Coordination polymer nano-objects into ionic liquids: Nanoparticles and superstructures

Inorganica Chimica Acta 361 (2008) 3988–3996

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Coordination polymer nano-objects into ionic liquids: Nanoparticles and superstructures Joulia Larionova a,*, Yannick Guari a,*, Alexei Tokarev a, Elena Chelebaeva a, Carlos Luna b,1, Claudio Sangregorio b,*, Andrea Caneschi b, Christian Guérin a a b

Institut Charles Gerhardt, UMR 5253, Chimie Moléculaire et Organisation du Solide, Université Montpellier II, Place E. Bataillon, 34095 Montpellier cedex 5, France INSTM Research Unit – Dipartimento di Chimica, Università di Firenze, via della Lastruccia 3, 50019 Sesto F.no, Firenze, Italy

a r t i c l e

i n f o

Article history: Received 13 February 2008 Accepted 10 March 2008 Available online 15 March 2008 This paper is dedicated to Prof. Dante Gatteschi. Keywords: Cyano-bridged coordination polymers Ionic liquids Nanoparticles Superparamagnetic Spin-glass-like Magnetic properties

a b s t r a c t A new exploit of ionic liquids as an alternative reaction media in the synthesis of cyano-bridged coordination polymers nano-objects such as nanoparticles and their superstructures is discussed. Stable colloidal solutions containing nanoparticles of cyano-bridged coordination polymers Cu3[Fe(CN)6]2/ [Cn-MIM][An] (where n = 2, 4; An = BF4, Cl) or their superstructures were prepared in the corresponding 1-R-3-methylimidazolium salts [Cn-MIM][An] which acts as both the stabilizing agent and the solvent. Different conditions, such as temperature, nature of the ionic liquid counter anion and N-alkyl substituted chain length, water content and microwave action have been varied in order to check their influence on the size, the shape and the organisation of the nanoparticles. A special emphasis is devoted to detailed studies of the magnetic properties of these frozen colloids. The dynamic study shows that the relaxation of magnetisation for the nanoparticles and their superstructures is influenced by interparticle interactions leading to appearance of a cluster-glass-like behaviour in these systems. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Cyano-bridged homo- and hetero-metallic coordination polymers belong to an important family of molecule-based materials presenting interesting magnetic, optic, photo-switchable and intercalation properties [1]. Consequently, during the last 30 years, numerous compounds of this family with various structures have been synthesised and extensively studied due to their fundamental interest as well as their technological applications in many fields [2]. About eight years ago, the research activity on the synthesis and studies of size and shape controlled cyano-bridged metallic coordination polymers at the nano-sized level regime started to develop [3]. Such interest is due to the fact that thanks to the very important surface/core atoms ratio or confinement effects, nanometer-scaled materials often exhibit the appearance of new interesting size-dependent physical and chemical properties, which cannot be observed in their bulk analogous [4]. For this reason, such nano-sized materials are interesting candidates for applications in many fields, including electronics, catalysis, separation, * Corresponding authors. Fax: +33 4 67 14 38 52 (J. Larionova). E-mail addresses: [email protected] (J. Larionova), [email protected] (Y. Guari), claudio.sangregorio@unifi.it (C. Sangregorio). 1 Present address: Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, Av. Pedro de Alba s/n, San Nicolás de los Garza, 66450 Nuevo León, Mexico. 0020-1693/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ica.2008.03.038

biology, medical imagery and others [5]. A pioneering work concerning the synthesis of cyano-bridged coordination polymer nano-objects has been realised by Mann and co-workers, who prepare cubic shaped nanocrystals of Prussian Blue of ca. 12–50 nm stabilized within reverse micelles [6]. Then, the synthesis of cyano-bridged metallic nanoparticles of different size by using reverse micelles [7], polymer [8] and biopolymer [9] as stabilizing agents, amorphous [10] and mesostructured silica [11] as matrixes were reported. Recently, we reported the synthesis of cyano-bridged coordination polymers nanoparticles of adjustable size by using ionic liquids (ILs) as both stabilizing agent and reaction media [12]. It should be noted that ILs are typically composed of organic cations with a variety of moieties such as quaternary ammonium cation, pyrrolidinium, phosphonium, sulfonium and other more exotic cations along with a variety of inorganic anions [13]. Their unique physico-chemical properties, such as a low melting point, a wide liquid range, negligible vapour pressure, good solubility characteristics, relatively low viscosity, high fluidity, non-flammability, a wide electrochemical window, tolerance to strong acids, and their excellent thermal and chemical stability provide their rapid emergence as alternative solvents for chemical reactions and separations [14]. ILs were also found interesting as a media for the synthesis of inorganic matters including the stabilization of various nano-sized objects [15]. As concerning coordination polymer

J. Larionova et al. / Inorganica Chimica Acta 361 (2008) 3988–3996

nanoparticles, we previously prepared soluble nanoparticles of cyano-bridged coordination polymers M3[M0 (CN)6]2/[Cn-MIM][BF4] (M2+ = Ni, Cu, Co, Mn; M0 = Fe, Cr) and Fe4[Fe(CN)6]3/[Cn-MIM][BF4] by using 1-R-3-methylimidazolium (with n = 4 or 10) tetrafluoroborates as ILs [12]. We show that stable nanoparticles of around 3 nm may be obtained with 3d metal ions and the size of these nanoparticles may be modified by heating. On the other hand, the nature of the transition metal ion used has no significant influence on the nanoparticle size. We also report that these colloids present a collective magnetic transition due to dipolar interparticle interactions. These results encouraged us to further investigate on these coordination polymer nanoparticles/ionic liquid systems and to analyse the influence of different factors on the shape, size, and organization and on the magnetic properties of the resulting nanoparticles. In this paper, we concentrate on the case of Cu3[Fe(CN)6]2/[Cn-MIM][An] system with various ILs and report on the influence of the temperature, the ionic liquid nature (N-substituted alkyl chain length and counter anion), water content, microwave action on the synthesis of spherical nanoparticles of different size and their organization into superstructures. We give a special emphasis to detailed magnetic studies of the frozen colloids of these nanoparticles by presenting a detailed study of their dynamic magnetic properties. 2. Experimental 2.1. Synthesis K3[Fe(CN)6], [Cu(H2O)x](BF4)2, [C4-MIM][Cl] (C4-MIM = 1-butyl3-methylimidazolium) and [C2-MIM][Cl] (EMIM = 1-ethyl-3-butylimidazolium) were purchased from Merck. AgBF4 was purchased from Alfa Aesar. [C4-MIM][BF4] [16] and [C4-MIM]3[Fe(CN)6] [12] were synthesized according to previously published procedures [12]. The quantity of water in ionic liquids was controlled by Karl–Fisher method. 2.1.1. Synthesis of Cu3[Fe(CN)6]2/[Cn-MIM][An] colloidal solutions (n = 2, 4 and An = BF4, Cl) In a typical synthesis, a [C4-MIM][BF4] solution (1 mL) of [Cu(H2O)x](BF4)2 (0.22 mmol) was added to a [C4-MIM][BF4] solution (1.5 mL) of [C4-MIM]3[Fe(CN)6] (0.15 mmol) at room temperature. The solution which changes the colour without any visible precipitate was stirred during 2 h at room temperature. The IL [C4MIM][BF4] may also replaced by [C2-MIM][Cl] or by a [C4-MIM][BF4] – 20% [C4-MIM][Cl] mixture and the temperature synthesis changed to 50 °C or 80 °C. 2.1.2. Synthesis of Cu3[Fe(CN)6]2/[C4-MIM][BF4] superstructures A Cu3[Fe(CN)6]2/[C4-MIM][BF4] solution prepared as reported above was placed into a microwave oven (100 W) for 3 min. No visible changes of the solution was observed. 2.2. Physical measurements IR spectra were recorded on a Perkin Elmer 1600 spectrometer with a 4 cm1 resolution. UV–Vis spectra were recorded on a Cary 5E spectrometer in solution or at the solid state in KBr disk. Transmission electron microscopy (TEM) observations were carried out at 100 kV (JEOL 1200 EXII). Samples for TEM measurements were prepared using ultramichrotomy techniques from a

3[Cu(H2O)6](BF4)2 + 2[C4-MIM]3[Fe(CN)6]

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frozen drop of solutions or from resin-embedded powder for solid materials and then deposited on copper grids. Magnetic susceptibility data were collected with a Quantum Design MPMS-XL SQUID magnetometer. The data were corrected for the sample holder contribution. 3. Results and discussion 3.1. Synthesis, characterisation and influence of different factors 3.1.1. Synthesis and characterisation Mixing two solutions of [C4-MIM]3[Fe(CN)6] and [Cu(H2O)x](BF4)2 in [C2-MIM][Cl], [C4-MIM][BF4] or a [C4-MIM][BF4] – 20% [C4-MIM][Cl] during 2 h at a given temperature leads to the formation of deeply coloured solutions of Cu3[Fe(CN)6]2/[Cn-MIM][An] (Scheme 1). These solutions are perfectly transparent and no precipitation occurred. All as-obtained solutions are stable for months. Adding alcohols CH3OH, or C2H5OH in these solutions induces immediate precipitation of coloured solids. The infrared spectra of the colloidal solutions beside the bands characteristic of the IL used clearly show the bands corresponding to the stretching vibrations of the bridging cyano groups [17]. Indeed, m(CN) observed in the [C4-MIM]3[Fe(CN)6] precursor is shifted to 40 cm1 toward higher frequency. UV–Vis absorption spectra of the colloidal solutions show broad intervalence charge-transfer bands in the visible region [12]. It is interesting to note that the maxima of intervalence bands for the samples are shifted toward higher wavenumber from that of the bulk materials by ca. 80 nm. Such shift in UV–Vis spectra has also been observed in the case of cyano-bridged nanoparticles incorporated into amorphous silica matrix [10] and was ascribed to the surface effect of the nanoparticles [18]. Textural observations of the nanoparticle-containing solutions were performed by using transmission electronic microscopy (TEM). Fig. 1a presents a TEM image of a Cu3[Fe(CN)6]2/[C4-MIM][BF4] colloidal solution obtained at room temperature showing uniformly sized spherical in shape nanoparticles, which are well dispersed in ILs with a size distribution centred at 3.3(0.6). 3.1.2. Influence of the temperature [C4-MIM][BF4] has a wide liquid range from its glass transition at 81 °C and its decomposition temperature at 250 °C. We studied the influence of the reaction temperature on the size of the nanoparticles following two protocols. On one hand, the colloidal solution synthesis is performed at room temperature during 5 min and then a 2 h post-synthetic treatment is applied. On the other hand, solutions of the two precursors are heated separately and then added on each other and allowed to react at the same temperature for 2 h. The post-synthetic heating of a colloidal solution prepared at room temperature induces slight changes of the nanoparticle size from 3.3(0.6) nm to 3.0(0.8) and to 2.4(0.5) nm with the heating at 50 and 80 °C, respectively [12a]. Concerning the second applied protocol, if the size distribution of the nanoparticles obtained between 50 °C and room temperature remains almost unchanged, heating at 50 °C induces an increase of the nanoparticles size to 5.2(1.4) nm [12b]. Performing the reaction at 80 °C leads to the formation of crystallites with regular geometric shapes (Fig. 1b) and a small amount of precipitate. The formation of larger nanoparticles can be attributed to both, a growth process dominating the nucleation one and to Ostwald ripening

[Cn-MIM][An]

Cu3[Fe(CN)6]2/[Cn-MIM][An]

Scheme 1. Schematic representation of the synthesis of cyano-bridged coordination polymer nanoparticles Cu3[Fe(CN)6]2/[Cn-MIM][An].

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Fig. 1. TEM images of the colloidal solutions (a) Cu3[Fe(CN)6]2/[C4-MIM][BF4] obtained at room temperature, (b) Cu3[Fe(CN)6]2/[C4-MIM][BF4] obtained at 80 °C; (c) Cu3[Fe(CN)6]2/[C4-MIM][An] (with An = Cl, BF4) and (d) Cu3[Fe(CN)6]2/[C2-MIM][Cl] obtained at room temperature. Scale bars = 100 nm.

[19]. These results suggest that the IL local structure during the nanoparticle growth, i.e. during the first minutes of reaction plays a major role on the nanoparticle size. Indeed, the increase of the temperature from the beginning of the reaction could result in a lower IL local structure and as a consequence to a size increase of the nanoparticles. 3.1.3. Influence of the IL nature Hydrogen bonding is supposed to play a major role on the ILs local structure. It was established that [C4-MIM][Cl] presents strong hydrogen bonding in the liquid phase between the [Cl] counter anion and the organic cation. On the contrary, imidazolium based ILs with the ½BF4   anions present relatively weak hydrogen bonds [20]. Then it seems interesting to check the influence of the IL counter anion on the resulting nanoparticles. Fig. 1c and d shows representative TEM images of the Cu3[Fe(CN)6]2/[C4-MIM][An] nanoparticles obtained in a [C4-MIM][BF4] – 20% [C4-MIM][Cl] mixture and of the Cu3[Fe(CN)6]2/[C2-MIM][Cl] nanoparticles. Note that the pure [C4-MIM][Cl] cannot be used at room temperature as reaction media is solid. In both cases, spherical homogeneous and non-aggregated nanoparticles are observed. In the former, the size distribution is equal to 4.8(0.8) nm. The observed nanoparticle size increase obtained as [C4-MIM][Cl] is added to [C4-MIM][BF4] suggests an influence of the IL counter anion. However, using [C2-MIM][Cl], the size distribution is centred at 3.3(0.9) as in the case of [C4-MIM][BF4]. It is then difficult to conclude on the exact role of the IL counter anion on the nanoparticle size. Note also that the nanoparticles obtained in [C2-MIM][Cl] are not very stable and appearance of a green precipitate was observed after 1 h suggesting that ILs with a too short N-substituted alkyl chain length is inadequate as stabilizing agent for the coordination polymer nanoparticles. 3.1.4. Influence of the water content [C4-MIM][BF4] is a hygroscopic IL completely miscible with water at room temperature. In our experiments, the water content was not exceeding 0.2 wt%. It should be noted that the presence of a small quantity of water is somewhat necessary to the synthesis as the precursors are insoluble in fully dehydrated ILs. We established that a minimum water content of 0.02 wt% is a requisite.

Fig. 2a–d shows TEM images of nanoparticle colloidal solutions containing 0.2, 0.7, 1.4 and 5 wt% of water. When the water content is low (0.02–0.2%), the TEM images show the presence of spherical uni-shaped, non-aggregated nanoparticles (Fig. 2a). As the water content increases, the progressive formation of aggregates or crystallites is observed beside spherical nanoparticles (0.7 and 1.4 wt% of water, Fig. 2b and c) and at 5 wt% of water, only crystallites formation with sizes of ca. 100–150 nm are observed. A water content superior to 6 wt% induces precipitation as for the use of pure water. It is noteworthy that the amount of water used in this study is far below the aggregation concentration values required in this family of LCs to observe appearance of a biphasic system [21]. It was proposed that imidazolium ring protons may act as hydrogen-bond donors to F atoms of the counterion in ILs with fluorine containing anion [22]. At low content, i.e. below 0.2 wt%, water can replace the C(sp2)–H  F interactions with hydrogen bonds involving water as an acceptor towards the cation and as a donor towards the [BF4] ion [23] without changing the local structure of the imidazolium entities. It is thus reasonable to consider that our primary building blocks which are soluble in water-rich areas of the IL, i.e. in the hydrophilic channels, are reacting at the vicinity of the imidazolium entities leading to the formation of IL-stabilized coordination polymer nanoparticles. The progressive water content increase can lead to a progressive IL local structure alteration which in turns lead to a nanoparticle size increase and aggregation. 3.1.5. Influence of microwave treatment Applying microwave irradiation to nanoparticle synthesis has been widely studied [24]. However, results concerning microwave irradiation of preformed nanoparticles are scarce. Microwave irradiation allows to heat for a short time and in a very homogeneous way which should result in the observation of significant differences with classical heating. For instance, a colloidal solution containing Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles was exposed to microwave heating with 10 W power during 10 s. No visual changes of the colloidal solution were observed but the TEM image of this solution shows the formation of spherical nanoparticle superstructures of 87(10) nm (Fig. 3). In the microwave frequency range, the IL tries to orientate with the electric field. As a consequence, the IL is highly disturbed which could results in a partial loss of its stabilizing agent ability, which can lead to the partial

Fig. 2. TEM images of Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles containing (a) 0.2 wt% (scale bar = 50 nm), (b) 0.7 wt%, (c) 1.4 wt% and (d) 5 wt% water. Scale bars = 100 nm.

J. Larionova et al. / Inorganica Chimica Acta 361 (2008) 3988–3996

Fig. 3. TEM image of Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles obtained with microwave treatment. Scale bar = 200 nm.

nanoparticle aggregation and thus to the formation of superstructures with a definite size. It should be noted that microwave irradiation for a longer time induces precipitation. 3.1.6. Influence of alcohol addition The Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles may be precipitated by adding a large amount of alcohols (methanol or ethanol) into colloidal solutions. The Cu/Fe atomic ratio inferred from elemental analysis for the so-obtained solids are closed to 1.5/1. Their IR spectra show the corresponding stretching vibrations of the bridging cyano groups (m = 2092, 2159 cm1) as well as the characteristic bands of [C4-MIM][BF4], proving the presence of the IL on the surface of the precipitated nanoparticles. The as-obtained nanoparticle precipitate is soluble into organic solvents such as toluene and THF. These nanoparticles are not affected by the precipitation process exhibiting a spherical in shape appearance with unchanged size. However, when using alcohols with higher water content, cubic shape nanoparticles with a size increased to ca. 15 nm were obtained (Fig. 4). 3.2. Magnetic study 3.2.1. Dynamic properties of Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles Magnetic properties of the colloidal solutions were previously studied by dc and ac modes by using SQUID-MPMS-XL magnetometer. It was shown that for all M3[Fe(CN)6]2/[Cn-MIM][BF4] nanoparticles the ZFC (zero field cooled)/FC (field cooled) magnetisation curves show an irreversibility and the ac susceptibility in the frequency range 1–1500 Hz shows frequency dependence [12]. The temperature dependence of the relaxation time was analysed with the Arrhenius and Power law and the presence of a spin-glass-like transition visibly induced by dipolar interparticle interactions was concluded. In this article we pursue the dynamic magnetic study of this system focusing on the sample Cu3-

Fig. 4. TEM image of Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles obtained after precipitation with methanol. Scale bar = 100 nm.

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[Fe(CN)6]2/[C4-MIM][BF4] in order to understand the nature of the magnetic behaviour. Fig. 5 shows the temperature dependence of the in-phase, v0 , and out-of-phase, v00 , components of the ac susceptibility for a Cu3[Fe(CN)6]2/[C4-MIM][BF4] sample measured in a zero external field in a wide frequency range, from 100 to 20,000 Hz. Both components, show frequency dependent behaviour where the temperatures of v0 and v00 peaks are shifted toward higher temperatures as the frequency increases. A parameter that is often used to distinguish different magnetic behaviours in nanoparticle systems is the temperature shift of the v00 peak (Tmax) per decade of frequency, which is determined by /  DTmax/[Tmax log (2pf)]. In the case of the Cu3[Fe(CN)6]2/[C4-MIM][BF4] sample was found the value / = 0.036, which is in the range of the frequency shifts found in canonical spin glasses and spin-glass-like materials (102–103) and rather smaller than the typical shifts found in superparamagnets (0.5–0.1). Different models were used in order to describe the temperature dependence of the relaxation time. Firstly, the frequency dependence of the v00 peak was analysed by the Arrhenius law, s = s0 exp (Ea/kBT), where Ea is the average energy barrier and is given by Ea = KV, K being the anisotropy energy constant and V the particles volume [25]. The energy barrier, Ea/kB, was estimated to be 120(2) K, and the pre-exponential factor, s0, 3.6(1.2)  1014 s (Table 1). This s0 value is close to what we observed previously in the frequency range of 1–1488 Hz (Table 1) [12] and it is too low compared to the commonly observed values for superparamagnetic systems, which are usually in the range 1010–1012 s [25]. Secondly, the temperature dependence of the relaxation time was fitted with the Vogel–Fulcher law, s = s0 exp (Ea/kB(T  T0)) in which the additional parameter T0 takes into account the interparticle interactions [26]. In this case, the value of the additional parameter, T0, was smaller than its error and the values of Ea/kB and s0 obtained in this fit were similar to those in the previous fit. These results are unsatisfactory and indicate that other models should be explored to analyse the magnetic dynamic properties of this sample. In this case unphysical values of the three parameters were obtained indicating this model is not appropriate to describe the relaxation dynamics. We further check if the dynamics of these samples would exhibit critical slowing down, as observed in canonical spin-glass systems. Two cases were considered depending on whether the transition temperature has a finite value or not. In the first case, an equilibrium ordered phase occurs at a finite critical temperature, Tg 6¼ 0 K, and the frequency relaxation time dependence may be fitted by the conventional critical scaling law of the spin dynamics, s = s0[Tg/ (Tmax  Tg)]zv, where Tg is the glass temperature and zv is a critical exponent [27]. The best fit gives Tg = 3.74(0.41) K, s0 = 2.64  106 s and zv = 7.41(1.89) (Table 1). The obtained zv value is in the range 4–12 expected for classical spin-glass systems. The s0 value is larger than the ones in conventional spin-glasses (1013 s), but close to what is observed in the case of cluster-spin-glass systems (106–1011 s) especially when the clusters are nanometric [27], as in our case. In the second case, the transition temperature occurs at Tg = 0 K and the frequency dependence of the relaxation time can be described by a generalised Arrhenius law s ¼ s0 expðEa =kB T zv max Þ [28]. The frequency dependence of s fitted with this law gives values of zv = 0.9(0.5), s0 = 2.75  1015 s, Ea/kB = 114(33) K indicating that also this model is not appropriate to describe our system. The relaxation time of the Cu3[Fe(CN)6]2/[C4-MIM][BF4] sample was also described using the Cole–Cole analysis [29]. This formalism is based on the assumption that the distribution of relaxation times is symmetrical on a logarithmic scale. This description introduces a parameter 0 < a < 1 which determines the width of the relaxation times distribution, g(ln s), around the median value, sC, through the following expressions [26]:

J. Larionova et al. / Inorganica Chimica Acta 361 (2008) 3988–3996

161.88 Hz 424.1 Hz 1.111 Hz 2.912 Hz 7.632 Hz 20.000 Hz

-4

4.0x10

-4

-4

-5

4.0x10

,,

2.0x10

,

χ (A. U.)

3.0x10

161.88 Hz 424.1 Hz 1.111 Hz 2.912 Hz 7.632 Hz 20.000 Hz

-5

6.0x10

χ (A. U.)

3992

-4

1.0x10

-5

2.0x10

0.0

0.0 0

2

4

6

8

10

0

12

2

Temperature (K)

4

6

8

10

Temperature (K)

Fig. 5. Temperature dependence of (a) in-phase, v0 , and (b) out-of-phase, v00 , components of the ac susceptibility for Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles.

Table 1 Some relevant magnetic data for the Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles in different state: as dispersed nanoparticles, as superstructures and as precipitated nanoparticles Frequency (Hz)

Dispersed nanoparticles Superstructures Precipitated nanoparticles

Tmaxa (K)

Power law fit

s0 (s)

Ea/kB

s0 (s)

Tg

zv

3.0  1018 3.6  1014 4.9  1014 2.7  1058

191(1) 120(2) 91(8) 1436(20)

1.3  108 2.6  106 3.4  106 1.9  1012

5.5 3.7 2.0 9.5

8.2 7.4 6.2 10

HC (Oe)

5.5

735

3 10

97 1940

Tmax was determined as the maximum of the ZFC curve.

v0  vS

1 þ ðixsÞ1a sinðapÞ gðln sÞ ¼ 2pfcosh½ð1  aÞ lnðs=sC Þ  cosðapÞg

ð1Þ

0.16 ð2Þ

where v0 and vS are the isothermal (low frequency limit) and adiabatic (high frequency limit) susceptibilities, respectively, and sC is the median relaxation time. a = 1 means an infinitely wide distribution and in the classical spin-glass systems it is expected close to 1, typically 0.8–0.9. If a = 0, the distribution width is zero and Eq. (1) reduces to a Debye equation suitable for relaxation with one single time constant [30]. Eq. (1) may be decomposed into its real and imaginary parts as [30] v  vS v0 ðxÞ ¼ vS þ 0 2 

 sinh½ð1  aÞ lnðxsC Þ cosh½ð1  aÞ lnðxsC Þ þ cosðð1  aÞp=2Þ   v  v sin½ð1  aÞp=2 S v00 ðxÞ ¼ 0 cosh½ð1  aÞ lnðxsC Þ þ cosðð1  aÞp=2Þ 2  1

0.12

,,

vðxÞ ¼ vS þ

χ / χ0

a

1–1500 100–20,000 1–1500 1–1500

Arrhenius law fit

0.08

4.00 K 4.25 K 4.50 K 4.75 K 5.25 K 5.50 K 6.00 K 6.50 K

0.04

0.00 0.0

0.2

0.4

0.6

0.8

1. 0

,

χ / χ0 ð3Þ ð4Þ

The fit of the experimental data of v00 expressed as a function of v0 following to the equation: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi v0  vS ðv0  vS Þ2 00 0 þ ðv0  vS Þðv0  v0 Þ þ v ðv Þ ¼  2 tan½ð1  aÞp=2 4 tan2 ½ð1  aÞp=2 ð5Þ is shown in Fig. 6. The obtained vs, v0 and a values are reported in Fig. 7 as a function of the temperature. The a values indicate a considerably wide s distribution with temperature. These values are much higher that the ones observed for classical superparamagnetic nanoparticles (a tend to 0). However they are lower than those expected for canonical spin-glass and cluster-glass systems (a tend to 1) [30]. The relaxation time distribution were calculated by applying Eqs. (2) and (3) and reported in Fig. 8. In conclusion the analysis of the ac susceptibility data with different models indicates the conventional critical scaling down model of the spin dynamics with Tg 6¼ 0 is the most appropriate,

Fig. 6. Cole–Cole diagram for selected temperatures obtained for Cu3[Fe(CN)6]2/[C4MIM][BF4] nanoparticles. Susceptibilities v0 and v00 are normalized to the isothermal susceptibility v0 determined by the fit. Symbols correspond to the experimental data and solid lines are fits of Eq. (5).

thus suggesting the presence of relatively strong interparticle interactions producing a nano-cluster-glass-like behaviour. 3.2.2. Temperature dependence of the coercive field for Cu3[Fe(CN)6]2/ [C4-MIM][BF4] nanoparticles The coercive field, HC, is a very important parameter considering particulate media. The field dependence of the magnetisation of the Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles measured at 1.8 K (lower than the ZFC peak temperature Tmax = 5.5 K) shows the presence of a hysteresis loop with HC = 735 Oe (Fig. 10a). The value of the coercive field, HC, decreases as the temperature increases and the hysteresis loop completely disappears as the temperature approaches to 5.5 K. The demagnetisation curves obtained at different temperatures from 1.8 to 5.5 K are shown in the inset of Fig. 10b. The thermal dependence of the coercive field of non-interacting and identical single domain particles with uniaxial anisotropy is

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0.7

0.2

α

0.6 0.1

0.4

0.000225

0.16 0.14

0

0.12 M emu/g

M emu/g

0.5

0.1 0.08 0.06

-0.1

χ s (A.U.)

0.04

0.000150

0.02 0 -1

-0.2

-0.5

00

0.000075 -10

-5

0

5

15

.5

20

2

25

H / kOe

0.000000 0.00045

0.8

0.00040

Experimental data Fit curve (k=0.5) Fit curve (k=0.77) Fit curve considering k as a free parameter

0.6

0.00035

0.4

C

H /kOe

χ 0 (A.U.)

10

.5 11 H / kOe

0.00030 4.0

4.5

5.0

5.5

6.0

6.5

0.2 0.0

T (K) Fig. 7. Thermal evolution of the parameters obtained with the fits to Eq. (5) for Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles.

-0.2 2

3

4

5

T/K Fig. 9. (a) Field dependence of the magnetisation performed for Cu3[Fe(CN)6]2/[C4MIM][BF4] nanoparticles. Inset: demagnetisation curves performed for different temperatures: 1.80 K (s), 1.92 K (d), 2.49 K (h), 2.99 K (j), 3.49 K (M) and 3.99 K (N); (b) temperature dependence of the coercive field for Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles.

0.20

0.16 0.12 0.08

0.16

g (ln τ)

0.20

30

0.04 0.00

0.12

0 4

5

T (K)

-30 6

Ln τ

6.5 K

0.24

g (Ln τ)

0.24

7

0.08 4.0 K

0.04 0.00 -20

0

ln τ Fig. 8. Distribution of relaxation times for Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles estimated with the Eq. (2) and the parameters a and sC.

" HC ðTÞ@HC ð0Þ 1 



T TB

k # ð6Þ

where HC(0) is the coercivity at T = 0 K and TB is the blocking temperature of the system. When the magnetic anisotropy axis of the particles are aligned, the expected value of k is 0.5 and when the particles are randomly oriented, k is 0.77 [31]. We observe that both models do not describe satisfactorily the experimental data in our system (see Fig. 9b). The values of the parameters obtained from the best fits are HC(0) = 1.75 (0.25) kOe and TB = 4.33 (0.32) K with

a coefficient of determination R2 of 0.87921, and HC(0) = 1.22 (0.18) kOe and TB = 4.23 (0.33) K with a coefficient of determination R2 of 0.8515, respectively. When the fit of the experimental data for relation (6) was done considering k as a free parameter (see continue line in Fig. 9b), the best fit gives unphysical values of the fit parameters with a large incertitude (k = 1.4  106 (0.99), HC(0) = 542513.79042 (4  1013) kOe, TB = 4.30 (0.33) K with a coefficient of determination R2 = 0.92359). Considering the conclusions of the Section 3.2.1, the unsatisfactory description of the temperature dependence of the coercivity in the studied sample with the Eq. (6) can be related to the presence of strong interparticle interactions. 3.2.3. Dynamic properties of Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles superstructures The magnetic properties of Cu3[Fe(CN)6]2/[C4MIM][BF4] superstructures resemble to those observed when the same nanoparticles are dispersed into ionic liquid mentioned previously. The FC/ ZFC curves show irreversibility with a maximum of the ZFC curve at Tmax = 3 K (Table 1, Fig. 1S, ESI). This value is lower than the value for the colloidal solution of the Cu3[Fe(CN)6]2/[C4MIM][BF4] nanoparticles (Tmax = 5.5 K, Table 1). The FC curve increases as the temperature decreases and never reaches the saturation. The temperature dependence of v0 and v00 , for the superstructures measured in a zero field in the 1–1500 Hz frequency range, are shown

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in Fig. 10. The parameter /  DTmax/[Tmax log (2pf)] in this case is equal to 0.08, that is in the range of the parameters observed in the case of spin-glass systems. However, this value is higher than the / parameter observed previously in the case of dispersed Cu3[Fe(CN)6]2/[C4MIM][BF4] nanoparticles (0.036). Both components of ac susceptibility are frequency dependent and the temperatures of v0 and v00 peaks are shifted toward low temperature in comparison to the colloidal solution of the dispersed nanoparticles. The Arrhenius fit of the temperature dependence of the relaxation time gives Ea/kB = 91(8) K and s0, of 4.99(2)  1014 s (Table 1), which suggests the presence of dipolar interparticle interactions [25]. The Vogel–Fulcher law does not provide a satisfactory result. We also checked if the dynamics would exhibit critical slowing down, as observed for dispersed nanoparticles. Indeed a satisfactory fit was obtained with s = s0[Tg/(Tmax  Tg)]zv law with the best parameters Tg = 2.02(0.41) K, s0 = 3.37  106 s and zv = 6(2) (Table 1). The value of zv is in the range 4–12 expected for classical spin-glass systems [27]. As in the case of the colloidal solution, the s0 value is larger than that in conventional spin-glasses (1013 s), but close to what observed for cluster-spin-glass systems (106–1011 s) especially when the clusters are nanometric. The second model, s ¼ s0 expðEa =kB T zv max Þ, does not seem to be appropriate to describe this system. These results show the presence of interparticle dipo-

1

χ' emu / L

0.8

0.6

0.4

0.2

0

2

3

4

5

6

7

8

9

10

T/K 0.14 0.12 0.1

χ" emu / L

lar interactions, which induces a spin-glass or a cluster-glass behaviour. The field dependence of the magnetisation performed at 1.8 K show a very small hysteresis loop with the coercive field of 97 Oe (Table 1). In comparison to the colloidal solution of the dispersed nanoparticles, the colloidal solution containing nanoparticle superstructures present increasing of the / parameter, decreasing of the Tmax on the ZFC curves, decreasing of the temperature peaks of both components of ac susceptibility, v0 and v00 , as well as the value of the coercive field. These results clearly indicate that in the case of dispersed nanoparticle system the magnetostatic interactions are more significant than in the case of their superstructures. This fact may be explained by the difference in their size. Indeed, the first system contains small homogeneously dispersed nanoparticles of 3.3(0.6) nm, while the second one contains nanoparticle’s superstructures of 87(10) nm. Both systems contain the same concentration of 1.4  106 mol. However, in comparison to the colloidal solution of dispersed nanoparticles, the colloidal solutions of the superstructures contain lower concentration in nano-objects and as a consequence we observe increasing intersuperstructures distances and decreasing of inter-superstructures interactions. TEM showed that the first system contains small homogeneously dispersed nanoparticles of 3.3(0.6) nm, while the second one contains nanoparticle’s superstructures of 87(10) nm. As the interactions are mainly dipolar we would thus expect larger interactions effect in the superstructure containing sample on the contrary of what experimentally observed. Moreover TEM also excludes the occurrence of 2D or 3D structural ordering into the superstructures making thus difficult to find a convincing explanation: Possibly the observed behaviour arises from a magnetic ordering of the particles easy axes inside the large structures producing an internal mean field which reduces the effect of interactions.

0.08 0.06 0.04 0.02 0 2

3

4

5

6

7

8

T/K Fig. 10. Temperature dependence of (a) in-phase, v0 , and (b) out-of-phase components of the ac susceptibility for Cu3[Fe(CN)6]2/[C4-MIM][BF4] superstructures. Frequency: 1 Hz (s), 36 Hz (d); 125 Hz (h), 498 Hz (j), 998 Hz (M).

3.2.4. Dynamic properties of precipitated Cu3[Fe(CN)6]2/[C4MIM][BF4] Nanoparticles The temperature dependence of v0 and, v00 , for precipitated Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles measured in a zero external field in the frequency range 1–1500 Hz are shown in Fig. 11. As in the previous cases, both components of ac susceptibility are frequency dependent. However, the temperature of v0 and v00 peaks are shifted toward higher temperature in comparison to the colloidal solution of dispersed nanoparticles and their superstructures. At 1 Hz, the maximum of v0 and v00 are found at 11.02 and 10.36 K. The / parameter is equal to 0.015 that is in the range of the values observed for classical spin-glass behaviour. The fit of the v00 peaks to the Arrhenius law, gives Ea/kB = 1436(20) K and a very small s0 value of 2.72  1058 (Table 1). The temperature dependence of the relaxation time was also fitted with the Power law, s = s0[Tg/(Tmax  Tg)]zv, providing the best fit parameters, Tg = 9.5 K, s0 = 1.909  1012 s and zv = 10(1), which are in good agreement with the values usually observed for classical spin-glass systems (Table 1). Thus the very strong dipolar interparticle interactions acting in the precipitated samples induce the appearance of a classical spin-glass regime. The field dependence of the magnetisation shows the presence of a hysteresis loop with a coercive field of 1.94 kOe, which is twice the value measured when the nanoparticles are in colloidal solution. Clearly, in the case of precipitated nanoparticles in comparison with dispersed into ionic liquid nanoparticles, we observed decreasing of / parameter, increasing of the Tmax on the ZFC curves, increasing of the temperature peaks of both components of ac susceptibility, as well as of the value of the coercive field. All obtained parameters for precipitated nanoparticles are characteristics of classical spin-glass behaviour. These results clearly indicate that in the case of precipitated nanoparticles the magnetostatic interactions are more significant than in the case of dispersed into ionic liquid nanoparticles. The large difference

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crease of the nanoparticle size and the influence of N-substituted alkyl chains showing that [C2-MIM][Cl] was found as a poor stabilising agent. We study the IL water content influence on the nanoparticles observing a progressive nanoparticle size increase and aggregation when increasing the water content with precipitation up to 6 wt%. Microwave heating of nanoparticle colloidal solutions was shown to generate superstructure while adding of alcohols leads to a nanoparticle precipitate that could be dissolved into organic solvents. The dynamic study of the magnetic properties of the obtained frozen colloids of nanoparticles shows the presence of relatively strong interparticles interactions inducing the appearance of cluster-glass-like behaviour. The stench of these interparticles interactions decreases in the nanoparticle’s superstructures. Compressing the nanoparticles by precipitation induces increasing of the interparticles interactions which induces an appearance of classical spin-glass behaviour.

0.007 0.006 0.005

χ" emu/g

3995

0.004 0.003 0.002 0.001 0 4

6

8

10

12

14

16 Acknowledgements

T/K

The authors thank C. Reibel (LPMC, Montpellier, France) for magnetic measurements and the network of excellence MAGMANET (NMP3-CT-2005-515767) for financial support.

-0.5 -1

Appendix A. Supplementary material

log(1/2πf)

-1.5

Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.ica.2008.03.038.

-2 -2.5

References

-3 -3.5 -4 0.7

0.8

0.9

1

1.1

1.2

1.3

log(Tg/(Tmax-Tg)) Fig. 11. (a) Temperature dependence of out-of-phase, v00 , component of the ac susceptibility and (b) Power law fitting of the temperature dependence of the relaxation time for precipitated Cu3[Fe(CN)6]2/[C4-MIM][BF4] nanoparticles. Frequency: 1 Hz (N), 10 Hz (}), 125 Hz (d), 498 Hz (j), 998 Hz (h), 1488 Hz (s).

of these magnetic properties with the ones found in the other samples are related to its larger compacting. 4. Conclusion In summary, room temperature imidazolium-based ILs were used to prepare soluble coordination polymer nanoparticles of controlled size Cu3[Fe(CN)6]2/[Cn-MIM][An] (where n = 2, 4 and X = Cl, BF4). These coordination polymer nanoparticles/IL colloidal systems are exceptionally stable and no ligands are required suggesting that the IL plays the role of the stabilizing agent. We focuses on Cu3[Fe(CN)6]2/[Cn-MIM][BF4] nanoparticles in order to establish the influence of different factors on the size and shape of the nanoparticles. We established the temperature influence as spherical nanoparticles of 3.3(0.9) nm were obtained in the temperature range 50 to 25 °C while increasing the reaction temperature to 50 °C induces a twice increase of the nanoparticles size and rising of the temperature to 80 °C induces the formation of the submicrometric crystallites. For comparison, the post-synthetic heating at 50 and 80 °C induces only a slight modification of the nanoparticle size. We discuss the influence of the IL counter anion as the adding of [C4-MIM][Cl] into [C4-MIM][BF4] up to 20% induces a weak in-

[1] M. Drillon, J. Miller, Magnetism: Molecules to Materials IV, Wiley-VCH, Weinheim, 2005. [2] (a) O. Hatlevik, W.E. Buschmann, J. Zhang, J.L. Manson, J.S. Miller, Adv. Mater. 11 (1999) 914; (b) S.M. Holmes, G.S. Girolami, J. Am. Chem. Soc. 121 (1999) 5593; (c) B.G. Morin, C. Hahm, A.J. Epstein, J.S. Miller, J. Appl. Phys. 75 (1994) 5782; (d) J.S. Miller, Adv. Mater. 6 (1994) 322; (e) S. Ferlay, T. Mallah, R. Ouahès, P. Veillet, M. Verdaguer, Inorg. Chem. 38 (1999) 229; (f) W.E. Buschmann, S.C. Paulson, C.M. Wynn, M. Girtu, A.J. Epstein, H.S. White, J.S. Miller, Adv. Mater. 9 (1997) 645; (g) W.R. Entley, G.S. Girolami, Science 268 (1995) 397; (h) S. Ferlay, T. Mallah, R. Ouahès, P. Veillet, M. Verdaguer, Nature 378 (1995) 701; (i) V. Gadet, T. Mallah, I. Castro, M. Verdaguer, J. Am. Chem. Soc. 114 (1992) 9213; (j) T. Mallah, S. Thiébaut, M. Verdaguer, P. Veillet, Science 262 (1993) 1554; (k) O. Sato, T. Iyoda, A. Fujishima, K. Hashimoto, Science 271 (1996) 49; (l) S. Ohkoshi, K. Hashimoto, J. Am. Chem. Soc. 121 (1999) 10591. [3] E. Dujardin, S. Mann, Adv. Mater. 16 (2004) 1125. and references cited therein. [4] G. Schmid, Nanoparticles: From Theory to Application, Wiley-VCH, Weinheim, 2004. [5] M.-I. Baraton, Synthesis, Functionalization and Surface Treatment of Nanoparticles, American Scientific Publishers, California, USA, 2003. [6] (a) S. Vaucher, M. Li, S. Mann, Angew. Chem., Int. Ed. 39 (2000) 1793; (b) S. Mann, J. Fielden, M. Li, E. Dujardin, S. Mann, Nano Lett. 2 (2002) 225. [7] L. Catala, T. Gacoin, J.-P. Boilot, E. Rivier, C. Paulsen, E. Lhotel, T. Mallah, Adv. Mater. 15 (2003) 826. [8] (a) T. Uemura, S. Kitagawa, J. Am. Chem. Soc. 125 (2003) 7814; (b) D.M. DeLongchamp, P.T. Hammond, Adv. Funct. Mater. 14 (2004) 224; (c) L. Catala, A. Gloter, O. Stephan, G. Rogez, T. Mallah, Chem. Commun. (2006) 1018; (d) D. Brinzei, L. Catala, N. Louvain, G. Rogez, O. Stéphan, A. Gloter, T. Mallah, J. Mater. Chem. 16 (2006) 2503. [9] (a) Y. Guari, J. Larionova, K. Molvinger, B. Folch, Ch. Guérin, Chem. Commun. (2006) 2613; (b) J.M. Domingez-Vera, E. Colacio, Inorg. Chem. 42 (2003) 6983. [10] (a) P. Zhou, D. Xue, H. Luo, X. Chen, Nano Lett. 2 (2002) 845; (b) J.G. Moore, E.J. Lochner, C. Ramsey, N.S. Dalal, A.E. Stiegman, Angew. Chem., Int. Ed. 42 (2003) 2741. [11] (a) B. Folch, Y. Guari, J. Larionova, C. Luna, C. Sangregorio, C. Innocenti, A. Caneschi, Ch. Guérin, New J. Chem. 32 (2008) 273; (b) G. Clavel, Y. Guari, J. Larionova, Ch. Guérin, New J. Chem. 29 (2005) 275. [12] (a) G. Clavel, J. Larionova, Y. Guari, Ch. Guérin, Chem. Eur. J. 12 (2006) 3798; (b) J. Larionova, Y. Guari, H. Sayegh, Ch. Guérin, Inorg. Chim. Acta (2007) 3829.

3996

J. Larionova et al. / Inorganica Chimica Acta 361 (2008) 3988–3996

[13] P. Wasserscheid, T. Welton, Ionic Liquids in Synthesis, Wiley-VCH, Weinheim, 2003. [14] (a) P. Wasserscheid, T. Welton, Ionic Liquids in Synthesis, Wiley-VCH, Weinheim, 2003; (b) R. Scheldon, Chem. Commun. (2001) 2339; (c) J.G. Huddleston, H.D. Willauer, R.P. Swatloski, A.E. Visser, R.D. Rogers, Chem. Commun. (1998) 1765; (d) A.B. McEwen, S.F. McDevitt, V.R. Koch, J. Electrochem. Soc. 144 (1997) L84; (e) E.V. Dickinson, M.E. Williams, S.M. Hendrickson, H. Masui, R.W. Murray, J. Am. Chem. Soc. 121 (1999) 613; (f) N. Kimizuka, T. Nakashima, Langmuir 17 (2001) 6759; (g) R.P. Swatloski, S.K. Spear, J.D. Holbrey, R.D. Rogers, J. Am. Chem. Soc. 124 (2002) 4974; (h) T. Nakashima, N. Kimizuka, Chem. Lett. (2002) 1018. [15] (a) G.-T. Wei, Z. Yang, C.-Y. Lee, H.-Y. Yang, C.R. Chris Wang, J. Am. Chem. Soc. 126 (2004) 5036; (b) H. Itoh, K. Naka, Y. Chujo, J. Am. Chem. Soc. 126 (2004) 3026; (c) K.-S. Kim, D. Demberelnyamba, H. Lee, Langmuir 20 (2004) 556; (d) J. Dupont, G.S. Fonseca, A.P. Umpierre, P.F.P. Fichtner, S.R. Teixeira, J. Am. Chem. Soc. 124 (2002) 4228; (e) C.W. Scheeren, G. Machado, J. Dupont, P.F.P. Fichtner, S.R. Texeira, Inorg. Chem. 42 (2003) 4738; (f) J. Huang, T. Jiang, B. Han, H. Gao, Y. Chang, G. Zhao, W. Wu, Chem. Commun. (2003) 1654; (g) V. Calo, A. Nacci, A. Monopoli, S. Laera, N. Cioffi, J. Org. Chem. 68 (2003) 2929; (h) R.R. Deshmukh, R. Rajagopal, K.V. Srinivasan, Chem. Commun. (2000) 1544; (i) Y.-J. Zhu, W.-W. Wang, R.-J. Qi, X.-L. Hu, Angew. Chem., Int. Ed. 43 (2004) 1410; (j) T. Nakashima, N. Kimizuka, J. Am. Chem. Soc. 125 (2003) 6386. [16] P.A.Z. Suarez, J.E.L. Dullios, S. Einloft, R.F. de Scuza, Polyhedron (1996) 1217.

[17] K. Nakamoto, Infrared and Raman Spectra, John Wiley and Sons Inc., New York, 1986. [18] D.L. Feldheim, C.A. Foss, Metal Nanoparticles, Marcel Dekker, Inc., New YorkBasel, 2002. [19] B.L. Cushing, V.L. Kolesnichenko, C.J. O’Connor, Chem. Rev. 104 (2004) 3893. [20] J. Holbrey, K.R. Seddon, J. Chem. Soc., Dalton Trans. (1999) 2133. [21] J. Bowers, C.P. Butts, P.J. Martin, M.C. Vergarra-Gutierrez, Langmuir 20 (2004) 2191. [22] A. Noda, K. Hayamizu, M.J. Watanabe, Phys. Chem. B 105 (2001) 4603. [23] A. Mele, C.D. Tran, S.H. De Paoli Lacerda, Angew. Chem., Int. Ed. 42 (2003) 4364. [24] (a) Y. Hasgawa, Y. Okada, T. Kataoka, T. Sakata, H. Mori, Y. Wada, J. Phys. Chem. B 110 (2006) 9008; (b) J. Liu, K. Li, H. Wang, M. Zhu, H. Yan, Chem. Phys. Lett. 396 (2004) 429; (c) I. Pastoriza-Santos, L.M. Liz-Marzan, Langmuir 18 (2002) 2888; (d) J. Knipping, H. Wiggers, B. Rellinghaus, P. Roth, D. Konjhodzic, C. Meier, J. Nanosci. Nanotech. 4 (2004) 1039. [25] (a) L. Nèel, Ann. Geophys. 60 (1949) 661; (b) J.L. Dormann, L. Bessais, D. Fiorani, J. Phys. Chem. C 21 (1988) 2015. [26] M.A. Girtu, J. Optoelectron. Adv. Mater. 4 (2002) 85. [27] (a) C. Djurberg, P. Svedlindh, P. Nordblad, M.F. Hansen, F. Bodker, S. Morup, Phys. Rev. Lett. 79 (1997) 5154; (b) J.A. Mydosh, Spin Glasses, Taylor and Francis, Washington, DC, 1993. [28] (a) G. Balaji, G. Wilde, J. Weissmuller, N.S. Gabhiye, V.K. Sankaranarayanan, Phys. Status Solidi 241 (2004) 1589; (b) N. Bontemps, J. Rajchenbach, R.V. Chamberlin, R. Orbach, Phys. Rev. B 30 (1984) 6514. [29] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341. [30] C. Dekker, A.F.M. Arts, H.W. de Wijn, A.J. van Duyneveldt, J.A. Mydosh, Phys. Rev. B 40 (1989) 11243. [31] B. Martínez, A. Roig, X. Obradors, E. Molins, A. Rouanet, C. Monty, J. Appl. Phys. 79 (1996) 2580.