Shaping Up Zn-Doped Magnetite Nanoparticles from Mono- and Bimetallic Oleates: The Impact of Zn Content, Fe Vacancies, and Morphology on Magnetic Hyperthermia Performance

Shaping Up Zn-Doped Magne i e Nanopa icles om Mono- and
Bime allic Olea es: The Impac o Zn Con en , Fe Vacancies, and
Mo phology on Magne ic Hype he mia Pe o mance
Idoia Cas ellanos-Rubio,*Oihane A io ua, Lou des Ma cano, I a i Rod igo, Daniela Iglesias-Rojas,
Ande Ba ón, Ane Olazagoi ia-Ga mendia, Luca Oli i, Fe nando Plazaola, M. Luisa Fdez-Gubieda,
Aina a Cas ellanos-Rubio, JoséS. Ga i aonandia, Inaki O ue, and Mai e Insaus i*
Ci e This: Chem. Ma e . 2021, 33, 3139−3154
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sıSuppo ing In o ma ion
ABSTRACT: The cu en ly exis ing magne ic hype he mia
ea men s usually need o employ e y la ge doses o magne ic
nanopa icles (MNPs) and/o excessi ely high exci a ion con-
di ions (H× >10
10 A/m s) o each he he apeu ic empe a u e
ange ha igge s cance cell dea h. To make his an icance
he apy uly minimally in asi e, i is c ucial he de elopmen o
imp o ed chemical ou es ha gi e ise o monodispe se MNPs
wi h high sa u a ion magne iza ion and negligible dipola
in e ac ions. He ein, we p esen an inno a i e chemical ou e o
syn hesize Zn-doped magne i e NPs based on he he molysis o
wo kinds o o ganome allic p ecu so s: (i) a mix u e o wo
monome allic olea es (FeOl + ZnOl), and (ii) a bime allic i on-
zinc olea e (Fe3−yZnyOl). These app oaches ha e allowed ailo ing
he size (10−50 nm), mo phology (sphe ical, cubic, and cuboc ahed al), and zinc con en (ZnxFe3−xO4, 0.05 < x< 0.25) o MNPs
wi h high sa u a ion magne iza ion (≥90 Am2/kg a RT). The oxida ion s a e and he local symme y o Zn2+ and Fe2+/3+ ca ions
ha e been in es iga ed by means o X- ay abso p ion nea -edge s uc u e (XANES) spec oscopy, while he Fe cen e dis ibu ion
and acancies wi hin he e i e la ice ha e been examined in de ail h ough Mossbaue spec oscopy, which has led o an accu a e
de e mina ion o he s oichiome y in each sample. To achie e good biocompa ibili y and colloidal s abili y in physiological
condi ions, he ZnxFe3−xO4NPs ha e been coa ed wi h high-molecula -weigh poly(e hylene glycol) (PEG). The magne o he mal
efficiency o ZnxFe3−xO4@PEG samples has been sys ema ically analyzed in e ms o composi ion, size, and mo phology, making use
o he la es -gene a ion AC magne ome e ha is able o each 90 mT. The hea ing capaci y o Zn0.06Fe2.94O4cuboc ahed ons o 25
nm eaches a maximum alue o 3652 W/g (a 40 kA/m and 605 kHz), bu mos impo an ly, hey each a highly sa is ac o y alue
(600 W/g) unde s ic sa e y exci a ion condi ions (a 36 kA/m and 125 kHz). Addi ionally, he excellen hea ing powe o he
sys em is kep iden ical bo h immobilized in aga and in he cellula en i onmen , p o ing he g ea po en ial and eliabili y o his
pla o m o magne ic hype he mia he apies.
1. INTRODUCTION
The success o magne ic hype he mia he apies depends on
he hea ing capaci y o specific abso p ion a e (SAR) o he
magne ic nanopa icles (MNPs) when hey a e exposed o an
al e na ing magne ic field (AMF).
1−3
As a ma e o cou se, o
achie e he desi ed he apeu ic effec unde a sa e equency
field p oduc (H× <1010 A/m s), he MNP hea ing powe
has o be op imized.
4,5
The design o new MNPs wi h
imp o ed magne o he mal efficiency is a challenging ask due
o he difficul y in con olling and p edic ing he complex
colloidal syn hesis o ino ganic nanoc ys als.
6−8
The p epa a-
ion o nanos uc u es wi h e y specific se s o cha ac e is ics
(size, mo phology, homogeneous chemical composi ion, high
pu i y, and low size/shape dispe si y) equi es an ex emely
fine con ol o e he syn he ic p o ocol.
9
In his sense, he
he mal decomposi ion o o ganome allic p ecu so s opened a
new a enue o syn hesizing no el i on oxide-based MNPs
wi h a well-defined size and mo phology.
10,11
The mos
commonly used i on oxide MNPs o biomedical applica ions
a e o magne i e (Fe3O4) due o hei high magne ic esponse,
good biocompa ibili y, chemical s abili y, and simple compo-
Recei ed: Decembe 16, 2020
Re ised: Ap il 2, 2021
Published: Ap il 19, 2021
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si ion.
12,13
Bu in e es ingly, he in oduc ion o a low quan i y
o di alen ansi ion-me al ions (MxFe3−xO4, M = Zn, Co, Mn,
Ni, e c.) wi hin he spinel s uc u e o magne i e NPs has
p o en o be a good s a egy o ob ain mixed e i es wi h
uned magne ic pe o mances,
14−17
al hough in some cases,
he e a e conce ns abou hei dubious biocompa ibili y.
Pa icula ly, Zn-con aining e i e NPs a e conside ed qui e
biocompa ible because zinc is an essen ial ace elemen o he
human body ha has a ela i ely high oxic dose, up o 450 mg
day−1.
18
Cu en ly, zinc e i es a e also being explo ed o
biomedical applica ions due o hei highe s abili y agains
oxida ion.
19,20
Addi ionally, as i is well-known, he in oduc-
ion o diamagne ic Zn2+ ions in he magne i e la ice
([Fe3+]A[Fe2+Fe3+]BO4) can p oduce significan enhancemen
o he pa icle′s magne ic momen , compa ed o pu e
magne i e.
21
This is because Zn2+ ions end o eplace Fe3+
in A si es, ein o cing he al eady exis ing unbalance be ween
an i e omagne ically coupled A and B subla ices. Un o u-
na ely, his mechanism holds up, in he bulk s a e, jus un il a
Zn con en o x≈0.4 (ZnxFe3−xO4), abo e which he lack o
magne ic momen s loca ed a A si es s ongly dis up s he
exchange in e ac ion be ween bo h subla ices, causing a
dec ease o he o al magne ic momen .
22
Ano he d awback
in he p epa a ion o doped e i e NPs is ha he dopan is
o en assimila ed in diffe en posi ions o he c ys al
la ice,
23−27
which ypically happens due o he nonequilib ium
na u e o hese chemical eac ions, making i difficul o
achie e he in ended heo e ical esul s and unning he isk o
de i ing mis aken conclusions. Thus, he fi s s ep in he
de elopmen o doped e i e nanoma e ials should be he
accu a e de e mina ion o he local geome y o he dopan
a oms o ensu e eliable p ope ies and us ul po en ial
applica ions.
I is clea , hen, ha a p io i a ema kable imp o emen o
he SAR can be achie ed i high-g ade Fe3O4NPs a e doped
wi h a sui able amoun o Zn2+ in he p ope la ice posi ion. In
addi ion, as has been epo ed ecen ly, he hea ing powe o
magne i e NPs wi h nonfluc ua ing magne ic momen (FM-
NP), whose a e age size is o e 20 nm, can be significan ly
g ea e han ha o he supe pa amagne ic NPs (SP-NPs < 20
nm) i high-enough fields (H>15−20 mT) a e used and
dipola magne ic in e ac ions a e minimized.
28,29
Howe e , as
one would expec , he syn hesis o high-quali y Zn-doped
magne i e FM-NPs is a mo e challenging han ha o
undoped magne i e. In ecen yea s, i has been common o
syn hesize Zn-doped e i e NPs by he mal decomposi ion o
me al ace ylace ona es
14,25,30
and by cop ecipi a ion o
co esponding me al chlo ide o ni a e sal s,
25,31−33
which in
mos o he cases ga e ise o polydispe se NPs in size and
shape. The decomposi ion o me al olea es has also been
explo ed in some s udies on Zn- e i es, bu i usually has he
downside o ha ing o deal wi h he o ma ion o he wus i e
(FeO)-phase byp oduc .
14,27
Ce ainly, wo ks desc ibing he
syn hesis o Zn-doped magne i e NPs wi h a well-defined
mo phology, a e age size la ge han 20 nm, and de oid o
seconda y phases a e a he sca ce and mos ly ocused on NPs
wi h a cubic mo phology.
20,26,34
The e is no doub ha he
de elopmen o new s a egies o p epa e Zn-doped e i es o
diffe en sizes and shapes would s imula e he p og ess o
nanopa icle-based pla o ms o he anos ics.
He ein, we p esen an imp o ed p o ocol o syn hesize
highly c ys alline ZnxFe3−xO4NPs wi h a low size/shape
dispe si y and enhanced sa u a ion magne iza ion. We ha e
explo ed a new syn he ic ou e based on he decomposi ion o
bime allic i on-zinc olea es, which has been compa ed o a
mo e common ou e employing a mix u e o monome allic
olea es (i on olea e + zinc olea e). To he bes o ou
knowledge, his is he fi s ime ha hese wo app oaches a e
ca e ully analyzed and compa ed. By finely modi ying he
syn hesis condi ions o bo h ou es, NPs o diffe en sizes (10−
50 nm), shapes (sphe es, cubes, and cuboc ahed ons), and zinc
con en s (0.05 < x< 0.25) ha e been ob ained. These samples
ha e been chemically, s uc u ally, and magne ically analyzed
wi h g ea accu acy making use o X- ay abso p ion nea -edge
s uc u e (XANES), DC magne ome y, and Mossbaue
spec oscopy. The s udy has allowed one o de e mine eliably
bo h he Zn posi ion/con en and he Fe dis ibu ion/
acancies, a subjec ha has no been sufficien ly explo ed
e en in he mos ecen wo ks on his opic.
35,36
Addi ionally, ZnxFe3−xO4NPs ha e been specifically
PEGyla ed o a oid NP agg ega ion in cell en i onmen s,
and iabili y assays ha e been ca ied ou o p o e hei good
biocompa ibili y.
Finally, he hea ing efficiency o ZnxFe3−xO4@PEG NPs has
been s udied in de ail by measu ing he dynamical hys e esis
loops a diffe en equencies (up o a field in ensi y o 90 mT)
and in se e al dispe sion en i onmen s (dis illed wa e , aga ,
and cell cul u e). The op imal exci a ion pa ame e s o
maximize he hea ing p oduc ion unde clinical sa e y limi s
ha e been de e mined o each sample.
2. RESULTS AND DISCUSSION
2.1. Role o Chemical Syn hesis on he Size, Shape,
C ys alline S uc u e, and Composi ion. By ca ying ou
he molysis o diffe en i on and zinc olea es, ZnxFe3−xO4NPs
o diffe en sizes, shapes, and composi ions we e ob ained.
Since ou goal is o ocus on zinc con en s x< 0.4 and he
dopan has ypically o be added in excess o each he
in ended compos ion,
23,37,38
Fe/Zn olea es wi h 5:1 and 2:1
a ios ha e been used in he p epa a ions, employing bo h
Table 1. Summa y o Syn hesis Condi ions and Samples Fea u es Ob ained by Mix u e o Monome allic Olea es (G ay Shade
Rows) And by Bime allic Olea es: Me al Olea e Used in he Syn hesis, Znx e3−xO4NPs Composi ion De e mined By ICP-MS,
Final Tempe a u e, Annealing Time, Pa icle Mean Dimension Ob ained By TEM, A e age C ys alli e Size Ob ained om
(311) And (400) Diff ac ion Peaks, Peak Posi ion o (311) And La ice Pa ame e a
sample me al olea e used in he
syn hesis sample composi ion
ICP-MS
final T
(°C) annealing
(min) DTEM
(nm) DXRD
(nm) 311 peak posi ion 2θ
(deg) la ice pa ame e a
(Å)
Zn0.15-10 2.5 FeOl + 0.5 ZnOl Zn0.15Fe2.85O4320 30 10 (1) 8.8 (4) 35.592 8.3910(1)
Zn0.1-48 2.5 FeOl + 0.5 ZnOl Zn0.1Fe2.9O4320 80 48 (4) 53 (5) 35.566 8.3940(5)
Zn0.1-24 Fe2.5Zn0.5Ol Zn0.1Fe2.9O4320 30 24 (2) 22 (2) 35.581 8.3913(3)
Zn0.1-34 Fe2.5Zn0.5Ol Zn0.1Fe2.9O4330 30 34 (3) 34 (3) 35.532 8.3961(4)
Zn0.25-39 Fe2Zn1Ol Zn0.25Fe2.75O4320 60 39 (3) 29 (3) 35.530 8.4016(4)
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monome allic olea es (FeOl + ZnOl) and bime allic olea es
(Fe3−yZnyOl) (y= 0.5 and 1) (see Sec ion 4 and Figu e S1,
Table S1 in he Suppo ing In o ma ion). The main s uc u al
diffe ence be ween he mix u e o monome allic olea es and
bime allic olea es is he p esence o he e ome allic b idging
coo dina ion in he la e (see Figu e S2 and Table S2 in he
Suppo ing In o ma ion), which educes he diffusion dis ance
be ween Zn−Fe cen e s, affec ing he g ow h dynamics o he
ZnxFe3−xO4NPs, as will be shown in he ollowing.
The ZnxFe3−xO4samples p esen a zinc con en (measu ed
by induc i ely coupled plasma mass spec ome y (ICP-MS))
anging om x= 0.1 o 0.25 and an a e age dimension om 10
o 50 nm. Wi h he aim o p o iding a clea pic u e o he main
syn hesis pa ame e s affec ing he p ope ies o he NPs, fi e
ep esen a i e samples ha e been chosen (see Table 1).
Samples ha e been named acco ding o he composi ion and
size as ollows: Znx-DTEM, whe e xis he zinc con en in he
NPs de e mined by ICP-MS and DTEM is he a e age
dimension ob ained by ansmission elec on mic oscopy
(TEM) analysis.
TEM mic og aphs in Figu e 1 show monodispe se samples
wi h sphe ical, cubic, and cuboc ahed al shapes. When FeOl
and ZnOl a e eac ed oge he a an Fe/Zn a io equal o 5:1,
using a final To 320 °C and 30 min o annealing, sphe ical
pa icles o 10 nm diame e (sample Zn0.15-10 in Figu e 1a) a e
ob ained. By inc easing he annealing ime o 80 min, he
shape o he nanoc ys als changes om sphe es o cubes and
he a e age dimension inc eases conside ably, om 10 o 48
nm (sample Zn0.1-48 in Figu e 1b). Samples Zn0.15-10 and
Zn0.1-48 seem o ha e ollowed he eac ion p ofile desc ibed
by Hyeon e al., in which he nuclea ion p ocess s a s be ween
310 and 320 °C and g ow h akes places g adually om 1 o 20
min o aging, p oceeding apidly a e wa d and causing he
mo phology o e ol e o he cubic ype.
39
On he o he hand, when bime allic Fe2.5Zn0.5Ol (Fe/Zn =
5:1) is eac ed a he same syn hesis condi ions as hose used
in sample Zn0.15-10 (see sample Zn0.1-24 in Table 1), he NPs
g ow u he and p esen a well- ace ed oc ahed al shape wi h
sligh unca ion (cuboc ahed ons) (Figu e 1c). The la ge size
ob ained when he bime allic Fe2.5Zn0.5Ol is used appea s o be
due o he sho e dis ance be ween Zn2+ and Fe3+ ca ions
wi hin he me allo-o ganic complex. The Zn2+ ions accele a e
he ans o ma ion o he bime allic olea e p ecu so , shi ing
i s decomposi ion empe a u e o lowe alues.
27
The e o e, as
could be expec ed, he eac ion o Fe2.5Zn0.5Ol a highe final T
(330 °C) p oduces e en la ge cuboc ahed al nanopa icles
(see sample Zn0.1-34 Figu e 1d). Thus, i also seems easonable
o pos ula e ha he changes in he decomposi ion p ofile o
he bime allic Fe2.5Zn0.5Ol no only speed up he g owing s age
bu also modi y he mo phology o esul ing nanoc ys als.
On he con a y, he me al olea e ype used in he syn hesis
(monome allic o bime allic) does no affec he amoun o
Figu e 1. TEM mic og aphs and co esponding size dis ibu ions o samples (a) Zn0.15-10, (b) Zn0.1-48, (c) Zn0.1-24, (d) Zn0.1‑34, and (e) Zn0.25-
39. (a) and (b) ha e been ob ained om a mix u e o monome allic olea es (FeOl + ZnOl). (c)−(e) ha e been ob ained om a bime allic i on-zinc
olea e (Fe3−yZnyOl). Whi e scale ba s a e 100 nm. Black scale ba s a e 10 nm.
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zinc inco po a ed in he NPs. All o he samples syn hesized
using an ini ial Fe/Zn a io o 5:1 gi e ise o NPs wi h a
simila zinc con en (x≈0.1) ega dless o he syn he ic ou e
employed. The sligh ly highe zinc con en in Zn0.15-10 is likely
due o i s la ge su ace- o- olume a io, assuming ha he
dopan concen a ion ends o be somewha highe on he NP
su ace because o in e nal diffusion cons ain s.
27,40
Wi h he
aim o inc easing he zinc con en wi hin he NP la ice while
acili a ing i s diffusion, a bime allic Fe2Zn1Ol wi h a highe
zinc concen a ion has been used (Fe/Zn = 2:1), expanding
he annealing ime o 60 min. In his way, he esul ing NPs
ha e a highe zinc concen a ion (x= 0.25), bu hey p esen
an i egula p isma ic shape wi h winning planes (sample
Zn0.25-39), as can be seen in Figu e 1e. I seems easible ha an
inc ease in Zn2+ subs i u ion causes la ice s ains and, hus,
some kind o c ys al dis o ion.
To gain u he in o ma ion on he s uc u al cha ac e is ics
o he nanopa icles, X- ay diff ac ion (XRD) has been
pe o med in powde samples. The whole se o ZnxFe3−xO4
samples (see Figu e 2a) shows an in e se spinel s uc u e wi h
he space g oup Fd3m, compa ible wi h he magne i e phase
(PDF #880866) and wi hou any ace o he wus i e phase,
which is a e y common byp oduc in his kind o i on oxide
nanopa icles.
25
A e Rie eld efinemen , no addi ional
impu i y phase has been de ec ed and he obse ed peaks
ha e been indexed as (111), (220), (311), (400), (422),
(511), (440), (620), and (533). The summa y o Rie eld
efined s uc u al da a is displayed in he Suppo ing
In o ma ion (Figu e S3 and Table S3), and he es ima ed
la ice pa ame e s (a) ha e been included in Table 1. The
diff ac ions peaks o Zn0.25-39 a e he mos shi ed owa d
lowe angles (see Figu e 2b), which gi e ise o he la ges
la ice pa ame e among he samples, i.e., 8.4016 Å, in
acco dance wi h i s highe zinc con en . When he x
de e mined by ICP-MS is aken in o accoun , he e is no
clea co ela ion be ween he la ice pa ame e and he zinc
concen a ion (see Figu e 2c). This seems o sugges ha a
ac ion o zinc may no be wi hin he e i e la ice. As will be
p o ed in he ollowing (by XANES, magne ome y, and
Mossbaue echniques), he e a e Zn2+ ions on he NP su ace;
hus, he Zn con en in he e i e la ice is lowe han he o al
zinc amoun de e mined by ICP-MS. I he co ec ed zinc
con en wi hin he e i e is plo ed e sus he la ice
pa ame e , a linea -like dependence can be obse ed (see
Figu e 2d). In any case, an in-dep h s udy o he physical
dimension o uni cells should also accoun o he possible
i on acancies in he c ys al la ice, a ma e ha will be
discussed in mo e de ail la e .
In ela ion o he a e age c ys alli e sizes, hey ha e been
calcula ed om (311) (Figu e 2b) and (400) diff ac ion peaks
and a e lis ed in Table 1 (see also Tables S4−S6 in he
Suppo ing In o ma ion). In all o he cases, excep o Zn0.25-
39, he a e age dimensions calcula ed om TEM measu e-
men s ma ch e y well wi h he c ys alli e sizes, meaning ha
samples Zn0.15-10, Zn0.1-48, Zn0.1-24, and Zn0.1-34 a e
composed o single c ys als. Ne e heless, he c ys alli e size
o Zn0.25-39 is smalle han he physical a e age size
de e mined by TEM, which implies ha he NPs o his
sample a e winned c ys als, in ag eemen wi h wha is seen in
Figu e 1e.
2.1.1. X- ay Abso p ion Nea -Edge S uc u e (XANES).
XANES is an elemen -specific echnique ha allows one o
gain in o ma ion abou he oxida ion s a e and he local
symme y o he abso bing elemen and can be used o iden i y
and quan i y ino ganic phases and coo dina ion com-
pounds.
41,42
In he p esen case, X- ay abso p ion nea -edge
s uc u e (XANES) has been pe o med a bo h Fe K-edge and
Zn K-edge o in es iga e i on and zinc a angemen s wi hin he
ZnxFe3−xO4NPs.
Figu e 3a shows he Fe K-edge XANES spec a o he se o
ZnxFe3−xO4NPs (x= 0.1, 0.15, and 0.25) oge he wi h
s oichiome ic magne i e (Fe3O4), Zn- e i e (ZnFe2O4), and
wus i e (FeO) as e e ences. The compa ison o he Fe K-edge
XANES spec a o Fe3O4and ZnFe2O4shows ha , apa om
ce ain diffe ences in he in ensi y below and abo e he edge
egion, he main changes expec ed om Zn doping should
Figu e 2. (a) X- ay powde diff ac ion pa e ns o samples Zn0.15-10, Zn0.1-48, Zn0.1-24, Zn0.1-34, and Zn0.25-39. (b) Zoom-in o he (311)
diff ac ion peak and he la ice pa ame e (a) ob ained by Rie eld efinemen e sus Zn con en (x) es ima ed by (c) ICP-MS and (d) Mossbaue
spec oscopy, espec i ely.
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appea a he edge ene gy (see he zoom-in o Figu e 3a). In
ac , he edge posi ion is a clea -cu indica o o he oxida ion
s a e o he abso bing a om. No e ha while magne i e is an
in e se spinel whe e he Fe2+ ions occupy oc ahed al (B) si es
and Fe3+ ions occupy bo h oc ahed al (B) and e ahed al (A)
si es, ZnFe2O4is a no mal spinel in which he Zn2+ ca ions
occupy he A si es and he Fe3+ a e loca ed in he B ones.
Thus, he oxida ion s a e o he Fe ions in magne i e (Fe2+/
Fe3+ a io o 1:2) is lowe han ha in ZnFe2O4(exclusi ely
Fe3+) and, consequen ly, he edge posi ion appea s ∼2eV
shi ed o lowe ene gies in compa ison wi h he ZnFe2O4
XANES spec um.
41
In he case o he ZnxFe3−xO4NPs, all samples excep o
Zn0.15-10 display e y simila spec a o he one o magne i e.
In samples Zn0.1-48, Zn0.1-24, Zn0.1-34, and Zn0.25-39, he
obse ed a ia ions in he edge posi ions wi h espec o
magne i e a e wi hin he e o (0.2 eV) (see he inse o Figu e
3a), sugges ing ha he Zn concen a ion in he e i e la ice
mus be somewha lowe han he Zn con en de e mined by
ICP-MS. In con as , he Zn0.15-10 sample shows a la ge shi
in he edge posi ion owa d highe ene gies (≈0.6 eV), which
can be explained by he p esence o he maghemi e (Fe2O3)
phase on he su ace (see Figu e S4 in he Suppo ing
In o ma ion). A pa ial oxida ion om magne i e o maghemi e
is no su p ising in he Zn0.15-10 sample conside ing he high
su ace-a ea- o- olume a io in NPs wi h an a e age dimension
o 10 nm. Addi ionally, he p esence o he maghemi e phase in
his sample is in acco dance wi h he lowe la ice pa ame e
ob ained om he Rie eld efinemen (see Table 1).
Figu e 3b displays he Zn K-edge XANES spec a o
ZnxFe3−xO4NPs compa ed o he ZnFe2O4 e e ence. The
edge posi ion o he syn hesized nanopa icles is coinciden
wi h ha obse ed in he ZnFe2O4XANES spec um, e ealing
aZn
2+ oxida ion s a e in he sample. Abo e he edge posi ion,
all spec a p esen h ee main peaks. Al hough he posi ions o
hose peaks a e compa able wi h ha obse ed in he ZnFe2O4
XANES spec um, he ela i e in ensi y o he peaks a ies
among he samples. Indeed, while ce ain simila i ies a e
obse ed be ween he Zn K-edge XANES spec a o he
ZnxFe3−xO4samples and ZnFe2O4, confi ming he inco po-
a ion o Zn ca ions in he inne s uc u e o he magne i e in
la ice A, an addi ional con ibu ion is necessa y o ep oduce
he expe imen al spec a. The e o e, he Zn K-edge XANES
spec a o he ZnxFe3−xO4samples we e fi ed o a linea
combina ion o ZnFe2O4and he a ailable s anda ds. The bes
linea combina ion fi was ound conside ing he coexis ence o
Figu e 3. (a) No malized XANES spec a a he Fe K-edge o ZnxFe3−xO4(x= 0.1, 0.15, 0.25) NPs compa ed o e e ence compounds: magne i e
(Fe3O4), Zn- e i e (ZnFe2O4), and wus i e (FeO). Zoom: de ail o he p e-edge egion. (b) Zn K-edge XANES spec a o ZnxFe3−xO4NPs
compa ed o ZnFe2O4. Zoom: de ail o he whi e line. (c) Linea combina ion fi (l.c.) o he Zn K-edge XANES spec a o sample Zn0.1-34 wi h
57(2)% ZnFe2O4and 43(2)% Zn2+ Td-complex. (d) Linea combina ion fi (l.c.) o he Zn K-edge XANES spec a o sample Zn0.25-39 wi h
79(1)% ZnFe2O4and 21(1)% Zn2+ Td-complex. The linea combina ion fi s o he es o he samples a e in Figu e S5 in he Suppo ing
In o ma ion.
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ZnFe2O4and Zn2+ adso bed on o a hyd oxyapa i e-like
s uc u e (see Figu e 3c,d), a pa ially dis o ed phase in
which Zn2+ a o s he e ahed al coo dina ion.
43,44
The
p esence o his e ahed al molecula geome y phase sugges s
ha a ac ion o Zn ca ions a e loca ed ou o he ino ganic
co e, p obably on he su ace o he NPs as zinc olea e ha
ha e no yielded decomposi ion. The highe decomposi ion
empe a u e o ZnOl seems o be he eason why a he final T
o he syn hesis (320−330 °C), he e a e s ill some zinc
cen e s ha ha e no been comple ely de ached om he
olea e ligands (see Figu e S6 in he Suppo ing In o ma ion).
Since his seconda y Zn phase is loca ed a he o ganic su ace
coa ing, i will no affec he magne ic p ope ies o he
ino ganic e i e co e.
The linea combina ion fi s p esen ed in Figu es 3c,d and S5
p o ide he pe cen age o zinc in he ino ganic co e (as
ZnxFe3−xO4) and on he su ace (as a me allo-o ganic s uc u e
wi h e ahed al coo dina ion); see Table 2. I becomes
appa en ha he zinc con en de e mined by ICP-MS eflec s
he o al zinc amoun in he NP sys em ( e i e co e + o ganic
su ace). Thus, o know he eal Zn con en in he e i e
la ice, he co esponding pe cen age (second column in Table
2) mus be applied o he o al zinc amoun (ICP-MS da a
p esen ed in Table 1). The ecalcula ed ZnxFe3−xO4
composi ions a e lis ed in Table 2. These co ec ed x alues
a e in ag eemen wi h he sligh edge-posi ion a ia ions
obse ed a he Fe K-edge (commen ed abo e) and he
s oichiome ies de e mined by Mossbaue ha will be
discussed in he ollowing (and a e p esen ed in Figu e 2d).
2.2. Magne ic Cha ac e iza ion. 2.2.1. DC Magne o-
me y. The magne ic field (M(H)) and he mal (M(T))
dependence o he magne iza ion be ween 5 and 300 K we e
ob ained in he whole se o samples and a e p esen ed in
Figu es 4 and 5. The main p ope ies o he hys e esis loops
(sa u a ion magne iza ion, Ms, coe ci e field, Hc, and educed
emanen magne iza ion, M /Ms) a e summa ized in Table 3.
As would be expec ed, Ms alues a 5 K eflec he inc ease
o he ne magne ic momen o he la ice as he Zn con en
inc eases due o he e ahed al Fe3+ subs i u ion. As shown in
Table 3,Ms anges om 122 Am2/kg in he Zn- iches sample
( o x≈0.25) o 105−108 Am2/kg in he samples wi h he
lowes Zn con en ( o x≈0.1). No e ha hese alues
significan ly exceed he sa u a ion magne iza ion o pu e bulk
magne i e (98 Am2/kg a 5 K). Howe e , ano he di ec
consequence o he Zn con en inc ease is he concomi an
dec ease o he Cu ie empe a u e, o igina ed by he
weakening o he supe exchange in e ac ion be ween A and
B subla ices. Such a empe a u e educ ion may be on he
o de o 200 K o a Zn con en o 0.4 ela i e o pu e
magne i e (∼950 K) and affec s s ongly he oom- empe a u e
magne iza ion alues.
45
This effec can be obse ed by plo ing
Msas a unc ion o empe a u e (Figu e S7, Suppo ing
In o ma ion). The cu e o sample Zn0.25-39 shows a s ong
he mal dependence in which he a io Ms(300 K)/Ms(5 K)
becomes much smalle (0.75) han o samples Zn0.1-24 (0.89)
o Zn0.1-48 (0.9). As a consequence, he oom- empe a u e Ms
o ZnxFe3−xO4samples wi h x> 0.1 can diffe li le om ha o
pu e bulk magne i e. Con e sely, mode a e doping le els (x<
0.1) can p o ide mo e benefi a RT; e.g., he Ms alues o
samples Zn0.1-48, Zn0.1-24, and Zn0.1-34 (96−97 Am2/kg a
RT; see Table 3) no ably imp o ed when compa ed wi h pu e
magne i e (92 Am2/kg a RT).
Addi ionally, om he hys e esis loops a 5 K shown in
Figu e 4, i can be s a ed ha he whole se o NPs is basically
single magne ic-phase objec s whose magne iza ion eaches
sa u a ion a fields smalle han 0.5 T. This is because he
cu es do no p esen kinks and/o linea con ibu ions o he
o al magne iza ion in he high-field egion, which would be
expec ed i pa amagne ic and/o diffe en e o-/ e i-magne ic
phases we e significan . The shape o he hys e esis loops a 5
K clea ly fi s wi h he S one −Wohl a model o uniaxial single
domains o all ZnxFe3−xO4samples (excep o Zn0.25-39
composed o winned NPs), as confi med by simula ions o
di ec hys e esis loops pe o med wi h his model (see Model
S1 in he Suppo ing In o ma ion). No e ha he model
p edic s a educed emanence (M /Ms) o abou 0.5 (Table 3).
In b ie , i sugges s ha in e pa icle in e ac ions play a mino
ole a 5 K, so ha he magne iza ion p ocess esul s om he
addi ion o andomly dis ibu ed o a ions o nonin e ac ing
supe spins loca ed a each indi idual pa icle. Below he
Ve wey ansi ion (VT) (T< 100 K), he effec i e magne ic
Table 2. A omic Pe cen age o Zn as Zinc Fe i e (in he
Ino ganic Co e) and as Zinc Me allo-O ganic Complex (on
he O ganic Su ace) Es ima ed om he Linea
Combina ion Fi o he Zn K-Edge XANES Spec a o
ZnxFe3−xO4Samples (Figu es 3c,d and S5)
a
sample Zn in he co e
(%) Zn on he su ace
(%) composi ion in he
co e
Zn0.15-10 64(1) 36(1) Zn0.1Fe2.9O4
Zn0.1-48 66(2) 34(2) Zn0.07Fe2.93O4
Zn0.1-24 59(2) 41(2) Zn0.06Fe2.94O4
Zn0.1-34 57(2) 43(2) Zn0.06Fe2.94O4
Zn0.25-39 79(1) 21(1) Zn0.2Fe2.8O4
a
The ZnxFe3−xO4composi ions ha e been ob ained by applying he
Zn % in he co e o he o al zinc amoun de e mined by ICP-MS
(Table 1).
Figu e 4. M(H) cu es o ZnxFe3−xO4samples a (a) 300 K and (b) 5 K in he low field egion.
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aniso opy (Ke ) a ises om he compe i ion o he uniaxial
magne oc ys alline effec , o igina ing om he monoclinic
dis o ion o he magne i e la ice
46
and he shape aniso opy.
In his case, he diffe ences in he alue o he coe ci e field
(Hc) (o effec i e magne ic aniso opy, Ke ) seem o be d i en
by he shape aniso opy con ibu ion, which depends on he
pa icle’s mo phology. No e ha he Zn con en , and he e o e
i s possible impac on monoclinic dis o ion, should be qui e
simila in samples Zn0.1-48, Zn0.1-24, and Zn0.1-34. O he wise,
he lowe Hc alue o Zn0.15-10 a 5 K is due o he non-
negligible he mal fluc ua ion effec s in NPs o 10 nm, which
a e in he SPM egime a RT. The he mal effec s a e also
isible in he es o he samples a RT gi en ha he hys e ical
p ope ies (Hcand M /Ms) a e conside ably educed. This
happens when he o al aniso opy ene gy Ke is compa able
o he he mal ene gy kBTand/o he dipola in e ac ion
ene gy.
M(T) cu es ob ained upon ze o-field cooling and field
cooling (ZFC and FC) condi ions a e p esen ed in Figu e 5.
The mos e iden sha ed ea u e is he la ge magne iza ion s ep
obse ed in he icini y o 100 K when he sample is wa med
up (ZFC) as well as cooled down (FC) ac oss i . This s ep is
usually he finge p in o he pu e magne i e phase and
o igina es om he Ve wey ansi ion (VT). In Figu e 5,i is
also obse ed ha his ansi ion sligh ly mo es up and down
in empe a u e om sample o sample (86 K in sample Zn0.1-
34 and a ound 100 K in samples Zn0.1-24, Zn0.1-48, and Zn0.25-
39; see Table 3). E en in sample Zn0.15-10 composed o
smalle NPs (whose blocking Tis a ound 55 K), a bump
be ween 80 and 100 is obse ed (ma ked in Figu e 5a).
Acco ding o he li e a u e, he lowe ing o he VT poin in
bulk magne i e is usually conside ed as a consequence o ei he
Fe defici (Fe3(1−δ)O4) in undoped magne i e and/o 3d
ansi ion-me al subs i u ion o Fe2+ ca ions (MxFe3−xO4, wi h
M = Zn, Mn, Co, e c.).
47
Besides, he shi ing effec also
in ol es he so ening o he ansi ion ha becomes g adually
one o a second o de ins ead o a fi s o de .
48
The poin is
ha alues o δ> 0.03 o x=3δ> 0.01 a e sufficien o emo e
he Ve wey ansi ion in bulk single c ys als, om which i
would be expec ed ha in ou ZnxFe3−xO4samples,
cha ac e ized by nominal x≥0.1, he magne iza ion s ep
should be no longe obse ed. Howe e , he e is clea
expe imen al e idence ha he Ve wey ansi ion is s ongly
affec ed by su ace p ope ies, pa icula ly significan a he
nanome e scale.
49
In he wo k o Guigue-Millo e al., he VT
shi ed owa d highe empe a u es and did no fi he ela ion
ha exis s o bulk single c ys als. The au ho s p oposed ha
he numbe o Fe2+/Fe3+ pai s pe o mula uni is he d i ing
o ce ha de e mines he VT in nanome ic g ains. The
numbe o Fe2+/Fe3+ pai s in ou ZnxFe3−xO4samples will be
es ima ed in he ollowing by ga he ing oge he he analysis o
Figu e 5. Ze o-field cooling and field cooling (ZFC-FC) cu es oge he wi h de i a i es o ZFC magne iza ion (black line) o samples: (a) Zn0.15-
10, (b) Zn0.1-48, (c) Zn0.1-24, (d) Zn0.1-34, and (e) Zn0.25-39. ( ) Ve wey ansi ion empe a u e (T ) e sus Fe2+/Fe3+ pai s ob ained by he
analysis o Mossbaue spec a.
Table 3. Summa y o Sa u a ion Magne iza ion (Ms), Coe ci i y (Hc), and Reduced Remanence (M /Ms) Ob ained om he
Hys e esis Loops a 300 and 5 K and he Ve wey T ansi ion T (T )
sample Msa RT (Am2/kg) Msa 5 K (Am2/kg) Hc(mT) a RT Hc(mT) 5 K M /Msa RT M /Ms5 K T (K)
Zn0.15-10 92 (2) 111 (2) 0.6 (1) 33.5 (1) 0.01 (2) 0.47 (2) 80−100 (1)
Zn0.1-48 97 (2) 108 (2) 6.7 (1) 61.0 (1) 0.28 (2) 0.44 (2) 103 (1)
Zn0.1-24 96 (2) 105 (2) 7.4 (1) 56.7 (1) 0.30 (2) 0.47 (2) 98 (1)
Zn0.1-34 97 (2) 106 (2) 3.4 (1) 50.8 (1) 0.19 (2) 0.48 (2) 86 (1)
Zn0.25-39 90 (2) 122 (3) 13.1 (1) 44.8 (1) 0.21 (2) 0.25 (2) 101 (1)
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Mossbaue spec a and he a ailable magne iza ion da a
ob ained a 5 K.
2.2.2. Mossbaue Spec oscopy. Mossbaue spec oscopy
can help de e mine he numbe o Fe2+/Fe3+ pai s by
compu ing he ela i e occupancy o Fe ions in he
inequi alen si es cha ac e is ic o he spinel la ice o e i es.
This can be easily achie ed om oom- empe a u e spec a in
samples abo e he SPM limi (D> 20 nm), i.e., in he whole
se o ZnxFe3−xO4samples excep in Zn0.15-10. Figu e 6 shows
he Mossbaue spec a o Zn0.1-48, Zn0.1-24, Zn0.1‑34, and
Zn0.25-39 NPs collec ed a oom empe a u e oge he wi h he
Mossbaue fi ing pa ame e s. Fo a be e compa ison, he
a ea o he spec a has been no malized o he Fe con en .
I he he mal fluc ua ion effec issufficien ly small,
Mossbaue spec a o he s oichiome ic Fe3O4magne i e
esul s om he supe posi ion o wo well- esol ed sex e s. The
sex e wi h he highe hype fine field (I) is ∼49 T, and i is
associa ed wi h Fe3+ ions in e ahed al si es (A), while he
componen wi h a lowe hype fine field (II) (∼46 T) is
assigned o Fe2+Fe3+ a oms in he oc ahed al (B) ones.
50
The
elec on hoping among he Fe2+ and Fe3+ a oms in he
oc ahed al (B) posi ion is much as e han he esolu ion ime
o he Mossbaue spec oscopy, and he hype fine alues o
bo h Fe2+ and Fe3+ canno be independen ly de e mined by
his echnique. The low hype fine field sex e is no mally
conside ed o be associa ed wi h an only componen wi h an
Fe2.5+ in e media e alence ep esen ing an Fe2+Fe3+ pai o
hopped a oms. The ela i e esonan a ea a io among wo
componen s is, hus, SI/SII = 0.5, in acco dance wi h he
popula ion o bo h c ys allog aphic posi ions A and B in a
s oichiome ic magne i e.
Spec a o he s udied ZnxFe3−xO4samples ha e been
p ope ly fi ed by supe posi ion o wo sex e s wi h hype fine
pa ame e s compa ible wi h hose expec ed om a magne i e
phase (Figu e 6). The spin elaxa ion supe pa amagne ic
effec s due o educed sizes o he NPs a e no mani es ed in
any spec a. The sligh ly lowe hype fine fields obse ed in he
spec al componen s o Zn0.1-24, Zn0.1‑34 and Zn0.25-39 NPs
can be a ibu ed o hei ela i ely smalle sizes and hei
opological cuboc ahed al shapes wi h lowe co e/su ace Fe
a oms in compa ison o he cubic-shaped Zn0.1-48 sample.
The SI/SII (Fe) ela i e esonan a ea a io o ZnxFe3−xO4-
s udied NPs can be ound in Table 4. Assuming ha Zn ions
a e loca ed in A si es, as in e ed om XANES, he no malized
a omic SI/SII (a .) a ios diffe om he 0.5 alue in all o he
samples, e idencing he diffe en s oichiome ic composi ions
o he NPs. Fe3+ ions a e subs i u ed by Zn2+ ones in A
e ahed al si es and, o conse e he cha ge neu ali y, a
con e sion o some Fe2+ ions in Fe3+ and/o gene a ion o Fe2+
acancies in B oc ahed al posi ion is p o oked. Fo mally, he
nons oichiome ic Zn-doped magne i e NPs can be ep e-
sen ed by he ollowing o mula
[
][ ]
δδδ
+
−
+
−−
+
−−
+
+
+
ZnFe(FeFe)Fe O
xx x x x
2
1
3
A13
2
13
3
52
3
B
4
(1)
whe e δand xsymbolize he acancies (0 ≤δ≤0.33) and zinc
concen a ion, espec i ely.
Following exp ession 1, he e a e 5δ+ 2x unbalanced Fe3+
ions in he B oc ahed al posi ion ha , as sugges ed by some
au ho s, do no con ibu e o Fe2+−Fe3+ elec onic hopping
bu ins ead o a high hype fine I sex e .
51
This ac mus be
eflec ed on he ela i e esonan a ea a io, being p ojec ed by
eq 2
δδ=++ −−
S
Sxx/(Fe) (1 5 )/(2 6 2)
III (2)
Based on eq 2, he numbe o Fe2+/Fe3+ pai s pe o mula uni
is gi en by
δ=− −px26 2 (3)
Figu e 6. Mossbaue spec a o he (a) Zn0.1-48, (b) Zn0.1-24, (c) Zn0.1‑34, and (d) Zn0.25-39 NPs collec ed a oom empe a u e oge he wi h
hype fine pa ame e s ob ained om he fi ings o he spec a. *IS ela i e o bcc-Fe.
Table 4. Summa y o Expe imen al SI/SII,Ms, and μand he
Calcula ed Fe Vacancies (δ), Zn Con en (x), Fe2+/Fe3+
Pai s, and S oichiome y Using Equa ions 3 and 4 o Zn0.1-
48, Zn0.1-24, Zn0.1-34, and Zn0.25-39 Samples
sample SI/SII
(Fe)
μ
(μB)δxFe2+/Fe3+
pai s s oichiome y
Zn0.1-48 0.52 4.41 ∼0 0.07 1.86 Zn0.07Fe2.93O4
Zn0.1-24 0.75 4.29 0,04 0.06 1.64 Zn0.06Fe2.9O4
Zn0.1-34 1.17 4.33 0,09 0.08 1.3 Zn0.08Fe2.83O4
Zn0.25-
39 0.43 4.96 ∼0 0.16 1.68 Zn0.16Fe2.84O4
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In addi ion, he ne magne ic momen in he amewo k o eq 1
can be calcula ed as
μ
δδ=−+xx(, ) 6 2 4 (4)
No e ha an inc ease in he Zn con en (x) ein o ces he ne
magne ic momen , while oc ahed al acancies (δ) end o
educe i . In such a con ex , eqs 2 and 4allow he calcula ion o
xand δ om expe imen al SI/SII (Fe) and μ alues (ob ained
om he Msda a a 5 K; see Table 3). Table 4 summa izes he
expe imen al SI/SII and μ, he ob ained δand x alues, he pai
numbe (p), and he co esponding s oichiome y o each
sample. Samples Zn0.1-24 and Zn0.1‑34 p esen acancy
concen a ions o δ= 0.04 and δ= 0.09, espec i ely. In
con as , Zn0.1-48 and Zn0.25-39 gi e ise o sligh ly nega i e
numbe s, leading us o conclude ha in hese samples he e is
an appa en absence o Fe2+ acancies, which seems chemically
plausible gi en ha Zn0.1-48 and Zn0.25-39 we e syn hesized
using qui e la ge annealing imes (see Table 1). Howe e , i
should be no ed ha Zn0.25-39 NPs p esen c ys al dis o ions
(see Figu e 1), so a p ecise in e p e a ion o SI/SII (Fe) could
equi e a mo e specific o mula ion- ame. I is no ewo hy o
men ion ha he Ve wey ansi ion empe a u e p esen s
app oxima ely a linea ela ion wi h Fe2+/Fe3+ pai s (see Figu e
5 ), which is in ag eemen wi h he hypo hesis p oposed by
Guigue-Millo e al.
49
commen ed in he p e ious sec ion.
Rega ding he x alues, hey a e qui e compa ible wi h he
ones ob ained om he XANES s udy (see Tables 2 and 4),
which suppo s he conclusion d awn p e iously abou being a
mino ac ion o Zn (ou o he e i e ino ganic co e) o ming
pa o he o ganic coa ing.
Addi ionally, he s oichiome ies de e mined by Mossbaue
spec oscopy and lis ed in Table 4 a e highly consis en wi h
he la ice pa ame e s (a) es ima ed by Rie eld efinemen in
he o egoing sec ion (see Figu e 2c). Gi en ha acancies
gene a e local elec os a ic epulsion among he emaining
ions, which in u n induces an inc emen o he la ice
pa ame e ,
52,53
i seems logical o suppose ha sample Zn0.1-34
(wi h a la ge numbe o acancies, δ= 0.09) p esen s a la ge
la ice pa ame e among he samples wi h simila Zn con en s
(Zn0.1-48, Zn0.1-24 and Zn0.1-34).
2.3. Biomedical Po en ial o ZnxFe3−xO4@PEG NPs.
A e ha ing pe o med a comp ehensi e physicochemical
s udy and a ho ough composi ion de e mina ion o he
ZnxFe3−xO4NPs, he wo k will be comple ed wi h a de ailed
discussion abou he biomedical po en ial o he samples.
2.3.1. Viabili y o ZnxFe3xO4@PEG Fo mula ions on Cells.
Fi s , o make he ZnxFe3−xO4samples hyd ophilic and
colloidally s able in physiological solu ions, samples we e
coa ed using he PMAO-PEG copolyme (see Sec ion 4 and
Table S7 in he Suppo ing In o ma ion) ollowing a p e iously
published p o ocol ha minimizes collec i e coa ings.
29
Sample Zn0.1-24 was unc ionalized using 10 kDa PEG, and
samples Zn0.1-34, Zn0.1-48, and Zn0.25-39, which a e composed
o la ge NPs, we e coa ed using longe PEG molecules (20
kDa) o be e coun e balance he dipola in e ac ion among
NPs. Due o he small size o he NPs o ming he Zn0.15-10
sample and, hus, i s low po en ial as a magne o he mal
ac ua o , om he e on, his sample will no longe be a pa o
he discussion.
The cy o oxici ies o Zn0.1-48@PEG, Zn0.1-24@PEG, Zn0.1-
34@PEG, and Zn0.25-39@PEG a e 96 hou s ha e been
s udied. Figu e 7 shows ha human colo ec al cance cells
(HCT116) incuba ed wi h ZnxFe3−xO4@PEG NPs g ow a he
same a e as cells wi hou NPs (whi e ba ), wi h no significan
diffe ences be ween he wo NP concen a ions (C1and C2,
g ey and black ba s, espec i ely). The zinc con en (0.05 < x<
0.25), size (24−48 nm), and mo phology (cuboc ahed al,
cubic, o p isma ic) o he samples did no affec he iabili y,
concluding ha hese ZnxFe3−xO4@PEG o mula ions a e no
oxic o he cells.
2.3.2. Magne ic Hype he mia Efficiency o ZnxFe3−xO4@
PEG Fo mula ions. The po en ial o MNPs o p oduce hea
depends c i ically on a numbe o ac o s, such as in insic
p ope ies (mo phology, size dis ibu ion, magne iza ion,
effec i e magne ic aniso opy, e c.), as well as “ex insic”
ones (collec i e assemblies, iscosi y o he medium, e c.).
Addi ionally, i is well-known ha any po en ially efficien
magne ic colloid can p oduce poo esul s i he adio-
equency exci a ion is a om ce ain op imal condi ions.
54
The hype he mia s udy de eloped in his wo k akes in o
accoun mos o hese issues, wi h he aim o analyzing he
impac o zinc doping and he NP shape on he pe o mance o
magne i e-based NPs. The specific abso p ion a e (SAR) was
ex ac ed om he analysis o he hys e esis loops ob ained a
h ee diffe en equencies (133, 305, and 605 kHz), which a e
in he ange usually employed in he hype he mia echnique.
The da a a e summa ized in Figu e 8 and Table 5.
AC hys e esis loops o samples composed o single c ys als
(Zn0.1-48@PEG, Zn0.1-24@PEG, Zn0.1-34@PEG), in Figu e 8,
a e simila o hose ob ained in pu e magne i e FM-NPs
p epa ed ollowing a simila syn he ic ou e.
29,55,56
Impo -
an ly, hese loops a e ypical o nea ly isola ed magne ic single
domains whose easy axes a e o ien ed a andom ela i e o he
ex e nally applied AC magne ic field. In consequence, he
S one −Wohl a h-based app oach
57
fi s easonably wi h mos
o he hys e esis loops p esen ed in Figu e 8d(123). The
simula ions (see Model S1 in he Suppo ing In o ma ion)
ha e been ob ained by assuming a Gaussian dis ibu ion o he
uniaxial effec i e aniso opy cons an s, ollowing he same line
o hough as ha used in he li e a u e
29,55
o compa able
magne i e pa icles. In his app oach, he magne ic aniso opy
s anda d de ia ion is unde s ood as eflec ing a mo phological
diso de , ha is o say, i egula i ies o igina ed by c ys allo-
g aphic di ec ions g owing a diffe en a es. No e ha
hys e esis loop a eas o samples Zn0.1-48@PEG and Zn0.1-
34@PEG, which a e composed o compa a i ely la ge pa icles,
a e equency-independen (as p edic ed by he model), while
in sample Zn0.1-24, wi h smalle pa icles o 24 nm, he a ea
Figu e 7. P oli e a ion assay o cells incuba ed wi h ZnxFe3−xO4@
PEG NPs o 96 hou s using wo diffe en concen a ions o NPs (C1
= 0.1 ngNP/cell and C2=1ng
NP/cell). G ow h a es we e plo ed as
ela i e inc ease compa ed o 0 h. Values a e ep esen ed as he mean
and s anda d e o o h ee independen expe imen s.
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