Optimizing and modeling of effective parameters on the structural and magnetic properties of Fe3O4 nanoparticles synthesized by coprecipitation technique using response surface methodology

Journal of Magnetism and Magnetic Materials 409 (2016) 134–142

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Optimizing and modeling of effective parameters on the structural and magnetic properties of Fe3O4 nanoparticles synthesized by coprecipitation technique using response surface methodology Mohammad Reza Ghazanfari a, Mehrdad Kashefi a,n, Mahmoud Reza Jaafari b a b

Department of Materials Science and Engineering, Ferdowsi University of Mashhad, 9177948974 Mashhad, Iran Biotechnology Research Center, Nanotechnology Research Center, School of Pharmacy, Mashhad University of Medical Sciences, Mashhad, Iran

art ic l e i nf o

a b s t r a c t

Article history: Received 16 October 2015 Received in revised form 24 February 2016 Accepted 29 February 2016 Available online 3 March 2016

In present work, the Fe3O4 magnetic nanoparticles were successfully synthesized by coprecipitation method. In order to study the effects of influential factors on the structural and magnetic properties of particles, the experimental runs were designed using response surface methodology (RSM) based on central composite design (CCD), while the reaction temperature, Fe2 þ /Fe3 þ cation ratio, and pH of reaction were defined as effective factors on the two responses include the amounts of crystallinity degree and saturation magnetization (Ms). The investigation of structural, magnetic, and microstructural properties of particles were carried out by X-ray diffraction (XRD), vibrating sample magnetometer (VSM), and dynamic light scattering (DLS) and transmission electron microscopy (TEM) analyses. As a result, the predictive quadratic models were fitted on the both responses while the R2 values were more than 0.97 for both models. The highest amounts of both responses (crystallinity degree: 88.07% and Ms: 65.801 emu/g) are presented when the reaction temperature, cation ratio, and pH amounts are equal to 90 °C, 0.60, and 10.5, respectively. Finally, the TEM results show the particles with size of about 10 nm and narrow size distribution. & 2016 Elsevier B.V. All rights reserved.

Keywords: Central composite design Superparamagnetism Cation ratio Bioapplications Nanostructures Chemical synthesis

1. Introduction Considering extremely development of nanotechnology in various sciences, the magnetic nanoparticles especially iron oxides particles like magnetite (Fe3O4) and maghemite (γ-Fe2O3) have found widespread applications such as electronic and microelectronic devices, mechanical sealing systems, heat transfer agents in chemical engineering, wastewater treatment, and many biomedical usages like MRI contrast agents, magnetic targeted drug delivery (MTDD), and magnetic hyperthermia (MHT) [1–5]. In order to use of these particles in mentioned applications, some special properties have considerable importance. The biomedical applications require the design and synthesis of nanoparticles with the perfectly controlled features such as magnetization of particles that is a size dependant property, so, it can utilize its size-independent version that is called saturation magnetization (Ms) [5– 8]. For instance, in the MTDD application, by increase the amounts of Ms of utilized particles the targeting process can be done more accurate [9–12]. Moreover, when the Ms amounts of nanoparticles n

Corresponding author. E-mail address: m-kashefi@um.ac.ir (M. Kashefi).

http://dx.doi.org/10.1016/j.jmmm.2016.02.094 0304-8853/& 2016 Elsevier B.V. All rights reserved.

have higher level, in order to carry out the suitable targeting process, the required time and applied field are usually increased [10–16]. Generally, the amount of Ms depends on the materials characteristics including their chemical compositions and crystal structures so that by changing each of them, the amount of Ms is considerably varied [17–22].Furthermore, the structural properties of materials not only effect on the magnetic properties, but also they can effect on the other features such as thermal properties, mechanical behaviors, chemical stabilization, and surface properties [22,23]. Accordingly, the crystallinity degree that is known as a one of the critical structural properties can be very important in structural studies of nanoparticles [24–28]. The structural characteristics and subsequently magnetic properties of materials are greatly originated from their synthesis process [22–25]. Hitherto, in order to synthesize Fe3O4 nanoparticles, the various techniques like coprecipitation, thermal decomposition, hydrothermal, microemulsion, sonochemical, sol– gel, and mechanical alloying are utilized while each of them has some benefits and disadvantages [29–31]. Amongst these synthesis techniques, the most common method is the coprecipitation owing to the relatively simple mechanism, abundant and nontoxic raw materials, moderately short production time, and

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Table 1 (a) Levels of selected factors for CCD experimental design. Effective factor

Temperature (°C) Cation ratio (Fe2 þ /Fe3 þ ) pH

Symbol

A B C

Levels Low axial

Low fractional

Center

High fractional

High axial

60 0.45 9

70 0.5 9.5

80 0.55 10

90 0.6 10.5

100 0.65 11

Table 1 (b) Selected responses to study the structural and magnetic properties of particles by CCD experimental design.

Table 2 The experimental design of RMS for three factors and obtained results. Run order

Response

Symbol

Crystallinity degree Saturation magnetization (Ms)

R1 R2

industrial scales yielding [32–35]. On the other hand, compared to some techniques like thermal decomposition and hydrothermal, the coprecipitation method has some disadvantages include low repeatability, inappropriate size distribution of synthesized particles, and low crystallinity degree [36–38]. Hence, in order to achieve the nanoparticles with desired properties using this method, the investigation and control of the effective parameters of synthesis process are absolutely essential. The temperature of synthesis reaction, pH amounts of reaction, initial cations ratio (Fe2 þ /Fe3 þ ), mixing rate, etc., are the most important parameters of synthesis process [37–39]. The utilization of statistic methods and design of experiments is a one of the most desirable approaches to the precisely studies of effects of main factors and their interactions on the synthesis process [39–42]. The design of experiments can be done based on the different techniques such as Taguchi, full/fractional factorial design (FFD), and response surface methodology (RSM) [41–43]. The RSM method using central composite design (CCD) with finite effective factors can be utilized to optimize process conditions and present a fitted model of factors behaviors on the one or more specific responses [41–44]. Since now, the RSM approach is successfully used in many researches like the study of size controlling of synthesized nanoparticles [43]. In present research, using the RSM method based on the CCD technique and by definition of three effective factors including reaction temperature, reaction pH, and cation ratio (Fe2 þ /Fe3 þ ), the main effects of factors and their interactions on the two independent responses consisting of the amount of Ms and the crystallinity degree of Fe3O4 nanoparticles synthesized by coprecipitation method are studied and optimized. Moreover, for both responses the appropriate fitted models are presented.

2. Material and methods 2.1. Materials In order to synthesize the Fe3O4 nanoparticles, the initial materials consisting of FeCl2  4H2O and FeCl3  6H2O (4 99%, Merck) as initial salts, NH4OH (Merck) as a reduction agent, Citric acid (4 99.5%, Merck) as a dispersant agent, and HCl (37%, Merck) were used based on stoichiometric ratios. Moreover, deionized water (DI) is selected as a solvent medium of reactions.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Factors

Responses

A (°C)

B

C

R1 (%)

R2 (emu/g)

70 90 80 70 80 80 80 90 80 80 80 60 80 70 100 70 80 90 90 80

0.6 0.6 0.55 0.5 0.55 0.55 0.55 0.6 0.55 0.55 0.55 0.55 0.65 0.6 0.55 0.5 0.55 0.5 0.5 0.45

9.5 10.5 10 9.5 10 10 10 9.5 10 10 9 10 10 10.5 10 10.5 11 9.5 10.5 10

83.13 87.49 79.49 73.15 78.92 76.78 76.13 80.07 75.01 79.18 70.82 79.55 87.63 76.46 93.84 64.82 71.05 75.61 80.21 72.07

54.397 66.591 63.172 47.478 65.257 61.202 62.123 60.269 62.455 61.657 50.314 52.291 56.259 62.189 67.104 58.415 63.208 57.261 61.978 46.582

2.2. Design of experiments In present research, the simultaneous effects of critical synthesis parameters (called factors) on the structural and magnetic properties of particles were investigated by the RSM method using DESIGN EXPERT (7) software. In order to achieve this aim, the CCD technique is a most common approach that is designed based on the five levels of effective parameters including  α,  1, 0, 1, and α. In the CCD approach, the effects of three independent factors can be studied by design with 20 experiment runs consisting of 8 full factorial points, 6 axial points in α distance from center point, and 6 replications of center point to determine the errors of design [44]. In addition, the factors can be classified in two actual and coded modes based on following formula [44].

xi = ( Xi −X 0 )/δX

(1)

where xi, Xi, X0, and δX are the coded values of factor, actual values of factor, actual values of factor in center point, and variation steps of factor, respectively. In present work, three effective factors on the structural and magnetic properties of particles such as Fe2 þ /Fe3 þ cations ratio (known by symbol A), reaction temperature (symbol B), and pH of reaction (symbol C) were selected which are presented in Table 1 (a). Furthermore, the values of crystallinity degree and saturation magnetization (Ms) of synthesized nanoparticles were opted as the responses of structural and magnetic properties. Table 1(b) shows the list of these responses and their symbols. According to RSM method, it can be fitted the quadratic polynomial equation for each response of CCD design as follows.

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Table 3 The results of ANOVA analysis for the response model of crystallinity degree amounts (R1). Source

Sum of squares

Degree of freedom

Mean square

F-value

P-value

Remarks

Model A B C AB AC BC A2 B2 C2 Residual Lack of fit Pure error

805.41 184.96 259.85 0.41 12.21 91.26 2.51 118.73 5.36 78.49 24.81 7.46 17.35

9 1 1 1 1 1 1 1 1 1 10 5 5

89.49 184.96 259.85 0.41 12.21 91.26 2.51 118.73 5.36 78.49 2.48 1.49 3.47

36.07 74.56 104.75 0.16 4.92 36.79 1.01 47.86 2.16 31.64

o 0.0001 o 0.0001 o 0.0001 0.6976 0.0509 0.0001 0.3383 o 0.0001 0.1722 0.0002

Significant Significant Significant Not significant Not significant Significant Not significant Significant Not significant Significant

0.43

0.8123

Not significant

Table 4 The results of ANOVA analysis for the response model of saturation magnetization (Ms) amounts (R2). Source

Sum of squares

Degree of freedom

Mean square

F-value

P-value

Remarks

Model A B C AB AC BC A2 B2 C2 Residual Lack of fit Pure error

670.83 177.21 88.68 192.91 1.18 7.39 0.29 10.66 186.07 48.25 20.47 10 10.47

9 1 1 1 1 1 1 1 1 1 10 5 5

74.54 177.21 88.68 192.91 1.18 7.39 0.29 10.66 186.07 48.25 2.05 2 2.09

36.42 86.58 43.33 94.25 0.58 3.61 0.14 5.21 90.91 23.57

o 0.0001 o 0.0001 o 0.0001 o 0.0001 0.4653 0.0866 0.7115 0.0456 o 0.0001 0.0007

Significant Significant Significant Significant Not significant Not significant Not significant Significant Significant Significant

0.96

0.5194

Not significant

Y = β0 +β1 × X1 +β2 × X2 +β3 × X3 +β12 X1 × X2 +β13 X1 × X3 +β23 X2 × X3 +β11 × X12 +β22 × X22 +β33 × X32 +β123 X1X2 × X3

(2)

where Y is the response amount, Xi is the actual values of factors, and Bi, Bii, and Biii are the first, second, and third degree coefficients, respectively. Moreover, the accuracy of presented models was evaluated by use of analysis of variance (ANOVA) tables while the conformity of actual values of responses and predicted amounts by models was studied using R2 (R-squared) diagrams. In addition, the investigation of effectiveness of each factor on the presented models was carried out by Pareto diagrams based on the following equation [45,46].

(

)

Pn (%) = 100 × βn2 / ∑ β2 If (n ≠ 0)

(3)

where, Pn is the effectiveness percentage of each factor and β is a mark of first order and/or quadratic coefficients of significant factors while the higher order coefficients are assumed not-significant. Finally, the study of interaction effects of factors on the responses and their optimization were done by CCD approach. 2.3. Synthesis of Fe3O4 nanoparticles In order to synthesize the Fe3O4 nanoparticles by coprecipitation method, the initial materials consisting of FeCl2  4H2O and FeCl3  6H2O were solved in 100 ml of deionized water according to designed stoichiometric ratio in each experiment run. The synthesis reaction was done at N2 atmosphere to prevent oxidation of Fe2 þ salt. After the complete string of salts solution in designed temperature, a certain amount of NH4OH was added to reaction solution as a reduction agent and the reaction pH was controlled based on the defined values. Afterwards, to homogenization the

solution was mixed by mechanical stirrer with speed of 3000 rpm for 1 h. Next, the critical amount of 1 M citric acid stock was added to the solution and it was aged for 1 h under string. Finally, the synthesized particles were separated by the magnetic separation and centrifuge, washed by DI water and ethanol for five times, and dried by freeze dryer. 2.4. Characterization Initially, in order to investigate the structural properties of synthesized nanoparticles, the X-ray diffraction (XRD) analyses were carried out by X-ray diffractometer (XRD, Bruker Advance 2) using a CuKα1,2 radiation set (at 40 kV and 40 mA at room temperature with a 2θ range of 20–80° with step size and rate of 0.03° and 6 s, respectively). After that, the phase studies of samples were done by utilization of Match software. Furthermore, in order to evaluate the crystallinity degree values of samples, the XRD results were analyzed using Materials Studio software (V 6.0) based on the intensity and broadening of standard peaks of crystalline Fe3O4 phase compared to peaks background. The magnetic properties (such as coercive field (Hc), remanent magnetization (Mr), and specially Ms as a one of the RSM design responses) of nanoparticles were studied by plotting of M–H curves of samples based on the vibrating sample magnetometer (VSM, Meghnatis Daghigh Kavir Co., Iran) analyses. Next, in order to carry out more investigations, the particle size analyses of optimized experiment runs were done by two methods. The hydrodynamic size of dispersed particles in aqueous media was measured by dynamic light scattering (DLS, MALVERN) technique. Moreover, using transmission electron microscope (TEM, JEOL 2010), the size and morphology of particles were studied.

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Fig. 1. The Pareto diagram of effectiveness percentages of different factors on the presented models for (a): crystallinity degree (R1) and (b): saturation magnetization (R2).

3. Results and discussion 3.1. Model equation Based on the CCD design for three independent factors, 20 experimental runs were defined such as the cubic points, axial points, and replications of center point. Table 2 demonstrates the list of these runs including the trend of factors variations and value of each response. The present research was done for two responses such as the crystallinity degree and the saturation magnetization (Ms) of the synthesized nanoparticles which were known by R1 and R2 symbols, respectively. Afterwards, according to experimental data of these responses, using software the quadratic polynomial equation was presented for each response that can predict the relationship of response value and the amounts of defined factors. The fitted model on the crystallinity degree of samples can be presented as follows.

R1 = 77.38 + 3.40 A + 4.03 B–0.16 C –1.23 AB + 3.38 AC + 0.56 BC + 2.17A2 + 0.46 B2 –1.77C 2

(4)

where R1 is a crystallinity degree (in unit %) of freeze dried particles and A, B, and C are the defined factors include temperature (°C), cation ratio, and pH, respectively. Furthermore, the model equation of Ms Values is calculated as follows.

Fig. 2. The diagrams of relationship between predicted and actual values for (a): R1 response (crystallinity degree) and (b): R2 response (saturation magnetization).

R2 = 62.82 + 3.33A + 2.35B + 3.47C – 0.38 AB – 0.96 AC – 0.19 BC – 0.65A2 – 2.72B2 – 1.39C2

(5)

where R2 is a saturation magnetization (in unit emu/g) of freeze dried particles and A, B, and C are the defined factors include temperature (°C), cation ratio, and pH, respectively. The ANOVA data of defined models of responses R1 and R2 are offered in Tables 3 and 4, respectively. Based on these tables, it is clear that the both presented models have high F-values and very low P-values (o0.0001) which illustrate their strongly significances [44–46]. The significant terms of factors include A, B, AC, A2, and C2 for the R1 response, and consisting of A, B, C, A2, B2, and C2 for the R2 response. In fact, the variations of these terms (such as main terms and interaction ones) can lead to logically affect on the related responses. Moreover, the “lack of fit” amounts in both

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Fig. 3. The 3D surface plots of simultaneous effects on responses. (a): The effects of temperature and cation ratio on the R1 (pH ¼ 10.5), (b): The effects of temperature and pH on the R1 (cation ratio¼ 0.5), (c): The effects of cation ratio and pH on the R1 (temperature¼70 °C), (d): The effects of temperature and cation ratio on the R2 (pH ¼ 10.5), (e): The effects of temperature and pH on the R2 (cation ratio¼0.5), and (f): The effects of cation ratio and pH on the R2 (temperature¼ 70 °C).

models are not significant because of their values are much more than 0.05 critical level; so, the pure errors have no effective impact in these models that it shows the credibility of models. The mounts of F-value parameter can be utilized to explain the effect intensity of each term factor such as main factors and/or their interactions. In addition, the effectiveness of these terms can be plotted as the Pareto diagrams. Fig. 1(a) and (b) show the Pareto diagrams of effectiveness percentage of critical terms on the R1 (crystallinity degree) and R2 (saturation magnetization) models, respectively. According to Fig. 1(a), the temperature of reaction (factor A) and the cation ratio (factor B) have a maximum effectiveness on the amount of crystallinity degree while the reaction pH has negligible impact on this response amount. Among factors interactions, the AC term (interaction of reaction temperature and pH) illustrates maximum effectiveness percentage. Furthermore, based on the Fig. 1(b), the reaction pH, temperature and cation

ratio are identified as the most effective terms on the Ms amounts of samples, respectively. Additionally, it can be mentioned that the BB interaction term has higher effect on the Ms amounts compared to B factor (cation ratio) that shows the importance of studies of interactions effects. Moreover, the amounts of Adjusted R-squared in both presented models are more than 94% while the amounts of their Predicted R-squared are about 90%. In fact, the low difference between these two ranges can be used as an evidence of conformity of predicted values by models with experimental data. Accordingly, the R-squared (R2) values are equal to 0.9701 and 0.9704 for R1 and R2 models, respectively; hence, it can be concluded that the presented models have considerable predictability. Fig. 2(a) and (b) indicate the relationship plots of actual data and predicted values by models for crystallinity degree and saturation magnetization responses, respectively. These plots show the significant matching between predicted values and actual data as a

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Fig. 4. The variation contour plots of factors effects on the optimized R1 and R2. (a): The effects of temperature and cation ratio on the R1 (pH ¼ 10.5), (b); The effects of temperature and pH on the R1 (cation ratio ¼ 0.5), (c): The effects of cation ratio and pH on the R1 (temperature¼ 70 °C), (d): The effects of temperature and cation ratio on the R2 (pH ¼ 10.5), (e): The effects of temperature and pH on the R2 (cation ratio¼0.5), and (f): The effects of cation ratio and pH on the R2 (temperature¼ 70 °C).

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Table 5 The most favorable amounts of factors to attain the optimum states of R1 and R2. Case

Target

A (oC)

B

C

R1 (%)

R1 R2 R1 and R2

Maximize Maximize Maximize

90 90 90

0.6 0.55 0.6

10.5 10.5 10.5

88.21 88.07

R2 (emu/g)

66.927 65.801

Fig. 5. The XRD pattern of optimum sample (run 2) with maximum amounts of R1 and R2. This pattern shows the peaks of only Fe3O4 phase.

reason of high values of R-squared. 3.2. RSM studies In this section, in order to more accurate investigate the effects of different factors, the 3-D plots of responses surface were used which were presented based on the related polynomial functions. The 3-D plots can illustrate the simultaneous effects of two independent factors on the response. Fig. 3(a-f) shows the 3-D plots of different factors on the response surface of R1 and R2 models. In Fig. 3(a), it can be seen the 3-D plot of simultaneous effects of reaction temperature and cation ratio (factors A and B) on the variation of crystallinity degree percentage. The increasing of temperature from 70 to 90 °C can lead to considerable augmentation of crystallinity degree from about 70% to 83% owing to the improvement of diffusion rate of solution ions to the initial nuclei and increasing of their growth by temperature increment [23–28]. Moreover, the crystallinity degree amount is significantly increased from 70% to more than 80% by Fe2 þ /Fe3 þ cation ratio augmentation from 0.50 to 0.60. In fact, when the cation ratio is about 0.50 the portion of Fe2 þ ions is oxidized to Fe3 þ cations that are caused to form some undesired phases such as goethite and other hydroxide structures, while by increasing of cation ratio to 0.60 the ratio of Fe3O4 phase to other phases is augmented and the measured crystallinity degree is detected at higher percentages. Based on this plot, in order to achieve higher crystallinity degree, the higher temperature and cation ratio can be defined as ideal conditions. Fig. 3(b) indicates the 3-D plot of reaction temperature and pH (factor A and C) on the amount of crystallinity degree. Although by temperature increasing the crystallinity degree percentage is raised, this variation is much more perceptible in high pH level compared to lower level of reaction pH. Furthermore, by pH variation from 9.5 to 10.25 the crystallinity degree is located in relatively plateau trend, but by enhance the pH amount to 10.5 in low level of temperature the crystallinity degree is suddenly fallen from 76 to about 70% due to the probable creation of hydroxide phases. On the other hand, in high level of temperature, the crystallinity degree is gradually increased from 77 to about 88% by pH augmentation from 9.5 to 10.5. Fig. 3(c) demonstrates the 3-D plot of effects of cation ratio and reaction pH on the variation of

Fig. 6. The results of magnetic properties of optimum sample (run 2) with maximum amounts of R1 and R2. (a) M–H curve of sample that shows the superparamagnetic behavior and high Ms amount. (b) Magnification of M–H curve in zero point range that shows very low amounts of Mr and Hc as an indication of perfect superparamagnetic properties.

crystallinity degree percentage. Accordingly, the crystallinity degree is climbed from 71 to 84% by increasing of cation ratio while the higher percentage of crystallinity degree is achieved in pH amount of 10. Fig. 3(d) shows the 3-D plot of temperature and cation ratio effects on the variation of saturation magnetization (Ms) amount. As a result, the temperature increase is caused to improve the amount of saturation magnetization from 58 to about 66 (emu/g) due to the enlargement of synthesized particles to higher scale of size while the saturation magnetization amount depends on the particles size [47]. Moreover, by cation ratio growth, the saturation magnetization amount is firstly increased and then is negligibly decreased because of partial formation of low-magnetic phases like maghemite (γ-Fe2O3) or even non-magnetic structures like hydroxide phases. Fig. 3(e) indicates the increasing of saturation magnetization amount from 50 to about 63 (emu/g) by augmentation of reaction temperature and pH from 70 to 90 °C and 9.5 to 10.5, respectively. Furthermore, the highest level of Ms (about 68 emu/g) is achieved in the maximum amounts of temperature and pH. Finally, in Fig. 3(f), it can be seen that the amount of saturation magnetization is firstly increased and then decreased by cation ratio growing, while the Ph rising is caused to the continuous increasing of Ms.

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be done point prediction for each point of responses. In addition, the appropriate amounts of different factors to achieve the maximum amounts of crystallinity degree (R1) and saturation magnetization (R2) are listed in Table 5. Based on these data, the highest amounts of both responses (crystallinity degree: 88.07% and Ms: 65.801 emu/g) are presented when the reaction temperature (factor A), cation ratio (factor B), and pH of reaction (factor C) are equal to 90 °C, 0.60, and 10.5, respectively. 3.4. Characterization

Fig. 7. (a): The histogram diagram and (b): the undersize plot of hydrodynamic size of particles (run 2) that is measured by DLS technique.

In order to study the other critical properties of synthesized nanoparticles, the results of structural, magnetic, and microstructural properties of optimized sample (run 2) are presented in this section. Fig. 5 illustrates the XRD pattern of nanoparticles that the peaks of Fe3O4 phase are clearly observed without any peaks of undesired phases like hematite (α-Fe2O3) and goethite (FeOOH). Furthermore, it can be seen that these peaks have relatively wide broadening as a result of the nanometric crystallite size of particles [11–13,48]. Fig. 6 demonstrates the M–H curve of sample that is plotted based on the results of VSM tests. Accordingly, the synthesized nanoparticles show no hysteresis loop owing to their absolute superparamagnetic behavior. Moreover, the amounts of their coercive field (Hc) and remanent magnetization (Mr) are measured equal to 0.5 (Oersted) and 0.05 (emu/g), respectively. Based on the low amounts of coercive field and remanent magnetization, the formation of structures with appropriate superparamagnetic properties can be concluded. Finally, Fig. 7(a) and (b) show the histogram diagram and undersize plot of hydrodynamic size of particles (run 2) that is measured by DLS technique. Based on this figure, the size of synthesized particles is varied in the range of 6 to 33 nm with a mean size of 15 nm. Considering the DLS technique measure the hydrodynamic size of particles that is considerably larger than real size, it is clear that the size of particles is located in the appropriate range for many applications like the biomedical ones, while the size distribution of particles is relatively narrow. In order to confirm the results of DLS analyses, the size and morphology of particles were studied by TEM. Fig. 8 indicates the TEM micrographs of sample that show the particles with size of about 10 nm and narrow size distribution.

4. Conclusion In present work, at first the Fe3O4 magnetic nanoparticles were successfully synthesized by coprecipitation method. Afterwards, using RSM statistic technique the effects of three factors such as the reaction temperature, Fe2 þ /Fe3 þ cation ratio, and pH of reaction (main terms and their interactions) on the structural and magnetic properties include the amounts of crystallinity degree and saturation magnetization (Ms) of nanoparticles. Accordingly, some results are concluded as following. Fig. 8. TEM micrograph of optimum sample (run 2) with maximum amounts of R1 and R2. This image shows that the particles size is about 10 nm with the narrow distribution.

3.3. Optimization In this section, the optimizing of suitable conditions of reaction was done using DESIGN EXPERT software, in order to achieve the optimum responses (maximum amounts of crystallinity degree and saturation magnetization). Fig. 4(a–f) shows the contour diagrams of optimum conditions variations of responses R1 and R2. Accordingly, it can be accessed to the certain ranges of responses by selection of desired amounts of effective factors. In fact, it can

1. Based on the CCD method, the predictive models are presented for both responses with R-squared values more than 0.97 that shows the considerable validation of models. 2. The temperature of reaction (factor A) and the cation ratio (factor B) have a maximum effectiveness on the amount of crystallinity degree while the reaction pH has negligible impact on this response amount. Among factors interactions, the AC term (interaction of reaction temperature and pH) illustrates maximum effectiveness percentage. 3. The reaction pH, temperature and cation ratio are identified as the most effective terms on the Ms amounts of samples, respectively. Additionally, it can be mentioned that the BB

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interaction term has higher effect on the amounts of Ms compared to B factor (cation ratio). 4. The highest amounts of both responses (crystallinity degree: 88.07% and Ms: 65.801 emu/g) are presented when the reaction temperature (factor A), cation ratio (factor B), and pH of reaction (factor C) are equal to 90 °C, 0.60, and 10.5, respectively. 5. Based on the results of DLS tests, the hydrodynamic size of synthesized particles is varied in the range of 6 to 33 nm with a mean size of 15 nm, while the TEM micrographs of sample show the particles with size of about 10 nm and narrow size distribution. It is clear that the size of particles is located in the appropriate range for many applications like the biomedical ones. Moreover, the amounts of their coercive field (Hc) and remanent magnetization (Mr) are measured equal to 0.5 Oersted and 0.05 (emu/g), respectively. Based on the low amounts of coercive field and remanent magnetization, the formation of structures with appropriate superparamagnetic properties can be concluded.

[21]

[22]

[23]

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