Measurement of the extinction coefficients of magnetic fluids
© Fang et al; licensee Springer. 2011
Received: 2 October 2010
Accepted: 18 March 2011
Published: 18 March 2011
A novel spectral transmittance approach for measuring the extinction coefficient of magnetic fluids is proposed. The measuring principle and accuracy of the approach are analysed. Experiments are conducted to measure the extinction coefficient of magnetic fluids with different particle volume fractions. The relative uncertainty of experimental data is less than 1.8%. The experimental results indicate that the extinction coefficient of magnetic fluids increases with increase of the volume fraction of suspended magnetic nanoparticles and the optical properties of the particle material have a significant effect on the extinction coefficient of the magnetic fluids.
Magnetic fluid is a kind of colloidal suspension containing surfactant-coated magnetic nanoparticles dispersed in carrier liquids such as water and oil. Since the emergence of magnetic fluid in the 1960s, researchers have conducted many investigations on the characters of magnetic fluids. When light is incident into the magnetic fluid, the magnetic nanoparticles suspended in the base fluid will interact with the incident light and affect the propagation of the incident light. Magnetic fluid presents some special optical characters such as birefringence [1–5] and magnetochromatics [6, 7]. Recently, the remarkable magneto-optical characters of magnetic fluids have attracted enormous attention of researchers who tried to apply magnetic fluids to optical devices such as fabricating optical switches , tunable filters , magnetic-field sensors  and tunable optical grating [11, 12]. Although the optical characters of the magnetic fluids have been studied for decades and novel phenomena have been discovered, there are few reports on the optical constants of magnetic fluids. Yang et a1.  measured the magnetic field-dependent refractive index of magnetic fluid films by total reflection technique. Pu et a1.  designed an experimental system for measuring the refractive index of magnetic fluid and studied the effect of particle volume fraction and temperature on the refractive index. Both of these investigations had the limitation of having one fixed wavelength, besides the experimental systems employed being complicated and expensive. So far, few investigations on the extinction coefficient of magnetic fluid have been reported. To promote the applications of magnetic fluids in different fields such as thermal and optical engineering, many more efforts toward further investigation of optical constants of magnetic fluids are needed. The purpose of this letter is to propose a simple method for measuring the extinction coefficient of magnetic fluids.
Experimental principle and apparatus
With the development of the manufacturing technique, the spectral transmittance of a translucent film can be accurately measured by a spectrophotometer. Based on the film transmission principle, the method for measuring the extinction coefficient of magnetic fluids can be established. The procedure of our method is as follows: first, two magnetic fluid films with different thicknesses are prepared. The spectral transmittance of these films can be accurately measured using a spectrophotometer. Then, based on the film transmission principle, two transmittivity equations of the magnetic fluid films with regard to the optical constant of the magnetic fluid are established. Finally, by solving the two equations, the extinction coefficient of the magnetic fluid can be obtained.
For fabricating a magnetic fluid film, two JGS3 glasses and a polyester film are needed. The glass has 50-mm width, 50-mm length and 1-mm thickness. The polyester film has a 30-mm-diameter circular hole in the central section. The polyester film is sandwiched in between the two glasses, and the magnetic fluid is injected into the circular hole. Then, the three-layer film is clamped by an attachment. We can obtain magnetic fluid film of different thicknesses by choosing polyester films of different thicknesses.
where n is the refractive index, k denotes the extinction coefficient, L denotes the thickness, λ denotes wavelength, and subscripts i and j represent the different media.
The data uncertainty results mainly from the measuring errors of structure parameters and transmittivity of the glass. To estimate the data uncertainty, Lw1 is used for denoting the thickness of the thin water film, Lw2 for the thickness of the thick water film, Teff 1 for the transmittivity of the thin water film and Teff 2 for the transmittivity of the thick water film. A micrometer with the measurement uncertainty of 1 μm is used. For the thin water film, the thicknesses of the two glasses L1 and L2 and the whole thickness of the three-layer film L are, respectively, measured using the micrometer. Thus, the thickness of the thin water film is obtained from L w1 = L - L1 - L2, and the measurement uncertainty of the film thickness from δL = δL1 = δL2 = 1 μm. Therefore, the uncertainty of Lw1 and Lw2 is determined as = 1.732 μm.
The relative uncertainty of the measured extinction coefficient of water at different wavelengths
Relative uncertainty (%)
Relative uncertainty (%)
Results and discussion
The relative uncertainty of the measured extinction coefficient of magnetic fluids with different particle volume fractions at different wavelengths
where εr,w is the dielectric function of water, εr,p is the dielectric function of Fe3O4 and ϕ is the particle volume fraction.
Since the complex refractive index of water can be obtained from Ref. , the dielectric function of water was calculated using Equations 13 and 14. So far, the dielectric functions of water and Fe3O4 are both available. Based on the MGT formula, the dielectric function of magnetic fluid is calculated. Then, according to Equations 15 and 16, the extinction coefficients of magnetic fluid were predicted. The predicted extinction coefficients of magnetic fluids with different particle volume fractions are shown in Figure 6. It can be seen from Figure 6 that the result of the MGT is a little higher than that of the experiment. This is because the MGT is a reduced model for the optical properties of magnetic fluid. The influence of both the Brownian motion of magnetic particles and the aggregation of magnetic particles on the optical properties of magnetic fluid is not considered in the MGT. Nevertheless, these two factors are not dominant for the optical feature of the magnetic fluid. Hence, the variation trend of the MGT result concurs with that of the experimental result.
From the curves in Figure 6, one learns that the extinction coefficient of magnetic fluid increases with the increase in the particle volume fraction. When the incident wavelength is 800 nm, the extinction coefficient of water is k = 1.25 × 10-7 from Ref.  and the extinction coefficient of magnetic fluid of 0.1% particle volume fraction (experimental result) is k = 2.06 × 10-4. The latter is 1647 times than the former. This is because the size of suspended magnetic nanoparticles is much smaller than the incident wavelength. According to the Mie's scattering theory, the absorption of the incident light is the main optical character of these magnetic nanoparticles. The presence of the magnetic nanoparticles in water greatly enhances the total absorption of light. With an increase of the particle volume fraction, the number of particles in the unit volume increases, and the total absorption of light further increases.
From Figure 6, it can be seen that in the continuous wavelength range of 500-800 nm, the extinction coefficients of magnetic fluids decrease with the increase of the incident wavelength. This is because the spectral features of the suspended magnetic nanoparticles are dominant for the optical feature of the magnetic fluid film. Since the extinction coefficient of Fe3O4 particles decreases with the increase of the wavelength (see Figure 7) and the scattering function of these nanoparticles is extremely weak, the absorption of light by the nanoparticles decreases with an increase in the wavelength. In other words, the above phenomenon further indicates that the optical properties of the nanoparticles play a significant role in affecting the optical properties of magnetic fluids.
In this study, a simple spectral transmittance method was proposed for measuring the extinction coefficient of magnetic fluids. The extinction coefficients of magnetic fluids with different particle volume fractions in the continuous wavelength range of 500-800 nm were measured. The experimental data have revealed that the extinction coefficient of magnetic fluids increases with increase of the particle volume fraction, and the optical properties of the particle material have a significant effect on the extinction coefficient of the magnetic fluids. It is feasible to control the optical character of the magnetic fluids by changing the optical properties of the nanoparticles.
Effective medium theory
This work was supported by the National Natural Science Foundation of China (Grant No. 50436020).
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