Optics Communications 336 (2015) 278–285

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Optics Communications

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Am Fass

journal homepage: www.elsevier.com/locate/optcom

The effect of suspended Fe3O4 nanoparticle size on magneto-opticalproperties of ferrofluids

Surajit Brojabasi, T. Muthukumaran, J.M. Laskar 1, John Philip n

SMARTS, Metallurgy and Materials Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, India

a r t i c l e i n f o

Article history:Received 30 July 2014Received in revised form10 September 2014Accepted 24 September 2014Available online 13 October 2014

Keywords:FerrofluidNanofluidScatteringDiffractionSpeckle patternAggregation kinetics

x.doi.org/10.1016/j.optcom.2014.09.06518/& Elsevier B.V. All rights reserved.

esponding author. Fax: þ91 44 27480356.ail address: philip@igcar.gov.in (J. Philip).esent address: Max Planck Institute for Dynberg 17, 37077 Göttingen, Germany.

a b s t r a c t

We investigate the effect of hydrodynamic particle size on the magnetic field induced light transmissionand transmitted speckle pattern in water based ferrofluids containing functionalized Fe3O4 nanoparticlesof size ranging from 15 to 46 nm. Three water-based magnetic nanofluids, containing Fe3O4 nanoparticlesfunctionalized with poly-acrylic acid (PAA), tetra-methyl ammonium hydroxide (TMAOH) and phos-phate, are used in the present study. In all three cases, the transmitted light intensity starts decreasingabove a certain magnetic field (called first critical field) and becomes a minimum at another field (secondcritical field). These two critical fields signify the onset of linear aggregation process and zipperingtransitions between fully grown chains, respectively. Both these critical fields shift towards a lowermagnetic field with increasing hydrodynamic diameter, due to stronger magnetic dipolar interactions.The first and the second critical fields showed a power law dependence on the hydrodynamic diameters.The dipolar resonances occurring at certain values of the scatterer size, leads to the field inducedextinction of light. Both the onset of chaining and zippering transitions were clearly evident in the timedependent transmitted light intensity. Above the first critical field, the lobe part of the transmittedintensity and the lobe speckle contrast values increase with increasing external magnetic field due toreduced Brownian motion of the field induced aggregates. The speckle contrast was highest fornanoparticle with the largest hydrodynamic diameter, due to reduced Brownian motion. These resultsprovide better insight into field dependent light control in magnetic colloids, which may find interestingapplications in magneto-optical devices.

& Elsevier B.V. All rights reserved.

1. Introduction

Magnetic colloids such as ferrofluids and ferro-emulsions areexciting systems for both fundamental studies and for practicalapplications, owing to their unique tunable optical properties inthe presence of an external magnetic field [1–9]. The tunableoptical properties originate from the external field induced struc-tural reorganization of suspended magnetic colloidal particles [10–13,14]. The field dependent tunable optical properties of ferro-fluids have been used in developing optical sensors [15,16],tunable optical filters [17], tunable photonic devices [18] etc. Theeffect of external magnetic field on aggregation of magneticnanoparticles and its influence on propagation of light have beenstudied extensively [19]. An understanding of various parametersinfluencing the aggregation process in magnetic nano-colloids is

amics and Self-Organization,

important from both fundamental and practical application pointof view [20].

Recently, the role of the applied field exposure time and viscousforce on the particle aggregation and de-aggregation kinetics inmagnetic nanofluids was studied experimentally using light scat-tering techniques [21]. Also, the kinetics of particle aggregation inmagnetic nanofluid have been studied using various techniques[22–25]. The functional groups adhered to the nanoparticles(stabilizers) can influence the kinetics of field induced chainlikeformation in magnetic nanofluid [26]. Among other influencingparameters, the dipolar interaction among the magnetic nanopar-ticles is the main driving force for particle aggregation process,and the field induced structural transitions [1]. However, for agiven condition (constant external magnetic field strength andparticle volume fraction), the particle size has a strong influenceon the dipolar interactions, that can affect the magneto-opticalproperties of nanofluids significantly. Studies show that the non-linear index of refraction and photon absorption in magneticnanofluids are affected by the nanoparticles size and its surfacecoating agents [27]. To the best our knowledge, no systematicexperimental study has been reported on the role of suspended

S. Brojabasi et al. / Optics Communications 336 (2015) 278–285 279

particle size on the external field induced particle aggregationprocess, and the resulting optical properties in magneticnanofluids.

In this paper, we have systematically studied the variation ofnormalized transmitted light intensity and transmitted specklepatterns as a function of external magnetic field in three differentwater based magnetic nanofluids containing magnetic nanoparti-cles with three different hydrodynamic diameters. The primaryobjective of this study is to obtain insight into the effect of particlesize on magnetic field induced aggregation and its kinetics.

2. Materials and experimental set-up

Three water-based stable magnetic nanofluids containing Fe3O4

nanoparticles coated with (i) poly-acrylic acid (PAA) (ii) tetra-methyl ammonium hydroxide (TMAOH) and (iii) phosphate wereused in our studies. The size distributions in dispersed mediumwere measured using dynamic light scattering (DLS). Fig. 1 showsthe size distributions of the three magnetic nanofluids. Themeasured average hydrodynamic sizes of the PAA, TMAOH andphosphate coated nanoparticles were 46, 30 and 15 nm, respec-tively. These suspensions showed excellent long-term stabilityeven after prolonged application of strong magnetic fields. Thevolume fractions (ϕ) for all the samples were kept constant at0.00916 in all our experiments. In all the three magnetic nanofluidsamples, the particle sizes were much less than the incident lightwavelength i.e. a⪡λ. The forward transmitted light intensity wasmeasured as a function of applied magnetic field, where thedirection of the applied field is perpendicular to the direction ofthe incident light. Details of the experimental technique andschematic of the experimental set up are described elsewhere[28,29].

3. Results and discussions

Fig. 2 shows the transmitted light scattering pattern projectedon a screen from three different magnetic nanofluids at theexternal magnetic fields 0, 100, 200, 300 and 400 G. Fig. 2(a–e)corresponds to PAA coated Fe3O4 nanofluid, Fig. 2(f–j) correspondsto TMAOH coated Fe3O4 nanofluid and Fig. 2(k–o) corresponds tophosphate coated Fe3O4 nanofluid. In all three cases ϕ¼0.00916.The external magnetic field was increased at a constant ramp rate

Fig. 1. Dynamic light scattering based characterization (size distribution) of threedifferent magnetic nanofluids with PAA, TMAOH, Phosphate as nanoparticlessurface coating agents.

of 2.5 G/s. In the absence of an external field (B¼0 G) only a brightcircular spot was observed. But on increasing the external mag-netic field, a straight line like pattern is observed. Similar trend isobserved in all three magnetic nanofluids. Nevertheless, featuresof the straight line pattern were slightly different for those threesamples. For the PAA coated Fe3O4 nanofluid, the straight linepattern was formed within a magnetic field strength of 100 G,whereas, in the other two samples they were discernible above100 G only. The straight line like pattern was observed at a lowerexternal magnetic field for the TMAOH coated Fe3O4 nanofluid,compared to the phosphate coated nanofluid. What is the origin ofthese straight line patterns? The suspended magnetic nanoparti-cles acquire dipole moments ( π χ=m a B( /6) 3 ) in the presence of anexternal magnetic field [30,31]. Here, a is the diameter of thesingle bare magnetic nanoparticle, χ is the effective susceptibilityof an individual nanoparticle, and B is the magnitude of externalmagnetic field. The anisotropic interaction energy Uij between twoidentical, parallel, point dipoles is given by [21,31]

⎛⎝⎜⎜

⎞⎠⎟⎟θ

μπ

θ=

−U r

m

r( , )

4

1 3 cos

(1)ij ij ij

ij

ij

20

2

3

where μ0 is the magnetic permeability of free space, rij is themagnitude of the vector describing the distance between thecenters of ith and jth nanoparticles, and θij is the angle betweenthe vector rij and the external field vector. The effective magneticinteraction between two magnetic nanoparticles is described bythe coupling constant πμ χ= − =L U k T a B k T/ /72B B0

3 2 2 [21,31]. Here,kB is the Boltzmann constant and T is the temperature. Themagnetic nanoparticles in the dispersion self-assemble into struc-tures that are aligned along the external magnetic field, when L⪢1[21,31]. Such field induced aggregation of magnetic nanoparticlesinto chainlike structures has been verified experimentally [32–34]and by computer simulation [35]. When light interacts with suchchain like structures with their axis perpendicular to the directionof the incident light, a straight line pattern is formed [36].

The optical properties of particle aggregates in dispersion isdifferent from that of solid particles, because the optical cross-sectional area of the particle aggregates in the former becomeslarger than the bare solid particles of the same mass [37]. Theexternal field induced evolution of transmitted light pattern(straight-line like), in magnetic nanofluid depends on the hydro-dynamic diameter (dh) of magnetic nanoparticles [36]. As thehydrodynamic diameter of the PAA coated nanoparticles was thehighest, the straight line like pattern was fully evolved within anexternal magnetic field strength of 100 G. On the other hand, forthe TMAOH and phosphate coated nanoparticles, straight line likepatterns were observed at a higher external magnetic field.Because the coating layer thickness in all the three cases arenearly same (�1–1.5 nm) and the primary Fe3O4 nanoparticle sizeis �10 nm, the observed hydrodynamic diameters indicates that2–4 primary particles form aggregates upon coating with differentfunctional groups.

Fig. 3 shows the normalized transmitted light intensity as afunction of external magnetic field for different magnetic nano-fluids. The inset of Fig. 3 shows the transmitted light pattern fromthe phosphate coated magnetic nanofluid (dh¼15 nm) at anexternal magnetic field of 430 G. In general, the normalizedtransmitted light intensity as a function of external magnetic fieldshows similar behavior for all the three samples. Initially, thenormalized transmitted light intensity increases and attains amaximum at a certain external magnetic field, called the firstcritical field (BC1).

Beyond BC1, the normalized transmitted light intensity de-creases continuously and becomes a minimum at a second criticalfield (BC2). The values of BC1 (and BC2) for the magnetic nanofluids

Fig. 2. Transmitted light intensity projected on a screen from three different magnetic nanofluid at external magnetic field 0, 100, 200, 300, 400 G. (a–e) PAA coated Fe3O4

nanoparticles. (f–j) TMAOH coated Fe3O4 nanoparticles. (k–o) Phosphate coated Fe3O4 nanoparticles. In all three cases ϕ¼0.00916.

Fig. 3. Normalized transmitted light intensity as a function of external magneticfield from three different magnetic nanofluids in the same dispersion (water) butwith different particle hydrodynamic diameters (46, 30, 15 nm) and surface coatingagents (PAA, TMAOH, Phosphate). ϕ is 0.00916 and the field ramp rate �2.5 G/s inall the three systems. Inset image shows the transmitted light pattern frommagnetic nanofluid at 430 G.

Fig. 4. Critical magnetic fields (BC1 and BC2) as a function of magnetic nanoparticleshydrodynamic diameter (dh). BC1 and BC2 follow power law decay with hydro-dynamic diameter (BC�dh

�x) where the exponents are 0.41 and 0.44, respectively.

S. Brojabasi et al. / Optics Communications 336 (2015) 278–285280

with phosphate, TMAOH, and PAA based magnetic nanofluids are126 (632), 98 (478) and 78 (382) G, respectively. This shows thatthe critical fields shift towards higher field values with decreasinghydrodynamic diameters of suspended nanoparticles. The earlierreports show that the magnitudes of the critical magnetic fields(BC1 and BC2) depend on the particle volume fractions and followpower law dependence [38] due to an disorder–order transition of

magnetic nanoparticles in the dispersion [28,39]. Here, we haveshown that for three different magnetic nanofluids, with samevolume fraction and varying hydrodynamic diameters, the criticalfields shift towards higher magnetic fields with decreasing thehydrodynamic diameter of dispersed magnetic nanoparticles.Fig. 4 shows the variation of the critical magnetic fields as afunction of the hydrodynamic diameters of the magnetic nano-particles. BC1, BC2 show a power law dependence with dh of thecoated magnetic nanoparticles in water (BC�dh

�x). The values ofthe exponent (x) for BC1, BC2 are 0.41, 0.44, respectively. The

Fig. 5. (a–c) The schematic of the aggregation process (left), the transmitted light pattern (centre) and the intensity profile of the scattered pattern across the distance(right), at B¼0, B4BC1 and B4BC2.

S. Brojabasi et al. / Optics Communications 336 (2015) 278–285 281

variation of transmitted intensity as a function of applied fieldstrength is the same irrespective of the polarization direction ofthe incident light [28].

Near the first critical field, the magnetic nanoparticles formsingle chainlike structure along the direction of the externalmagnetic field and the aspect ratio of these nanochains increasesprogressively with increasing external magnetic field. Beyond thesecond critical field, structural rearrangement occurs due to lateralaggregation of the nanochains where several chains are zipped toform bundles [31]. This aggregation process depends on theexternal magnetic field and exposure time [21,31]. Fig. 5 showsthe schematic of the aggregation process, the transmitted lightpattern and the intensity profile of the scattered pattern at B¼0,B4BC1 and B4BC2. In the absence of an external magnetic field,the magnetic nanoparticles are in random motion where thetransmitted light shows a circular spot with the entire lightintensity distributed within the spot. For B4BC1, the magneticnanoparticles form single chainlike structure along the direction ofthe external field, where some intensity of the transmitted light isdistributed in the straight line like pattern. At B4BC2, nanochainsare zippered due to lateral attraction where the intensity distribu-tion along the line was significantly larger compared to the earliertwo cases.

For a given volume fraction, a nanofluid sample with smaller dhrequires a higher external field strength to meet the condition L⪢1.The observation of shifting of BC1 and BC2 towards higher magneticfields with decreasing the hydrodynamic diameters (Fig. 4) was ingood agreement with the above condition.

The external magnetic field induced aggregation increases theparticle aggregate size and is related to Stokes–Einstein's relation,[40,41].

πη=D

k Td3 (2)

B

h

Here D is the diffusion coefficient of the dispersed nanoparticleand η is the viscosity of the dispersion medium. Therefore, withincreasing hydrodynamic diameter of magnetic nanoparticles, thediffusion coefficient decreases [42,43]. Thus, for particles withlarger diameter, the onset of chain formation commences at alower magnetic field, which is in good agreement with the shiftingof the critical fields to lower external magnetic field with increas-ing hydrodynamic diameter of the magnetic nanoparticles(Figs. 3 and 4).

The optical absorption studies in magnetic nanofluid show thatthere is no absorption peak in the visible region in presence of aweak external magnetic field [28]. Therefore, the extinction oftransmitted light from a magnetic nanofluid in the presence of anexternal magnetic field is due to the increase in light scatteringfrom the induced chain like structures (cylinders) oriented alongthe external magnetic field direction [38]. According to Miescattering theory (applicable when the scatterer size becomescomparable to the incident light wavelength), the total lightextinction efficiency factor (Qext) and transport mean free path( )tr are given by the following expressions [44,45].

Fig. 6. (a) Total scattering extinction efficiency (Qext) as a function of size parameterka. (b) Transport mean free path ( )tr as a function of size parameter ka.

Fig. 7. Normalized transmitted light intensity as a function of time at criticalmagnetic fields 382, 478, 632 G from three different magnetic nanofluids.

S. Brojabasi et al. / Optics Communications 336 (2015) 278–285282

∑= + +=

∞

Qka

n a b2

( )(2 1)Re( )

(3)ext

nn n2

1

θ=

− < >1 cos (4)tr

Here, the Mie scattering parameters an and bn depend on thesize parameter and refractive index of the scattering medium,

θ⟨ ⟩ = +⁎a b a bcos Re( )/( )i i i i2 2

is the forward anisotropy factor, kais the size parameter and is the photon mean free path. Formagnetic nanofluids, the refractive index increases with externalmagnetic field [46,47] and hence affects the Mie scattering para-meters. Recently, we have experimentally demonstrated that theimaginary part of the refractive index of a ferrofluid emulsionincreases with increasing volume fraction and the external mag-netic field strength [48]. Further, an increase in scatterer size, dueto increased dipolar attractions leads to an enhancement of thetransport mean free path ( )tr [38]. At certain values of externalmagnetic fields (called critical fields), the scatterer sizes are suchthat dipolar resonances occur, which significantly increases lightscattering and thereby causing a field induced extinction of light.Recently a theoretical analysis by Bhatt et al. [47] in bidispersedmagnetic colloid composed of micrometer size magnetic spheresdispersed in a nonmagnetic liquid carrier shows that field depen-dent oscillatory behavior in θ⟨ ⟩cos , k tr , energy transport velocity(VE) and light diffusion constant that produces standing wavesinside the field induced scatterers. The external field inducedresonant behavior causes a buildup of standing waves inside thescattering medium and leads to a significant decrease in thetransmitted light through magnetic nanofluids [28,49]. Fig. 6shows the theoretical plot of total light extinction efficiency(Qext) and transport mean free path ( )tr as a function of the sizeparameter, where the resonant behaviors can be observed atcertain ka. With increasing hydrodynamic diameters of the mag-netic nanoparticles, the onset of external field induced aggregationtakes place at a lower field value.

When an incident light gets scattered from a cylindrical sur-face, the scattered pattern takes the shape of a cone. The inter-section of the cone of the scattered light on the observation screengives the scattered pattern. The shape of the scattered patterndepends on the angle between the incident light and the cylinderaxis [36]. When the incident angle is 90° with the cylinder axis,the scattered pattern takes the shape of a straight line with a spotat the centre [Figs. 2, 3, 5 and 8]. Therefore, the observed scatteredpattern under the applied field, a straight line with a laser spot atthe centre, is due to the scattering of light from the linear chainlike aggregates of nanoparticles (cylinders). If there is only onescattering cylinder, then the incident laser spot contains a diffrac-tion pattern. However, under an applied field, large number ofcylindrical aggregates of magnetic nanoparticles are formed in themagnetic nanofluid, which results in multiple light scattering fromthe cylinders inside the nanofluid. The maxima and minima of thediffraction pattern from different cylinders overlap each other,resulting in a diffused pattern, which is a cumulative effect of lightscattering from many cylindrical surfaces [36]. Therefore, theobserved scattered straight light pattern is a surface scatteringphenomenon that depends only on the incident angle and it doesnot contain information regarding the detailed internal structuresinside the magnetic nanofluid.

If the dispersed magnetic nanoparticle size is large (�40 nm)[50], the magnetic dipolar interaction is very strong and theparticles are no longer single domain. It is well established thatthe particle size should be below 10 nm to be free from sedimen-tation and dipolar aggregation [1]. Also, when the size of dispersedparticles is larger, the dispersion becomes prone to sedimentation.The magnetic nanofluid used in the present experiment is highly

stable against sedimentation (shelf life 45 years) and dipolaraggregation, and the observed scattered pattern is perfectlyreversible and are the same irrespective of the sample position.Fig. 7 shows the normalized transmitted light intensity as afunction of time at the second critical fields 382, 478 and 632 Gfor the PAA, TMAOH and phosphate coated magnetic nanofluids,respectively for a ϕ¼0.00916. The higher critical fields occur dueto the zippering of magnetic field induced chains due to attractive

Fig. 9. Lobe speckle contrast (CL) as a function of external magnetic field in threedifferent magnetic nanofluids. Solid lines correspond to linear regression analysisof the experimental data. Inset image (a) the scattered pattern from magneticnanofluid (phosphate coated Fe3O4 nanoparticles in water) at B¼300 G and image(b) the 3D surface plot for intensities of speckles on small portion of the scatteredlobe part at B¼300 G.

S. Brojabasi et al. / Optics Communications 336 (2015) 278–285 283

energy between them when the chain is off registry [31]. It can beobserved from Fig. 7 that the normalized light intensity decreaseswith time and reaches a minimum value. The time correspondingto the minimum value of the normalized transmitted light in-tensity is designated as tmin. Beyond tmin, the normalized trans-mitted intensity is found to increase with time. It is speculatedthat after achieving equilibrium zipped structures, more space isavailable between them, which causes the normalized transmittedlight intensity to increase again. The effect of hydrodynamicdiameters on the tmin is also evident from Fig. 7. For the PAAcoated magnetic nanoparticles (dh�46 nm), the decay of normal-ized transmitted light intensity is fastest with lowest tmin. On theother hand, the rate of increase of normalized transmitted lightintensity is slowest for the phosphate coated magnetic nanopar-ticles (dh�15 nm). Overall, tmin shifts towards lower values withincrease in hydrodynamic diameter.

The straight line lobe part in the transmitted light pattern isdue to scattering of incident light from the chain like structuresoriented towards the direction of the external magnetic field,which was perpendicular to the direction of the incident light inthe present case. Fig. 8 shows the variation of the intensity of aportion of the lobe part (indicated in the inset of Fig. 8 forphosphate coated magnetic nanofluid at an external magneticfield of 400 G) as a function of external magnetic field for the threemagnetic nanofluids with different hydrodynamic diameters. Itcan be seen that for all the three samples, the intensity of the lobepart remained constant at a very low value up to a certain externalmagnetic field, designated as lobe critical field (BLC). Beyond thislobe critical field, the intensity of the lobe part increases con-tinuously with increasing external magnetic field. Beyond BLC, theintensity of the lobe part increases due to field induced chainlikestructure formation. The BLC is highest for the phosphate coatedmagnetic nanoparticles dispersed in water with a smallest dh (i.e.15 nm) whereas, the BLC was the lowest for the PAA coatedmagnetic nanoparticles. Therefore, the critical lobe field shifts tohigher values with decreasing hydrodynamic diameters.

The combination of bright and dark intensity points and theirradiance level in-between these two extremities on the lobe partof the transmitted light intensity pattern constitutes speckles[51,52]. Light propagation through disordered colloidal media likemagnetic nanofluid produces speckle pattern due to interferenceof the de-phased scattered wavelets emanating from the randommedia [53–56]. Measurement of speckle parameters can provide

Fig. 8. Lobe intensity as a function of external magnetic field from three differentmagnetic nanofluids. (Inset) the transmitted light from magnetic nanofluid at400 G.

valuable information about soft condensed system [57–60].Furthermore, structural transition during disorder–order or viceversa in colloidal media is studied by measuring speckle para-meters [61]. If the randomness of the media dies out andapproaches towards an ordered state, the probability that thescattered wavelets from media will be in phase rather thandephased is higher. This leads to the enhanced probability ofconstructive interference of the scattered waves [51]. In thepresent case, the speckles on the lobe part of the transmitted lightintensity pattern become prominent after the first critical field.The speckle contrast (C) is defined as the ratio of the standarddeviation (s) of the intensity (I) to the mean intensity ⟨I⟩ of thespeckle pattern, as described below [51].

σ≡ =−

CI

I I

I (5)

2 2

For a static speckle pattern, the speckle contrast is equal tounity (maximum value), which is called a ‘fully developed’ specklepattern [62]. In dynamic systems, the speckle contrast is less thanunity due to the motion of scattering centers and the overallspeckle pattern appears blurred. Fig. 9 shows the variation of thespeckle contrast on a lobe part as a function of external magneticfield for all three magnetic nanofluids. The measurement of thespeckle contrast is done in the external magnetic field range of100–600 G. The speckle contrast on the lobe part originates due tothe scattering from the ordered internal structure (i.e. linearaggregates). The inset of Fig. 9 shows the lobe speckle patternfor the phosphate coated magnetic nanofluid at an externalmagnetic field of 300 G.

Fig. 9 inset (a and b) shows the scattered light pattern from thephosphate coated nanofluid and the 3D surface plot of speckleintensity distribution of a part of the lobe, respectively. It isobserved that the speckle contrast (CL) in the lobe part increaseslinearly with increasing external magnetic field. This shows thatthe random Brownian movement of the aggregates decreases withincreasing external magnetic field strength. Similar trend isobserved in all three samples. For a given external magnetic field,

S. Brojabasi et al. / Optics Communications 336 (2015) 278–285284

CL is higher for magnetic nanofluid with larger hydrodynamicdiameter.

It should be noted from Fig. 9 that the speckle contrast value issignificantly lower than unity at higher external fields (B4500 G),though the scatterers are almost stationary in the dispersionmedium-water. This is probably due to the surface roughness inthe external magnetic field induced chain like structures. Also, thethermal fluctuations in the carrier liquid can restrict the specklepattern from being ‘fully developed’ [51]. For a given external fieldstrength, the nanoparticles with the highest particle diameter willhave the strongest coupling within the chains. Therefore, withincreasing hydrodynamic diameter, a reduced thermal fluctuationand a higher value of speckle contrast is expected, which is in goodagreement with our experimental findings (Fig. 9).

4. Conclusions

The effect of hydrodynamic particle size on the magnetic fieldinduced light transmission and transmitted speckle pattern inwater based magnetic nanofluids, containing poly-acrylic acid(PAA), tetra-methyl ammonium hydroxide (TMAOH) and phos-phate functionalized Fe3O4 nanoparticles of size ranging from 15to 46 nm, is studied. In all three nanofluids, the transmitted lightintensity shows two distinct critical magnetic fields, correspond-ing to the onset of aggregation and the onset of zippering. Both thecritical fields shift towards lower magnetic fields, as the hydro-dynamic particle diameters increases and also shows a power lawdependence on the hydrodynamic diameters. The extinction oflight occurs at some critical fields due to dipolar resonances. Thetime dependent study shows that the transmitted intensitybecomes a minimum prior to zippering transition but increaseson zippering transitions due to opening up of the otherwise filledspace between chains. The first critical field decreases withincreasing hydrodynamic diameter. Above the first critical field,the lobe part of the transmitted intensity and the lobe specklecontrast increases with increasing magnetic field. The specklecontrast is higher for nanoparticles with larger hydrodynamicdiameters, due to reduced Brownian motion of the aggregatesdue to stronger coupling.

Acknowledgements

The authors thank Dr. T. Jayakumar and Dr. P.R. Vasudeva Raofor fruitful discussions. J.P. thanks the Board of Research NuclearSciences (BRNS) (Grant no. 2009/38/01/BRNS) for support througha research grant for the advanced nanofluid developmentprogram.

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