Optimization and modeling of synthesis parameters of neodymium(III) bromide by dry method using full factorial design analysis

Yassine Bounouri; Madjid Berkani; Abdelmalek Zamouche; Leszek Rycerz

doi:10.1016/j.arabjc.2017.05.003

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Review

13 (

); 366-376

doi:

10.1016/j.arabjc.2017.05.003

Optimization and modeling of synthesis parameters of neodymium(III) bromide by dry method using full factorial design analysis

Yassine Bounouri^{^a}, Madjid Berkani^{^a,⁎}, Abdelmalek Zamouche^{^a}, Leszek Rycerz^{^b}

a Laboratoire de Physico-chimie des Matériaux et Catalyse, Faculté des Sciences Exactes, Université de Bejaia, Targa ouzemmour 06000, Algeria

b Chemical Metallurgy Group, Department of Chemistry, Wroclaw University of Technology, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland

⁎Corresponding author. berkanima@yahoo.fr (Madjid Berkani)

Received: 2017-1-19, Accepted: 2017-5-6, Published: 2017-01-01

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The synthesis of neodymium(III) bromide (NdBr₃) by sintering brominating of neodymium oxide (Nd₂O₃) with ammonium bromide (NH₄Br) was investigated. The influence of various synthesis parameters (temperature, contact time and stoichiometry) on the reaction yield was studied and optimized. The main interaction effects of the synthesis parameters on the reaction yield were also determined by a full 2³ factorial designs with six replicates at the center point.

This study showed that the optimum conditions for the synthesis of NdBr₃ are following: contact time t = 60 min, stoichiometry in moles Nd₂O₃:NH₄Br = 1:24 and temperature T = 400 °C. The reaction yield for these parameters was equal to 97.80%. The first order model was obtained to predict the reaction yield as a function of these three parameters. It was shown that all parameters have a significant positive influence on reaction yield. In addition it was pointed out also that the interaction effects between them are significant.

Keywords

Neodymium(III) bromide

Lanthanide halides

Reaction yield

Full factorial design

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1 Introduction

In the past 50 years, lanthanide halides were the subject of several studies. The majority of these studies were focused on their chemical and physical properties. The physicochemical properties of the compounds they form, for instance with the alkali halides, can be examined and correlated in a way which is unique since the lanthanides regularly vary along the series they form in the periodic table. This is due to the presence of f electrons in the lanthanide ions, which do not participate in the formation of the chemical bonding (Gschneidner et al., 2003). These compounds are used in various fields such as: reprocessing of nuclear wastes (Kobayashi et al., 1998), recycling of spent nuclear fuel (Ogawa et al., 1995; Ogawa and Igarashi, 1998), catalysis and chemical synthesis (Doty et al., 2007), medical imaging (Beckert et al., 2016), and in the lighting industry (Muklejohn et al., 1993; Markus et al., 2005). These different applications require knowledge of their physicochemical, structural and thermodynamic properties. The study of these properties requires high purity of these salts in order to have accurate data (Rycerz and Gaune-Escard, 2008; Kolodziej et al., 2009; Chojnacka et al., 2014 ). These anhydrous salts that are commercially available still contain small amounts of water and cannot be used for such a study. Therefore, good control of the different stages of synthesis and optimization of parameters that can affect the synthesis reaction is the preliminary step to cross (Gaune-Escard et al., 1994; Peringer et al., 2008; Mendil et al., 2013 ). The determination of these optimum conditions requires a large number of experiments and takes a lot of time. These drawbacks can be avoided by applying the experimental design method, which allows studying the effects of several factors on one or more responses, and to find a mathematical model that connects the response to the factors (Kincl et al., 2005). This method has several advantages such as: providing maximum information with minimum experiments, the possibility of increasing the number of factors studied or their levels, taking into account possible interactions between factors, simple modeling results and a good search of the optimal response (Lazic, 2006; Tinsson, 2010). The aims of the present work were as follows: firstly, optimization of synthesis parameters (temperature, contact time and molar ratio neodymium oxide: ammonium bromide) of neodymium(III) bromide (NdBr₃) by sintering brominating of neodymium oxide (Nd₂O₃) with ammonium bromide (NH₄Br), secondly, application of a 2³ full factorial design in order to determine a mathematical model connecting these three factors with reaction yield and to gain insight into how the various factors interact and influence the response.

2 Experimental

NdBr₃ was synthesized from neodymium oxide Nd₂O₃ (Sigma-Aldrich, 99.9%) by sintering brominating with NH₄Br (Sigma-Aldrich, 99%). A mixture of Nd₂O₃ and NH₄Br in well-defined proportions was ground and homogenized in a mortar, and placed into alumina crucible. Then, the crucible was inserted into a quartz reactor and placed in an electric furnace. The furnace temperature was controlled by the programmer EUROTHERM 2404. This resulted in a process where volatile products were absorbed in a scrubber filled with sodium hydroxide. The entire experiments were carried out in an argon atmosphere. The yield of the reaction was determined by chemical analysis. Neodymium(III) bromide is soluble in water whereas unreacted neodymium oxide is water insoluble. Thus dissolution of the reaction product transfers neodymium bromide into solution, whereas neodymium oxide stays in insoluble solid residue. The resulting product of the reaction was cooled down, and then dissolved in 150 cm³ of 0.05 M HCl solution using magnetic stirrer for 10 min. In this step obtained neodymium(III) bromide was transferred to the solution. The solution of 0.05 M HCl was used to prevent hydrolysis of neodymium ions formed during the dissolution of the neodymium bromide. Buchner funnel with hard paper filter was used to separate the leach solution from the sediments. Filtrates (leach solutions) were collected in a 200 cm³ volumetric flask, and filled by the solution of 0.05 M HCl to the mark. Then a 20 cm³ of the resulting solution was diluted 10 times in a 200 cm³ volumetric flask. Next, 10 cm³ of the diluted solution was transferred to a conical flask and 10 cm³ of buffer solution (CH₃COOH/CH₃COONa), pH = 5.6 was added. The prepared solution was heated almost to boil (80 °C), and then four drops of xylenol orange solution were added. The chemical analysis of the content of Nd was performed by a complexometric titration with a standard EDTA solution until the color changed from purple–red to light yellow. The titration was repeated 3 times.

3 Full factorial designs

A full factorial design is an experimental design with a number of levels limited to two (low and high) for each factor; it takes into account all the combinations between the levels of factors during the experiment. The full factorial design allows modeling of the first degree with or without interactions and it quickly finds the application limits when the number of factors increases. This design also allows us to determine the effects of the factors on the response and the effects of interactions between different factors (Montgomery, 2012).

4 Results and discussion

4.1

4.1 Thermodynamic aspect of the reaction

Before synthesis of NdBr₃ by sintering brominating with NH₄Br, we performed a thermodynamic study of the reaction to determine the standard thermodynamic parameters such as enthalpy, entropy and the standard Gibbs free energy of this reaction. These thermodynamic parameters provided information about the exothermic or endothermic synthesis process, the degree of disorder, and clarified the possibility of spontaneous synthesis process.

The synthesis of NdBr₃, from Nd₂O₃ and NH₄Br by dry route, can be described by the following reaction:

(1)

{Nd}_{2} O_{3} (s) + 6 {NH}_{4} Br (s, g) \to 2 {NdBr}_{3} (s) + 6 {NH}_{3} (g) + 3 H_{2} O (ℓ, g)

The standard thermodynamic quantities (

Δ_{r} H_{T}^{0}

Δ_{r} S_{T}^{0},

Δ_{r} G_{T}^{0}

) were calculated using the thermodynamic data obtained from the literature (Lide, 2007; Barin, 1995). The results of above calculation are presented in Fig. 1.

Thermodynamic functions: (a) Standard enthalpy of reaction, (b) Standard entropy of reaction, and (c) Standard Gibbs free energy of reaction.

The results of Fig. 1a show that the reaction is endothermic between room temperature and T = 606 K (sublimation temperature of NH₄Br). The sudden increase of enthalpy observed at 373 K is associated with the passage of water from liquid to a gaseous state.

Fig. 1b shows that the entropic contribution is positive over the entire temperature range, this is due to the increase in disorder, which can be explained by the increase in the number of moles of gas.

The free enthalpy of reaction as a function of the temperature was calculated according to the equation:

(2)

Δ_{r} G_{T}^{0} = Δ_{r} H_{T}^{0} - T Δ_{r} S_{T}^{0}

Fig. 1c shows that the

Δ_{r} G_{T}^{0}

decreases with increase in temperature. This means that the synthesis of NdBr₃ is promoted by an increase in temperature. Also, we can deduce graphically an inversion temperature T = 571 K, beyond which the reaction is favorable.

4.2

4.2 Thermal analysis of reagents by TG–DTG

The two reagents (Nd₂O₃ and NH₄Br) used for the synthesis of NdBr₃, have been analyzed with TG–DTG in order to verify their stability in function of the temperature. The TG–DTG curves obtained with heating rate 10 °C/min under a nitrogen atmosphere are shown in Figs. 2 and 3.

Curves TG-DTG of ammonium bromide NH4Br obtained at 10 °C/min under nitrogen atmosphere.

Curves TG-DTG obtained at 10 °C/min under nitrogen atmosphere of neodymium oxide Nd2O3.

Fig. 2 shows that NH₄Br begins to lose the weight at 179 °C and greater weight loss, corresponding to decomposition temperature according to the reaction (3), was observed at 333 °C.

(3)

{NH}_{4} Br (s) \to {NH}_{3} (g) + HBr (g)

Sintering brominating of neodymium oxide takes place with NH₄Br and also with HBr formed during thermal decomposition of NH₄Br. (Mendil et al., 2013; Chen et al., 2008).

The curves TG–DTG of Nd₂O₃ (Fig. 3) shows that the oxide does not lose any weight and that during this process the oxide remained stable. This observation confirms the literature information concerning the lanthanide oxides (Sarbak et al., 2005).

4.3

4.3 Optimization of the synthesis parameters

In this work, we studied the influence of three main synthesis parameters (contact time, stoichiometry and temperature) on the reaction yield.

4.3.1

4.3.1 Influence of the contact time

The study of contact time influence on the reaction yield was realized by varying it from 10 to 120 min while maintaining the two other parameters constant (the molar ratio Nd₂O₃: NH₄Br = 1:6 and experimental temperature T = 250 °C).

The reaction yield, noted R, was calculated with the following equation:

(4)

R = \frac{number of experimental moles}{number of theoretical moles} \times 100

The number of experimental moles is the number of moles of NdBr₃ obtained during reaction. The theoretical number of moles is the number of moles corresponding to a yield of 100% calculated from the mass of the neodymium oxide. The results are presented in Fig. 4.

Effect of contact time on variations of yield.

This figure shows that the yield of the reaction R (%) increases with the increase in reaction time up to 60 min. Beyond this value, the yield remains almost constant and stabilizes at an average of 30%. Therefore, the optimum contact time of this reaction is 60 min, and for this reason, we set the contact time to 60 min in order to study the effect of the stoichiometry and temperature.

4.3.2

4.3.2 Influence of the stoichiometry

The study of this parameter was carried out in order to see the effect of excess NH₄Br on the reaction yield. It is based on the variation of the stoichiometry in moles of Nd₂O₃:NH₄Br from 1:6 to 1:30. The two other parameters were kept constant (t = 60 min and T = 250 °C). The results obtained are represented in Fig. 5.

Effect of the stoichiometry on variations of yield.

Increase in the reaction yield R (%) was observed with excess of NH₄Br up to the molar ratio Nd₂O₃:NH₄Br = 1:24. Beyond this value, the yield was stabilized at a level of about 46%. The optimal molar ratio Nd₂O₃:NH₄Br was found to be 1:24.

4.3.3

4.3.3 Influence of the temperature

The thermodynamic study of the synthesis reaction of NdBr₃ showed that the synthesis is promoted by an increase in temperature. According to this result, we have chosen to vary the temperature from 250 to 450 °C, and kept the two other parameters at their optimum level (t = 60 min and molar ratio Nd₂O₃:NH₄Br = 1:24). Fig. 6 represents the experimental results of this study.

Effect of the temperature on variations of yield.

It is evident that an increase in temperature up to 400 °C has a positive effect on the reaction yield. Beyond this value, the yield decreases slightly. This is probably due to the loss of NH₄Br related to its decomposition at high temperatures (Mendil et al., 2013). As a result, the optimum temperature for synthesis of NdBr₃ by sintering brominating with NH₄Br is 400 °C for which yield reaches 97.80%.

4.4

4.4 Factorial design analysis

After optimization of the three factors influencing the reaction yield of the synthesis of NdBr₃, we have applied the experiment design method to model the reaction yield depending on the three factors. This method allows us to find a mathematical model that links the reaction yield to the three factors, and allows us to examine the main and interaction effects of factors on the reaction yield.

In this study, a full factorial design 2³ with six experiments at the central point and therefore a total of 14 experiments were used. The replication of experiments in central point is in order to evaluate the experimental error (Mendonça et al., 2011). The high, center and low levels defined for the 2³ factorial designs were listed in Table 1. The low and high levels of the factors were selected according to the optimization results.

Table 1 Factors and levels used in the factorial design.

Factors	Low level (−1)	Center level (0)	High level (+1)
( $x_{1}$ ) Contact time (min)	10	35	60
( $x_{2}$ ) Stoichiometry in moles (Nd₂O₃:NH₄Br)	1:6	1:15	1:24
( $x_{3}$ ) Temperature (°C)	250	325	400

The mathematical model in the coded form for the full factorial design 2³ is given as follows:

(5)

\hat{R} = b_{0} + b_{1} x_{1} + b_{2} x_{2} + b_{3} x_{3} + b_{12} x_{1} x_{2} + b_{13} x_{1} x_{3} + b_{23} x_{2} x_{3} + b_{123} x_{1} x_{2} x_{3}

where

\hat{R}

is the predicted reaction yield,

b_{0}

is the global mean,

b_{i}

represents the other regression coefficients and

x_{1}

x_{2}

x_{3}

, stands for contact time, stoichiometry and temperature, respectively.

The results obtained from the 14 experiments are shown in Table 2, with the low (−1), center (0), and high (+1) levels as specified in Table 1.

Table 2 Design matrix and the results of the 2³ full factorial design.

Experiments	$x_{1}$	$x_{2}$	$x_{3}$	R (%)
1	−1	−1	−1	7.40
2	1	−1	−1	30.84
3	−1	1	−1	14.99
4	1	1	−1	46.04
5	−1	−1	1	21.84
6	1	−1	1	79.76
7	−1	1	1	30.07
8	1	1	1	97.80
9	0	0	0	47.40
10	0	0	0	48.55
11	0	0	0	48.17
12	0	0	0	49.32
13	0	0	0	47.01
14	0	0	0	50.86

4.4.1

4.4.1 Statistical analysis

After realization of the 14 experiments, we have calculated the various coefficients of the model ( $b_{i}$ ), and then we have determined the main effects and interactions between different factors. This effect which represents the difference between the average value of the response (R) at the high level (+) and the average value of the response at low level (−) was determined using the formula (6) (Cavalitto and Mignone, 2007).

(6)

E_{i} = \frac{\sum R_{(i +)}}{n} - \frac{\sum R_{(i -)}}{n}

where E_i is the effect of the variable, R is the experimental response, and n is the number of experiments at each level (− or +).

The significance of the different calculated coefficients has been checked by the Student's t-test, which allows us to determine whether among the coefficients of the model, there are no significant coefficients, which will be eliminated from the regression equation because their influence on the reaction yield is negligible (Erto et al., 2010).

The t_i value which represents the ratio of the coefficient to the estimated parameter and standard deviation residual are calculated using the following equation:

(7)

t_{i} = \frac{| b_{i} |}{\sqrt{\frac{1}{N} (\frac{\sum_{j = 1}^{m} {(R_{0 j} - \overline{R_{0}})}^{2}}{m - 1})}}

where

b_{i}

: coefficient, N: number of experiments (N = 8), m: number of experiments at the central point (m = 6),

R_{0 j}

: observed value of reaction yield at the j central point,

\overline{R_{0}}

: mean reaction yield at the central point.

The regression coefficients, the effects and t values are shown in Table 3.

Table 3 Statistical parameters for 2³ designs.

Term	Effects	Coefficients	Standard error	t_i	Significance
b₀	41.09	41.09	0.9506	83.15	S
b₁	45.03	22.51	0.9506	45.55	S
b₂	12.27	06.13	0.9506	12.41	S
b₃	32.55	16.28	0.9506	32.95	S
b₁₂	04.36	02.18	0.9506	4.41	S
b₁₃	17.79	08.90	0.9506	18.01	S
b₂₃	00.87	00.44	0.9506	0.89	NS
b₁₂₃	00.55	00.28	0.9506	0.57	NS

S: Significant, NS: Not Significant.

For a 95% confidence level and 5 degrees of freedom (m-1), the tabulated value of STUDENT (t_crit value) is 2.57.

The results are illustrated by means of Pareto charts (Fig. 7). The vertical line in Pareto charts indicates minimum statistically significant effect magnitude for a 95% confidence level. The effects which have t_i less than 2.57 are statistically insignificant (Montgomery, 2012; Carmona et al., 2005).

Pareto chart of the standardized effects.

According to the Pareto chart (Fig. 7), the interaction, stoichiometry - temperature (coded $x_{2} x_{3}$ ) and time-stoichiometry-temperature (coded $x_{1} x_{2} x_{3}$ ) are insignificant for a 95% confidence level.

Thus, the reduced model, represented by (Eq. (5)) in terms of coded parameters after excluding the insignificant terms for the predicted reaction yield $\hat{R}$ (%) is as follows:

(8)

\hat{R} = 41.09 + 22.51 x_{1} + 6.13 x_{2} + 16.28 x_{3} + 2.18 x_{1} x_{2} + 8.90 x_{1} x_{3}

4.4.2

4.4.2 Variance analysis (ANOVA)

The significance and adequacy of the regression model after excluding insignificant coefficients was evaluated by the analysis of variance (ANOVA) (Sen and Swaminathan, 2004).

The ANOVA is based on the comparison of the variation associated with the model that represents the sum of the quadratic variation of the experimental yield (R) and the predicted yield ( $\hat{R}$ ) to the experimental average yield ( $\bar{R}$ ) and variation associated with experimental error which represents the sum of the squared residual between the experimental and predicted yields (Kasiri and Khataee, 2011).

The sum of squared total (SST), sum of squares for regression (SSR) and sum of squared errors (SSE) were computed from the reaction yield as follows (Tinsson, 2010):

(9)

SST = \sum_{i = 1}^{N} {(R_{i} - \overline{R})}^{2}

(10)

SSR = \sum_{i = 1}^{N} {({\hat{R}}_{i} - \overline{R})}^{2}

(11)

SSE = \sum_{i = 1}^{N} {(R_{i} - {\hat{R}}_{i})}^{2}

These parameters are shown in Table 4.

Table 4 Analysis of variance-reduced model fit for reaction yield.

Experiments	$R_{i}$	${\hat{R}}_{i}$	${(R_{i} - {\hat{R}}_{i})}^{2}$	${({\hat{R}}_{i} - \bar{R})}^{2}$	${(R_{i} - \bar{R})}^{2}$
1	7.40	7.25	0.022	1145.32	1135.19
2	30.84	30.11	0.533	120.62	105.12
3	14.99	15.15	0.026	673.02	681.35
4	46.04	46.73	0.476	31.78	24.48
5	21.84	22.01	0.029	364.15	370.66
6	79.76	80.47	0.504	1550.58	1495.17
7	30.07	29.91	0.026	125.05	121.50
8	97.80	97.09	0.506	3135.71	3215.84
SUM	–	–	SSE = 2.121	SSR = 7146.222	SST = 7149.300

The validity of the regression equation is based on the statistical of Fisher, which consists in comparing of F-value defined as the ratio between the mean-square-effect and the mean-square-error, and the tabulated value of the F-distribution at a level of significance and a certain number degrees of freedom.

The value of F is calculated by the following equation:

(12)

F = \frac{SSR / (ℓ - 1)}{SSE / (N - ℓ)} = \frac{\sum_{i = 1}^{N} {({\hat{R}}_{i} - \overline{R})}^{2} / (ℓ - 1)}{\sum_{i = 1}^{N} {(R_{i} - {\hat{R}}_{i})}^{2} / (N - ℓ)}

where

ℓ

: number of the significance parameters.

The model is a good predictor of the experimental results if the F-value is greater than the tabulated value of the F-distribution (Yetilmezsoy et al., 2009; Liu et al., 2004).

The calculated F-value for reaction yield “F = 1347.57” is much greater than the tabulated ( $F = 19.3$ at the 95% significance), the regression equation is thus very significant on the response, and the adjustment of the model is adequate.

4.4.3

4.4.3 Correlation coefficients

The correlation coefficient or determination coefficient (R²) is the ratio between the variation due to the regression and the total variation, this coefficient enable us to check the correlation between the experimental and the predicted responses (Liu and Chiou, 2005; Santos and Boaventura, 2008; Deming and Morgan, 1993 ), it is calculated as follows:

(13)

R^{2} = \frac{SSR}{SST} = \frac{\sum_{i = 1}^{N} {({\hat{R}}_{i} - \overline{R})}^{2}}{\sum_{i = 1}^{N} {(R_{i} - \overline{R})}^{2}}

The calculated R² (R² = 0.999) is very close to 1, which explains a strong linear relationship between the experimental responses and that given by the model. The values of R² indicate that the model does not explain only about 0.001 of the variations. This result is confirmed by the representation of the experimental results and those calculated by the model (Eq. (8)) in Fig. 8, which shows a good correspondence between the experimental and predicted values.

Plot of the measured and model predicted values of the response variable.

The goodness of fit of the model was also checked by adjusted coefficient $R_{Adj}^{2}$ (Eq. (14)), which corrects the correlation coefficient value R² for the sample size and the number of terms in the model.

(14)

R_{Adj}^{2} = 1 - (1 - R^{2}) \frac{N - 1}{N - ℓ - 1}

when the sample size is not very large and the number of terms in the model is not great, the adjusted

R_{Adj}^{2}

may be smaller than R² (Santos and Boaventura, 2008).

In our study, the value of $R_{Adj}^{2}$ (0.993) was found very close to the corresponding value R².

4.4.4

4.4.4 Residual analysis

The residuals analysis, which represents the difference between the experimental and predicted responses, allows us to represent the unexplained part of the model and check whether there is a failure in the latter. This test consists of analyzing the plot of observed residues depending on the predicted responses (Fig. 9) (Kasiri and Khataee, 2011; Sado and Sado, 2000).

Residual plots for reaction yield R (%).

The look of the graph shows a random distribution of points, confirming the nonexistence of a relationship between predicted responses and residue. So the model of first level that we have established well explains the experimental results (Kasiri and Khataee, 2011; Goupy and Creighton, 2006).

4.5

4.5 Main and interaction effects

A main effect can be defined as the effect of one factor on the response, ignoring the effects of all other factors, it represents the change in the response when the factor changes from low to high levels. The effect of a factor is positive if the response R (%) increases when the factor changes from low to high levels. Otherwise (the response R (%) decreases when the factor changes from low to high levels) the effect is negative (Ponnusami et al., 2007).

The main effects of the experimental results for the respective low and high levels of contact time, molar ratio and temperature were illustrated in Fig. 10.

Main effects plot for reaction yield R (%): (a) contact time, (b) stoichiometry, and (c) temperature.

From the graph (Fig. 10), we can see that an increase in contact time (a), stoichiometry (b), temperature (c), from low to high levels resulted in an increase in the reaction yield R (%). This indicates that all factors have a positive effect on the response (Palanikumar et al., 2009; Lorenzen and Anderson, 1993).

Contrast to the main effect, the interaction effect represents the effect of a factor on the response as a function of other factors. An interaction between two factors is significant when the effect of a factor on the response depends on the level of the other factor, i.e. whether the lines of the two factors are not parallel (Lazić, 2004; Mathialagan and Viraraghavan, 2005).

The interactions between factors were illustrated in Fig. 11.

Interaction effects plot: (a) time/stoichiometry, (b) time/temperature, and (c) stoichiometry/temperature.

Fig. 11 shows the significant interactions between contact time and stoichiometry (Fig. 11a), as well as between the contact time and the temperature (Fig. 11b). However, the interaction between stoichiometry and temperature (Fig. 11c) is neglected (the lines are almost parallel). These plots also indicate that the interaction between the contact time and the temperature ( $x_{1} x_{3}$ ) is stronger than between the contact time and stoichiometry ( $x_{1} x_{2}$ ). These plots also show that the effect of the contact time is larger when the temperature and the stoichiometry are at high (+1) levels.

5 Conclusion

In these study, the synthesis parameters (contact time, stoichiometry and temperature) of neodymium(III) bromide by dry method are optimized. According to the results, the optimum conditions for the synthesis of NdBr₃ are as follows: contact time (t = 60 min), stoichiometry in moles (Nd₂O₃:NH₄Br = 1:24) and temperature (T = 400 °C), for which the reaction yield reached 97.80%.

The full factorial design was used to allow the evaluation of the most important factors for synthesis of neodymium(III) bromide. This modeling leads to a first degree mathematical model, which relates the yield to the three operating parameters. It has also shown that an increase from lower to higher levels in factors has a significantly positive influence on reaction yield R (%), with presents of significant interaction between contact time (t) and stoichiometry, and between contact time (t) and temperature. The validity of this study was limited to, contact time between 10 and 60 min, stoichiometry between 1:6 and 1:24 and temperatures between 250 and 400 °C.

Acknowledgments

The work was finances by a statutory activity subsidy from the Polish Ministry of Science and Higher Education for the Faculty of Chemistry of Wroclaw University of Technology.

Financial support by the Thematic Agency for Research in Science and Technology (ATRST) from the Algerian Ministry of Higher Education and Scientific Research is gratefully acknowledged.

M. B and Y. B wish to thank the Department of Chemistry of Wroclaw University of Technology for hospitality and support during this work.

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Introduction

Experimental

Full factorial designs

Results and discussion

Thermodynamic aspect of the reaction
Thermal analysis of reagents by TG–DTG
Optimization of the synthesis parameters
Factorial design analysis
Main and interaction effects

Conclusion

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[Google Scholar]

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[36] Santos S.C.R., Boaventura R.A.R., . Adsorption modelling of textile dyes by sepiolite. Appl. Clay Sci.. 2008;42:137-145.
[Google Scholar]

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[Google Scholar]

[39] Tinsson W., . Plans d'expérience: constructions et analyses statistiques. Berlin: Springer Science & Business Media; 2010.

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Optimization and modeling of synthesis parameters of neodymium(III) bromide by dry method using full factorial design analysis

Abstract

Keywords

Neodymium(III) bromide

Lanthanide halides

Reaction yield

Full factorial design

1 Introduction

2 Experimental

3 Full factorial designs

4 Results and discussion

4.1 Thermodynamic aspect of the reaction

4.2 Thermal analysis of reagents by TG–DTG

4.3 Optimization of the synthesis parameters

4.3.1 Influence of the contact time

4.3.2 Influence of the stoichiometry

4.3.3 Influence of the temperature

4.4 Factorial design analysis

4.4.1 Statistical analysis

4.4.2 Variance analysis (ANOVA)

4.4.3 Correlation coefficients

4.4.4 Residual analysis

4.5 Main and interaction effects

5 Conclusion

Acknowledgments

References

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