The increase of the light transparency induced by a magnetic field for the colloid film based on α–FeOOH nanoparticles

Jian Li; Anrong Wang; Yueqiang Lin; Xiaodong Liu; Jun Fu; Lihua Lin; Longlong Chen

doi:10.1364/OME.2.001760

1. Introduction

Interest in the physical properties of colloid dispersions has grown because of their widespread technological applications [1]. Magnetic colloids in particular, i.e., ferrofluids, which are composed of magnetic nanoparticles with sizes of the order of 10 nm dispersed in a carrier liquid [2], have the possibility to control the properties and flow of these liquids using a moderate magnetic field. Thus, such magnetic colloids are regarded as interesting materials, in particular for engineering applications [3]. The optical transmission of a ferrofluid film under an applied magnetic field has recently attracted the attention of many researchers [4–13]. Experiments have shown that the transmission of light is generally reduced for the ferrofluid film because the magnetic nanoparticles form chain-like structures when an external magnetic field is applied. Using a special design, a ferrofluid-based optical switch device has been produced, in which the transmittance is enhanced with the application of an external magnetic field [7,12]. The switching speed of such a device is mainly determined by the field-induced agglomeration rate of the ferrofluid nanoparticles [12]. In addition, when a magnetic field with gradient is applied, the transmittance of the ferrofluid demonstrates as a non-monotonic relaxation process due to motion of the chains, from both magnetic convergent force (MCF) and magnetic divergent force (MDF) processes [14].

Generally, the particles in ferrofluids are ferromagnetic or ferrimagnetic [2]. The colloids based on paramagnetic particles, known as “parafluids” [15], are seldom studied because the magnetic interaction between particles is so weak that they cannot cluster into chain-like structures under an applied external magnetic field. Therefore, such weakly magnetic colloids have been regarded as of little value other than being used as a model system to investigate complex liquids [15–18]. Bulk α–FeOOH is an antiferromagnetic material and when finely divided such materials can exhibit weak ferromagnetism or superparamagnetism resulting from the uncompensated surface spins [19,20]. In this study, we investigate the field-induced optical properties of the apparently paramagnetic fluid based on α–FeOOH nanoparticles. The enhancement of the transmission of light through the fluid film in the presence of an applied magnetic field is revealed.

2. Experiments

2.1 Description of the samples

The particles were fabricated using chemical precipitation. Analysis of the X-ray diffraction (XRD) data indicated the particles to be α–FeOOH [21]. The magnetization curve of the nanoparticles powder was measured by a vibrating sample magnetometer (VSM) using go-and-return magnetic field cycles at room temperature, as shown in Fig. 1 .

Fig. 1 Magnetization curve of the powder. The inset is a typical TEM picture of the particles and the size bar is 100 nm.

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The particles are apparently paramagnetic and the effective initial susceptibility $χ_{e f f}$ ( = M/H) is calculated to be 1.29 × 10⁻². Transmission electron microscopy (TEM) observations indicated that the particle’s morphology is spherical (see the inset in Fig. 1), and the average diameter of the particles is 8.16 nm and the standard deviation of average size is 0.26. For antiferromagnetic nanoparticles, their magnetization M can be described using the modified Langevin formula [20], M = M_sL(α) + χ_aH, where M_s is the saturation magnetization, L(α) = coth(α)−1/α is the Langevin function and α = µ₀mH/k_BT is known as the Langevin parameter, χ_a is the susceptibility. The value $μ_{0}$ is the permeability of free space, k_B is the Boltzmann constant, T is the absolute temperature, H is the applied magnetic field and m = πd³M_s/6 is a particle magnetic moment, where d is the average diameter of the particles. Since χ_a is generally very small [20], when a applied magnetic field is not high enough, the magnetization law of the antiferromagnetic nanoparticles can be described as M = M_sL(α). Under low field limit, χ_aH $\to$ 0, $μ_{0}$ mH<<k_BT, so that M = M_sL(α) and L(α)≈α/3, i.e., M = $μ_{0}$ πd³M_s²H/18k_BT, so the effective initial susceptibility $χ_{e f f}$ can be described as $χ_{e f f}$ = $μ_{0}$ πd³M_s²/18k_BT. Thus, from the experimental data for $χ_{e f f}$ and d, M_s is estimated to be 21.79 kA/m, and the dipolar coupling constant $λ$ = $μ_{0}$ m²/2πd³k_BT can be calculated as 3.22 × 10⁻³(<<1). Therefore, it is judged that the particles cannot form any aggregates as a result of their magnetic interactions [22]. The α-FeOOH colloids with 0.2% particle volume fraction ( $φ$ ) were synthesized by the Massart method, without a surfactant [23], and appeared similar magnetization behavior to the particles.

2.2 The magneto-optical experiment

The colloids were sealed in a rectangular glass cell to form a colloidal film of thickness 0.3 mm. The light source for the magneto-optical measurement was a 10 mW He-Ne laser with 632.8 nm wavelength. The incident light was parallel to the applied magnetic field and normal to the film. The transmitted light was measured by a photoelectric cell. The details of the experimental set were shown in [24]. The measurement of the absolute amount of light transmitted can be greatly influenced by the cleanliness of the glass surface of the sample, so the normalized transmission was generally used to characterize the magneto-optical effects [25]. Therefore, in the present work, the action of the applied magnetic field is described as the variation of relative transmission coefficient T, which is defined as

T = {(I}^{a} {/I}_{i} {)/(I}^{o} {/I}_{i}) = I^{a} {/I}^{o}

where I_i is the intensity of incident light, and I^a is the intensity of transmitted light after the magnetic field was applied and I^o is the one under zero field.

3. Results and discussion

Figure 2 plots the time-dependent applied magnetic field and shows the corresponding response of the relative transmission coefficient T. The experimental results show that the intensity of the light transmitted is stable before a magnetic field was applied.

Fig. 2 The variation of the transmission T as a function of field strength. The external magnetic field was applied during the period 50 to 100 s.

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From Fig. 2, it can be found that when a magnetic field exceeding 20 Oe was applied, the transmittance was clearly enhanced, whereas when the field was removed, the change in T vanished. At H = 500 Oe, the enhancement of T reached about 30%. The relationship between the relative transmission coefficient T and the applied magnetic field H is shown in Fig. 3 . From Fig. 3, it can be seen clearly that the transmittance increased nonlinearly and exhibited a saturation tendency with applied magnetic field.

Fig. 3 The relation between T and H. The error bars represent the fluctuation region of the T values as Fig. 2 shown.

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It is apparent that the phenomenon of transparency enhancement cannot result from field-induced microstructure transformation in the α-FeOOH colloids since the dipolar coupling constant $λ$ (<<1) is too small to make the colloidal particles cluster, even pair correlations exist among them [26,27] as a result of magnetic interactions. In addition, for weakly magnetic colloids, self-assembled droplet-like aggregates may be formed in zero field due to nonmagnetic colloidal forces [28]. However, the behavior of such aggregates is similar to those of individual large particles [29]. And, the experiments shown that the optical behavior of the colloids based on ZnFe₂O₄ particles, whose magnetic coupling constant $λ$ ( = 3.16 $\times$ 10⁻¹) is larger than the α-FeOOH particles, was not influenced by the magnetic field [30]. As a consequence, it is determined that for α-FeOOH colloids, the enhancement of the transparency cannot result from the particles being drifted apart from the place of the light beam by the gradients of the magnetic field. Accordingly, the magnetic enhancement could instead be attributed to the optical absorption behavior of the colloids in relation to the coupling of magnetic and dielectric properties of the colloidal particles. This can be explained as follows.

When a beam of light with intensity I_i is directed at a medium containing nonmetallic nanoparticles, the intensity I of the light transmitted a distance l through the medium can be described as

I = I_{i} e^{- τ 1}

where

τ

is the turbidity of the medium, and is related to the number density of the particles N (

\propto

φ

) and their individual extinction cross-sections

σ_{e x t}

by

τ = N σ_{ext}

. Extinction is due to both scattering, which removes light from the incident path, and absorption, which converts the light into other forms of energy (e.g., heat), i.e.,

σ_{e x t} = σ_{s c a t} + σ_{a b s}

, where

σ_{s c a t}

and

σ_{a b c}

are the scattering cross-section and absorption cross-section, respectively. Because the α-FeOOH particle size parameter

Γ

( = 2πd/

λ

, d is diameter of the particle and

λ

is the wavelength of the incident light) <1, the particles can be regarded as Rayleigh scatters [29], in which σ_scat<<σ_abs. Hence, for the α−FeOOH colloids, σ_ext≈σ_abs. The Rayleigh absorption cross-section is

σ_{a b s} = - \frac{8 π d^{3}}{λ} \cdot \frac{3 {E^{″}}_{2} E_{1}}{{({E^{'}}_{2} + 2 E_{1})}^{2} + {E^{″}}_{2}^{2}}

where,

{\tilde{n}}_{1}

,

{\tilde{n}}_{2}

are the complex refraction indices of both the carrier liquid and the particles system, respectively, and Im indicates the imaginary part [31]. Because the magnetism of both the α−FeOOH nanoparticles and the aqueous carrier liquid are very weak, their permeability is taken as μ = 1. Thus,

{\tilde{n}}_{1} =

E₁^1/2 and

{\tilde{n}}_{2} =

E₂^1/2. The relationship between refraction indice

\tilde{n}

and permittivity E (or ε) is

{\tilde{n}}^{2} = {(n + i κ)}^{2} = n^{2} - κ^{2} + 2 i n κ

E = E' -iE'', E' = n^{2} - κ^{2}, - E'' = 2 n κ

where n is the refractive index and κ is the absorption coefficient [32], and the minus sign in E is used to make the observed imaginary part positive. For the medium, which absorbs only slightly in a given range of frequencies, the imaginary part of the permittivity E'' may be neglected, i.e.,

{\tilde{n}}^{2} = n^{2} = E' = E

.So, neglecting the absorption of the carrier liquid, which is independent of the magnetic field, the imaginary part can be written as

i m (\frac{{\tilde{n}}_{2}^{2} - {\tilde{n}}_{1}^{2}}{{\tilde{n}}_{2}^{2} + 2 {\tilde{n}}_{1}^{2}}) = \frac{3 E_{2}^{'' 2} E_{1}}{{(E_{2}^{'} + 2 E_{1})}^{2} + E_{2}^{'' 2}}

where E₁ is the permittivity of the carrier liquid, and E₂' and E₂'' are the real and imaginary parts of the permittivity of the colloids, respectively. Thus,

σ_{a b s} = - \frac{8 π d^{3}}{λ} \cdot \frac{3 E_{2}^{''} E_{1}}{{(E_{2}^{'} + 2 E_{1})}^{2} + E_{2}^{'' 2}}

Therefore, the relative transmission coefficient T can be written as

T = \frac{I^{a}}{I^{o}} = e^{- l N (σ_{a b s}^{a} - σ_{a b s}^{o})}

where I^a and

σ_{a b s}^{a}

is the intensity of the transimission light and the absorption cross-section of the colloids after the magnetic field is applied, and I^o and

σ_{a b s}^{o}

is the intensity of the transimission light and the absorption cross-section of the colloids in zero field, respectively. From the experimental results, it can be determined that the absorption cross-section is constant before the application of the magnetic field. So, formula (8) can be written as

T = A e^{- l N σ_{a b s}^{a}}

A ( = exp(lN

σ_{a b s}^{o}

)) is in relation to l, N and

σ_{a b s}^{a}

independent from magnetic field. Therefore, T varies with

σ_{a b s}^{a}

since l and N are constant.

α–FeOOH has an orthorhombic crystal structure and is antiferromagnetic material, with a sublattice magnetization that lies essentially along the [010] direction [33]. For the orthorhombic crystal structure, the three principal values of the permittivity tensor, ε_x, ε_y, and ε_z, are different and the positions of the principal axes coincide with the three crystal axes within the crystallographic unit [28]. The permittivity is, in general, complex and can be written as: ε_x = ε_x'–iε_x'', ε_y = ε_y'–iε_y'', and ε_z = ε_z'–iε_z''. For a colloid comprised the nanoparticles with permanent moments, the permittivity tensor of the colloidal system under an external magnetic field can be anisotropic [34]. While the light propagates along the direction of the external magnetic field, its absorption should be described by the permittivity perpendicular to the magnetization of the medium. For the α–FeOOH system, the direction of the magnetization, which is fixed inside the grains and lies essentially along the [010] direction, is defined as y, and the magnetic field/light path is defined as the Y direction. Consequently, when a magnetic field is applied along the direction defined, the direction of magnetization, i.e. [010] crystallographic direction of α–FeOOH nanocrystals tends to realign the Y direction, and the permittivity perpendicular to the direction of the magnetic field (Y direction) E_X = E_Z ( = E₂) is

\begin{array}{l} E_{X} = E_{X}^{'} - E_{X}^{''} \\ = (ε_{x}^{'} + ε_{z}^{'}) (1 - L (α) / α) / 2 + ε_{y}^{'} L (α) / α - i [(ε_{x}^{''} + ε_{z}^{''}) (1 - L (α) / α) / 2 + ε_{y}^{''} L (α) / α] \end{array}

From Eq. (10), it can be seen that when H→0, i.e. α→0, L(α) = α/3, and E_X = (ε_x' + ε_y' + ε_z')/3– i(ε_x'' + ε_y'' + ε_z'')/3 is just the permittivity of the system before the application of the magnetic field. For a moderate field, as in the experiment, L(α) can be taken as L(α) = α/3– α³/45, so L(α)/α = 1/3– α²/45, 1–L(α)/α = 2/3 + α²/45. Thus, when the incident light was parallel to the magnetic field (Y direction) and normal to the α−FeOOH colloidal film (XZ plane), according to Eq. (7) and Eq. (10),

σ_{a b s}^{a}

can be described as

σ_{a b s}^{a} = \frac{8 π d^{3}}{λ} \cdot \frac{E_{1} [ε_{x}^{''} + ε_{y}^{''} + ε_{z}^{''} + \frac{α^{2} (ε_{x}^{''} + ε_{z}^{''} - 2 ε_{y}^{''})}{30}]}{{[\frac{1}{3} (ε_{x}^{'} + ε_{y}^{'} + ε_{z}^{'}) + \frac{α^{2} (ε_{x}^{'} + ε_{z}^{'} - 2 ε_{y}^{'})}{90} + 2 E_{1}]}^{2}^{} + {[\frac{1}{3} (ε_{x}^{''} + ε_{y}^{''} + ε_{z}^{''}) + \frac{α^{2} (ε_{x}^{''} + ε_{z}^{''} - 2 ε_{y}^{''})}{90}]}^{2}}

Although the details of the permittivity of the α−FeOOH particle are unknown so that the

σ_{a b s}^{a}

is difficult to be calculated theoretically, it can be known still from the Eq. (11) that the

σ_{a b s}^{a}

will reduce with increasing magnetic field because, in the formula, the numerator increases with the α²(∝H²) and the denominator with the α⁴(∝H⁴). Consequently, the relative transmission coefficient T increases with the magnetic field, while l and N are constants. However, the variation of T will gradually slow down as α (or H) increases. While α² is large enough,

σ_{a b s}^{a} \to 0

and

T \to A

, so T will tend to a saturation with increasing applied magnetic field. Obviously, the maximum value of T depends on the absorption cross-section of the colloids in zero field, i.e. on the intrinsic dielectric properties of the colloids besides the thickness of the film and the particle volume fraction of the colloids.

4. Conclusions

The colloidal film based on spherical α−FeOOH nanoparticles exhibits a novel enhancement effect of transmitted light when an external magnetic field is applied. The magnetization of the particles is so weak that the effect cannot be attributed to field-induced particle aggregation. In addition, the size of the particles is only 8 nm or so, so enhancement of the light transmitted through α−FeOOH colloidal film can be regarded as a reduction of absorption cross-section in the applied magnetic field. It is apparent that the mechanism of the magnetic enhancement effect from the α−FeOOH colloids is not only different from the similar effect found with ferrofluids but also that of liquid crystals, whose additional magneto-optical effects result from the orientation of the anisotropic building blocks in the field [35,36]. The magnetic field in technical devices usually exhibits non-uniformity of the order of 10⁴-10⁵Gs/m [37], which would result in a relaxation process during the transmission of the light through the ferrofluid film [24]. Therefore, optical switching devices made using weakly magnetic α−FeOOH colloids could give faster and more stable responses compared with the general ferrofluids based on strongly magnetic nanoparticles, because the field-induced response is independent of the chain-like formation of the colloid nanoparticles and the motion of the chains.

Acknowledgment

The work has been supported by the Natural Science Foundation Project of P. R. China (11074205).

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The increase of the light transparency induced by a magnetic field for the colloid film based on α–FeOOH nanoparticles

Abstract

1. Introduction

2. Experiments

2.1 Description of the samples

2.2 The magneto-optical experiment

3. Results and discussion

4. Conclusions

Acknowledgment

References and links

Cited By

Figures (3)

Equations (11)

Optical Materials Express