J. Phys. Chem. 1996, 100, 14269-14271
14269
Electron Paramagnetic Resonance of Doped Magnetic Fluids: A New Approach To Probe the Particle Size Polydispersity Geraldo Jose´ da Silva and Paulo Ce´ sar de Morais* Departamento de Fı´sica, UniVersidade de Brası´lia, 70910, Brası´lia, DF, Brazil
Francisco Augusto Tourinho Departamento de Quı´mica, UniVersidade de Brası´lia, 70910, Brası´lia, DF, Brazil ReceiVed: March 11, 1996; In Final Form: May 30, 1996X
Electron paramagnetic resonance is introduced as a characterization technique to obtain the particle size polydispersity of a Cu2+-doped CoFe2O4 water-based magnetic fluid. The polydispersity parameters based on a log-normal distribution f(R,R0,σ) were obtained from the line-shape analysis of the Cu2+ resonance line. Excellent agreement between the data obtained from the resonance measurements (R0 ) 7.8 nm and σ ) 0.23) and from electron microscopy (R0 ) 7.8 nm and σ ) 0.25) was obtained for a large range of doping concentration.
Stable suspensions of magnetic nanoparticles in either organic or inorganic solvents are called magnetic fluids. Applied and basic research have both contributed to the enormous progress in this field in the past three decades; the chemical synthesis of new ferrite-based ionic magnetic fluids being a recent example.1 Magnetic fluid standard characterization techniques are X-ray diffraction, electron microscopy, and magnetization, for crystallographic structure, particle size polydispersity, and magnetic anisotropy represent the most important parameters to be determined.2 Despite the special interest in concentrated magnetic fluids and the strong optical absorption in the visible range, birefringence and dichroism measurements have been used to characterize ferrite-based magnetic fluids as well.3 More recently however, magnetic resonance has been proposed as a promising technique to study many of the very properties related to magnetic fluids, as for instance magnetic and electric particle-particle and particle-carrier fluid interactions4, magnetic anisotropy of single nanoparticles,5 and Brownian rotational time.6 As far as magnetic resonance is concerned, all the data published to date however present the magnetic nanoparticles themselves as the resonant centers. Actually, the resonance measurements have been lately performed at a fixed microwave frequency and sweeping the external field rather than at zero external field and varying the microwave frequency.4-10 In this case the effective magnetic field at the particle site is a combination of the external field, the anisotropy field, and the fluctuation field.11 As a consequence highly anisotropic magnetic fluids may require very low excitation frequencies.6 In addition, larger sample quantities may be required as well. Indeed, for highly anisotropic magnetic fluids magnetic resonance at a fixed frequency may not represent a promising characterization technique as it does for moderated anisotropic magnetic fluids. In this letter we propose a simple way to overcome the difficulties mentioned above; namely, we doped a highly anisotropic magnetic fluid sample with a well-known paramagnetic center. The magnetic resonance is now focused on the dopant center instead of focusing on the magnetic particle. In what follows we will discuss the first magnetic resonance results using a cobalt-ferrite water-based magnetic fluid doped with Cu2+. X
Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00736-8 CCC: $12.00
A water-based magnetic fluid containing 2 × 1016 particles of CoFe2O4/cm3 and saturation magnetization of Ms ) 300 G was used in this work.12 Electron microscopy was previously used to determine the particle polydispersity based on a lognormal distribution with a mean value for the particle radius of Ro ) 7.8 nm and a characteristic width of σ ) 0.25. A set of five aqueous solutions containing Cu2+ at different molar concentrations (0.10, 0.20, 0.30, 0.40, and 0.60) were prepared and used to perform the doping of the magnetic fluid sample. The set of five Cu2+-doped magnetic fluid samples were prepared by mixing the undoped magnetic fluid sample/aqueous Cu2+ solution at a volume ratio of 3:1. As far as phase separation is concerned, the molar concentration of the Cu2+ aqueous solutions and the mixing volume ratio used were such that the ionic strength of the doped magnetic fluids still fall within the stable monophasic region.3 Paramagnetic resonance measurements were performed at room temperature using an X-band spectrometer tuned at 9.65 GHz. No magnetic resonance was observed with the undoped magnetic fluid sample in the range of our experiment, i.e., from 2.2 to 4.0 kG. The magnetic resonance spectra of the five Cu2+-doped magnetic fluid samples are quite different from the spectra obtained from the Cu2+ in aqueous solution. However, except for the signal amplitude, no significant difference was found among the magnetic resonance spectra of the five Cu2+-doped magnetic fluid samples. The differences we found in the resonance spectra of the Cu2+-doped magnetic fluid samples, as compared to the corresponding Cu2+ aqueous solutions, were a broadening of the resonance line of the order of 35 G and a shift in the resonance field of a few tens of gauss. The single transition we observed (eg f t2g) is typical of Cu2+ distorted octahedral complexes and in aqueous solution the line width is often of order of 100 G-broad with no discernible hyperfine structure at room temperature.13 The open circles in Figure 1 describe the first derivative of the magnetic resonance absorption spectra of the Cu2+. From top to bottom in Figure 1 we have the resonance spectrum of Cu2+ in aqueous solution and five resonance spectra of Cu2+-doped magnetic fluids at different Cu2+-doping concentration. The changes we observed in the resonance spectra of the Cu2+ in the doped samples, i.e., the broadening of the resonance line and the shift in the resonance field are both associated to the presence of the anisotropy field on the Cu2+ © 1996 American Chemical Society
14270 J. Phys. Chem., Vol. 100, No. 34, 1996
Letters
Figure 1. Open circles: experimental points of the first derivative of the magnetic resonance absorption curve. The full lines are the fitting according to a Lorentzian line shape (a) and a modified Lorentzian line shape (b-f) as described by eqs 1-3. The values of molarity quoted on the right-hand side of each spectrum (b-f) represent the final Cu2+-ion concentration in the doped magnetic fluid sample. The resonance spectra (a-f) were normalized to unit. The signal-to-noise ratio, however, ranges from 7 for spectrum b up to 40 for spectrum f.
site due to the surrounding magnetic nanoparticles. The shift on the resonance field due to the contribution of the anisotropy field to the effective field at the Cu2+ site is qualitatively obvious. The broadening of the resonance line of the Cu2+ center in the doped magnetic fluid will be discussed below. From now on we will focus our attention on the resonance line-shape description of the Cu2+ in the doped magnetic fluids. The resonance line shape of all doped magnetic fluids analyzed here are quite similar, no matter what Cu2+ doping we refer, within the range of our experiment, i.e., from 0.025 through 0.150 M. This is strong evidence that the magnetic fluid stability was preserved despite the increasing in the ionic strength due to Cu2+-ion addition. Considering the mixing procedure used and going beyond 0.150 M in Cu2+ concentration one could induce phase separation as expected from the phase diagram of the magnetic fluid sample. To describe the Cu2+ resonance line shape in doped magnetic fluids, we start averaging out a Lorentzian-shaped resonance line to the angular dependence of the anisotropy field of the surrounding magnetic particles. This is done by considering the effective field at the Cu2+ site as a combination of the external field and the parallel component of the anisotropy field. The contribution to the effective field due to the fluctuation field is completely ruled out here. By parallel component of the anisotropy field we mean the component of the dipolar field due to the surrounding magnetic particles parallel to the external magnetic field, here taken as the z direction. The angular average of the dipolar field over the resonance line shape is performed by integrating the effective field from θ ) 0 through θ ) π, being θ the angle with respect to the z direction. In a second step we performed a radial averaging of the parallel component of the dipolar field to the resonance line shape by integrating from a radial distance close to the particle surface (R1) to a radial distance greater than the particle radius (R2). In a third and last step we took into account the particle size polydispersity considering a lognormal distribution of the particle radius, and we average out
the particle radius from zero to infinity. Indeed the resonance line shape of the Cu2+ ion in the doped magnetic fluid is described by
L ) 2πA∫0 f(R,R0,σ) dR∫R r2 dr∫0 g(H,Hd,H0,γ) sin θ dθ 1 (1) ∞
R2
π
where A is the Cu2+ molar concentration in the doped magnetic fluid, H is the external sweeping field, f(R,R0,σ) is the log-normal distribution function
f(R,R0,σ) ) (x2πPσ)-1exp{-[ln(R/R0)]2/2σ2}
(2)
and g(H,Hd,H0,γ) is the normalized first derivative of a lorentzian function
(H - H0 + Hd) g(H,Hd,H0,γ) ) (2γ/π) 2 [γ + (H - H0 + Hd)2]2
(3)
The average value of the particle radius and the broadening of the particle size distribution are described by the parameters R0 and σ, respectively. In eq 1 the limits R1 and R2 are given by R1 ) mR and R2 ) nR, m and n being fitted parameters. The values we found for the parameters m and n indicates that the resonant centers (Cu2+ ions) are located midway between the magnetic particles, mostly in a layer of tickness equals to R0/2, with the average particle-particle distance equals to 4.8R0. The resonance field and the line width at half-height of the Cu2+ ion in aqueous solution are H0 ) 3.15 kG and γ ) 77.3 G, respectively. The component of the dipolar field parallel to the external field H is Hd ) (4π/3)Ms(R/r)3 sinθ cos(θ + φ)(3 cos2 θ + 1)1/2, where φ ) tan-1 (1/2 tan θ). The full lines in Figure 1 represent the best fit of the experimental points according to eq 1. The most relevant parameters we obtained from our fitting procedure are summarized in Table 1. We first observe from
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J. Phys. Chem., Vol. 100, No. 34, 1996 14271
TABLE 1: Fitted Values for the Particle Radius (R0) and Width (σ) According to Eqs 1-3, Considering the log-normal Distribution Function f(R,R0,σ), for the Five Cu2+-Doped Magnetic Fluid Samples Analyzed Here Cu2+ doping (M)
R0 (nm)
σ
0.025 0.050 0.075 0.100 0.150
7.80 7.79 7.80 7.81 7.81
0.22 0.22 0.23 0.23 0.23
Table 1 the regularity of the parameters R0 and σ throughout all doped magnetic fluid samples. Such a regularity supports the assumption that our doping procedure preserves the integrity of the magnetic fluid samples. Second, we observe the excellent agreement between the parameters R0 and σ obtained from magnetic resonance (R0 ) 7.8 nm and σ ) 0.23) as described in this work and the same parameters as obtained from electron microscopy (R0 ) 7.8 nm and σ ) 0.25). We can draw some conclusions from our experiment and from our analysis based on eqs 1-3. The enhancement of the ionic strength of the magnetic fluid due to the Cu2+-doping procedure, in a large range of Cu2+ concentration, does not induce any phase separation, i.e., the addition of Cu2+ does not compromise the magnetic fluid stability. In terms of establishing magnetic resonance as a characterization technique, this is an important point to be considered. The excellent fitting of the magnetic resonance data indicates that the basic aspects which determine the resonance lineshape of the Cu2+ ion as a dopant for magnetic fluids were included in eqs 1-3. As a consequence the characteristic parameters of the log-normal distribution for the particle size, i.e., R0 and σ are obtained from the magnetic resonance data according to the scheme proposed in this work. The excellent agreement between the parameters R0 and σ obtained from both techniques electron microscopy and magnetic resonance and the stability of the parameters for a large range of Cu2+ doping points out magnetic resonance as an alternative characterization technique for the determination of
the particle polydispersity in the case of highly anisotropic magnetic fluids. In addition, the sample preparation is much simpler and the time of measurement much shorter than in the case of both electron microscopy and magnetization, which are considered the standard techniques used for that purpose. Finally, as long as the paramagnetic probe is adequately chosen, the doping procedure proposed here could be useful for further studies of many different properties associated with magnetic fluids. Acknowledgment. This work was partially supported by the Brazilian agencies FAP-DF, PADCT, CAPES, and CNPq. References and Notes (1) Tourinho, F. A.; Morais, P. C.; Souza, M. H.; Macedo, L. G., to be published. (2) Tourinho, F. A. Thesis; Universite´ Pierre et Marie Curie: Paris, 1988. Tourinho, F. A.; Franck, R.; Massart, R.; Perzynski, R. Prog. Colloid. Polym. Sci. 1989, 128, 134. (3) Neveu-Prin, S.; Tourinho, F. A.; Bacri, J. C.; Perzynski, R. Colloids and Surf. A: Phys. Eng. Aspects 1993, 80, 1. (4) Tronconi, A. L.; Morais, P. C.; Pelegrini, F.; Tourinho, F. A. J. Magn. Magn. Mater. 1993, 122, 90. Morais, P. C.; Tourinho, F. A.; Gonc¸ alves, G. R. R.; Tronconi, A. L. J. Magn. Magn. Mater. 1995, 149, 19. (5) Bakuzis, A. F.; Morais, P. C.; Tourinho, F. A., to be published. (6) Konn, A. M.; Laurent, P.; Talbolt, P.; Le Floch, M. J. Magn. Magn. Mater. 1995, 140-144, 367. (7) Morais, P. C.; Tronconi, A. L.; Skeff Neto, K. J. Appl. Phys. 1984, 55, 3744. (8) Morais, P. C.; Lara, M. C.; Skeff Neto, K. Philos. Mag. Lett. 1987, 55, 181. (9) Sastry, M. D.; Babu, Y.; Goyal, P. S.; Mehta, R. V.; Upadhyay, R. V.; Srinivas, D. J. Magn. Magn. Mater. 1995, 149, 64. (10) Nagata, K.; Ishihara, A. J. Magn. Magn. Mater. 1992, 104-107, 1571. (11) Raikher, Y. L.; Stepanov, V. I. J. Magn. Magn. Mater. 1995, 104107, 34. (12) Tourinho, F. A.; Franck, R.; Massart, R. J. Mater. Sci. 1990, 25, 3249. (13) Bleaney, B.; Bowers, K. D.; Pryce, M. H. L. Proc. R. Soc. London A 1955, 228, 166. McConnell, H. M. J. Chem. Phys. 1956, 25, 709.
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