Revisiting MRI Contrast Properties of Nanoparticles: Beyond theSuperparamagnetic RegimeMichael Levy,† Florence Gazeau,*,† Claire Wilhelm,† Sophie Neveu,‡ Martin Devaud,† and Pierre Levitz‡,§

†Laboratoire Matiere et Systemes Complexes (MSC), UMR 7057 CNRS/Universite Paris-Diderot, 10 rue Alice Domon et LeonieDuquet, F-75205 Paris Cedex 13, France‡Laboratoire Physico-Chimie des Electrolytes, Colloıdes et Sciences Analytiques, UMR 7195 CNRS/Universite Pierre et Marie Curie,4 place Jussieu, F-75252 Paris Cedex 05, France

ABSTRACT: Recent developments in magnetic resonance imaging (MRI)have led the community to consider more complex nanostructures than theregular superparamagnetic iron oxide nanoparticles (NPs) as potential efficientcontrast agents. These nanostructures present a magnetic dynamical behaviorthat may stand beyond the superparamagnetic regime and then affect theproton relaxation in a way that is not described by the existing models. Here,we focus on the longitudinal relaxation rate R1 = 1/T1 and revisit the seminalmodel of relaxation in order to consider any dynamical behavior of the NPmagnetic moment. Our new model is validated experimentally, reproducing thenuclear magnetic relaxation dispersion (NMRD) profiles of colloidal NPs inthe two extreme dynamical regimes, the superparamagnetic one and the rigiddipole one. In particular, it predicts an unexpected low field contribution of thetransverse component of the NP magnetic moment to the proton relaxation.This new contribution accounts for the disappearance of the high field R1 maximum when the dynamics of the magnetic momentslows down.

■ INTRODUCTION

Magnetic nanoparticles (NPs) uniquely have the propertiesboth of contrast agents in magnetic resonance imaging (MRI)and of therapeutic agents for magnetically targeted andthermally actuated therapy.1 These properties rely on thecapacity of the NP magnetic moment to interact with a remotemagnetic field and to exhibit a dynamical behavior specific tothe nanometer scale. The recent developments in molecularand cellular MRI face the long-standing challenge of contrastagent quantification.2 It requires theoretical models to relate theability of NPs to increase proton relaxation rates with theirmagnetic dynamics in a peculiar environment. Iron oxide NPsin the superparamagnetic regime, that is, governed by thermallyactivated Neel fluctuations, have been well understood by theseminal theory developed by Roch, Muller, and Gillis,3 which isbuilt on the original outersphere theory4,5 including a Curierelaxation.6,7 However, in an attempt to improve the efficiencyof MRI contrast agents, nanostructures with various materials,8

unconventional shape,9,10 or complex architecture11,12 havebeen proposed, which fail to be described by the seminalmodel. Moreover, the transformations operated by thebiological environment on NPs (cellular confinement, bindingto a molecular target, etc.) also affect their magnetic propertiesand may compromise their superparamagnetic behavior.13,14

Therefore, we thought to revisit the model of NMR relaxationin order to take into account any dynamical behavior of the NPmagnetic moment.

Here, we focus on the longitudinal relaxation rate R1 = 1/T1

and show that its field dependence, that is, its nuclear magneticrelaxation dispersion (NMRD) profile, may be derivedquantitatively for any dynamical behavior provided that thetransverse and longitudinal correlation times of the NPmagnetic moment are known. In contrast to the seminalmodel that considers the NP as a quantum superspin, wedescribe the NP as a classical magnetic moment and rely on theextensive theory of NP dynamics15 to explore NP-inducedproton relaxation.Our general model is validated experimentally for colloidal

suspensions of NPs that differ by their size and magneto-crystalline anisotropy, spanning from the superparamagneticregime to the rigid dipole (RD) regime of magnetic momentfluctuations. In particular, in contrast to the previous models,the revised theory fully reproduces the disappearance of thehigh field maximum of R1, which is experimentally observedupon increasing the anisotropy energy and freezing Neelfluctuations. This evolution of the NMRD profile, dependingon the NP dynamics, is comprehensively explained by anunexpected low field contribution to the proton relaxation,originating from the transverse component of the NP magneticmoment. This newly understood relaxation mechanism high-lights the potential of Brownian nanostructures beyond the

Received: April 28, 2013Revised: June 25, 2013Published: June 25, 2013

Article

pubs.acs.org/JPCC

© 2013 American Chemical Society 15369 dx.doi.org/10.1021/jp404199f | J. Phys. Chem. C 2013, 117, 15369−15374

superparamagnetic regime as highly effective MRI contrastagents.

■ EXPERIMENTAL SECTIONExperimental Procedures. We performed experiments on

dilute colloids of γFe2O3 (weak magnetocrystalline anisotropy)and CoFe2O4 (strong magnetocrystalline anisotropy) citrate-coated NPs of two different sizes.Chemical Synthesis. The magnetic suspension used in this

study consisted of citrate-coated anionic NPs dispersed inwater. The ferrite Fe2O3 (maghemite) and CoFe2O4 (cobaltferrite) NPs were chemically synthesized with Massart’sprocedure by alkaline coprecipitation of iron(III) (1.5 mol)and iron(II) (0.9 mol) (respectively cobalt(II)) salts.16 Afterbeing decantation-sieved, the NPs were suspended in waterwith 70 g of sodium citrate before heating at 80 °C for 30 min.The particles were washed with acetone and dispersed in water.Colloidal stability was ensured by electrostatic repulsionsbetween the citrate anions at the ferric-oxide surface. Colloidalstability was confirmed over a wide temperature range and inexternal fields up to 800 kA/m by means of small-angle neutronscattering.17 The precursor ferrofluid was size-sorted by asuccession of phase separations induced by an increase in ionicstrength, that is, screening of electrostatic repulsions. Becausethe phase diagram is dependent on the particle size, thesuccessive phase separation procedure was used to reduce thesize polydispersity of each sample.18

Determination of the Particle Size Distribution fromMagnetization Curve Measurements. The magnetizationcurves of the NP suspensions were determined by using ahomemade vibrating magnetometer. The magnetization curveM(H) of a suspension of monodisperse iron oxide NPs can bedescribed by a Langevin function. For a polydisperse sample,M(H) is adjusted by weighting the Langevin expression by alog-normal distribution of particle diameters d:

π σ σ= −

⎡⎣⎢

⎤⎦⎥P d

dd d

( )1

2exp

ln ( / )20

20

02

(1)

where d0 is the characteristic diameter and σ0 the polydispersity.The diameter d allows one to compute the NP magneticvolume Vm. As shown in the insets of Figure 1a and b, eq 1allows one to obtain a good fit of the normalized magnetization,providing a determination of d0 and σ0.

19

NMRD Experiments. The NMRD profiles of these sampleswere measured over the frequency range of 0.01−15 MHzusing a Stelar fast field cycling NMR relaxometer.Experimental Results. The NMRD experimental results

are reported in Figure 1a and b.While γFe2O3 NPs with a characteristic magnetic size of 7

and 9.2 nm display the regular high-frequency maximum, it isno longer the case for CoFe2O4 NPs of 6.2 and 7.9 nm. For thelatter, the NMRD profiles continuously decrease withfrequency. As mentioned here above, such a shape cannot beinterpreted in the framework of the existing high-anisotropyNMRD model,3,20 which always predicts a maximum. Toexplicate our experimental observations and other reports in theliterature,10,21,22 the seminal model has to be modified.

■ THEORETICAL MODELLet us consider a proton with magnetic moment μp = γII, whereγI is the nuclear gyromagnetic ratio and I the proton spin,interacting with a static magnetic field B0 = B0ez and a

perturbing fluctuating magnetic field B1(t) created by amagnetic NP of classical magnetic moment μ(Ωμ(t)), Ωμ(t)being the μ direction at a given moment. The Hamiltonian ofthe proton spin can be written23 H(t) = H0 + H1(t), where H0= −μp·B0 = −ωIIz, ωI = γIB0, and H1(t) = −μp·B1(t) = (μ0/4πr3)[μp·μ − 3(μp·u )(μ·u )] = ∑q F

(q)(t)A(q), with r(r(t),Ω(t))= ru as the vector from the proton to the center of the NP, u asa unit vector, q as an integer between −2 and 2, F(q)(t) asclassical functions following F(0) = −(16π/5)1/2(Y20(Ω)/r3), F(1)= −(8π/15)1/2(Y2−1(Ω)/r3), F(2) = −(32π/15)1/2(Y2−2(Ω)/r3),F(q) = F(−q)* (the Yl

m being the normalized sphericalharmonics), and the A(q)(t) quantum operators following A(0)

= a[−(2/3)μzIz + (1/6)(μ−I+ + μ+I−)], A(1) = a(μ+Iz + μzI+),

A(2) = (a/2)μ+I+, and A(q) = A(−q)†, with a = −(3μ0γI/8π).We want to study the evolution of the mean z-component

⟨Iz⟩ = Tr{ρIz} of I (ρ being the mean density operator takenover all the possible system histories). This evolution isdescribed by the master equation derived in ref 24 (Chapter XI,eq 11.19) up to the second order in H1. Expressing thisequation in the Schrodinger picture instead of the interactionpicture gives

Figure 1. Experimental NMRD profiles and theoretical fits (solidlines) of suspensions of (a) γFe2O3 and (b) CoFe2O4 NPs (ironconcentration [Fe] = 1 mM). The fits are obtained as explained in thetext using T = 298 K, η = 0.89 × 10−3 Pa·s, and Ms as the bulk value(412 kA·m−1 for γFe2O3 and 398 kA·m−1 for CoFe2O4). Theadjustable parameters used for each sample are the following. ForFeO1, K = 9000 J·m−3, τ0 = 6 × 10−8 s, α = 0.11, and δ = 1.8 nm. ForFeO2, K = 6000 J·m−3, τ0 = 5 × 10−9 s, α = 0.19, and δ = 1.4 nm. ForCoFe1, δ = 1.5 nm. For CoFe2, δ = 0.5 nm. Insets show thenormalized magnetization curves fitted with polydisperse Langevinfunctions (solid lines) to determine the characteristic diameter d0 andpolydispersity σ0 of the NP log-normal size distributions. We found forFeO1 d0 = 9.2 nm and σ0 = 0.22, for FeO2 d0 = 7 nm and σ0 = 0.2, forCoFe1 d0 = 7.9 nm and σ0 = 0.32, and for CoFe2 d0 = 6.2 nm and σ0 =0.4.

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ρ ρ⟨ ⟩

= −ℏ

−It

td

d1

Tr{( ( ) ) }z2 0 (2)

with

∫ τ τ= −τ τ∞

− ℏ ℏH t H t Id [e ( )e , [ ( ), ]]H Hz

0

i /1

i /1

0 0

as the “fluctuation operator” in the Schrodinger picture and ρ0as the stationary equilibrium density operator. The upper linerepresents a classical average over all of the possible systemhistories (or equivalently over a statistical ensemble), and H1 isconsidered as a stationary perturbation. Furthermore, it isknown that

τ δ τ− =− ′′F t F t G( ) ( ) ( )q q

qqq( ) ( ) ( )

(3)

where the correlation function G(q)(τ) is both even and real.23

The perturbing Hamiltonian H1 consisting in five terms,should be equivalent to the sum of 25 terms, but because of eq

3, only the five terms q( ) for which q = q′ remain:

= ∑qq( ) and

∫ τ τ τ=∞

G Cd ( ) ( )q q q( )

0

( ) ( )(4)

where

τ τ= −τ τ− ℏ − ℏC A A I( ) [e ( )e , [ (0), ]]q H q H qz

( ) i / ( ) i / ( )0 0

The commutators in C(q) can be explicitly evaluated using theA(q) expressions

μ μ μ μ ω τ

μ μ ω τ

= + = ℏ +

+ = ℏ

τ τ

τ

−

−

C C C a I

C C a I

9 ( ) cos( )

4 cos( )

x x y y z

z z z

(0) ( 2) (2) 2 20 0 I

( 1) (1) 2 20 I (5)

where μi0 ≡ μi(0) and μiτ ≡ μi(−τ), i being x, y, or z. To obtaineq 5, we considered that μ±0μzτ = μz0μ±τ = 0 because μ has nocertain transverse component.The μi autocorrelation functions appearing in eq 5 actually

depend on the NP characteristics. Let us now assume a NPwith uniaxial magnetic anisotropy. The NP energy is thenexpressed by15 U = −μ·B0 − KVm(μ·n )2/μ2, with K as theanisotropy constant and n(Ωn(t)) as the anisotropy axis. Ωn(t)defines the orientation of n(Ωn(t)) in the laboratory referenceframe. We assume that the μi autocorrelation functions aremonoexponential for a given μ and n initial condition

Figure 2. Theoretical predictions for 7 nm NPs in the two considered cases NR (black) and RD (red). The following parameters are used: T = 298K, η = 0.89 × 10−3 Pa·s, dm = 7 nm, δ = 1 nm, Ms = 412 kA·m−1, K = 6000 J·m−3, τ0 = 10−9, and α = 0.01 s. (a) Theoretical NMRD profiles andillustration of the μ dynamics in each case. (b) The contributions of the three R1 constitutive terms appearing in eq 10 are isolated. (c) The Ayant j0function as a function of τ for four fixed ωI values.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp404199f | J. Phys. Chem. C 2013, 117, 15369−1537415371

∫μ μ μ μ

μ

μ μ μ δμ

+ ≃ Ω Ω Ω Ω

× Ω

≃ +

τ τ μ μ

μτ τ

ττ τ

⊥− Ω Ω

−

μ⊥

Pd d ( , )

( )e

e

x x y y n n

z z z z

0 02 / ( , )

02 2 /

n

(6)

where Ω Ω =μ−P( , ) e /n

U k T/ B is the probability density of Ωμ

and Ωn with being the partition function, μ⊥ the μ transversecomponent, μ μ ξ= ( )z its mean z-component ( being theLangevin function and ξ = μB0/kBT the Langevin parameter),

and δμ μ ξ ξ ξ= − −[1 2 ( )/ ( )]z2 2 2 the mean-squared

fluctuating μz component.25 The correlation times τ∥ and τ⊥characterize respectively the longitudinal and transverse μdynamics. Rigorously, τ∥ could depend on Ωμ and Ωn as τ⊥,leading to an integration over these variables also in the secondequality in eq 6. However, in the case of superparamagneticNPs, the longitudinal correlation time is usually identified tothe Neel time and is thus independent of the direction of themagnetic moment with respect the anisotropy axis.15 In the RDapproximation where the magnetic moment is attached to theparticle, τ∥ and τ⊥ are strictly independent of Ωμ and Ωn (seebelow).

In order to calculate the five q( ) terms in eq 4 and accordingto eqs 5 and 6, expressions such as ∫ 0

∞ dτ G(0)(τ) cos(ωIτ)e

−τ/τ⊥ = Re[∫ 0∞ dτ G(0)(τ)e−(iωI+1/τ⊥)τ] have to be

evaluated. For this purpose, we use the following Freed−Ayant result obtained considering a proton diffusing around aNP of radius R4,5

∫ τ ττ

=στ∞

−GNR

j xRe[ d ( )e ]4

27( )q

0A( ) d

3 0 (7)

where GA(q)(τ) = FA

(q)(0)FA(−q)(τ), FA

(q)(t) = Y2q(θ,φ)/r3, σ is a

complex variable, N is the NP density, and τd = R2/D. R isdefined by the boundary condition for the diffusion of a watermolecule close to the NP. D is the water diffusion coefficient. τdis commonly considered as the motional (diffusion) passagetime of a water molecule in the vicinity of the NP.

= ++ + +

⎡⎣⎢

⎤⎦⎥j x

xx x x

( ) Re1 /4

1 4 /9 /90

1/2

1/2 3/2(8)

and x = στd. Then, we deduce

∫

∫

μ

μ δμ

μ

= ℏ Ω Ω Ω Ω

+ = ℏ +

+ = ℏ Ω Ω Ω Ω

μ μ

μ μ

⊥ ⊥

−

−⊥ ⊥

c P j x I

c j x j x I

c P j x I

d d ( , ) ( )

6 [ ( ) ( )]

6 d d ( , ) ( )

n n z

z z z

n n z

(0) 2 20

( 1) (1) 2 20 I

20

( 2) (2) 2 20 (9)

with c = (γI2μ0

2/135π)(Nτd/R3), x⊥(Ωμ,Ωn) = iωIτd + τd/

τ⊥(Ωμ,Ωn), x∥ = iωIτd + τd/τ∥, and xI = iωIτd. Finally, adding

these q( ) terms, eq 2 is rewritten as d⟨Iz⟩/dt = −R1(⟨Iz⟩ −⟨Iz⟩0), with ⟨Iz⟩0 = Tr{ρ0Iz}, the ⟨Iz⟩ value at Boltzmannequilibrium, and

∫ μ μ

δμ

= Ω Ω Ω Ω +

+

μ μ ⊥ ⊥R c P j x j x

j x

{7 d d ( , ) ( ) 6 ( )

6 ( )}

n n z

z

12

02

0 I

20 (10)

This expression is accurate as long as the NP is big enough toconsider μ as a classical moment. The second and third termsof eq 10 describe the relaxation arising from the proton

diffusion in the field created respectively by the static part of μ(the so-called Curie relaxation) and by the fluctuating part ofμz. They also appear in the seminal model. As far as we knowhowever, the first term that represents the relaxation inducedby the transverse component of μ is of a new form. Hereafter,we discuss the relative contributions of these three mechanisms(see Figure 2b).To our knowledge, there are no general analytic expressions

in the literature for the correlation times τ⊥ and τ∥. The authorsonly evaluate them with asymptotic expressions in variouscases. We now focus on the two cases relevant to interpret ourexperiments.(i) KVm ≳ kBT, but thermal fluctuations are still able from

time to time to make μ overcome the U energy barrier during ameasurement, inducing a Neel relaxation (NR). Moreover, theweakest thermal fluctuations, too small to induce the energybarrier overcome, only move μ aside from its equilibriumposition in one of the potential wells. Then, μ relaxes to itsequilibrium orientation, spiraling around the effective field Be =−(∂U/∂μ) = B0 + (2KVm/μ

2)(μ·n)n . According to ref 15, wehave in such a case τ⊥ = τsτB/(τs + τB) and τ∥ = τNτB = (τN +τB), where τs, τB, and τN are, respectively, the damping time, theBrownian time depending on the NP hydrodynamics radius RH,and the Neel time, defined as

τα γ

τπη

τ τ=| |

= =B

Rk T

1 4eKV k T

se

BH3

BN 0

/m B

(11)

with α as the dimensionless damping parameter used in the NPLandau−Lifshitz−Gilbert equation (see ref 15). α takes intoaccount the fluctuations of the magnetic moment orientationwithin the crystal lattice that dissipate energy transferred to thelattice through vibrational modes. Thus, the magnetic momentrelaxes toward its equilibrium position by dissipating energy.15

This effect is equivalent to a “magnetic” viscous friction. |γ| isthe absolute value of the electronic gyromagnetic ratio, and η isthe viscosity of the carrier fluid.(ii) KVm is so large compared to kBT that the NR is frozen.

The NP is thus considered as a RD, μ being completely stuck tothe crystal. Consequently, μ has a rotational Browniandynamics in a B0 field, characterized by15

τ ξξ ξ

τ τ ξξ

τ=−

=⊥2 ( )

( )d ln ( )

d lnB B(12)

To sum up, one advantage of our model is the possibility tointroduce any expressions of the correlation times of thatmagnetic moment that are established or measured independ-ently. Therefore, it could account for modifications of NPbehavior in various carriers and/or in the biological environ-ment. It could give access to some parameters beyond theirintrinsic properties (such as Ms, K, and d), which characterizethe dynamics of magnetic moments in their local environment(magnetic interactions, aggregation state, coating modification,encapsulation into the carrier, degradation, and so on).Therefore, the NMRD experiment could also provideinformation on the magnetic behavior of NPs in more complexsystems.

■ RESULTS AND DISCUSSIONWe present in Figure 2a the theoretical NMRD profiles ofmonodisperse NPs (magnetic diameter dm = 7 nm) accordingto eq 10 in the two cases discussed in the previous section (NR

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dx.doi.org/10.1021/jp404199f | J. Phys. Chem. C 2013, 117, 15369−1537415372

and RD). The three terms involved in R1 (see eq 10) areisolated in Figure 2b. We first note that the NR profile shape inFigure 2a corresponds to the common profiles usually discussedin the literature and to our γFe2O3 experiments. The μ Neeldynamics is actually the one traditionally considered. Let usnote that the transverse dynamics that we modeled, consistingof an attenuated precession, is however different from the oneconsidered in the seminal model, which reduced to a regularprecession. Our model predicts in the RD case a significantincrease of the low field relaxation, which induces thedisappearance of both the low field dispersion and the highfield maximum, which are characteristic of the NR case. Theresulting profile shape is in line with that from our experimentson CoFe2O4 NPs with high anisotropy. According to Figure 2b,such an increase comes from the higher contribution of both ofthe relaxations related to μ⊥ and δμz. In order to interpret themodifications in relaxivity related to these two contributions,we plotted in Figure 2c the Freed−Ayant function j0(iωIτd +τd/τ) as a function of τ for different Larmor frequencies ωI. Wenotice that j0 becomes significant for τ ≥ τd and that itssaturation value decreases with ωI. The μ dynamics beingactually slower in the RD case than that in the NR case, the twocorresponding Freed−Ayant terms j0(x⊥) and j0(x∥) have largervalues and increase the relaxation rate R1.In order to quantitatively compare the theoretical eq 10 to

our experiments, we introduce the sample polydispersity in themodel in the following way

∫=R R d P d d( ) ( ) d1poly

1 m m m (13)

where P(dm) is the distribution of the NP magnetic diametersdm, as discussed in the Experimental Section (see eq 1).The obtained NMRD fitting curves using eq 13 are presented

in Figure 1a) and b) with the experimental data. For these fits,we have considered that R = d/2 + δ, δ being the thickness ofthe nonmagnetic layer and the surface coating. Moreover, wehave made the approximation RH = R. The set of parameters(K, δ, d0, and σ0) may be obtained experimentally frommagnetization measurements. The particle size distribution isdeduced from the field-dependent magnetization of isolatedNPs, which fits a size-weighted Langevin function. On the otherhand, the anisotropy constant may be eventually derived fromthe temperature dependence of the zero-field-cooled (ZFC)magnetization, also weighted by the size distribution.14 Incontrast, the intrinsic parameters τ0 and α characterizing theinternal fluctuations of the magnetic moment are not readilyobtained and can be considered as adjustable parameters in themodel. In this particular study of maghemite NP and to adjustthe experimental curves shown in Figure1, we have fixed onlythe particle size distribution (d0 and σ0) deduced frommagnetization curves and let free the thickness of thenonmagnetic layer δ, the anisotropy constant K, and theintrinsic parameters τ0 and α. For cobalt ferrite NPs having alarge enough anisotropy (RD: KVm > kBT), the only remainingadjustable parameter left is δ.Remarkably, the modified model quantitatively describes our

experiments both in the RD and NR regimes. To ourknowledge, this is the first model able to interpret NMRDprofiles that do not present the characteristic high fieldmaximum, such as those represented in Figure 1b.The model developed here sheds light on the importance of

tuning the NP dynamics to significantly increase the 1H NMRrelaxivity. It appears that slowing down the μ dynamics by

increasing the coupling between μ and the NP lattice (i.e.,increasing anisotropy) drastically enhances the μ⊥, and the δμzcontributions to the proton longitudinal relaxation.This increased coupling should also affect the proton

transverse relaxation because at low field, both the longitudinaland transverse relaxations converge. The transverse relaxationshould then increase as the longitudinal relaxation does. It is animportant aspect because NPs are clinically used as T2 contrastagents. The calculation of the transverse relaxation rate R2 isunder way to quantify such an effect. Consequently, accordingto this model, NPs with high anisotropy energy present asignificant potential as MRI contrast agents, in particular, forthe emerging field of micro-Tesla MRI.26

An important difference between the model presented in thispaper and the seminal model is the way that μ is considered.Here, we analyze it as a classical magnetic moment, while it istreated as a quantum superspin in the seminal model. Ourclassical view has two major advantages. First, the obtained R1expression given by eq 10 is easily computable, whereas theseminal model solution requires such a long calculation timethat the authors propose a heuristic expression to fitexperiments. Second, a classical μ allows us to make use ofthe abounding literature devoted to its dynamics, whichsystematically employs the classical view. Approximateexpressions for τ⊥ and τ∥ are then available almost whateverthe case and, in particular, whatever the NP anisotropy. Itmakes eq 10 not only a general theoretical expression but also ausable one in almost all of the experimental situations involvingdilute magnetic colloids.

■ CONCLUSIONWe have presented a model that is directly usable to fit NMRDexperiments and explain for the first time the high field NMRDmaximum disappearance in the case of highly anisotropic NPs.Importantly, our model gives evidence of a new contribution tothe proton relaxation arising from the transverse fluctuations ofthe NP magnetic moment. Owing to this contribution, themodel quantitatively demonstrates the evolution of the NMRDprofile when the μ dynamics evolves from a Neel regime to apurely Brownian one. In principle, our model could apply for allcoupling strengths between μ and the NP crystal, provided thatthe correct τ⊥ and τ∥ corresponding expressions are known.Finally, according to this model, NPs with slowered dynamicsshould be considered as a new class of MRI contrast agentswith exceptionally high low field relaxivity.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: florence.gazeau@univ-paris-diderot.fr.NotesThe authors declare no competing financial interest.§E-mail: pierre.levitz@upmc.fr (P.L.).

■ ACKNOWLEDGMENTSThe authors thank Aude Michel for iron quantification andJean-Claude Bacri and Lam Vuong Quoc for fruitful discussion.This work was supported by the European project Magnifyco(Contract NMP4-SL-2009-228622).

■ REFERENCES(1) Yoo, D.; Lee, J.; Shin, T.; Cheon, J. Theranostic MagneticNanoparticles. Acc. Chem. Res. 2011, 44, 863−874.

The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp404199f | J. Phys. Chem. C 2013, 117, 15369−1537415373

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The Journal of Physical Chemistry C Article

dx.doi.org/10.1021/jp404199f | J. Phys. Chem. C 2013, 117, 15369−1537415374