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The role of diffusion-controlled growth in formation of uniform iron oxide nanoparticles with a link to magnetic hyperthermia Ilona S. Smolkova, Natalia E. Kazantseva, Vladimir Babayan, Jarmila Vilcakova, Nadezda Pizurova, and Petr Saha Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.6b01104 • Publication Date (Web): 10 Apr 2017 Downloaded from http://pubs.acs.org on April 15, 2017

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Crystal Growth & Design

The role of diffusion-controlled growth in formation of uniform iron oxide nanoparticles with a link to magnetic hyperthermia Ilona S. Smolkovaa, Natalia E. Kazantsevaa*, Vladimir Babayana, Jarmila Vilcakovaa, Nadezda Pizurovab, Petr Sahaa a

Centre of Polymer Systems, Tomas Bata University in Zlin, Trida Tomase Bati 5678, 760 01

Zlin, Czech Republic b

Institute of Physics of Materials of the Academy of Sciences of the Czech Republic, Zizkova

22, 616 62 Brno, Czech Republic Corresponding Author * Natalia E. Kazantseva, Tel.: +42057 603 8114; fax: +420 57 603 1444, E-mail address: [email protected] [email protected] KEYWORDS Crystal nucleation and growth, iron oxide nanoparticles, coprecipitation, magnetic interaction, multicore particles, magnetic hyperthermia.

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ABSTRACT

Uniform superparamagnetic iron oxide nanoparticles were obtained by coprecipitation under synthesis conditions that guarantee diffusion-controlled growth. Study of nanoparticles crystal structure formation by HRTEM showed that at the earlier stage of the reaction some nanoparticles consist of crystalline core and amorphous surface layer, whereas resulting particles display high degree of crystalline order. This result suggest that nanoparticles are formed from fusion of non-crystalline primary particles of iron(hydr)oxide. Slow addition of iron salts to excess ammonia restricts the amount of primary particles; as a result, their diffusion is the limiting step of the reaction, which provides the formation of uniform nanoparticles. Importantly, five-minute reaction product shows the same polydispersity and heating efficiency as final product. Thus, monodispersity guarantees precision of particles properties, facilitating control over heat generation for given amplitude and frequency of AMF. Magnetic dipole interactions between single nanoparticles lead to the formation of dense aggregates (multicore particles) at the beginning of the reaction. The dispersions of separated multicore particles with hydrodynamic size of about 85 nm shows higher heating efficiency than dispersion of asprepared nanoparticles. Increase of aggregate size leads to decrease of heating efficiency to the value of as-prepared nanoparticles due to demagnetizing effect.

INTRODUCTION

Magnetic iron oxide nanoparticles (NPs) are thoroughly investigated for application as a magnetic phase of heat mediators in magnetic hyperthermia [1-3]. In magnetic hyperthermia, the magnetic material is deposited inside the tumour and generates heat when exposed to low-power alternating magnetic fields (AMF), i.e. at frequencies (from 100 kHz up to 1.5 MHz) and


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amplitudes (≤ 15 kA/m) standardized for medicine [4]. The heating potential of magnetic material in AFM is characterized by specific loss power (SLP), which reflects the amount of heat generated by unit mass of magnetic material. SLP depends on the intrinsic properties of NPs (magnetic anisotropy, saturation magnetization) and dispersion media (viscosity and specific heat capacity), as well as by experimental conditions (AFM parameters, magnetic phase concentration). In the ensemble of non-interacting (weak interacting) single-domain NPs, the energy losses are associated with Neel − Brown relaxation process [5]. Since Brown relaxation is largely suppressed when the particles are immobilized in a viscous medium such as a tumour tissue, there is clear need for experimental studies of SLP in Neel-dominated systems [6]. Several key structural parameters of NPs were revealed that favor high energy losses: (1) high crystallinity; (2) narrow particle size distribution, i.e. polydispersity index (σ) ≤ 0.3; (3) particle size corresponding to the stable-single domain state [7-9]. Each of these parameters as well as interparticle magnetic interactions, leading to the formation of aggregates, contribute to the effective value of magnetic anisotropy, which ultimately determines the degree of freedom of particle magnetic moment rotation and, therefore, governs energy loss in the system [10]. However, there is no unique opinion on the dynamic behavior of magnetic NPs in the presence of magnetic interactions, and, therefore, it impacts on heat generation under exposure to AMF is still unclear. Besides, data from literature show contrariety in the hyperthermia performance as a function of particle concentration and amplitude of AMF [2, 11-16]. As an example, Landi at el. have shown that even moderate changes in the particle concentrations may have substantial effects on the magnetization dynamics of the system, being capable of increasing or decreasing the heat released by order the magnitude, depending on the specific characteristics of NPs and AMF parameters [11]. The differences in hyperthermia response of magnetic NPs systems


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reported in the literature has been comprehensively explained by Conde-Leboran et al. in accordance with the differences in frequency and amplitude of AMF, specific characteristics of tested magnetic materials, and material concentration (dosage) in dispersive media [1]. Generally, studying of heat generation in interacting particle system requires investigation of time-dependent relaxation processes in terms of: (i) specific characteristics of NPs and their aggregates, (ii) concentration of magnetic phase in dispersive media, (iii) viscosity of dispersive media, (iv) frequency and amplitude of AMF, etc.

The highest reported up-today SLP values of about 1 – 2 kW/gFe [3, 12, 17, 18] were obtained in AMFs with amplitudes of 20 – 35 kA/m, which are not tolerated by the patients [19, 20]. Moreover, these SLP values are obtained usually for the dispersions of NPs in low viscosity medium, where both relaxation mechanisms account for heat generation. Therefore, fine-tuning of NPs size, shape and interparticle interaction that determine effective magnetic field of anisotropy is strictly required to prepare the material, which could be intrinsically used in magnetic hyperthermia.

As to the methods for preparation of magnetic iron oxides NPs with required properties, the most frequently used method is thermal decomposition of iron-organic compounds. By this method, it is possible to obtain highly monodisperse NPs as the nucleation and growth stages are separated, as far as they take place at different temperatures [21]. To obtain NPs in stable single domain state by this method, two-step seed-mediated NPs growth is required. However, this may lead to the formation of the defect crystal structure of NPs and as a result the material does not display the expected high heating efficiency [22]. Another popular synthesis route is the coprecipitation of iron salts with alkalis. This method is simple, rapid and inexpensive, does not require toxic


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initial components and yields gram quantities of NPs. The main drawback reported for this method is high polydispersity of particle size and nonstoichiometric crystal structure, explained by inability to control the nucleation and growth processes. Moreover, coprecipitation method suffers from spontaneous aggregation of NPs resulting in formation of aggregates with broad hydrodynamic size distribution. As in coprecipitation reaction nucleation and growth of NPs occur simultaneously and it is not possible to study each process independently, and the mechanisms of crystallization are still not completely understood. Indeed, despite the obvious potential of coprecipitation method, there are only a few systematic studies aimed at the optimization of NPs synthesis [23-26]. The parameters that usually studied are: ratio of hydroxide ions to total iron concentration, iron salt concentration (total amount of iron), reaction temperature and steering speed, Fe3+/Fe2+ ratio. The influence of these parameters is evaluated according to average particle size and magnetic properties. Namely, it was established that formation of magnetite proceeds at pH above 8, therefore the ratio of hydroxide ions to total iron salts concentration should be more than one [26, 27]. Recently, Baumgarther et. al. have shown that nucleation and growth of magnetite NPs during coprecipitation in alkaline media proceed through rapid fusion of metastable primary particles, 1−2 nm in size, consisting of a disordered iron oxide phase [28]. It was also verified, that an increase of iron salts concentration, while keeping all other reaction parameters constant, leads to an increase in NPs size [26]. This is explained by the enhancement of the nucleation rate with the increase of iron salts concentration. The effect of reaction temperature and steering speed on the particle size is also connected with their influence on the nucleation, to be precise increase of reaction temperature leads to an increase of particle size, whereas increase of the steering speed leads to a decrease of the particle size. [26, 28, 29]. However, though the influence of synthesis parameters on the average particle


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size is well established, the polydispersity of the obtained NPs is still high, above 0.3. A general strategy to obtain monodisperse particles requires rapid homogeneous nucleation [30]. Size distribution can be further varied during growth of NPs depending upon the growth mechanism. The growth process involves two steps: (1) movement of the monomer (NPs building material) to the surface of the NP, and (2) adsorption of the monomers by the growing particle. Depending on the velocity of these two processes, one distinguishes diffusion-controlled and adsorptioncontrolled growth. Based on the classical and non-classical nucleation theory, Wen et al. proposed a generalised diffusion model for growth of NPs synthesized in the liquid phase [31]. It was established that diffusion-controlled growth would result in monodisperse NPs, while adsorption-controlled growth would give polydisperse NPs.

In our previous work, we have shown how the coprecipitation reaction parameters determine the nucleation mechanism and consequently the magneto-structural properties of iron oxide NPs that manifest itself in their heating efficiency in AMFs [32]. It was demonstrated that the changing of mixing order of the initial reagent leads to different pH of reaction media and, as a consequence, formation of uniform or polydisperse NPs. Uniform NPs are formed if the reaction is carried out in an alkaline medium with slow addition of iron (II) and iron (III) solution to excess alkali; this provides immediate supersaturation promoting rapid homogeneous nucleation and rapid growth of NPs at the first minutes of the reaction, which is than replaced by slow growth process.

In the current work, we continue to investigate the iron-oxide NPs formation by coprecipitation within the frames of nucleation and growth phenomena. It is demonstrated, that slow velocity of precursor (iron salts) addition provides a narrow alkaline pH window during the reaction and determines the diffusion-controlled growth of uniform NPs. Contrariwise, abrupt addition of


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precursor leads to the higher polydispersity of NPs and lower heat generation in AMF compared to uniform NPs. The effect of polydispersity on the magnetic properties and heating efficiency in AMF was investigated. Along with the effect of polydispersity, we considered the effect of interparticle magnetic interactions on the heating efficiency of NPs incorporated into aggregates by study the dependence of SLP on hydrodynamic size of aggregates, viscosity of dispersive media and parameters of AMF.

EXPERIMENTAL PART Synthesis of magnetic iron oxide NPs

Magnetic NPs were prepared by coprecipitation of iron salts in an alkaline medium according to the synthesis protocol described in [32]. Solution containing ferrous and ferric chlorides with molar ratio of ½ was added dropwise into the excess of aqueous ammonia with pH ~ 11. The salts solution addition rate was 30 ml/min and 0.3 ml/min for Sample A and Sample B respectively. Excess of alkali was deliberately taken in order to keep the alkaline pH during the salts addition process, since magnetite is rapidly formed through a single intermediate stage, namely, through the formation of ferrihydrite with incorporated iron (II) cations, only in alkaline pH [25, 28, 32]. The reaction was performed in argon atmosphere with a continuous stirring, at 70 °C. After complete addition of iron salts solution, the reaction was left for an hour at 70 °C and stirring. The black powder of magnetic particles formed in the reaction was separated by a permanent magnet, washed with distilled water and dried in air at room temperature. Both samples were prepared and investigated at least three times to verify the reproducibility of the results.


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To analyze the kinetics of magnetic NPs formation the magneto-structural properties and heating efficiency of reaction intermediates were studied. To this end, the reaction was stopped at different stages, and the reaction products were separated. To ensure the reproducibility of properties of the reaction intermediates the synthesis was performed at least three times.

To separate NPs aggregates with certain hydrodynamic size, the peptization of as-prepared NPs was done by the treatment of the NPs sediment with 0.001 M hydrochloric acid till pH ~ 2.5 and sonication in ultrasonic bath. The dark-brown supernatant containing electrostatically stabilized NPs aggregates was collected by holding the remained sediment by permanent magnet. The addition of water to the sediment and ultrasonication also resulted in the formation of supernatant with dispersed NPs aggregates. Increase of pH of the dispersive media leads to the formation of NPs aggregates with larger hydrodynamic size then the former ones. To obtain the dispersions of NPs aggregates in agar matrix, 3.4 wt. % of agar was mixed with the water dispersions of NPs aggregates and heated under continuous stirring to 70 °C. After this, the mixture was placed in a fridge to form the solid matrix.

Characterization Transmission Electron Microscopy / High Resolution Transmission Electron Microscopy (TEM / HRTEM, JEOL JEM - 2100F) was used to establish the morphostructure of NPs. The statistical analysis of the average particle size was carried out on several TEM and HRTEM images with different magnification to detect both small and large NPs with the help of Digital Micrograph software (Gatan). For each sample, 250 particles were counted at least and numerical and volume distributions were obtained. The estimation of NPs volume distribution was done with the assumption of the spherical shape of particles.


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X-Ray diffraction (XRD, PANalytical X-Ray powder diffractometer) was used to determine the crystal structure, crystal lattice strains and the average crystallite size using Scherrer’s formula. The XRD data were refined by the Rietveld method using the Fullprof program. The average crystallite size was determined using Scherrer’s formula (incorporated into Rietveld's refinement codes). The magnetization measurements were performed with a Vibrating Sample Magnetometer (Lake Shore 7407) at room temperature in air atmosphere in a magnetic field of up to 10 kOe. The 57Fe transmission Mössbauer spectra of samples were recorded using a standard Mössbauer spectrometer in a constant acceleration mode with the 57Co (Rh) gamma-ray source in zero field at 293 K. Zero-field-cooled (ZFC) and field-cooled (FC) temperature dependent magnetization measurements were performed with a superconducting quantum interference device, SQUID magnetometer, Quantum Design MPMS XL-7. The measurements were carried out in the temperature range 50 - 300 K at magnetic fields of 500 and 1000 Oe. The concentration of iron oxide and iron content in the dispersions were determined by Energy Dispersive X-ray Fluorescence spectroscopy by ARL Quant’X EDXRF Analyzer, Thermo Scientific. Electrical conductivity was measured on impedance material analyzer Novocontrol Concept 50. Thermal conductivity of NPs in a powder form and the dispersions of NPs in glycerol and agar was measured by TCi™ Thermal Conductivity Analyzer, C-Therm Technologies at ambient temperature. Concentration of NPs in dispersions was 5 wt. %, i.e. the same as during SLP test.


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Hydrodynamic size of NPs aggregates in water dispersions was measured by Dynamic Light Scatering (DLS) on Zetasizer Nano ZS, Malvern Instruments. Specific loss power (SLP) of as-prepared iron oxide NPs and their aggregates were measured in AMF of 1048 kHz, 5.9 kA/m. For the measurement powder of as-prepared NPs was dispersed in both glycerol (viscosity 1.41 Pa s) and agar (viscosity ~140 Pa s) matrix with concentration of 5 wt. %. To study the dependence of SLP on the field amplitude for NPs aggregates we applied AMF of 525 kHz as at this frequency it is possible to perform measurements in a broader amplitude range (4.0 – 7.6 kA/m) than at 1048 kHz due to the technical reasons. Measurements of separated NPs aggregates were carried out on water and agar dispersions with concentration of 1 wt %. During the experiment the temperature was measured with fiber optic temperature monitoring system (ReFlex 4, Neoptix) and fiber optic temperature probe (T1S-02-WNO-PT05) inserted directly inside the sample dispersions. The SLP was calculated as follows: ܵ‫ = ܲܮ‬1/݉ · ሾሺ݀ܶ/݀‫ݐ‬ሻ · ‫ܥ‬ሿ, where m is the mass of iron in the dispersion; dT/dt is the slope of the time-dependence of temperature; and C is the heat capacity of sample. RESULTS AND DISCUSSION In the current work, two samples of magnetic iron oxide particles were prepared. In the case of Sample A the solution of iron salts was quickly added (30 ml/min) to the aqueous ammonia. In the case of Sample B the iron salts solution was added dropwise with the rate of 0.3 ml/min. According to XRD both reactions yield magnetic iron oxide NPs with inverse spinel structure (Figure 1). The values of saturation magnetization (MS) and coercivity (HC) of samples (Table 1) display lower values of saturation magnetization compared to bulk magnetite and maghemite,


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which is usually observed for nanomaterials due to spin disorder on the surface, the so-called “dead layer” [33-35].

Figure 1. XRD of samples. Table 1. Structural and magnetic properties of iron oxide particles.

Property dTEM, (nm) σTEM Shape Surface to volume ratio, nm-1 dXRD, (nm) ε, % MS, (emu·g–1) HC, (Oe) Electrical conductivity, S·cm–1

Sample A 13 0.4 Irregular

Sample B 13 0.3 Nearly spherical

Sample B_5 min 9 0.3 Nearly spherical

0.2

0.3

-

13 0.3 58 ± 2 10 ± 2

12 0.3 56 ± 2 11 ± 4

8 0.3 48 ± 3 1±2

3.7 ⋅ 10-7

6.9 ⋅ 10-9

-

As can be seen from the TEM images of dry aqueous dispersion (Figure 2 a, b), single NPs of samples have different morphology and are incorporated into aggregates. NPs of Sample A have irregular shape and different sizes, whereas NPs in Sample B are mostly spherical and have


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almost the same size. The average particle size (dTEM) and size distribution (σTEM) determined from TEM images, average crystallite size determined from XRD patterns (dXRD), as well as crystalline lattice strain (ε) evaluated by Rietveld refinement are summarized in Table 1. Though, the average particle size is almost the same for the samples, the size and volume distribution for Sample A are higher (Figure 2 c, d). Indeed, the presence of large NPs with diameters over 60 nm was detected for Sample A, which occupy more than 50 vol. %. According to micromagnetic modelling, 60 nm sized NPs are pseudo-domain and 80 nm sized are multi-domain [36]. This fact is reflected in slightly higher saturation magnetization (Table 1) but lower heating efficiency for this sample (Figure 3), that will be discussed later.

Figure 2. (a) TEM of Sample A, (b) TEM of Sample B, (c) number and (d) volume particle size distributions of samples. Unlike the majority of published results on SLP where NPs are dispersed in media with low viscosity (water, saline, glycerol), the heating efficiency of obtained materials was studies also


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on their agar dispersion, as it eliminates the contribution of Brown relaxation into the heat generation and thus emulate biological tissues with different viscosity [2, 3, 37]. The parameters of AMFs were the following: frequency and amplitude of 1048 kHz and 5.8 kA/m, respectively. Figure 3 shows the temperature rise of glycerol and agar dispersions of both samples. According to the results obtained, Sample B demonstrates significantly higher heating efficiency than Sample A in glycerol: heating rate of 16 ± 1 °C/min for Sample A and 21 ± 1 °C/min for Sample B. However, this difference is not so pronounced in the case of agar dispersion. What is also important, five-minute reaction product of Sample B dispersed in glycerol is heated almost as fast as the final product, and much faster than Sample A.

Figure 3. Temperature increase in (a) glycerol and (b) agar dispersions of NPs subjected to AMF of 1048 kHz, 5.8 kA/m In order to estimate the effect of polydispersity (surface area to volume ratio) on heat conduction of materials obtained and its possible impact on heating efficiency in AFM, we performed investigations of thermal conductivity (k) of NPs (in powder form) and their dispersions in glycerol and agar; obtained values are depicted in Table 2.


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Table 2. Thermal conductivity of NPs in a powder form and in glycerol and agar dispersions.

Sample

Sample A

Sample B

Dispersion media

k, W/m·K

Powder form

0.627 ± 0.25

Glycerol

0.337 ± 0.15

Agar

0.661 ± 0.11

Powder form

0.736 ± 0.03

Glycerol

0.367 ± 0.13

Agar

0.740 ± 0.03

Thermal conductivity of Sample B in a powder form is slightly higher than for Sample A, though the electrical conductivity of Sample A (3.7·10-7 S/cm) is in two orders higher than for Sample B (6.9·10-9 S/cm) due to the presence of large NPs in Sample A. Presence of magnetic NPs of both samples leads to an increased heat conductivity of the dispersions compared to pure glycerol (0.285 W/m·K) and agar (about 0.580 − 0.560 W/m·K). Samples demonstrate relatively the same thermal conductivity even though monodisperse Sample B has higher surface to volume ratio (0.3 nm-1) compared to polydisperse Sample A (0.2 nm-1). Therefore, it is possible to conclude, that for the investigated dispersions thermal conductivity does not contribute to the heat outcome in AMF. To explain a difference in heating efficiency between the samples, let us consider the issues of nucleation and growth of iron oxide NPs in aqueous media. During the synthesis of the samples the iron salts solution was added to the excess ammonia with pH ~ 11. In this condition crystalline magnetic iron oxide phase is formed from intermediate products, namely by fusion of primary particles with the size of 1−2 nm, as it was demonstrated by Baumgartner et al. [28]. The


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primary particles consist of non-crystalline iron(hydr)oxide arising from interaction of ferrous ions with ferrihydrite, formed from the reaction of ferric ions with alkali. Primary particles are thermodynamically metastable and serve as building blocks for magnetic iron oxide formation. It is believed that electron hoping between Fe2+ ions and ferrihydrite in primary particles is a driving force for final crystalline phase formation [25]. In the synthesis conditions used, at highly alkaline pH, the process of primary particles formation is very rapid, thus supersaturation is easily reached leading to the burst homogeneous nucleation. Subsequent growth of NPs occurs due to the adsorption of primary particles onto the surface of a growing particle, which is true for both samples (Sample A and Sample B). Therefore, the main difference in the morphology of the final products of Sample A and Sample B is due to the difference in the mechanism of particle growth. Since during the synthesis of Sample B, a solution of iron salts was slowly added to alkali solution, it is possible to propose that the diffusion of the primary particles to the growing crystals is a limiting step. On the contrary, in the case of Sample A as the salts solution is quickly added to alkali solution, the primary particles are presented in large amount in the reaction media, therefore, NPs growth is limited by the adsorption of primary particles on the particle surface. For diffusion controlled growth process, after burst nucleation, NPs grow rapidly until their size exceeds twice the critical nucleation size (RC), then the growth rate quickly decreases [31]. Meanwhile, smaller NPs grow more rapidly until they reach the 2RC size border. Consequently, the growth rate of larger NPs remains slower than the growth rate of smaller ones which results in NPs with narrow particle size distribution. To verify the hypothesis of the diffusion-controlled growth for Sample B we investigated the change in average crystallite size during the reaction obtained from XRD data (Figure 4)


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including its the reproducibility. As can be seen from Figure 4 a, the dependence of mean crystallite size on the reaction time is nonlinear, rapid increase of the mean size during the first minutes of the reaction is followed by slow growth. It is important to emphasize that nonlinear increase of crystallite size is consistent with nonlinear decrease of pH of reaction mixture. It is known that average crystallite size dependents on the pH of the reaction media, namely increases with decrease of pH [28, 38]. Indeed, the five-minute reaction product of Sample B represents NPs with average size of 8 − 9 nm (according to XRD and TEM, respectively), which is smaller than that for the final NPs (12 − 13 nm, according to XRD and TEM, respectively) but polydispersity is the same (σTEM = 0.3) (Figures 2 and 5). It means that small NPs formed at the beginning of the reaction continue growing simultaneously with the formation of new NPs with bigger sizes.

Figure 4. (a) The dependence of average crystallite size and pH of the reaction mixture on the reaction time for Sample B. Black dots are the experimental values of crystallite size, measured from the peak broadening of XRD patterns. Red solid line is the best fit to the experimental data in the given range of reaction time. Blue dots are values of pH in the reaction media. Blue solid


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line is guide for eyes. (b) The dependence of the saturation magnetization on the average crystallite size.

Figure 5. (a) TEM image of five-minute reaction product for Sample B and (b) particle size distribution histogram. Among the NPs formed at the earlier stage of the reaction, two types of NPs can be recognized: (1) NPs consisting of magnetite core and amorphous surface layer and (2) fully crystalline magnetite NPs with faceted surface (Figure 6 a, b). The observed amorphous surface layer most probably represents the non-crystalline, non-magnetic primary particles attached to the surface of the growing NP. The final product displays high degree of crystalline order; both NPs of magnetite and maghemite were detected (Figure 6 c, d). It is known that NPs obtained by coprecipitation constitute also non-stoichiometric magnetite due to partial oxidation of Fe2+ ions, however it is difficult to distinguish between magnetite/non-stoichiometric magnetite/maghemite crystal structures by methods like HRTEM, XRD and Mössbauer spectroscopy [37]. After the complete addition of the salts solution to the alkali (80 minutes), the reaction mixture was aged for an hour at the same conditions. As can be seen from Figure 4, during this time, the


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average crystallite size slightly increases from 11.8 nm to 12 nm with slight decrease of pH from 8.7 to 8.5. In this period of NPs growth, the increase of their average size occurs due to the accomplishment of crystallization at the expense of primary particles attached to the surface and no amorphous layer was observed for the final reaction product. The increase of crystalline size leads to the increase of saturation magnetization of NPs (Figure 4 b). It is can be explained by accomplishment of crystallization and by the decrease of the surface layer effect.

Figure 6. HRTEM images of NPs of five-minute reaction product of Sample B: (a) NPs with amorphous surface layer, (b) NPs with faceted surface, and HRTEM images of NPs of final product of Sample B: (c) magnetite NP, (d) maghemite NP. The growth rate as a function of particle size, derived from the dependence on Figure 4, is plotted on Figure 7, whence it follows that the growth rate of bigger particles is slower than that


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of the smaller ones, which it typical for the diffusion-controlled growth mechanism (Figure 8) [31].

Figure 7. Growth rate of NPs of Sample B as a function of particle size.

Figure 8. Theoretically obtained growth rate of NPs as a function of particle size: (a) diffusion controlled growth and (b) adsorption controlled growth. Reprinted from [31], with permission from Elsevier.


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Therefore, differences in mechanisms of NPs formation for Sample A and Sample B are reflected on their morpho-structural properties, i.e. NPs of Sample A are polydisperse and of irregular shape, whereas NPs of Sample B are uniform according to the size and shape. Sample A contains equal parts of superparamagnetic NPs and NPs with a size of about 60 and 80 nm (~ 50 vol. %, Figure 2) that are in pseudo- and multi-domain states according to micromagnetic simulation [36]. Sample A demonstrates lower heating efficiency than Sample B in both type of dispersion media (Table 3), since pseudo- and multi-domain NPs do not contribute to heat generation as they are in a blocked state in the experimental conditions applied (moderate frequency and amplitude of AMF). This finding correlates with the theoretically predicted effect of the influence of polydispersity on the dynamic magnetic susceptibility [39, 40]. Noting that the SLP values for agar dispersions for both samples are lower than for glycerol dispersions due to higher viscosity of agar. As a result, Brownian relaxation is suppressed in agar dispersion and heat output is determined solely by Neel relaxation [6]. Table 3. SLP values of glycerol and agarose dispersions (5 wt. % of NPs) of samples in the AMF of 1048 kHz and 5.8 kA/m.

Sample SLP, glycerol dispersion, W/gFe SLP, agar dispersion, W/gFe Sample A 15.0 ± 1.3 7.8 ± 1.1 Sample B 23.0 ± 0.6 10.5 ± 1.4

Along with polydispersity, the interparticle interactions can affect significantly magnetization dynamics of NPs since they lead to aggregation especially when particles are without surface coating. The aggregation process starts at the beginning of the coprecipitation reaction once magnetic NPs are formed (Figure 5). It is driven by attractive/repulsive interaction between NPs:


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van der Waals, magnetic, electrostatic, solvophobic [41]. The former two interactions hold NPs together and usually magnetic interactions coexist with van der Waals forces. However, the formation of dense aggregates that are stable against segregation into individual NPs is attributed to the magnetic interactions: magneto-dipole and exchange interactions. Exchange interaction can be neglected when interparticle spacing is of the order of 2 nm [42], that approximately corresponds to the distance between two NPs with dead layer of the thickness of about 1 nm. In most cases, the dominant contribution to interparticle energy is from magnetic-dipole coupling that increases with the NPs volume and depends on the mutual distance between particles [41, 43]. Dipole-dipole interactions can be either attractive (in-line dipoles) or repulsive (antiparallel align dipoles). Predominant type of configuration of dipoles is the antiparallel orientation of the magnetic moments of a pair of particles [44]. Subsequently, the pair of dipoles stick together to form larger aggregates. In the absence of an external field, these aggregates have close magnetic flux with random orientation of magnetic moments of individual NPs [44, 45]. In spite the fact that according to HRTEM and XRD data particles in Sample B are singledomain NPs in the superparamagnetic state, the sample demonstrate ferromagnetic-like behavior, which is evidenced by distinct sextets on Mössbauer spectrum and blocking temperature well above room temperature on FC/ZFC curves (Figure 10). This ferromagnetic-like behavior is apparently attributed to magnetic dipolar interactions within the superparamagnetic NPs incorporated to the dense aggregates (multicore particles) [46]. Indeed, when we separated NPs aggregates with certain hydrodynamic size, they demonstrate significantly higher SLP in agar compared to as-prepared NPs (Figure 11). NPs aggregates demonstrate saturation magnetization of 51 ± 4 emu/g and zero coercivity, regardless their hydrodynamic size.


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Figure 10. (a) Mössbauer spectroscopy and (b) FC/ZFC magnetization measurements for Sample B.

Figure 11. SLP for water and agar dispersions of NPs aggregates as a function of hydrodynamic size in an AMF of 1048 kHz and 5.8 kA/m. Depending on the hydrodynamic size, SLP attains a maximum value for 85 nm-sized multicore particles for both water and agar dispersions. The increase of the hydrodynamic size of


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aggregates leads to the significant decrease of SLP for both dispersions, where the decrease of SLP in water dispersion is more pronounced. Moreover, the difference in SLP between water and agar dispersions becomes minor for aggregate size greater than 85 nm. It seems that the higher SLP in the water dispersion of 85 nm-sized multicore particles is due to the coexistence of Neel and Brownian relaxations, whereas, in the agar dispersion, it is due the Neel relaxation alone. An increase in the hydrodynamic size above 85 nm mediated by intra-aggregate dipolar interaction results in a decrease in SLP due to demagnetizing effects [47].

To understand the modulation of SLP via interparticle magnetic interactions, we investigate the dependence of SLP on the AMF amplitude (Figure 12).

Figure 12. Amplitude dependence of SLP for water and agar dispersions of multicore particles (85 nm, 1 wt. %) at 525 kHz. Depending on the field amplitude, water and agarose dispersions of multicore particles (85 nm, 1 wt. %) demonstrate different trends of rise in SLP. The SLP increases with amplitude linearly for the water dispersion and nonlinearly for the agarose dispersion. Meanwhile, SLP for the


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water dispersion is significantly higher than that for the agarose in a whole range of amplitudes. It is clear that Brownian relaxation is restrained in the agarose dispersion, where Neel relaxation is dominant. The increase of SLP with field amplitude for both dispersions can be explained by the increase of the Zeeman energy in a higher magnetic field, which may overcome the anisotropy energy of NPs and increase Neel relaxation. CONCLUSIONS Despite the fact that coprecipitation method is widely applied for synthesis of magnetic iron oxide NPs, the issues of nucleation and growth mechanisms are rather rarely addressed in the literature. In the current study, we demonstrated for the first time that slow velocity of iron salts addition provides a narrow alkaline pH window during the reaction and determines the diffusioncontrolled growth of NPs. Initial highly alkaline pH of the reaction media provided rapid nucleation, namely formation of NPs building material, so called primary particles that fuse to form magnetic iron oxide crystals. For Sample A rapid addition of iron salts solution to alkali results in excess of primary particles and apparently their adsorption on the growing crystals is a limiting step of the reaction. The NPs obtained in this rote have irregular shape and polydispersity of about 0.4. On the contrary, for Sample B slow addition of iron salts solution to excess ammonia restricts the amount of primary particles, and as a result, the diffusion of primary particles limits the reaction. This synthesis yields highly crystalline, round-shaped NPs with polydispersity of about 0.3. Dependence of particles growth rate on their size complies with the theoretical model for the diffusion-controlled growth mechanism. Samples display the same static magnetic properties but significantly differ in dynamic magnetic properties that is evidenced from their heating efficiency in AMF. Dispersions of uniform NPs of Sample B demonstrate higher heating rate than the dispersions of polydisperse Sample A. The difference in


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heating efficiency of samples is not connected to the thermal conductivity of dispersions, as it is almost the same for both samples. The main role in the difference of the heat outcome belongs to the relaxation phenomena in the samples with different particle size distribution. Polydisperse Sample A represents an ensemble of NPs with various magnetization states, i.e. has a distribution of magnetic properties. It contains large volume of pseudo- and multi-domain NPs that do not contribute to heat generation as they are in a blocked state in the experimental conditions applied (moderate frequency and amplitude of AMF). Along the polydispersity, the magnetic dipole interactions also play an important role in the heat generation. NPs aggregate already at the beginning of the reaction and form stable multicore particles that account for ferromagnetic-like behavior of the material. Separation of those multicore particles with a certain hydrodynamic size resulted in increased SLP of their dispersions compared to the dispersions of as-prepared NPs. ACKNOWLEDGEMENT This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic – Program NPU I (LO1504) as well as with the support of Operational Program Research and Development for Innovations co-funded by the European Regional Development Fund (ERDF) and national budget of the Czech Republic, within the framework of the project CPS strengthening research capacity (reg. number: CZ.1.05/2.1.00/19.0409). REFERENCES [1] I. Conde-Leboran, D. Baldomir, C. Martinez-Boubeta, O. Chubykalo-Fesenko, M.D. Morales, G. Salas, D. Cabrera, J. Camarero, F.J. Teran, D. Serantes, A Single Picture Explains


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FOR TABLE OF CONTENTS USE ONLY The role of diffusion-controlled growth in formation of uniform iron oxide nanoparticles with a link to magnetic hyperthermia Ilona S. Smolkova, Natalia E. Kazantseva, Vladimir Babayan, Jarmila Vilcakova, Nadezda Pizurova, Petr Saha TABLE OF CONTENTS GRAPHIC

SYNOPSIS Uniform iron oxide nanoparticles were obtained by coprecipitation method under synthesis conditions providing rapid homogeneous nucleation and growth controlled by diffusion. Obtained nanoparticles form dense aggregates (multicore particles) due to magnetic interactions. The dispersion of multicore particles in viscous media demonstrates high heating ability in lowpower alternating magnetic field allowed in magnetic hyperthermia.


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The Role of Diffusion-Controlled Growth in the ... - ACS Publications

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