frequency ranges of 10 Hz to 10 kHz and 200 Hz to 1 MHz at room temperature and the AC-option of a Quantum Design MPMS-5S for lower frequencies (0.1−1500 Hz) at variable temperatures (5−300 K) for a detailed mapping of relaxation processes. To study the influence of the amplitude of the ACmagnetic field on the Brownian relaxation time, a fluxgate-based setup, originally built for measurements of the MNP dynamics in a rotating magnetic field,44 was used. This allows measurements of the AC-susceptibility between 2 Hz and 10 kHz for field strengths up to 9 mT.

consistent with the peculiar alignment behavior of larger, agglomerated particles as seen in Mössbauer spectroscopy, while sample S displays weak alignment in the low-field region. Data of samples S and M were then evaluated in the lowfield region via the Langevin equation, yielding particle magnetic moments mM(H), which are in general agreement with those from Mössbauer spectroscopy and calculated values mcalc (based on average particle core volumes from TEM analysis and MS ≈ 400 kA/m) shown in Table 1, considering a Table 1. Particle Core Diameters DC,TEM from TEM, Hydrodynamic Diameters DH,MS from Mössbauer Spectroscopy, DH,ACS from ACS Analysis (77 nm from LowField Rotation Frequency and 64−90 nm Inferred from the Agglomerate Net Magnetic Moment meff), and Magnetic Moments of Individual, Nonagglomerated Particles from Magnetometry mM(H), Mössbauer Spectroscopy mMS, and Theory Values (Excluding Effects from Spin Canting) mcalc sample DC,TEM (nm) DH,MS (nm) DH,ACS (nm) mM(H) (A m2) mMS (A m2) mcalc (A m2)

S

M

L

6.0 ± 0.5 16 ± 2

14.8 ± 1.6 33 ± 3

22.0 ± 1.9 68 ± 2 77 (64−90)

2.9 × 10−20

6.4 × 10−19 6.8 × 10−19 7.6 × 10−19

4.8 × 10−20

■

2.4 × 10−18

Corresponding Author

*E-mail: [email protected].

minor decrease in mcalc by a fraction of canted surface spins in the experimental data. Sample L, however, displays orientational behavior matching A23(H), which is not reproducible via the Langevin function with a constant magnetic moment, further substantiating the assumption of particle agglomeration.

ORCID

Joachim Landers: 0000-0002-4506-6383 Heiko Wende: 0000-0001-8395-3541 Notes

The authors declare no competing financial interest.

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CONCLUSIONS Detailed information on particle orientation, Brownian motion, and Néel relaxation was obtained simultaneously from Mössbauer spectra, usually possible only via the combination of complementary techniques, such as ACS (dynamic processes) and static magnetization measurements (orientation), while additionally enabling a precise investigation of the magnetic structure and spin canting behavior. These combined abilities are essential for the analysis of field-induced phenomena not only in ferrofluids but even more so for soft magnetic hybrid materials. In 6 nm particles, a field-driven transition from Néel-type superparamagnetism to a magnetically blocked state was observed, while the particle mobility was determined at the same time. Larger, magnetically mostly blocked particles even allow the simultaneous determination of Néel relaxation, Brownian motion, and particle orientation. Furthermore, the degree of agglomeration and surface spin canting of MNPs in the ferrofluidic samples have been extracted from field- and temperature-dependent Mössbauer spectroscopy experiments. Agglomeration in sample L, containing the largest particles, was also verified via fielddependent ACS by modeling the increase of the net magnetic moment upon rising field, yielding effective agglomerate diameters matching Mössbauer results.

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AUTHOR INFORMATION

ACKNOWLEDGMENTS We want to thank Dr. M. Heidelmann (ICAN, University of Duisburg-Essen) for performing the TEM measurements on the ferrofluid sample L. This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) within SPP1681 (WE2623/7-3, LU800/4-3), FOR 1509 (WE2623/13) and Projektnummer 278162697 − SFB 1242 (TP A5).

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REFERENCES

(1) Schmauch, M. M.; Mishra, S. R.; Evans, B. A.; Velev, O. D.; Tracy, J. B. Chained Iron Microparticles for Directionally Controlled Actuation of Soft Robots. ACS Appl. Mater. Interfaces 2017, 9, 11895− 11901. (2) Zimmermann, K.; Naletova, V. A.; Zeidis, I.; Böhm, V.; Kolev, E. Modelling of Locomotion Systems Using Deformable Magnetizable Media. J. Phys.: Condens. Matter 2006, 18, S2973−S2983. (3) Vega, J. C.; Kaufhold, T.; Böhm, V.; Becker, T.; Zimmermann, K.; Martens, M.; Schilling, M.; Gundermann, T.; Odenbach, S. FieldInduced Plasticity of Magneto-Sensitive Elastomers in Context with Soft Robotic Gripper Applications. PAMM 2017, 17, 23−26. (4) Odenbach, S. Magnetoviscous Effects in Ferrofluids; SpringerVerlag: Berlin, Heidelberg, 2002. (5) Zhou, M.; Liebert, T.; Müller, R.; Dellith, A.; Gräfe, C.; Clement, J. H.; Heinze, T. Magnetic Biocomposites for Remote Melting. Biomacromolecules 2015, 16, 2308−2315. (6) Salunkhe, A. B.; Khot, V. M.; Pawar, S. H. Magnetic Hyperthermia with Magnetic Nanoparticles: A Status Review. Curr. Top. Med. Chem. 2014, 14, 572−594.

EXPERIMENTAL SECTION

The three studied ferrofluids containing monodisperse IONPs of 6− 22 nm, capped by a shell of oleic acid and an amphiphilic polymer of d ≈ 4−5 nm thickness, dissolved in 70 vol % glycerol solution, were H


Research Article

ACS Applied Materials & Interfaces (7) Fock, J.; Hansen, M. F.; Frandsen, C.; Mørup, S. On the Interpretation of Mössbauer Spectra of Magnetic Nanoparticles. J. Magn. Magn. Mater. 2018, 445, 11−21. (8) Landers, J.; Stromberg, F.; Darbandi, M.; Schöppner, C.; Keune, W.; Wende, H. Correlation of Superparamagnetic Relaxation with Magnetic Dipole Interaction in Capped Iron-Oxide Nanoparticles. J. Phys.: Condens. Matter 2014, 27, 026002. (9) Keller, H.; Kündig, W. Mössbauer Studies of Brownian Motion. Solid State Commun. 1975, 16, 253−256. (10) Fornal, P.; Stanek, J. Mobility of Hematite Submicron Particles in Water Solutions of Sugar. Acta Phys. Pol., A 2008, 114, 1667−1673. (11) Plachinda, A. S.; Sedov, V. E.; Khromov, V. I.; Suzdalev, I. P.; Goldanskii, V. I.; Nienhaus, G. U.; Parak, F. Mössbauer Studies of Bound Diffusion in a Model Polymer System. Phys. Rev. B: Condens. Matter Mater. Phys. 1992, 45, 7716−7723. (12) Landers, J.; Roeder, L.; Salamon, S.; Schmidt, A. M.; Wende, H. Particle-Matrix Interaction in Cross-Linked PAAm-Hydrogels Analyzed by Mössbauer Spectroscopy. J. Phys. Chem. C 2015, 119, 20642−20648. (13) Landers, J.; Salamon, S.; Remmer, H.; Ludwig, F.; Wende, H. Simultaneous Study of Brownian and Néel Relaxation Phenomena in Ferrofluids by Mössbauer Spectroscopy. Nano Lett. 2016, 16, 1150− 1155. (14) Mørup, S.; Hansen, M. F.; Frandsen, C. Comprehensive Nanoscience and Technology; Academic Press, 2011; Vol. 1, pp 437− 491. (15) Segur, J. B.; Oberstar, H. E. Viscosity of Glycerol and its Aqueous Solutions. Ind. Eng. Chem. 1951, 43, 2117−2120. (16) Schröter, K.; Donth, E. Viscosity and Shear Response at the Dynamic Glass Transition of Glycerol. J. Chem. Phys. 2000, 113, 9101−9108. (17) González, J. A. T.; Longiotti, M. P.; Corti, H. R. The Viscosity of Glycerol-Water Mixtures Including the Supercooled Region. J. Chem. Eng. Data 2011, 56, 1397−1406. (18) Bachler, J.; Fuentes-Landete, V.; Jahn, D. A.; Wong, J.; Giovambattista, N.; Loerting, T. Glass Polymorphism in GlycerolWater Mixtures: II. Experimental Studies. Phys. Chem. Chem. Phys. 2016, 18, 11058−11068. (19) Néel, L. Théorie du Traı̂nage Magnétique des Ferromagnétiques en Grains Fins avec Applications aux Terres Cuites. Ann. Geophys. 1949, 5, 99−136. (20) Demortière, A.; Panissod, P.; Pichon, B. P.; Pourroy, G.; Guillon, D.; Donnio, B.; Bégin-Colin, S. Size-dependent properties of magnetic iron oxide nanocrystals. Nanoscale 2011, 3, 225. (21) Takei, H.; Chiba, S. Vacancy Ordering in Epitaxially-Grown Single Crystals of γ-Fe2O3. J. Phys. Soc. Jpn. 1966, 21, 1255−1263. (22) Ludwig, F.; Balceris, C.; Jonasson, C.; Johansson, C. Analysis of AC Susceptibility Spectra for the Characterization of Magnetic Nanoparticles. IEEE Trans. Magn. 2017, 53, 6100904. (23) Fock, J.; Balceris, C.; Costo, R.; Zeng, L.; Ludwig, F.; Hansen, M. F. Field-Dependent Dynamic Responses from Dilute Magnetic Nanoparticle Dispersions. Nanoscale 2018, 10, 2052−2066. (24) Havriliak, S.; Negami, S. A Complex Plane Representation of Dielectric and Mechanical Relaxation Processes in Some Polymers. Polymer 1967, 8, 161−210. (25) Dieckhoff, J.; Eberbeck, D.; Schilling, M.; Ludwig, F. Magneticfield dependence of Brownian and Néel relaxation times. J. Appl. Phys. 2016, 119, 043903. (26) Remmer, H.; Gratz, M.; Tschope, A.; Ludwig, F. Magnetic Field Dependence of Ni Nanorod Brownian Relaxation. IEEE Trans. Magn. 2017, 53, 1−4. (27) Yoshida, T.; Enpuku, K. Simulation and Quantitative Clarification of AC Susceptibility of Magnetic Fluid in Nonlinear Brownian Relaxation Region. Jpn. J. Appl. Phys. 2009, 48, 127002. (28) Ludwig, F.; Eberbeck, D.; Löwa, N.; Steinhoff, U.; Wawrzik, T.; Schilling, M.; Trahms, L. Characterization of Magnetic Nanoparticle Systems with Respect to their Magnetic Particle Imaging Performance. Biomed. Tech. 2013, 58, 535−545.

(29) Schaller, V.; Wahnström, G.; Sanz-Velasco, A.; Gustafsson, S.; Olsson, E.; Enoksson, P.; Johansson, C. Effective Magnetic Moment of Magnetic Multicore Nanoparticles. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 80, 092406. (30) Roca, A. G.; Marco, J. F.; Morales, M. d. P.; Serna, C. J. Effect of Nature and Particle Size on Properties of Uniform Magnetite and Maghemite Nanoparticles. J. Phys. Chem. C 2007, 111, 18577−18584. (31) Winkler, H.; Heinrich, H.-J.; Gerdau, E. Relaxation Phenomena in Ferrofluids. J. Phys., Colloq. 1976, 37, 261−267. (32) von, U. Hö rsten Pi Program Package. www.unidue.de/ hm236ap/hoersten/home.html (accessed Nov 20, 2017). (33) Jones, D. H.; Srivastava, K. K. P. Many-state relaxation model for the Mössbauer spectra of superparamagnets. Phys. Rev. B: Condens. Matter Mater. Phys. 1986, 34, 7542. (34) da Costa, G. M.; De Grave, E.; Vandenberghe, R. E. Mössbauer studies of magnetite and Al-substituted maghemites. Hyperfine Interact. 1998, 117, 207−243. (35) Nedkov, I. Nanosized magnetite for biomedical applications. J. Optoelectron. Adv. Mater. 2007, 9, 24−29. (36) Singwi, K. S.; Sjölander, A. Resonance Absorption of Nuclear Gamma Rays and the Dynamics of Atomic Motions. Phys. Rev. 1960, 120, 1093−1102. (37) Kachkachi, H.; Ezzir, A.; Noguès, M.; Tronc, E. Surface effects in nanoparticles: application to maghemite γ-Fe2O3. Eur. Phys. J. B 2000, 14, 681−689. (38) Tronc, E.; Prené, P.; Jolivet, J. P.; Dormann, J. L.; Grenèche, J. M. Spin Canting in γ-Fe2O3 Nanoparticles. Hyperfine Interact. 1998, 112, 97−100. (39) Shendruk, T. N.; Desautels, R. D.; Southern, B. W.; van Lierop, J. The effect of surface spin disorder on the magnetism of γ-Fe2O3 nanoparticle dispersions. Nanotechnology 2007, 18, 455704. (40) Cullity, B. D.; Graham, C. D. Introduction to Magnetic Materials, 2nd ed.; John Wiley & Sons, Inc.: Hoboken, New Jersey, 2009; p 183. (41) Green, E.; Parke, J. P. Density and Viscosity of Glycerol Solutions at Low Temperatures. J. Soc. Chem. Ind. 1939, 58, 319−320. (42) Heilmann, I.; Olsen, B.; Jensen, J. H. Non-Lorentzian Diffusion-Broadened Mössbauer Lines. J. Phys. C: Solid State Phys. 1974, 7, 4355−4360. (43) Afanas’ev, A. M.; Hendriksen, P. V.; Mørup, S. Influence of Rotational Diffusion of the Mössbauer Spectrum of Ultrafine Particles in a Supercooled Liquid. Hyperfine Interact. 1994, 88, 35−48. (44) Dieckhoff, J.; Schilling, M.; Ludwig, F. Fluxgate Based Detection of Magnetic Nanoparticle Dynamics in a Rotating Magnetic Field. Appl. Phys. Lett. 2011, 99, 112501.

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Dynamics of Ferrofluids Studied by MÃ¶ssbauer Spectroscopy

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