Fabrication of spherical CoFe₂O₄ nanoparticles via sol–gel and hydrothermal methods and investigation of their magnetorheological characteristics

Abstract

CoFe₂O₄ nanoparticles are synthesized through sol–gel and facile hydrothermal methods, and their magnetorheological (MR) characteristics are evaluated. X-ray diffraction results indicate the formation of single phase CoFe₂O₄ after the prepared samples were sintered at 550 °C for 2 h, which was further confirmed by DSC, TG and FT-IR analysis. TEM results exhibit a narrow particle size distribution in the range of 5–40 nm with an average size of 21 nm for the samples prepared via the hydrothermal method. On the other hand, the particle size distribution was in the range of 15–120 nm and an average size of 42 nm was obtained via the sol–gel method. To prepare an MR fluid, CoFe₂O₄ nanoparticles were added to a micron-sized soft magnetic carbonyl iron (CI)-based suspension and MR effects were measured via rotational tests under different magnetic field strengths. The results reveal that the CoFe₂O₄–CI-based MR fluids present a higher yield stress with an enhanced MR effect compared to the CI-based MR fluid due to increased magnetic properties. This suggests that the CoFe₂O₄ nanoparticles fill the cavities of micron-sized CI particles and form chain-like structures, which orient in the direction of the applied magnetic field. On the other hand, depending on the employed synthetic route, the obtained results display slightly higher stress behaviors in the samples prepared via the hydrothermal method. The sedimentation ratio was also evaluated to further confirm the effects of the nanoparticle additive.

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1. Introduction

The spinel ferrite structure, which has the general chemical formula MFe₂O₄ (M = Co, Ni, Zn, or other divalent metals), is characterized as a cubic, closely packed arrangement of oxygen atoms, and M²⁺ and Fe³⁺ ions occupy either tetrahedral (A) or octahedral (B) sites.¹ Nano-sized particles of spinel ferrites have been the focus of extensive research primarily due to the fact that most technological and medical applications require nanoparticles with small sizes and narrow size distributions, which subsequently result in uniform physical and chemical properties. Indeed, small sized particles with a large surface-to-volume ratio result in distinct magnetic properties which are different from those of their bulk counterparts.^2–5

Among the spinel ferrites, cobalt ferrite, CoFe₂O₄ is particularly interesting due to its high cubic magnetocrystalline anisotropy, moderate saturation magnetization (M_s), high coercivity (H_c), high Curie temperature (T_c) of about 793 K, strong anisotropy along with good mechanical hardness and chemical stability. Such properties make CoFe₂O₄ a superior candidate for recording media applications.^5–7 Furthermore, it is widely used in electronic devices, ferrofluids, magnetic delivery microwave devices and high density information storage,^6,8,9 and is also known as a photomagnetic material which displays an interesting light-induced coercivity change.¹⁰

CoFe₂O₄ has an inverse spinel structure in the ideal state, in which all Co²⁺ ions are in B sites and Fe³⁺ ions are equally distributed between A and B sites. Its magnetic characteristics are strongly dependent on its particles size, shape, and purity, which are influenced by chemical composition and microstructural characteristic and can be controlled by fabrication and synthesis processes.^1,9,11,12 Various preparation techniques, such as sol–gel, microemulsion, hot spraying, evaporation condensation, matrix isolation, laser-induced vapor phase reaction, aerosol, coprecipitation, hydrothermal, and solid state routes are employed to prepare cobalt ferrite nanoparticles.^6–13

Magnetorheological (MR) fluids are known to be colloidal suspensions of magnetizable particles dispersed in a nonmagnetic fluid, such as mineral oils, and are capable of being solid-like under an applied magnetic field, thus display non-Newtonian behavior. On the other hand, they present liquid-like behavior by the removal of the magnetic field, which is characteristic of the Newtonian behavior.^14–16 The rheological characteristics of MR fluids, such as yield stress and shear viscosity, can be reversibly altered quickly as a consequence of dispersed magnetizable particles building a chain-like structure under an applied magnetic field due to magnetic dipole–dipole interaction between particles. This phenomenon has great potential in the design of diverse high performance engineering products including MR polishing equipment, torque transducers and active damper systems.^17–19 Generally, low apparent viscosity and high yield stress in the absence of a magnetic field as well as good durability and stability have become key factors for the application of MR fluids.

Among the wide range of magnetic materials, carbonyl iron (CI) particles have been adopted as a superior candidate for MR fluids due to their high permeability, low coercivity and high saturation magnetization, as well as appropriate particle size.^19–21 On the other hand, the large density mismatch between CI particles and carrier fluids results in the serious drawback of sedimentation. Therefore, many strategies have been employed to address this issue.^17,19,20 Examples of these strategies include the addition of nanoparticles, introduction of bidispersed particles into MR fluids,^15,16 and coating the surface of magnetic CI particles with shell materials such as inorganic polymers.^22,23 On the other hand, the coating method was found to be a complex process which makes it very challenging to commercialize. In fact, the coating thickness is remarkably influenced by reaction time in the case of polymers or the molar ratio among reactive agents, and temperature.²³ Hence, the inclusion of nanoparticles as an additive to CI-based MR suspensions is primarily considered. Several types of nano-sized additives, including carbon nanotubes and carbon fibers, Fe₃O₄, Fe₂O₃, fumed silica, CI and clays, have been added to MR suspensions to improve their rheological properties and the dispersion stability of heavy magnetizable particles.^{15,19,20,21,24} Since non-magnetic particles have negative effects on rheological behavior, e.g. decreasing the relative effect of the MR fluid, the inclusion of additives with nanoscale particles is recommended. In this work, CoF₂O₄ nanoparticles were synthesized by sol–gel and hydrothermal methods and subsequently added to a micron-sized CI-based MR fluid to improve its yield stress. The rheological features of the MR fluids under various applied magnetic fields were evaluated using a rotational rheometer with a parallel-plate measuring cell. The flow and yield behaviors were measured from steady-state experiments and their improvements compared.

2. Experimental

To prepare cobalt ferrite nanoparticles, stoichiometric molar amounts of cobalt(II) nitrate hexahydrate [Co(NO₃)₂·6H₂O], iron(III) nitrate nonahydrate [Fe(NO₃)·9H₂O₂] and citric acid (C₆H₈O₇) were mixed in 20 mL of distilled water. The mixture was stirred with a magnetic stirrer until the reactants were dissolved completely. In the sol–gel method, the prepared solution was place in a beaker, whereas the prepared mixture in the hydrothermal method was placed in an autoclave. Subsequently, both samples were left in an oven at 150 °C for 24 h and allowed to cool down to room temperature. Then, the samples were placed in an oven at 120 °C for 24 h in order to get dried powders. Finally, to establish the formation of a single phase, the obtained powders were sintered at 550 °C for 2 h at a constant heating rate of 10 °C min⁻¹.

Phase transformation and structural changes were evaluated by X-ray diffraction (XRD) in a Philips X' PERT MPD diffractometer using filtered Cu Kα radiation (λ = 0.15406 nm).

The morphological changes of the samples were characterized by field emission scanning electron microscopy (FESEM) equipped with energy-dispersive X-ray spectroscopy (EDX) using an FEI NOVA NanoSEM 230 machine. Transmission electron microscopy (TEM) analysis of the samples was carried out using a Hitachi 7100 TEM (Tokyo Japan).

A vibrating sample magnetometer (VSM; lakeshore 7404) was used to study the magnetic properties of the samples at room temperature. The B–H hysteresis loop of the bulk samples was studied using a MATS-2010SD Static Hysteresisgraph.

The precursors of the samples were subjected to thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) analysis between 25 °C and 1000 °C using a TGA/SDTA 51E/LR1600/MT5/347 in static air atmosphere, and heating rate of 5 °C per minute.

To prepare 15 mL of MR fluid, CI particles with the average particles size of 4 μm and density of about 7.87 g cm⁻³ were procured from BASF with an OM series. Polyalphaolefin (PAO) oil (density: 0.81 g mL⁻³) and oleic acid (density: 0.9 g mL⁻³) were supplied by R&M and used as carrier fluid and surfactant, respectively. Three types of MR fluids were prepared: without additives, including 30 wt% CI particles + 70 wt% carrier fluid, and surfactant. Other MR fluids were prepared by 1 wt% CoFe₂O₄ nanoparticles additive, which were produced by the two different routes of sol–gel and hydrothermal, considering 1 wt%-CoFe₂O₄–CI-based MR fluids.

MR characteristics were measured using a rotational rheometer (MCR 302 Anton Paar) with an MR instrument (MRD 70 Anton Paar), which generates a homogeneous magnetic field. The parallel-plate configuration with a diameter of 20 mm at a gap of 1 mm was employed. The magnetic field from 100 mT to 700 mT with 100 mT increments in the perpendicular direction to the flow was set to evaluate the rheological properties at 25 °C.

3. Results and discussion

The TG/DSC curves of the precursors are shown in Fig. 1. Four stages of weight loss are observed in the TG curve for the samples prepared by the hydrothermal method. The first thermal event at a temperature below 190 °C, with the mass loss of 10.50%, is attributed to the loss of water molecules, which is determined by the small endothermic peak in the DSC curve. The second stage in the range of 195–220 °C in the TG curve, with a mass loss of 8.67%, is due to spontaneous combustion induced by interactions of the nitrate ions in the solution. This behavior is supported by an exothermic event in the DSC analysis. The third stage in the TG curve, in the temperature range of 220–275 °C, with a mass loss of 2.87%, results from the chain decomposition of the components. The fourth stage in the temperature range of 275–365 °C, with the mass loss of 1.63% is due to the loss of structural water and the further thermal decomposition of residual compounds and onset of the crystallization process. After that, the mass change is negligible with a further increase in temperature up to 1000 °C, which signifies the completion of the crystallization process, and is accompanied by a large exothermic peak in the DSC curve. This suggests that single phase CoFe₂O₄ forms at a temperature above 400 °C. An approximately similar trend was observed in the TG curve of the samples prepared by the sol–gel method, except that a discrepancy in the maximum weight loss of about 10.69% occurs in the range of 220–270 °C (third stage). This indicates that the gel decomposition needs more energy than that of samples prepared by the hydrothermal route. This is why the weight loss was about 5.30, 3.08 and 1.28% in the first, second and last stages, respectively. The corresponding DSC curve, however, represents a desired phase formation after 400 °C, and the exothermic peak observed is not as noticeable as the exothermic peak observed in the sample prepared by the hydrothermal route.

Fig. 1 DSC and TG traces of the samples prepared by (a) hydrothermal, and (b) sol–gel methods.

The XRD patterns of the samples prepared by the sol–gel and hydrothermal methods as well as samples sintered at 550 °C are shown in Fig. 2. Before the sintering process, however, the CoFe₂O₄ phase was formed in both cases. The presence of a small amount of Fe₂O₃ and Co₃O₄ phases indicates that the reaction was not completed and an external source of thermal energy, i.e. heating, needs to be provided. These phases can be indexed to JCPDS cards of 01-079-1741 for Fe₂O₃ and 01-076-1802 for Co₃O₄. After sintering at 550 °C, single phase CoFe₂O₄ was formed for both methods and no undesirable second phase was detected. Based on the XRD diffractograms various diffraction peaks appeared at different planes of (1 1 1), (2 2 0), (3 1 1), (2 2 2), (4 0 0), (4 2 2), (5 1 1), and (4 4 0). It is evident that all the diffraction peaks are either all even or all odd which signify that the samples are spinel in phase. The average crystallite size was calculated by employing the Debye–Scherrer equation and the procedure utilized in ref. 24. The average crystallite size was found to be about 13 nm in the samples prepared by the hydrothermal and 22 nm in the samples prepared by the sol–gel method after sintering at 550 °C. The crystallite growth activation energy (Q) for both samples was evaluated using the Scott equation as follows:

D = C exp(−Q/RT) (1)

where, D is the average crystallite size, R is the ideal gas constant, T is the absolute temperature and C is a constant that is equal to 177.67.⁴ The values of activation energy were found to be around 17.892 and 14.293 kJ mol⁻¹, respectively for the samples prepared by the hydrothermal and sol–gel methods. These values are in agreement with the equation, thus indicating a lower activation energy with the crystallite growth. This simply means that the crystallite growth rate is higher in the samples prepared by sol–gel. Furthermore, the diffusion kinetics sequence can be identified as: through the surface area > grain boundary > volume (lattice)^4,25 by assuming the identical sintering conditions for both samples. It can be expressed that for the CoFe₂O₄ samples prepared by the sol–gel route the diffusion coefficient is higher due to the inverse proportion with Q according to

d = d₀ exp(−Q/RT) (2)

where, d is the diffusion coefficient and d₀ is the constant, On the other hand, the lower values of Q for both the samples indicate that the crystallite growth primarily takes place through an interfacial reaction and surface area.

Fig. 2 XRD patterns of the samples prepared by (a) hydrothermal, (b) sol–gel, (c) hydrothermal and sintered at 550 °C and (d) sol–gel and sintered at 550 °C.

The lattice parameter of CoFe₂O₄ synthesized through hydrothermal and sol–gel methods are estimated to be a = b = c = 0.84172 ± 0.00261 nm and 0.84034 ± 0.00351, respectively. The lattice parameters of the ferrite nanocrystals synthesized by both methods are in agreement with the previously reported values of 0.8445 (ref. 6) and 8.3971 nm.^10,13 These values were found to be larger than the reported value of 0.83390 nm for the bulk CoFe₂O₄ materials. This reveals the expansion of the lattice as the size of the CoFe₂O₄ particles is reduced. These values also indicate that the structural characteristics depend on the employed synthetic method. X-ray density and measured density were found to be about 5.23 and 2.91 g cm⁻³, respectively, for the sample prepared by the hydrothermal method. These values were about 5.09 and 2.93 g cm⁻³, respectively, for the sample prepared by sol–gel.

FESEM images of the cobalt ferrite samples (before and after sintering) are shown in Fig. 3. These images indicate that there is no certain border between particles in the case of before sintering for both types of the samples. This means that particles stick together and become agglomerated. This condition is more evident in the samples prepared by the sol–gel method (Fig. 3a) compared to the sample prepared via the hydrothermal method (Fig. 3c). During the sintering process, the particle shape becomes almost spherical and they make contact to their adjacent particles via neck formation. Indeed, the sintering at 550 °C gives rise to the rearrangement of the particles and concave neck formation in the contact point of particles. The bonds created between particles lead to matter transport. This results in increments of crystallinity, which is further manifested by the noticeable increase in the XRD patterns peaks intensity. Comparison of the FESEM images revealed that the samples prepared by the hydrothermal method have a smaller particle size which is confirmed by the TEM images (Fig. 4).

Fig. 3 FESEM images of the prepared samples by (a) sol–gel, (b) sol–gel and sintered at 550 °C, (c) hydrothermal, and (d) hydrothermal and sintered at 550 °C.

Fig. 4 TEM images of the prepared samples by (a) sol–gel, (b) sol–gel and sintered at 550 °C, (c) hydrothermal, and (d) hydrothermal and sintered at 550 °C.

TEM images revealed that the samples prepared by the hydrothermal method have a particle size distribution in the range of 5–40 nm with the average size of 21 nm. In contrast, the particle size ranged between 15–120 nm with the average size of 42 nm in the sol–gel method. The images also exhibit that the particles do not have a regular shape. This is because of either particle agglomeration or magnetic behavior of the particles (particle attraction) which increases by employing the sintering process.

EDX measurement from different points (as exemplified in Fig. 3b and d) exhibited all the expected elements including Fe, Co and O in the spectra of both samples (Fig. 5). No impurities were introduced in the products. The presence of C atoms may also be a result of the carbon-coating for FESEM measurement which was applied prior to the EDX measurement.

Fig. 5 EDX spectra of the (a) sol–gel and sintered at 550 °C, and (b) hydrothermal and sintered at 550 °C samples.

Room temperature M–H and B–H hysteresis loop curves for the sintered samples are shown in Fig. 6. Their magnetic behavior values i.e. saturation magnetization (M_s), coercivity (H_c) and retentivity (M_r) are represented in Table 1. The samples prepared by the hydrothermal method have higher M_s, H_c and M_r compared to the other method. If this phenomenon is examined in terms of particle size, it is expected that the larger particles possess higher magnetic properties. In other words, the samples prepared by the sol–gel method possess higher M_s, which is in contradiction with the experimental results. In fact, once the particles become bigger, the number of particle sizes exceeding the single-domain-to-multi-domain critical particle size also increases. Therefore, the number of domain walls increases and thus the contribution of the domain wall movement to ease of magnetization, which requires a lower energy than domain rotation, increases.^1,25 Thus, it can be concluded that the lower value of M_s (about 24 emu g⁻¹) obtained for the sample prepared by the sol–gel method with larger particles size compared to the other method (M_s: about 52 emu g⁻¹) is associated with the large amount of amorphous phases formed, which result in lowering the magnetic properties. Furthermore, the represented data in Table 1 indicate that the M_s, M_r and H_c values are not symmetrical in the sample prepared by the sol–gel method. This indicates a canted spin arrangement and non-equilibrium cation distribution in the particles, which results in a lower M_s and higher H_c. Indeed, CoFe₂O₄, with a partially inverse spinel structure, is considered by the general formula (Fe³⁺_x1, Co²⁺_x2, M²⁺_x3)[Fe³⁺_y1, Co²⁺_y2, M²⁺_y3], where x₁, x₂, x₃ and y₁, y₂, y₃ are the normalized concentrations for the A- and B-sites, respectively, and x₁ + x₂ + x₃ = 1, y₁ + y₂ + y₃ = 1.⁸ By considering the Bohr magneton (μ_B) for Fe³⁺ and Co²⁺ to be 5 and 3 μ_B, respectively, and also that the magnetic moments are not affected by non-magnetic atoms or vacancies (0 μ_B), the cation distribution can be written as: (Co_0.828Fe_0.570)[Co_0.172Fe_1.43] and (Co_0.622Fe_0.055)[Co_0.378Fe_1.945] for the samples prepared by the sol–gel and hydrothermal methods, respectively. On the other hand, the spin disorder in nanoparticles is due to broken exchange bonds in the near-surface layers and magnetocrystalline anisotropy.^3,26 It has been stated that the reduction of saturation magnetization of nano-sized ferrites by considering a spin configuration differs from the Neel type observed in large particles.²⁶ In fact, the spins are canted at the surface of the nanoparticles; i.e., the ions in the surface layer are inclined at different angles with respect to the direction of the net moment. In this state, particle magnetization cannot be observed as uniform through the nanoparticle, which is the result of a magnetic ordered core and surrounding surface shell of disordered spins.²⁶

Fig. 6 Room temperature (a) M–H, and (b) B–H hysteresis loops for CoFe₂O₄ nanoparticles.

Table 1 Magnetic behaviour of the samples prepred by sol–gel and hydrothermal methods

Property	Sol–gel method		Hydrothermal method
	Positive side	Negative side	Positive side	Negative side
Ms (emu g^−1)	24.58	22.77	52.00	51.98
Mr (emu g^−1)	4.88	5.22	22.44	22.43
Hc (G)	262.74	294.69	1114.6	1117.6

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The remanent to the saturation magnetization (R = M_r/M_s) values for the samples prepared by the sol–gel and hydrothermal were found to be 0.198 and 0.431, respectively. This indicates that the particles interact by magnetostatic interactions (R < 0.5) for both samples. This is why the exchange-couple exists when R > 0.5 and for R = 0, the randomly oriented non-interacting particles undergo coherent rotations.²⁷ Furthermore, from the values of R, it can be concluded that the samples should be subjected to higher sintering temperatures so that particle aggregation will start to dominate. This gives rise to the rapid formation of grain boundaries which greatly affect the exchange coupling interactions.

Different values of coercivity and saturation magnetization have been reported elsewhere as well.^27,28 In fact, the magnetic behavior is strongly dependent on the average particle size, which is induced from the preparation methods employed.

On the other hand, the higher value of H_c in the sample prepared by the hydrothermal method can be explained in terms of the average particle size; H_c ∝ 1/d, where d is the average particle size. It is believed that grain boundaries are the key factors contributing to H_c in the case of large-grained polycrystalline nanomaterials (d > L_exch). Thus, fine-grained magnetic materials are often magnetically harder than coarse-grained materials with identical compositions. Consequently, H_c had a tendency to increase as the particle size decreases, according to the well-accepted 1/d law.^29,30

The B–H hysteresis loop (Fig. 6b), which is obtained from a toroidal-shape sample with inner and outer diameters of 10 and 20 mm, respectively, confirms the M–H results. It indicates a well-defined sigmoid-shape hysteresis loop for the sample prepared by the hydrothermal method, which suggests strong ferromagnetic behavior. This is why a narrowly bulging but linear-looking loop with a low saturation induction, B_s, suggests a small amount of ferromagnetic phase. Its significant coercivity with somewhat elongated shape is due to necking (shape anisotropy).

To further study the single-phase CoFe₂O₄ features and chemical bands, FT-IR spectroscopy was carried out (Fig. 7). Waldron identified the continuously bonded crystals in the ferrite structure³¹ and they involve two octahedral (O-band) and tetrahedral (T-band) sub-lattices, which are attributed to the intrinsic vibration of divalent cations.³¹ The absorption bands of solids at 100–1000 cm⁻¹ are often attributed to the ion vibrations in the crystal lattice.^32–34

Fig. 7 FT-IR spectra of the Co ferrite samples.

The oxide absorption bands are often observed in the range of 400–1100 cm⁻¹. For example, the stretching vibration bands of Zn–O, Ni–O and Fe–O are detected in the range of 450–700, 400–500 and 900–1000 cm⁻¹, respectively.^32–34 In the case of cobalt ferrite, the bands at around 400 cm⁻¹ are assigned to the vibration modes of octahedral groups (Fe³⁺–O²⁻), whereas bands at around 600 cm⁻¹ belong to the stretching vibrations of tetrahedral groups (Fe³⁺–O²⁻).³⁵ The FT-IR spectra show that these bands are at 555.60 and 460.98 cm⁻¹, respectively, for the sample prepared by the hydrothermal method and at 541.92 and 458.29 cm⁻¹, respectively, for the sample prepared by sol–gel. However, these bands shift to 563.92 and 459.72 cm⁻¹, and 573.31 and 463.20 cm⁻¹, respectively, after sintering at 550 °C (refer to inset in Fig. 7). These variations in the absorption bands can be associated with particle growth and release of internal lattice strain with the sintering process, which result in a variation in the cation distribution and consequently in the T- and O-bands positions in the FT-IR spectra.³⁶ It was noticeable that CoFe₂O₄ prepared by the sol–gel method shows a decrease in the intensity for the tetrahedral absorption band as compared to the sample prepared by the hydrothermal route. This indicates that the intensity of the absorption bands depends largely on the cation substitution and synthesis route. A change in bond length with the internuclear distance (dμ/dr) largely affects this intensity ratio. Thus, the ionic Fe–O bond length has a greater contribution based on its dipole moments. The Fe–O bond length depends normally on the synthetic method. The two absorption bands observed at around 1370 and 1600 cm⁻¹ are associated with hydrocarbonal impurities in the raw materials and moisture absorbed through the powders when exposed to ambient air.²⁴

In order to design MR devices and to predict how they work, one should recognize the specific relation between shear stress (τ) and shear rate ([small gamma, Greek, dot above]) in the flow curves of MR fluids.¹⁶ One of the most widely used models to describe the MR fluid flow curve behavior is the Bingham model,³⁷ in which the dynamic yield stress (τ_y) for each flow curve is extracted from interpolation at zero shear rate.³⁸ The shear stress versus shear rate ([small gamma, Greek, dot above]) for the CI-based and CoFe₂O₄–CI-based suspensions is shown in Fig. 8. The concentration of CI was 70 wt% in all the systems, and that of the CoF₂O₄ nanoparticles additives was considered to be 1 wt% with regards to the suspending medium. The externally applied magnetic field strength ranged from 0 to 700 mT with 100 mT increments, which is evident in all systems that display non-Newtonian behavior in the absence of a magnetic field. This phenomenon is associated with the remnant magnetization of magnetic particles.¹⁹ Furthermore, comparison of the flow curves (Fig. 8) indicates that the MR effect increases with the inclusion of nano-sized additives in the CI-based MR suspensions. For instance, the shear stress value of the CI-based MR fluids increased from 0.3822 Pa to 1.7616 Pa for the CoFe₂O₄–CI-based MR fluids, in which, the CoFe₂O₄ nanoparticles were prepared by the hydrothermal method. This value was 0.8212 Pa for the MR fluids, in which the CoFe₂O₄ nanoparticles were synthesized by sol–gel. This discrepancy in MR effect can be associated with the strong chain-like structure formed in the presence of nanoparticles additives. Moreover, the type, size and shape of these nano additives also affect the chain-like structure formation mechanism and consequently influence the MR effect in the samples prepared by different methods.³⁸

Fig. 8 Flow curves for (a) CI-based MR fluid, (b) CoFe₂O₄–CI-based MR fluid (additive prepared by sol–gel method), and (c) CoFe₂O₄–CI-based MR fluid (additive prepared by hydrothermal method) under different magnetic field strengths.

On the other hand, in the presence of a magnetic field, both the CI-based MR fluid and 1 wt% CoFe₂O₄–CI-based MR fluids exhibited typical Bingham plastic behavior. This is attributed the strong and robust chain-like structure formed by the magnetic particles in the carrier fluid, as schematically illustrated and shown in Fig. 9. Indeed, the magnetizable particles are randomly distributed in the carrier fluid in the absence of a magnetic field, however they orientate in direction of the applied magnetic field and form a chain-like structure under an applied magnetic field.^{14,19,23,39,40} The degree of variation in the MR effect is mostly affected by the formed structure, in which it is strongly dependent on the strength of the applied magnetic field, volume fraction of magnetic particles and some other physical behaviors.^15,16 Patel reported that the formation of the chain-like structure in the presence of nanoparticles is quite different from that of conventional MR fluids.³⁹ This is because the additive nanoparticles (CoFe₂O₄ nanoparticles) fill the structural microcavities produced due to the association of large magnetic particles (CI particles) (Fig. 9b). Furthermore, the introduction of nano-sized additive particles restricts the aggregation of the micron-sized CI particles, which gives rise to field induced phase separation in the MR fluid. Hence, the CoFe₂O₄–CI-based MR fluids are more stable than the CI-based MR fluid and therefore more favorable for engineering applications. On the other hand, the size and shape of the nanoparticles, which were synthesized by two different methods, strongly affect the MR effect of the CoFe₂O₄–CI-based MR fluids, which have a 55 638 and 43 921 Pa shear stress at an applied magnetic field of 700 mT for the samples prepared by the hydrothermal and sol–gel methods, respectively (refer to Fig. 8). This confirms the utilized synthesis method-dependent MR effect of the samples due to the variation in size and shape of the nanoparticles. Thus, this would cause a chain-like structure to form by different mechanisms in the MR suspensions.³⁸

Fig. 9 Schematic of chain formation of micron-sized CI-based and CoFe₂O₄–CI-based MR fluids.

It is believed that there are two possible ways that the small particles can attach to the large particles and form the chain-like structures in the carrier fluid in the presence of a magnetic field.^39,41 The first way is by movement in the transverse direction perpendicular to the chain axis and being trapped at the triangular position constructed by two connecting large particles. The second way is that the small particles may attach to the end of the chain made by large particles. Once the dipole moment of the small particle orients parallel to the chain axis produced by the large particles, the maximum attractive energy is achieved, however this energy is not stronger than kT in the first state.^39,41

Consequently, the chain-like structures formed in any case would prevent fluid movement and accordingly enhance the suspension viscosity. The mechanical energy needed to overcome these structures is enhanced with an increase in the applied magnetic field strength.¹⁷ Once the shear rate exceeds a critical value, the chain-like structures break down and thereby the fluid starts to flow. The stress which the MR fluid sustains at this intense shear rate is considered as the MR fluid's apparent yield stress.¹⁶ It simply means that the yield stress is the maximum stress which can be applied before the MR fluid starts to flow, which is a function of the magnetic field strength¹⁸ and gives rise to an increase in viscoelasticity behavior.⁴² Yield stress is an important factor in the industrial applications of MR fluids, which varies between 10 and 100 kPa in a specific magnetic field range.¹⁸ This is normally dependent on factors such as particle interaction and formation of agglomerates,²⁹ strength of the applied magnetic field,¹⁶ particle volume fraction, and particle size, shape and distribution.^15,16 Thus far, several models have been proposed to describe the yield stress dependency with these factors.^38,43,44,45 All of them generally originate from the “polarization model”, which is associated with the attractive force between particles to Maxwell–Wagner's interfacial polarization, and use the point-dipole approximation.^38,43 With respect to this, the yield stress (τ_y) is given as:

τ_y ∝ ∅K_fE₀²f(β) (3)

where, E₀, β and ∅ are parameters related to the applied electric field, the dielectric permittivity of a MR fluid and the volume fraction of magnetic particles, respectively. This polarization model is in good accordance with the data for a small E₀ and volume fraction of particles.^38,44 Hence, τ_y deviates noticeably from eqn (3) at high E₀, and the power law (τ_y ∝ E₀^m; m < 2) is a good model for the explanation of τ_y of ER fluids.^43,44 By assuming similarity between ER and MR fluids, these evaluations are also valid for MR fluids. In fact, at a low magnetic field (H₀), τ_y is proportional to H², due to the magnetic polarization of the magnetized particles. On the other hand, at high H₀, τ_y is proportional to H^3/2, due to the local saturation magnetization of the magnetic particles at high applied fields. Thus, τ_y is expressed by:^20,38where, μ₀ is the free space permeability and M_s is the saturation magnetization at the maximum applied field. Furthermore, at H₀, the magnetic field is enough to obtain M_s in all the magnetic particles so that the τ_y and modulus do not respond to an externally applied magnetic field. Thus, it can be concluded that there is a critical value of H₀ that divides the τ_y into two regimes; H > H_c where τ_y ∝ H² and H < H_c, where τ_y ∝ H^3/2.^20,38 In order to quantify the τ_y data for a wide electric field strength range, a simple equation is introduced as follows:where, α is dependent on ∅ and β, which were described above. E_c is the critical electric field induced from the nonlinear conductivity model, and is descriptive for crossover behavior and defines (or links) the two regimes in the E₀ versus τ_y plot. This equation has two limiting traits at low and high electric field intensity, which are respectively given as follows:

τ_y = αE₀² ∝ E₀², E₀ ≪ E_c (6)

These equations confirm the above-mentioned relationships between τ_y and E₀. Now, by assuming similarity between ER and MR fluids and using a magnetic field instead of electric field in the mentioned equations, all the equations are applicable for MR fluids, which are given as:

where, α is associated with the fluid susceptibility and ∅ or other analogous physical parameters. In this case, τ_y also has two limiting traits with regards to H₀ as follows:

τ_y = αH₀² ∝ H₀², H₀ ≪ H_c (9)

Fig. 10a displays the dynamic yield stress attained from Fig. 8 in terms of the magnetic field strength for the CI-based MR fluid and CoFe₂O₄–CI-based suspensions, which are in good accordance with eqn (8)–(10) with the H_c of 319 kA m⁻¹. This signifies that the formation of the chain-like structure through the magnetic particle attraction is caused by the magnetic polarization force in the presence of a magnetic field. On the other hand, once the magnetic field is high enough to magnetically saturate all the particles, the force will not enhance with an increase in the magnetic field strength and thereby the exponent will decline from 2.0 to 1.0. It should also be mentioned that the slope variation from 2 to 1.5 is considered as a critical magnetic field in dynamic yield stress versus magnetic field strength.

Fig. 10 (a) Dynamic yield stress vs. magnetic field strength, (b) τ′ vs. H′ and (c) τ′′ vs. H′′ for CI-based and CoFe₂O₄–CI-based MR fluids.

By scaling eqn (8) through H_c and τ_y(H_c) = 0.762αH_c², a generalized scaling relationship is attained as follows:

In this case, the data obtained from Fig. 10a collapse onto a single curve by utilizing eqn (9), as exhibited in Fig. 10b.

A modification in eqn (11) is employed to confirm the experimental data fit and a universal correlation is obtained, as shown below. This equation includes an additional parameter of b. It is generally used for systems that are partly discord with eqn (11) although the plots seem to track an alternative curve.³⁸ Thus, τ′ is rescaled with τ′′ = τ′H^4b and H′ with H′′ = H^1+2b and eventually a modified scaling equation is derived as:

By plotting τ′′ versus H′′ (Fig. 10c), the points (τ′′, H′′) are confirmed by substituting b = 0.35. Thus, this equation is used to construct the master curve for MR fluids due to smaller deviations compared to the points (τ′, H′) along the curve of eqn (9). Moreover, the deviations of H_c do not vary the scaled yield stress equation, whereas the point tracks the universal yield stress equation,⁴⁶ by moving down for a lower H_c and moving up for a higher H_c. Eventually, from these explanations it can be concluded that the dynamic yield stress of the MR fluids is strongly dependent on the externally applied field strength.

Fig. 11 represents the shear viscosity of the CI-based MR fluid and CoFe₂O₄–CI-based MR fluids in terms of the shear rate ([small gamma, Greek, dot above]) in the presence and absence of externally applied fields. It is evident that the shear viscosity of all the systems is affected by the variations in the internal structure which are induced by the [small gamma, Greek, dot above]. The shear viscosity declines as [small gamma, Greek, dot above] is enhanced, which is shear thinning behavior.⁴⁷ This is because the magnetizable particles orientate in the parallel direction of the externally applied field, however the velocity gradient of the flow is perpendicular to the applied magnetic field direction under shear formation.⁴⁷ Thus, this results in the creation of an angle between the magnetic moment and magnetic field which leads to a magnetic torque that declines the particles free rotation and increases the fluid's shear viscosity.⁴⁶

Fig. 11 Shear viscosity vs. shear rate curves of (a) CI-based MR fluid, (b) CoFe₂O₄–CI-based MR fluid (additive prepared by sol–gel), and (c) CoFe₂O₄–CI-based MR fluid (additive prepared by hydrothermal method) under different magnetic field strengths.

Fig. 12 shows that the role of the CoFe₂O₄ nanoparticles in the sedimentation ratio, which was recorded as a function of time, was much improved in comparison with that of the CI-based suspension. In other words, even though the dispersion stability of the CoFe₂O₄–CI-based suspension was more stable than the CI-based system, it was dependent on the synthetic route. Thus, the role of additives for CI-based suspensions could be established.⁴⁶ Some analogical additives were also added to the CI-based suspension to reduce sedimentation.^20–23,46 The sedimentation rate of the CoFe₂O₄–CI-based suspensions is relatively large during the first 1000 min, and then it became slower until it reached a steady-state after 4000 min. Furthermore, the dispersion stability of the samples prepared by the hydrothermal method was higher than that of the samples prepared by the sol–gel method. On the other hand, the sedimentation rate of the CI-based suspensions is relatively high during the first 500 min before reaching a steady state. This indicates that inclusion of nanoparticles in micron-sized CI-based suspensions remarkably declines the settling rate of the particles. This relates to the increased frictional forces between the particles and carrier fluid. Indeed, these forces are greater in nanoparticles due to their higher surface areas compared to micron-sized particles. Therefore, the addition of CoFe₂O₄ as an additive to CI-based suspensions enhances the sedimentation stability of MR fluids.

Fig. 12 Sedimentation ratio versus time for CI-based and CoFe₂O₄–CI-based suspensions.

4. Conclusion

CoFe₂O₄ nanoparticles were synthesized by sol–gel and hydrothermal methods. The XRD results of samples sintered at 550 °C indicate the formation of single phase CoFe₂O₄ in both methods. The samples prepared by the hydrothermal method had a smaller particle size and higher saturation magnetization compared to the samples prepared by the sol–gel method. The introduction of a CoFe₂O₄ nanoparticle additive to a micron-sized CI-based MR fluid was investigated and better results were achieved in the samples prepared via the hydrothermal method. Also, rheological behavior, i.e. shear stress and shear viscosity, improved in the presence of additives. This is due to the filling of nanoscale particles in the microcavities formed by micron-sized particles, and the formation of robust chains in the presence of additive nanoparticles. Finally, the introduction of CoFe₂O₄ nanoparticles significantly reduced the sedimentation rate, improved the redispersibility and enhanced the MR fluids rheological performance.

Acknowledgements

The authors would like to acknowledge MOHE and UTM, with grants PRGS (Vote No. 4L667) and PDRU (Vote No. 02E72) for providing financial support of this work.

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