IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004
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Anomalous Magnetic Aftereffect of a Frozen Magnetic Fluid Susamu Taketomi, Rosetta V. Drew, and Robert D. Shull
Abstract—A very stably dispersed magnetic fluid (MF) was zero-field-cooled from room temperature to 5 K followed by the application of a magnetic field of 2.86 MA/m for 300 s. After the was field was removed ( = 0), its residual magnetization measured as a function of time for 80 000 s. After measurement, the MF sample was heated to room temperature, and the experiment was repeated after zero-field cooling to 5 K and again applying and removing the 2.86 MA/m field. We performed the versus same experiment several times, and obtained a different curve each time. With each cycle, the average (at = 0) increased and the versus curve converged to a universal surprisingly increased curve. In the early cycles’ experiments, with during the later stages of the experiment. From other different experiments, it was concluded that the isolated surfactant molecules in the MF solvent played an important role. We propose a model wherein the magnetic colloids form closed magnetic flux circuits by forming collective micelle structures with temperature decrease. It is suggested that after application and removal of the field at 5 K, the micelles in the frozen MF break spontaneously, leading to an increase in the residual magnetization. Index Terms—Magnetic after effect, magnetic fluid, magnetic spin entropy, micelle, surfactant.
I. INTRODUCTION
A
MAGNETIC FLUID (MF) is a colloidal suspension containing magnetic particles of about 5 nm in diameter. The surfaces of the particles are covered with surfactant molecules in order to prevent the agglomeration of the colloidal particles because of their magnetic dipolar attraction. Accordingly, the MF forms a very stable colloidal suspension [1], [2]. At room temperature, the colloidal particles in the MF move and rotate freely in the solvent. However, upon decreasing the temperature and freezing the solvent, the particles become fixed in the solvent and can no longer move or rotate. Therefore, the frozen MF resembles an alloy containing a nonmagnetic matrix with dispersed ferromagnetic clusters. Accordingly, the presence of a magnetic anisotropy and a magnetic aftereffect have been found in the past in frozen MFs; see the references cited in . In order to clarify whether or not the individual particle’s magnetic moment obeys the Néel rotational relaxation process or deviates from it due to the dipole–dipole interaction between the colloidal particles, we studied the magnetic aftereffect of a frozen MF. The
Manuscript received September 23, 2003. S. Taketomi was with the National Institute of Standards and Technology, Gaithersburg, MD 20899-8552 USA. He is now with Matsumoto Yushi-Seiyaku Co., Ltd., Osaka 581-0075 Japan (e-mail:
[email protected]). R. V. Drew and R. D. Shull are with the National Institute of Standards and Technology, Gaithersburg, MD 20899-8552 USA (e-mail:
[email protected];
[email protected]). Digital Object Identifier 10.1109/TMAG.2004.830619
result was far from our expectation; it was inconsistent with the conventional concept of a MF. II. EXPERIMENT I AND RESULTS We used the magnetic fluid “Marpomagna” FV-42 made by Matsumoto Yushi-Seiyaku Co., Ltd., (magnetite colloid of 0.104 volume fraction, alkylnaphthalene solvent).1 Two different anion surfactants were used for this MF and their molar weight was much less than that of the solvent. The colloidal dispersivity of this MF was excellent, which was confirmed by different experiments [4], [5]. Detailed properties of FV-42 were shown in these references. For the measurement of the magnetization, two different sample holders , were used. One was a glass tube (inner diameter ) and glass lid which were glued together axial length with an epoxy adhesive after the tube was filled with the MF. The other sample holder was made of Teflon with similar dimensions. In this case, the tube and lid were fastened only by the threaded lid after filling with the MF. The seal on the first holder was hermetically good while that of the latter holder was poor. In this experiment, we used a SQUID magnetometer made by Quantum Design Co. We kept the cryostat temperature at 5 K during the experiment. Before inserting the sample into the cryostat, we quenched the superconducting magnet and zeroed the magnet field. For the zero-field-cooled condition, the sample was then lowered from room temperature at the top of the cryostat to the center of the cryostat at 5 K. Inside the cryostat the chamber was in vacuum. A magnetic field of 2.86 MA/m was subsequently applied to the sample in the axial direction for 300 s, and the field was removed by again quenching the superconducting magnet. It took approximately 2 min to stabilize the cryostat temperature after quenching. After the temperature was stabilized, measurement of the sample’s residual magnetiand continued for zation as a function of time began is not in 80 000 s. Therefore the residual magnetization at reality the “initial” residual magnetization. After measurement, the MF sample was taken out of the cryostat and left at room temperature for a few days. The experiment was repeated after inserting the sample in the cryostat at 5 K and again applying and removing the 2.86 MA/m field. We performed the same versus experiment several times, and obtained a different curve each time. For sample A, the glass sample holder was used. With each (at ) increased and the versus cycle, the average 1The use of manufacturers’ names in this paper is only for specifying the experimental conditions and does not imply an endorsement by the National Institute of Standards and Technology
0018-9464/04$20.00 © 2004 IEEE
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Fig. 1
IEEE TRANSACTIONS ON MAGNETICS, VOL. 40, NO. 4, JULY 2004
Residual magnetization M as a function of time t for sample A.
Fig. 3 Residual magnetization M as a function of time t for samples C and D.
Fig. 2 Residual magnetization M as a function of time t for sample B. M means that the true M value is the value on the graph : . :
1 17
+1 17
0
curve converged to a universal curve. Fig. 1 shows the versus data for the second and sixth cycles. Note decreased in produring the sixth cycle as expected for a system portion to where the field has been reduced. However, during the second being much less, fluctucycle, in addition to . ates greatly and surprisingly “increases” with for With the repetition of measurement cycles, the versus curve converged to a single curve which was almost the same as that shown for the sixth measurement cycle. Hereafter, we will call versus curve the universal curve. this sixth cycle’s The same series of experiments were conducted on sample B inserted in the same glass sample holder as used by sample A. However, when the holder’s lid and tube were glued with adhesive, both parts were fixed and tightly pressed together using a vice. Therefore the hermetic seal for sample B was much better versus results than that for sample A. Fig. 2 shows the for sample B. Though in general the residual magnetization at increased with the cycle number (for small cycle numvalue of bers), all their values were much lower than the the limiting universal function, and all curves had an versus region with a positive slope. Sample C was contained inside a Teflon sample holder. In addition, before filling the holder with the MF, we placed the for 1 h. As menMF under vacuum tioned before, the Teflon sample holder did not possess a good hermetic seal. Therefore, it is conceivable that during the experiment, some amount of the surfactant in the MF might have
Fig. 4 Micelle structure in the magnetic field. (a) Schematic structure of the micelle in the magnetic fluid. (b) Schematic magnetic dipole configuration in the micelle before and after the breaking of the micelle in the frozen magnetic fluid.
escaped into the vacuum. Fig. 3 shows the versus curves measured for sample C. It shows that from the very first cycle versus curve almost coincides with the universal curve. the III. EXPERIMENT II AND RESULTS Residual magnetization versus experiments were also performed on a solid polymerized MF, sample D. In this case, we vigorously mixed the MF and an epoxy adhesive prior to and during the polymerization of the epoxy to form a solid mixture. Scanning electron microscopy showed that in this sample D, the MF solvent had been consumed in the epoxy polymerization and the MF was dispersed as particles of 1 diameter in the solid adhesive matrix. Also, no large aggregates of the colloidal particles larger than a few hundred nanometers were observed. versus curves for this mixture sample D are shown The in Fig. 3. As the MF weight fraction in the solidified adhesive values by a was unknown, we multiplied the experimental constant so that the sample’s residual magnetization at coincided with that of the universal curve for sample A. Note versus curve coincided perfectly with the that sample D’s universal curve. Other experimental results are shown and discussed in [3].
TAKETOMI et al.: ANOMALOUS MAGNETIC AFTEREFFECT OF A FROZEN MAGNETIC FLUID
IV. DISCUSSION We interpret the present experimental results by suggesting the low-temperature physical picture for the MF shown in Fig. 4. In addition to the surfactant molecules which cover the surface of the colloidal particles to prevent their coagulation, there is also a considerable amount of isolated surfactant in the MF solvent. In general, when the MF is prepared, an excess amount of surfactant over that theoretically needed is used so that there is a minimal chance that the magnetic colloidal particles would coagulate. Here, the theoretically needed amount is the surfactant amount which is needed exactly to cover the surface of all the colloidal particles with one-molecular layer. We consider that these isolated surfactant molecules generate micelles when the MFs temperature is decreased. This means that a phase transition occurs in the MF from a monodispersed phase (i.e., with isolated surfactant molecules in the solvent) to a micelle phase (i.e., with clustered surfactant molecules) upon temperature decrease from 300 K. The MFs micelle differs from ordinary micelles in the respect that some fraction of the magnetic colloidal particles sticks to the surface of the micelles as shown in Fig. 4(a). Accordingly the micelle generation resembles the coagulation of the colloidal particles. In addition, the magnetic moments of the colloids on the micelle surface make a closed magnetic flux circuit. These micelles are fixed in the frozen solvent with further temperature decrease. When a strong magnetic field is applied to these micelles, the strong magnetic force resulting distorts the shape of the micelles. After removal of the field, the magnetic moments of the colloids on the micelle once again form a closed magnetic flux circuit and accordingly the residual magnetization, , in such a frozen MF is much smaller than that described by the universal residual magnetization curve for isolated particles slowly randomizing their moment directions. The micelle shape distortion by the strong field results in a residual stress in the micelle. After a certain amount of time has elapsed following field removal, the micelle breaks spontaneously due to the internal stress. This mifor the celle’s breaking generates a finite magnetic moment micelle [see Fig. 4(b)]. At the same time the micelle’s breaking increases the surfactant molecules’ configurational entropy. The appearance on breaking of the micelle is the origin of the increase in with time. In general, the spontaneous increase of the magnetization under zero field contradicts the second law of the thermodynamics. However, in the present case, the increase of the surfactant molecules’ configurational entropy compensates for the decrease in magnetic spin entropy or the increase in the residual magnetization with time. In sample C, the isolated surfactant evaporated in the vacuum prior to cooling and field application, and no micelles were generated in this MF even at a low temperature. Accordingly, its versus curve coincided with the universal curve. first cycle In the solid mixture sample of the MF and the adhesive (sample D), no micelle was generated, and naturally its versus curve coincided with the universal curve. Finally, the micelles are generated in the MF not only by the temperature decrease but also by magnetic field application at room temperature. However, in the latter case, the elongated
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micelles are generated in the field direction. This is the origin of the MFs unusual magnetooptical phenomena reported earlier [6], [7]. Further experimental evidence for this paper’s physical picture of the MF is presented in [3]. V. CONCLUSION A very stably dispersed MF was zero-field-cooled from room temperature to 5 K followed by the application of a magnetic field of 2.86 MA/m for 300 s. After the field was removed , its residual magnetization was measured as a function of time for 80 000 s. After measurement, the MF sample was heated to room temperature, and the experiment was repeated after cooling to 5 K and again applying and removing the 2.86 MA/m field. We performed the same experiment several times, and obtained a different versus curve each time. With increased and the versus curve each cycle, the average converged to a universal curve. In the initial few cycles, the value was very small and surprisingly increased with in some of time region. When we used a hermetically sealed sample holder, versus curve did not converge to the universal curve, the versus curve coincided with the universal curve while the if we used a poorly sealed sample holder. A solid mixture of the versus MF and an epoxy adhesive also showed the universal curve. In order to interpret the present experimental results, we propose the following physical model. When the MF was cooled down, isolated surfactant molecules in the MF solvent trigger the generation of micelles to which the colloidal particles stick and result in their magnetic moments making a closed magnetic flux circuit. Consequently, the residual magnetization is anomalously small. After removal of the magnetic field, the micelles in to inthe frozen MF spontaneously break with time causing crease with . The conventional MF model must be significantly changed in order to explain the present experimental results. ACKNOWLEDGMENT The authors would like to thank Dr. A. J. Shapiro for observing the samples by scanning electron microscopy. REFERENCES [1] R. E. Rosensweig, Ferrohydrodynamics. Cambridge, U.K.: Cambridge Univ. Press, 1985. [2] S. Taketomi and S. Chikazumi, Magnetic Fluids-Principle and Application. Tokyo, Japan: Nikkan Kogyo Shinbun, 1988. [3] S. Taketomi, R. V. Drew, and R. D. Shull, “Phase transition between a micelle and a mono-dispersed colloid in a magnetic fluid,” Phys. Rev. E, 2004, submitted for publication. [4] S. Taketomi, H. Takahashi, N. Inaba, and H. Miyajima, “Experimental and theoretical investigations on agglomeration of magnetic colloidal particles in magnetic fluids,” J. Phys. Soc. Jpn., vol. 60, pp. 1689–1707, 1991. [5] S. Taketomi and R. D. Shull, “Experimental study of magnetic interactions between colloidal particles in magnetic fluids,” J. Appl. Phys., vol. 91, pp. 8546–8548, 2002. [6] S. Taketomi, N. Inaba, H. Takahashi, and H. Miyajima, “Field dependence of magnetic bifringence of magnetic fluid in low field region,” J. Phys. Soc. Jpn. Lett., vol. 59, pp. 3077–3080, 1990. [7] S. Taketomi, C. M. Sorensen, and K. J. Klabunde, “Calorimetric study of magnetic fluids under magnetic field,” Phys. Rev. E, vol. 68, pp. 21501–1–21501–8, 2003.
