Concentration and temperature effect in microstructure of ferrofluids

ARTICLE IN PRESS

Journal of Magnetism and Magnetic Materials 300 (2006) e221–e224 www.elsevier.com/locate/jmmm

Concentration and temperature effect in microstructure of ferrofluids Gy. To¨ro¨ka,, V.T. Lebedevb, D. Bicac, L. Ve´ka´sc, M.V. Avdeevd a

Research Institute for Solid State Physics and Optics, Budapest, Hungary Petersburg Nuclear Physics Institute, 188300 Gatchina, St. Petersburg district, Russian Federation c Center of Fundamental and Advanced Technical Research, Timisoara Branch of RAS, Romania d Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, Dubna, Russian Federation b

Available online 15 November 2005

Abstract The spatial correlations in magnetite-based ferrofluids (FF) with pentanol carrier have been investigated by small-angle neutron scattering, as dependent on the concentration of magnetic phase (C ¼ 0:6220 vol%) and temperature (20–85 1C). Some peculiarities in the structure of FF were detected. An anomalous increase of short range order by heating of low-concentrated FF (C
0:624:0 vol%); the formation of short range order at ambient temperature which weakens at growing concentrations C ¼ 7214 vol% and the existence of a stable structure at the highest concentration C
20 vol% when particles’ shell interpenetrate. Neutron scattering data are discussed with regard to the particles’ intrinsic magnetisation enhancement induced by ordering. r 2005 Elsevier B.V. All rights reserved. PACS: 61.12.Ex, 82.70.g, 83.80.Gv Keywords: Neutron scattering; Ferrofluid; Structure

1. Introduction Traditional approaches used in neutron studies of ferrofluids (FFs) (e.g. Guinier, model of spheres scattering independently) do not give any direct information, and real description of the structural peculiarities arises from a fine balance of particle interactions via dipole and molecular forces. This balance is influenced by temperature and concentration of magnetic phase, as well as the changes in state of surfactant layers due to both factors. A surfactant shell can be frozen or melted, deformed, weakened or strengthened under external factors and neighbouring particles. The knowledge of FFs’ behaviour at the nanoscale level promises a good progress in magnetic colloids technology. 2. Experimental We have carried out a series of SANS experiments on FFs of different concentrations (C ¼ 0:6220 vol%) at Corresponding author. Tel.: +36 1 392 2222; fax: +36 1 392 2501.

E-mail address: [email protected] (G. To¨ro¨k). 0304-8853/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2005.10.084

temperatures 20 and 85 1C in the range of momentum transfer q ¼ 0:0324:5 nm1 (BNC ‘‘Yellow Submarine’’ SANS facility) [1]. The sample pentanol-based FFs, stabilised by oleic acid [2], were prepared in the Magnetic Fluid Laboratory (Timisoara Branch of Romanian Academy). There was no applied magnetic field and we used the same samples at temperatures 20 and 85 1C. The raw data were treated in the usual procedures and normalised to the water standard. The detailed analyses were carried out using inverse Fourier transform (Program package ATSAS) [3]. 3. Results and discussion Data treatment in q-space does not allow to distinguish clearly the effects of particle form factor and interparticle correlations. These effects are mixed strongly. In order to get more information from scattering data we have done the Fourier analysis using the regularisation method, giving a real space presentation of the neutron scattering data. This is especially effective in dense FFs where approximation by the model of independently scattering particles is not correct.

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A spherical particle (homogeneous, radius Ro) can be characterised by individual correlation function [4] gðrÞ ¼ 1  ð3=4Þðr=Ro Þ þ ð1=16Þðr=Ro Þ3 in the range of radii 0prp2Ro . Obviously, any correlation exists only interior of the particle volume, and at r ¼ 2Ro the function g(r) gets a zero value. [3,5]. The function g(r) can be obtained from Fourier transform of the scattering intensity distribution I(q) measured in the neutron scattering experiment in the case of a diluted system. It is convenient to use a modified function PðrÞ ¼ gðrÞr2 showing correlation in the spherical layer. It takes a maximum at rm ¼ 1:0494 Ro . So the radius of particle from the position of maximum can be calculated. In dilute systems there are no structural peculiarities at r42Ro where PðrÞ  0. At high content of magnetic phase, the interparticle correlations at r42Ro come into view and dominate when the average distance between particles is close to their diameter. In concentrated systems at r42Ro we observe density fluctuations gðrÞ
hDCð0ÞDCðrÞi or other possible short range order in the particles arrangement. The latter is examined for a series of FF samples with a magnetic phase concentration C ¼ 0:6220 vol% at ambient (20 1C) and

high (85 1C) temperature. In Fig. 1(a) and (b) the scattering intensity distributions and the P(R) correlation function are shown at temperatures 20 and 85 1C at C
0:6 vol% of magnetite. A temperature-dependent interference effect is visible at small momentum transfers. It means that the interparticle correlations depend on temperature, and weaken when it increases. At moderate content of magnetite (C
4214 vol%, Figs. 2–4) a short range order is more pronounced than at a low concentration. At the same time, this ordering is more stable and weakly influenced by temperature. Correlation functions in all the samples show a strong maximum at Rm1
7 nm corresponding to the radius of the core Rm1
Ro . At doubled distance
2Rm1 the correlation function approaches zero because of limited core correlation length Lp2Ro
2Rm . The core is covered by a double surfactant layer (thickness d
4 nm). Therefore, the forbidden distances are 2Ro oRo2ðRo þ dÞ
20 nm if the shells repulse and do not interpenetrate. Indeed, in diluted FF we observe a minimum of the correlation function at R
15220 nm at low and

100 FF2, C=3.80 % vol. 20°C 85°C

10

10 FF1, C=0.584 % vol.

0.1

I(q), a.u.

I(q), a.u.

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1E-3 0.05

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FF2, C=3.80 %vol. 20°C 90°C

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0.4

15 0.05

0.1

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q, nm-1

(a) 2

q, nm-1

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0.3 FF1, C=0.584 % vol. 20°C 1

85°C

P(R), a.u.

P(R), a.u.

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0.1

FF2, C=3.80 % vol. 20°C 85°C 0

0.0

-0.1

-1 0

(b)

10

20

30

40

50

R nm

Fig. 1. (a) Measured patterns at magnetite C ¼ 0:6 vol% at T ¼ 201 and 85 1C. (b) The P(R) function at C ¼ 0:6% at T ¼ 201 and 85 1C.

0 (b)

10

20

30

40

50

R, nm

Fig. 2. (a) Measured patterns at C ¼ 3:8 vol%, T ¼ 201 and 85 1C; (b) The P(R) function found at C ¼ 3:8 vol%, T ¼ 201 and 85 1C.

ARTICLE IN PRESS G. To¨ro¨k et al. / Journal of Magnetism and Magnetic Materials 300 (2006) e221–e224

100

100

FF5, C=14.0 % vol. 20°C 85°C

FF3, C=7.00% vol. 20˚C 85˚C

10

10

200

I(q), a.u.

200

1 I(q), a.u.

I(q), a.u.

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0.01

100

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FF3, C=7.00 % vol. 20˚C 90˚C 20 0.05

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1 P(R), a.u.

P(R), a.u.

0.1

(a)

0

0

-1 -2

-2 0 (b)

10

20

30

40

50 0

R, nm (b)

Fig. 3. (a). Measured patterns at C ¼ 7%, T ¼ 201 and 85 1C; (b) The P(R) function obtained at C ¼ 7 vol%, T ¼ 201 and 85 1C.

moderate concentrations, C ¼ 4214 vol% (Figs. 2–4). At these concentrations a short range order exists that is proved by a well-defined maximum at Rmax
25–30 nm 42ðRo þ dÞ. At the highest amount of magnetite (C
20 vol%) the interference effects are damped. We interpret it as a result of particle shells’ interpenetration near the upper limit in the magnetic phase content. The spacing between particles gets a minimum value Rmax
18 nmo2ðRo þ dÞ. At the content C
20 vol% the temperature practically does not disturb the particles arrangement. Oppositely, at a low concentration of the magnetic phase we observe a temperature-dependent short range order, but it demonstrates an anomalous behaviour. As we found, at the lowest magnetite content the ordering appears at high temperature. It means that local interactions (clustering) are destroyed, and symmetric repulsive forces (pressure) create an order (C ¼ 0:6 vol%). This inverse temperature effect is visible at C ¼ 3:8 vol%, but at C ¼ 729 vol% it is not revealed.

10

20

30

40

50

R, nm

Fig. 4. (a). SANS patterns at C ¼ 14:0%, T ¼ 201 and 85 1C; (b) The P(R) function found at C ¼ 14:0 vol%, T ¼ 201 and 85 1C.

From data at high q we found the total surface area of magnetite cores. At qb1/Ro in Porod approximation the scattering intensity is equal to IðqÞ ¼ A=q4 þ B. Here, the parameter A
2pSt ðDKÞ2 is proportional to the squared contrast factor DK and the total surface of particles in the sample. The constant B is an incoherent background. Such a Porod approximation gives a Fe3O4-particles’ surface. We normalized the measured magnetization of the fluid to the total particles’ surface, and found an anomalous increase of this modified magnetization at C ¼ 0:627:0 vol%. Then, at C ¼ 9220 vol% the magnetization maintains at the same level (Fig. 5). This behaviour can be explained by the action of internal magnetic field, generated by the particles ensemble to each particle. This field induces a higher magnetization of the particle. If the field is weak (diluted system) we observe a well-known effect when particles’ saturation depends on their size (surface/volume ratio) [6] measured with the ferromagnetic resonance method. Due to the internal field this saturation grows up till the theoretical value (Fig. 6).

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400

100 FF6, C=20.1 % vol.

C

20°C 85°C

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300 M / St, a.u.

I(q), a.u.

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0.1 FF6, C=20.1 % vol. 20°C 90°C

0.01

200

Magnetization per particle (in arb.units) dependent on particles' concentration

100

20 0.05

0.1

0.5

1E-3 (a)

0

0.05

0.1

1

5

0

q, nm-1

5

10 C, % vol.

15

20

Fig. 6. Magnetization, normalized to total surface area of particles vs. volume content of magnetite.

4

FF6, C=20.1 % vol. 20°C 2

colloidal particles contacting by their shells or being tightly packed at content C
20 vol% when shells interpenetrate. The cross-over in the structure leads to an anomalous behaviour of magnetisation per particle. It reveals the kink at the characteristic concentration C*
7 vol%. Below the threshold CoC  , a growth of the particle moment is observed with concentration, while at CXC  a saturation is achieved. Thus, we proved first the effect of short range order on the intrinsic magnetic properties of particles influenced by internal mean field in a magnetised ferrofluid.

P(R), a.u.

85°C

0

-2 0 (b)

10

20

30

40

50

R, nm

Fig. 5. (a) SANS patterns at C ¼ 20:1 %vol, T ¼ 201 and 85 1C; (b) The P(R) function obtained at C ¼ 20:1 vol%, T ¼ 201 and 85 1C.

4. Conclusion A series of SANS measurements on ferrofluids with different concentrations of magnetite at ambient and high temperature (85 1C) showed the evolution of spatial particle correlations from a rare ensemble of magnetic dipoles slightly correlated to the ordered system of

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