Stati Magneto Optial Birefringene of
New Eletri Double Layered Magneti Fluids
J. Depeyrot 1
, G. J.da Silva 1
, C. R. Alves 1
,E. C. Sousa 1
,M. Magalh~aes 2
,
A. M. Figueiredo Neto 2
,M. H. Sousa 3
, and F. A. Tourinho 3
1
ComplexFluidsGroup,Instituto deFsia,
UniversidadedeBraslia,CaixaPostal04455,70919-970, Braslia(DF),Brazil
2
Institutode Fsia, UniversidadedeS~aoPaulo,
CaixaPostal66318, S~ao Paulo(SP),Brazil
3
Complex FluidsGroup,Institutode Qumia,
UniversidadedeBraslia,CaixaPostal04478,70919-970 Braslia(DF),Brazil
Reeivedon27May,2001
MagnetibirefringenemeasurementsareperformedunderastatieldonEletriDoubleLayered
Magneti Fluids based on opper and zin ferrite nanostrutures. The optial birefringene is
related to a single-partile eet and well desribed by a Langevin model whih inludes a
log-normaldistributionofpartiles. Bytheeld-induedbirefringenelevel,thesenewmagnetiuids
are omparabletousualones,aresultwhihouldoeranewwayforbiologialappliations.
I Introdution
Nowadays, Magneti Fluids (MF) or Ferrouids are
stable olloidal suspensions of magneti monodomain
nanosizedpartilesdispersedin aspeiliquidarrier
[1℄. Dueinparttotheoexisteneofastrong
magneti-zationwithuiditypropertiesandalsoto the
versatil-ityofmoleularliquidsarrierwhih anbeemployed,
suhartiialsystemsleadsto numeroustehnologial
appliations[2℄. Fundamentalstudiesaregenerally
per-formedineletridoublelayeredmagnetiuids
(EDL-MF) [3℄ where the stabilization is ahieved by
intro-duing,betweenpartiles,eletrostatirepulsivefores
obtainedbyanadjustablesurfaehargedensity.
MF have long been investigated using
magneto-optialbirefringenemeasurements. Forinstane,
mag-neti olloidal sols based on Fe
3 O
4
[4℄, -Fe
2 O
3 [5℄,
CoFe
2 O
4
[6℄andNiFe
2 O
4
[7℄nanopartilesareoptially
ative and exhibit strong optial birefringene under
magneti elds. In diluted solutions (typially of the
order of 10 16
partiles per m 3
), the magneto-optial
behavior of MF an be well desribed by a Langevin
formalismthat inludes a log-normalsize distribution
ofroughlyspherialpartiles[4,8℄.
Nevertheless, until now, the origin of the MF
magneto-optialbirefringeneisnotwellunderstood. A
possibleeld-induedeetonthepartilematerial,the
ubi(spinel)rystalstrutureandthenearlyspherial
partileshapeobservedbyeletronmirosopydonot
explain the optial anisotropy. Optial birefringene
anddihroismofsurfatedMFhavebeeninterpretedin
termsoforientationoraggregationinthepreseneofa
magnetieldofpartileaggregatesalreadypresentin
thesolutionintheabseneoftheeld[9℄. However,in
EDL-MF,reentSmallAngleX-raysattering
measure-mentsperformedonalargenumberofsamplesshowat
zeroeldalowdegreeofpartileaggregation[10℄. F
or-mationofhain-likeaggregatesintheappliedeld has
alsobeenproposed toaountforthemagneto-optial
behaviorof MF[11℄. Nevertheless,suh model results
inonsiderabledeviationfromexperimentsatloweld.
Furthermore,aeldinduedaggregationofpartilesin
EDL-MFisrejetedbySmallAngleNeutronSattering
resultsiftheionistrengthofthesolutionsislessthan
0.05 mol L 1
with partiles of surfaeharge density
about0.2Cm 2
[12℄.
Morereently, stati magneto-optialbirefringene
of size sorted-Fe
2 O
3
nanopartilesindiated[13℄, on
the ontrary, that the optial anisotropy observed in
EDL-MF is not due to ooperative proessof partile
agglomerationintheeldbuttoapartilesurfae
mag-netianisotropy,omingfromthedisontinuityof
netiinterationsbetweenindividualspinswhihreside
at thepartilesurfae,oupledtoaslightelliptiityof
thepartiles.
The aim of the present work is to investigate the
stati magneto-optial birefringene of new EDL-MF
based on opper and zin ferrite nanopartiles. The
hemial synthesis of these ferrouidsas well as their
magneti properties have already been presentedin a
previouspaper[14℄. Suh MF ouldoer anew
alter-native for biologial appliations sine their iron
on-tent is redued and they would therefore be notably
easier to titrate in biologial in vivo experiments. In
suhaontext,itisessentialtohektheiroptial
bire-fringenelevelsineoptialbirefringenemeasurements
haveshowntobeausefultoolintestingthegraftingof
magnetinanopartilesbyantibodies[15℄.
The urrent work is dividedas follows. In setion
II,wegiveabriefdesriptionoftheEDL-MF hemial
synthesisaswell as ahemialand struturalanalysis
of thesynthesizednanopartiles. Partsofourprevious
magnetization dataobtainedat 300Karereviewedin
setionIII.Then,in setionIV,statimagneto-optial
measurements are presented and disussed within the
frameworkoftheLangevinmodel.
II Chemial synthesis and
par-tile haraterization
EDL-MF synthesis. The EDL-MF elaborationis
ar-ried out on three basi steps [14℄: rstly, the
fer-rite nanopartilessynthesis,then thehemialsurfae
treatment, and nally thepeptization of the partiles
in a stable aqueous olloidal solution. CuFe
2 O
4 and
ZnFe
2 O
4
oxidenanopartiles were prepared using
hy-drothermalopreipitatingaqueous solutionofCuCl
2
-FeCl
3
and ZnCl
2 -FeCl
3
mixtures,respetively,in
alka-line medium. After the opreipitation step, the
pre-ipitate is washed in order to suppress the high ioni
strength of the medium and the partile surfae is
leanedbya(2molL 1
)HNO
3
solution. Moreover,to
ensurethethermodynamialstabilityofthepartilesan
empirial proess hasbeenproposed: thepreipitated
isboiledwitha0.5molL 1
Fe(NO
3 )
3
solution. Then,
thepartilesareonvenientlypeptized inaidmedium
by theadjustmentof theionistrength, resultingin a
stable solofhighquality.
Chemialanalysis. OnetheEDL-MFsynthesishas
been performed, the sample omposition is ontrolled
by hemial analysis: iron(III) titration isdetermined
by dihromatometry. Copper(II) titrationis done by
volumetri analysis with iodine and zin (II) is
quan-tiedusing plasma emissionspetrosopy. Then, eah
MF preursor solution is diluted at two volume
fra-tion of magneti nanomaterial, = 0.73% and =
0.15%for Cu-basedsamples and =0.75% and =
0.16%forZn-basedones. Thesevolumefrationvalues
have been hosen in order to perform magnetization
and magneto-optial measurements on suÆiently
di-lutesampleswhere the inter-partiles interationsan
beonsideredasnegligibleandtheindependentpartile
modelwellworks.
Magneti material yield. The experimental
proe-dureusedtodeterminethebestvalueindivalentmetal
molarfrationisanadaptationofthemethodof
ontin-uousvariationor\Job'smethod". Aseriesofsolutions
ofequal totalonentrationin metal[M 2+
+ Fe 3+
℄ is
prepared with dierent relative amounts of M 2+
and
Fe 3+
reating in exess of sodium hydroxide in order
to obtainthe ferrite nanopartiles. Foreah solution,
theorrespondingmagnetimaterialyieldismeasured
usinganadaptationoftheGouymethod,wherean
ap-parentinreasein massmanbedetetedwhenthe
solutionissubmittedtoamagnetieldgradient. Fig.
1displaysthevariationsofthenormalizedvalueofthe
magneti material yield as a funtion of the divalent
metal molar fration X
M
2+. As it an be seen, our
measurements show a very good agreement with the
theoretialurvededuedfromthehemialreationof
ferriteformation[14℄. Themaximumyieldorresponds
tothatprovidedbytheexatferritestoihiometrywith
avalueofX
M
2+ equalto0.33.
X-raysdiration. Inordertoharaterizethe
rys-tallinestruture ofourmagnetinanopartiles,X-rays
diration measurements were performed on powder
samples obtained after evaporation of the liquid
ar-rier, using a Rigaku/Denki X-rays diratometer and
theCuK radiationat1.54
A. Wepresentin Fig. 2a
typial powder diration pattern whih exhibits
sev-eral lines orresponding to the harateristi
interpla-nar spaing [220℄, [311℄, [400℄, [422℄, [511℄, [440℄ and
[533℄ofthespinel struture[16℄. Table1omparesfor
both kindof nanomaterialthemeasured peak
intensi-tieswiththeAmerianSoietyforTestingand
Materi-als(ASTM) values[17℄ andalsogivestheubilattie
elldedued from the peak position with average
val-uesof 0.828 nm and 0.832 nmto be ompared to the
ASTMones 0.835 nmand0.844 nmfor CuFe
2 O
4 and
Figure1.X-raypowderdifratogramsofopperandzin
fer-ritenanopartiles. The harateristi dirated diretions
[220℄,[311℄, [400℄,[422℄, [511℄, [440℄and[533℄ ofthe spinel
strutureareindexed.
Figure2. Normalizedmass variationm=mmax or
mag-netimaterialyieldasafuntionofthedivalentmetalmolar
ratio,X
M 2+.
Moreover, the observed line width arises from the
nite dimension of the rystal (polyrystalline
spei-mens)andisrelatedtotheroughlyspherialpartile
di-ameter. Additionalsouresofbroadening,arisingfrom
theexperimental setupandinstrumentation,were
dis-ounted hereusing a Si standard monorystal. Then,
terd
XR
=8:4nmintheaseofCu-basednanopartiles
andd
XR
=6:3nmin theaseofZn-basedones.
Table 1: Crystallographi analysis of Fig. 1 for
CuFe
2 O
4
and ZnFe
2 O
4
nanopartiles. The
interpla-nar spaing d
hk l
is alulated from the line
posi-tion by using the Bragg law and the orresponding
ubi lattie ell a is dedued. The experimental
peakintensities I
exp
are omparedto theASTMones.
III Magnetization results
Magneti properties ofMagneti Fluidsarise from the
dispersionofmagnetinanopartilesinaliquidarrier.
Inspinel-typenanopartiles,theexhangeinterations
betweenionsofthetetrahedralandtheotahedralsites
leadtoaglobalferrimagnetiorderinthepartilesore
andduetotheirsmallsize,eahmagnetipartiles
be-havesasasinglemagnetidomainofvolumeV bearing
apermanentmagnetimomentofmodulusm
S V,m
S
beingthenanomaterialmagnetization. Then,at300K
and for enoughdilute solutions(for avolume fration
< 2%), the magneti uid response to an applied
eld H resultsfrom the progressive orientationin the
eld of an ensemble of non interating magneti
mo-mentwhiharefreetorotateinthesolvent. This
super-paramagnetibehavioriswelldesribedbyaLangevin
formalism inluding a log normal size distribution to
take into aount the size polydispersion of partiles
[19,20℄. Thus,atT =300Kandatzeroeldthe
mag-netization is zero due to thermal utuations; as the
magnetieldinreases,thesolutionmagnetization
in-reasestooanddoesnotpresentanyhysteresis. Inthe
limit ofsmall elds, themagnetization isproportional
toH andatlargemagnetields,allthemagneti
mo-mentare alignedin theeld diretionand the
formagnetiuidsbasedon10nmsized-Fe
2 O
3
par-tiles, using ananomaterialmagnetization about75%
ofthebulkone. Nevertheless,astheproportionofspins
loated in theneighborhoodof thepartilesurfae
in-reaseswhenthepartilesize isredued,themagneti
propertiesofverysmallpartiles(typiallyinferiorto5
nm) isstrongly inuenedbythe spinarrangementof
thepartile surfae. Theloweroordinationofsurfae
ions doesmodifythe exhangeinterationsand it has
been shown the existene of a superial shell where
thespinongurationanbedisorderedresultingthen
in a redued average net moment [21, 22℄. EDL-MF
basedon4.4nmsizedNiFe
2 O
4
nanopartilesexhibita
substantial partile surfae disorder and the resulting
magnetization does not follow a simple single-domain
partilemodel[23℄. Evideneforspin-glass-like
behav-ior ofsurfae spinsin -Fe
2 O
3
partiles hasalso been
reportedusingquasi-elastineutronsattering[24℄and
FMR [25℄measurements.
However, the magneti behavior of Cu- and
Zn-based samples exhibited in Fig. 3 shows that, in
bothasesthesolutionmagnetizationtendstowardand
nearlyreahesthesaturation. Thistypial
superparam-agnetibehaviorallowstheuseoftheindependent
mo-mentmodelsinethemagnetizationisproportionalto
thevolume frationof magnetinanomaterial. F
ur-thermore,inthelimitofhighelds,asimpleestimation
of thesaturationmagnetizationof themagneti
parti-les an be made. Then, from the omplete analysis
of these urves,ithasbeendedued [14℄,thepartiles
meanmagnetisizeandpolydispersion.Theresultsare
listedin Table2.
Figure3. Log-log representationofthenormalized
magne-tizationM=asafuntionoftheappliedmagnetieldH.
Thefull lineisthebesttobtainedbyusing theLangevin
formalismoupledwithalog-normaldistribution(seeTable
Table 2: Mean nanopartile size dedued from X-ray
diration D
XR
, magneti size D mag
0
and
polydisper-sity s mag
dedued from magnetization measurements
andomparedtotherespetivebirefringeneonesD bir 0 ands bir . D bir LF andD bir HF
arethesizesdeterminedfrom
theloweld analysisandthehigheldone.
IV Magneto-optial behavior
BirefringeneLangevinformalism. Isotropiatzero
ap-plied eld, magneti uid solutions beome optially
ativewhentheeldisturned on,duetosomeoptial
anisotropy along the magneti easy axis of partiles.
For a magneti solutionof volume fration of
inde-pendentpolydispersepartiles,theLangevinformalism
givesthestatield-induedbirefringeneata
temper-atureT as[6,8,13℄:
n(H) n 0 = R 1 0 D 3 L 2 ((D))P(D)dD R 1 0 D 3 P(D)dD ; (1)
where =H=k
B
TistheLangevinparameter,L
2 ()=
1 3L
1
()=istheseondLangevinfuntion,L
1 ()
be-ing thewell known rst Langevin funtion. n
0
or-responds to the optial anisotropy (shape anisometry
and/ormagnetianisotropy)ofone partilein
suspen-sionand slightly depends on thepartile size [13℄.The
partiles diameters distribution is generally well
de-sribedbyalog-normallaw:
P(D)= 1 p 2Ds exp[ ln 2 (D=D 0 ) 2s 2 ; (2)
whereDisthepartilediameter,sisthestandard
devi-ationandlnD
0
orrespondstothemeanvalueoflnD.
Themomentsofthelog-normalsize distribution
fun-tionaredened by:
<D n >= Z 1 0 D n
P(D)dD=D n 0 exp n 2 s 2 2 : (3) Sine m S
is determined by magnetization
measure-ments,theurveN(H)=thereforereduestoa
fun-tionoftwoparametersD
0
ands ifn
0
an be
refer-usingthewholebirefringeneurvewiththoseobtained
byusingboththelimitsoflowandhigheldsallowsa
gooddeterminationofthesizedistributionparameters.
Forhighelds,1 3[L
1
()=℄=1 (3=)andthe
solu-tionbirefringeneanbelinearlywritten asafuntion
of1=H as:
n =n 0 18k B T m s <D 3 > 1 H : (4)
Forlowelds, 1 3[L
1
()=℄= 2
=15andthe
solu-tionbirefringeneisproportionalto H 2 : n = n 0 m 2 S 2 <D 9 > 540k 2 B T 2 <D 3 > H 2 : (5)
Both equations show that the high eld diameter
is related to the third moment of the log-normal size
distributionwhereastheloweldoneorrespondstoa
higher moment of the distribution. Furthermore, the
high elds analysis allows a simple determination of
n
0 :
Birefringene measurements. Theexternal-eld
in-duedbirefringeneismeasureduptoamagnetield
about 1:510 3
kA m 1
, by enapsulating magneti
uidsamples innon-birefringentglassellsafew
hun-dredmirometers thikand usingtheonventional set
up well desribed in referenes13 and 26. Whenthe
magnetieldisswithedon,theferrouidellbehaves
as a birefringent plate haraterized by a phase-lag'
related to thebirefringeneof the sampleof thikness
e by ' = 2en= where is the wavelength of the
inidentlight. Inourexperiments,thedetetiondevie
inludesaphotoelastioptialmodulatorandalok-in
amplier whih omparesthedetetedsignalfromthe
photoell to the referene signal from the modulator.
Then,theomponentatpulsation!ofthetransmitted
lightintensityI
!
isproportionaltosin'. Ifthesample
thikness and the volume fration of nanomaterial
are well hosen, several osillationsouras it an be
seen on Fig. 4whih showsthe variationsof I
! as a
funtion of the applied eld in the ase of Zn- based
magnetiuidsample(=0.75%).
Theorrespondingbirefringenevariationsan
eas-ily bededued from suh measurements and the
bire-fringenedataareplotted in linearoordinatesin Fig.
5a and Fig. 5b forCu- and Zn-based samples
respe-tively. The same qualitative behavior is observed for
all our samples: n is an inreasing funtion of the
applied eld and tends toward the saturation at our
maximum eld value. Moreover, asit an be seenon
theinsetsof Figs. 5aand 5b,thebirefringeneis
pro-portional to showing, as expeted for the values of
usedin ourexperiments,thatthemeasured
birefrin-gene is related to a single-partileeet. Indeedthe
oinideneofthedatawhennormalizedbythevolume
ontentofnanoferriteonrmstheappliabilityof the
independentpartilemodeldesribedin thebeginning
of this setion. To determine the saturationbehavior
ofn,theresultsareexhibitedinFig. 6aandFig. 6b
in double-logarithmioordinateswherethefulllineis
the result of abest t obtained by using equations 1
and 2. Fig. 7a and 7b present, in linear oordinates,
thehigh eld data(H >500kA m 1
) insuha
man-nerthatn
0
isdeterminedbythevalueofn=when
1=Htendstowardzero. Furthermore,theinsetsofboth
Figuresillustrate,inlog-logrepresentation,theloweld
behavior(H <10kAm 1
)ofnproportionalto H 2
.
ThisH 2
variationsalsoindiatesthatatlowelds,the
birefringenesamplesomes fromindividualpartiles.
Using both the limits of low and high elds, one
an alsoobtainthesizedistribution parameters. Then
a rossing of these results with those obtainedby
us-ing thewhole birefringeneurveallowsagood
deter-mination of the nanopartile size and the
polydisper-sion. In suh a ontext, the analysis of our
birefrin-gene urves givesthe resultssummarized in Table 3,
where weompareD bir
0
, themeanvalueofD dedued
from the whole urve, with D bir LF =D bir 0 exp(6s 2 ) and D bir HF =D bir 0 exp(1:5s 2
), theaveragedvalues of D
ob-tainedfromthelow-eldandhigh-eldanalyses
respe-tively. As it anbe seen,the standarddeviations s bir
are lose to those found from magnetization
measure-ments(s mag
)whereasissigniantlylargerthan
show-ing as expeted that the optial birefringene is more
sensibletolargepartiles. IntheaseofCu-based
sam-ples, thedierenebetweenthededuedaveraged
val-ues ofthe nanopartilesizes islargerdue to thequite
broadsizedistribution(s=0.5)whenomparedto
Zn-basedones(s=0.3)andisdiretly relatedtothe
syn-thesisproess.
Figure4. ComponentI!atpulsation !ofthetransmitted
lightintensityasafuntionoftheappliedeldforZn-based
sample. I
!
Figure5a. Birefringenenandnormalizedbirefringenen=(inset)ofopperferritesamplesasafuntionoftheapplied
magnetield. (Æ;=0.73 %;2,=0.15%).
Figure5b. Birefringene nandnormalizedbirefringenen=(inset)ofzinferritesamplesasafuntionoftheapplied
magnetield. (Æ,=0.75 %;2,=0.16%).
Figure 6a. Log-log representation of the normalized
bire-fringene n=of Cu-based samples as a funtionof the
appliedmagnetield. Thefulllineisthebesttobtained
byusing eq. (1)(see Table 2for the resulting parameters
size distribution).
Figure 6b. Log-log representation of the normalized
bire-fringene n= of Zn-basedsamples as a funtionof the
appliedmagnetield. Thefulllineisthebesttobtained
by usingeq. (1)(seeTable 2for the resulting parameters
Figure 7a. High eld analysis of birefringene data for Cu-based samples. The inset illustrates the low eld behavior
n/H 2
:
Figure 7b. High eld analysis of birefringene data for Zn-based samples. The inset illustrates the low eld behavior
n/H 2
:
Table 3: Saturation magnetization and optial
anisotropy of ferrite nanopartiles (hemially
opre-ipitated)withtheirrelevantreferenes.
Finally, Table 3 summarizes the saturation
mag-netization and the optial anisotropyvalues of ferrite
nanopartiles,allobtainedbythesameopreipitation
method inorder toomparethebirefringenelevelsof
orresponding ferrouid solutions. As it an be seen,
ournew EDL-MF samplespresentaomparable
opti-alleveltothatofmoreommonmagnetiuids
show-ing that theyalso ouldrepresent good preursorsfor
V Conlusion
EDL-MF based on opper and zin ferrite
nanoparti-les havebeensuessfully synthesized. Thepartiles
rystallographistruturehasbeenhekedbyusing
X-raysdirationandidentiedasspinel-type. The
mag-neti behavior of suh ferrouid solutions is typially
superparamagneti and anbe readily interpreted, in
the lowonentrationrangeinvestigated here,using a
simple single-domainpartile Langevin model. In the
sameway,theirmagneto-optialbirefringenehasbeen
measuredinthediluteregimeandisrelatedtoasingle
partile eet. In the investigated range of magneti
elds,theLangevinbirefringeneformalismwellworks
andithasbeenpossibletodeterminetheparametersof
eld-induedbirefringenelevel,opperandzinferrite
based MFare omparableto usualones. Due to their
reduedironontent,suhmagnetiolloidswould
rep-resentanewalternativeforbiologialappliations. In
future,itwillbeinterestingtoinvestigatetheiroptial
propertiesfrom adynami point ofview. Inaddition,
optial birefringenemeasurementsperformed on Ni-,
Cu- and Zn-based EDL-MF samples synthesized with
nanopartilesofdierentsizesareinprogress.
Aknowledgments
TheauthorsaregreatlyindebtedtoDr. Itri(USP)
for X-ray diration measurements. They also thank
theBrazilianageniesCNPq/Pronex,CAPES,FAPDF
andFAPESP fortheirnanialsupport.
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