J. Phys. Chem. B 2000, 104, 7919-7922
7919
A Chemometric Approach for Predicting the Size of Magnetic Spinel Ferrite Nanoparticles from the Synthesis Conditions Adam J. Rondinone, Anna C. S. Samia, and Z. John Zhang* School of Chemistry & Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400 ReceiVed: June 1, 2000
Magnetic CoFe2O4 spinel ferrite nanoparticles are synthesized by a microemulsion method using sodium dodecyl sulfate as the surfactant to form micelles. A statistical method of factorial design is used to establish a mathematical model from a series of synthesis experiments. This chemometric model quantitatively correlates the size of the nanoparticles with the experimental conditions. It has demonstrated the capability of predicting the mean diameter of nanoparticles from the synthesis conditions with a precision of 1-3 nm over a range from 5 to 35 nm. This quantitative correlation between the size of nanoparticles and the synthesis condition provides the rationale for choosing experimental conditions to control the nanoparticle sizes.
Introduction Materials consisting of nanometer-scale particles have attracted broad interest in fundamental sciences and in technological applications. Nanoparticles usually possess some novel and/or enhanced physical and chemical properties.1,2 The unique properties of nanoparticles originate in the nanometer scale size of the materials. Since the particle size is a crucial parameter for understanding and controlling the properties of nanoparticles, utilizing the nanoparticulate materials on large scales for their desired properties requires the particle size to be predictable and controllable. Although the size of the nanoparticles may be controlled by intuition in the synthesis process, it has not been achieved to quantitatively predict the size of the nanoparticles from experimental conditions. The targeted size of the nanoparticles is usually reached by a trial and error process of varying experimental conditions. The capability of predicting the size of nanoparticles from the synthesis conditions will not only enhance our ability to control the particle size, but also facilitate the industrial-scale production of nanoparticles with a desired size. Spinel ferrites as a group of the most important magnetic materials have been widely used in modern electronic technologies.3,4 The unique properties and sizes of spinel ferrite nanoparticles can play crucial roles in the fast paced miniaturization of modern electronic devices and in biomedical applications.5 We have employed the statistical method of factorial design to quantitatively correlate the particle size with the experimental conditions in microemulsion synthesis of magnetic CoFe2O4 spinel ferrite nanoparticles. A mathematic model based on chemometric principles is established to provide the capability of predicting the size of spinel ferrite nanoparticles from the synthesis conditions with a deviation of 1-3 nm. Experimental Results and Discussion We have used a microemulsion method to synthesize CoFe2O4 spinel ferrite nanoparticles.6,7 The starting reagents were CoCl2‚ 6H2O and FeCl2‚4H2O salts. An aqueous surfactant of sodium dodecyl sulfate (SDS) was used to form a micellar Fe(DS)2 and Co(DS)2 solution. An organic base of methylamine, CH3NH2 * To whom correspondence should be addressed.
aqueous solution was then added to adjust pH level for the formation of CoFe2O4 nanoparticles:
Fe(DS)2 + Co(DS)2 + O2/H2O + CH3NH2 f CoFe2O4 + DS- + CH3NH3+ (1) Various synthesis experiments were performed at different temperatures (40 °C-80 °C) with varying metal salt (0.010 M-0.025 M for iron; 0.005 M-0.0125 M for cobalt), surfactant (0.020 M-0.060 M), and methylamine (1.16 M-5.82 M) concentrations. The [Fe(DS)2]/[Co(DS)2] ratio was kept to 2 in all experiments. The nanoparticles have a pure spinel phase characterized by X-ray and neutron powder diffraction studies. Neutron diffraction studies show that these CoFe2O4 spinel nanoparticles have an inversion degree of 72% in cation distribution. The particle size of the nanoparticles has been determined from the peak broadening in X-ray diffraction patterns and confirmed by transmission electron microscopy (TEM) studies. We have synthesized the nanoparticles with a fairly uniform size from 5 nm to about 35 nm. Figure 1 is a TEM micrograph of the CoFe2O4 nanoparticles with a size of 6.6 ( 0.6 nm. High resolution TEM confirms that the nanoparticles are single crystals (inset in Figure 1). The chemical composition of the nanoparticles has been determined by inductively coupled plasma-atomic emission spectroscopy (ICP-AES) analysis. The ICP results show that the iron-to-cobalt ratio is 1.99 ( 0.046 consistent in all the samples. Mo¨ssbauer spectroscopy studies confirm that the Fe cations have a +3 oxidation state, which indicates that our nanoparticles have a stoichiometry close to a standard spinel with four oxygen per formula. The starting Fe2+ cation has been oxidized during the reaction by the oxygen molecules naturally dissolved in the solution. Chemometric Modeling Results and Discussion Factorial design method is used to build a quantitative correlation model between the particle size and the synthesis conditions. The control factors for the particle size are identified. The concentration of the metal salt reagents, Fe(DS)2 and Co(DS)2, should be a control factor. The reagent of CH3NH2 is
10.1021/jp002001j CCC: $19.00 © 2000 American Chemical Society Published on Web 07/18/2000
7920 J. Phys. Chem. B, Vol. 104, No. 33, 2000
Rondinone et al. TABLE 1: Results of Four-Factor Two-Level Design size Fe(II) (M) Co(II) (M) SDS (M) CH3NH2 (M) temp (°C) (nm) 0.010 0.020 0.010 0.020 0.010 0.020 0.010 0.020 0.010 0.020 0.010 0.020 0.010 0.020 0.010 0.020
0.005 0.010 0.005 0.010 0.005 0.010 0.005 0.010 0.005 0.010 0.005 0.010 0.005 0.010 0.005 0.010
0.020 0.040 0.030 0.060 0.020 0.040 0.030 0.060 0.020 0.040 0.030 0.060 0.020 0.040 0.030 0.060
2.32 2.32 2.32 2.32 4.66 4.66 4.66 4.66 2.32 2.32 2.32 2.32 4.66 4.66 4.66 4.66
50 50 50 50 50 50 50 50 70 70 70 70 70 70 70 70
8.7 10.2 8.5 13.4 10.8 21.3 12.4 19.8 17.3 23.7 20.3 26.9 23.4 22.6 20.6 23.4
Figure 1. TEM micrograph (150 K magnification) of CoFe2O4 nanoparticles. The inset is the micrograph at high magnification (1500 K magnification).
used to adjust the pH level for the formation of CoFe2O4 spinel, and the concentration of CH3NH2 becomes the second factor. The temperature is a key element in crystal growth, and therefore is the third factor. The concentration of the surfactant is the fourth factor since it could have a possible effect on the nanoparticle size. To verify the effect of these four factors to the particle size, a series of experiments have been systematically carried out. Our initial approach is a two-level-four-factor factorial design system. The level here means the setting of the individual factor. A two-level experimental system uses a high value and a low value of each factor. The effect of each factor is then evaluated as the difference between the average response of the particle size to experiments at the high and low level of the factor. The effect of factor A would be calculated as follows:
effect of factor A ) [average response at high A] [average response at low A] The statistical method of two-level-four-factor factorial design requires a minimum of 16 (24) systematic experiments. The experimental results and factor effects from the first batch of 16 screening experiments are listed in Table 1. The data imply that nanoparticle size increases with increasing concentrations of metal cation salt and methylamine, and temperature. The evaluation of surfactant concentration effect indicates that the variation of surfactant concentration has a negligible effect on the particle size. This result is consistent with some reported experimental data.8 Thus, the surfactant concentration has been kept at a constant 3:1 ratio to iron concentrations in the subsequent modeling experiments. The control factors to the particle size are reduced to three. With three control factors, we are able to increase the level of our design system to three without drastically increasing the number of systematic experiments that are required. The BoxWilson design or known as central composite design (CCD)
Figure 2. Schematic illustration of a Box-Wilson or central composite design. O and ] represent the corner and axial points for factor settings, respectively. b is the combined center point.
approach is used for this three-level-three-factor system because of its flexibility and efficiency.9 This approach consists of a cube and a star sharing a common center (Figure 2). Each corner of the cubic box represents a set of factors. Changing factors from one corner to another along the axis gives the first order response of the particle size. Moving diagonally provides the information on the effect from the interactions among factors. The star is added to provide the axial points for testing the possible second-order quadratic effects of the factors. A minimum of 15 systematic experiments is required to build a valid chemometric model using this system. The factor level limits (i.e., maximum and minimum temperature) have been determined by initial experiments judging by producing adequate samples with minimal particle size distribution. The experimental settings and results from this central composite design approach are listed in Table 2. On the basis of these experimental data, a matrix calculation method has been performed using Mathcad 8.0 computer software to generate a mathematic model for particle size prediction. Three control factors form a factor matrix, X:
[
S .01 .02 X) .01 .02
A 2.33 2.33 4.66 2.33
T 50 50 50 70
S2 .0001 .0004 .0001 .0004
SAT 1.165 2.33 2.33 3.26
]
(1)
Where the concentrations of metal salt S and methylamine A are in molar unit, and temperature T is in °C. The corresponding particle sizes obtained from the experiments form a response
Magnetic Spinel Ferrite Nanoparticles
J. Phys. Chem. B, Vol. 104, No. 33, 2000 7921
TABLE 2: Experimental Parameters and Results for Central Composite Design metal salt (M)
CH3NH2 (M)
temperature (°C)
size (nm)
0.010 0.020 0.010 0.020 0.010 0.020 0.010 0.020 0.015 0.015 0.015 0.015 0.015 0.015 0.005 0.025
2.328 2.328 4.656 4.656 4.656 4.656 2.328 2.328 3.492 3.492 3.492 3.492 3.492 3.492 3.492 3.492
50 50 50 50 70 70 70 70 60 60 60 60 40 80 60 60
8.5 7 12.3 19.8 20.3 26.9 20.6 23.4 14.2 14.3 13.2 13.1 0.0a 22 8.1 18.3
a
Amorophous.
matrix, Y:
[ ]
size (nm) 8.5 7 Y) 12.3 23.4
(2)
Following the principles of factorial design, the particle size can be mathematically expressed in the model by the experimental factors: metal salt concentration (S), methylamine concentration (A), and temperature (T) in first, second, and interacting terms:
size(S,A,T) ) β0 + β1S + β2A + β3T + β4S2 + β5A2 + ... + βnSAT (3) The coefficient β terms are the elements of a parameter matrix M obtained from the matrix calculation:
M ) [(XT × X)-1] × (XT × Y)
(4)
where is the transpose of matrix X and M is a (1 × n) matrix where n is the number of experiments performed. To simplify the calculations, the values for each factor level have been coded and normalized around zero. For example, a series of experiments with concentrations of factor A that would normally be recorded as 0.1, 0.2, and 0.3 M are recorded as -0.1, 0, and 0.1. A detailed discussion of the mathematics and modeling principles is available elsewhere.9 The calculations have been performed with two subsets.10 The first subset is using the cube to calculate only first-order effects and cofactor interactions, which gives XT
size(S,A,T) ) 17.4 + 385S + 0.851A + 0.545T + 110SA + 8.50ST - 0.058AT - 4.47SAT (5) The second subset is on the star to provide first- and secondorder effects of the factors:
size(S,A,T) ) 14.2 + 880S - 0086A + 0.652T + 2700S2 + 0.018A2 - 0.00288T2 (6) Averaging all overlapping terms yields a single model. Further tests have demonstrated that the second-order effect of methylamine concentration factor is negligible. Subsequently, the
Figure 3. The three-dimensional cross sections of a four-dimensional chemometric model for predicting nanoparticle size from the experimental conditions. S and A axes are the concentrations of metal cation and methylamine, respectively. T is the temperature axis. The cross section in A is along a constant temperature of 60 °C. The cross section in B is at a constant methylamine concentration of 3.49 M. The cross section in C is along a constant metal cation concentration of 0.015 M.
second-order term of methylamine is removed from the model. The overall empirical formula for the model of particle size prediction becomes
size(S,A,T) ) 16.8 + 447.5S + 0.851A + 0.55T 10000S2 - 0.008T2 + 110SA + 8.5ST - 0.058AT 4.467SAT (7) Although in principle only 15 systematic experiments are required for establishing a valid chemometric model, more than 40 experiments have been conducted to analyze the noise level in our model and to test the consistency of the experiments. The model has been tested against the experimental data used to generate the model, and yielded a “goodness of fit” χ2 of 5.58, which indicates that this is an adequate model at the 97.5% confidence level.11 Similarly, the critical Fisher ratio for this model at 99.0% confidence is 26.6 while the calculated Fisher ratio is 12.9. Thus, this model is valid with a 99.0% confidence level.12 The factorial design method provides a four-dimensional chemometric model with one response axis of nanoparticle size and three-factor axes of temperature and concentrations of metal salt and methylamine. This four-dimensional model is obtained by totally fitting all the experimental data. Three threedimensional cross sections along a constant axis in this model are displayed in Figure 3 as various response surfaces between the particle size and the control factors. Figure 3A shows strong effects of metal salt and methylamine on the nanoparticle size with the temperature factor kept as a
7922 J. Phys. Chem. B, Vol. 104, No. 33, 2000 constant. The saddle shape response implies a strong interaction between metal salt factor and methylamine factor. The extent of the effect from one factor heavily depends on the other factor. For instance, the particle size can either increase or decrease with increasing metal salt concentration when the methylamine concentration changes. Such a strong interaction roots in the synthesis reaction 1. Metal salt and methylamine are the starting reagents. When the setting of one reagent shifts, the effect to the reaction from the second reagent will change greatly. The response surface of the particle size to metal salt concentration and temperature is displayed in Figure 3B with methylamine concentration as a constant. This surface shows that the metal salt factor and the temperature factor are independent to each other. The variation of the particle size due to changing metal salt concentration is almost the same at different temperature. It indicates that these two control factors are independent from each other. Such an independence of these two control factors may suggest that the effect of metal salt concentration is in the formation of CoFe2O4 compound. The temperature factor controls the subsequent crystallization of nanoparticles. Figure 3C shows the particle size variation from temperature factor and methylamine factor. The relationship between these two factors should be the same as the one between metal salt factor and temperature factor. However, the response surface in Figure 3C implies the mutual dependence between methylamine factor and temperature factor. Because methylamine has a relatively low boiling point of 48 °C, this dependence is believed due to the increase of methylamine vaporization rate in the aqueous solution with increasing temperature. Analysis of the effects from three factors indicates that the best approach for size control is varying temperature and metal salt concentration while holding methylamine concentration steady. The change of particle size in Figure 3B is almost linear along temperature and metal salt concentration axis. However, the rate of the size change is different between these two factors. This allows the system to be highly tunable. Adjusting the temperature will yield large changes of predictable particle size while adjusting the salt concentration will give smaller and predictable changes in particle size. Therefore, a rough tuning can be achieved through temperature, and a fine-tuning will be conducted through metal salt concentration. The model has been tested against several types of spinel ferrite nanoparticles
Rondinone et al. TABLE 3: Comparison of Nanoparticle Size between Model Predicted Value and Experimental Measurement CoFe2O4 (nm)
CoxZn(1-x) Fe2O4 (0 < x
