Syntheses of ultra-fine barium carbonate powders by homogeneous precipitation method

2.1 Materials

All chemicals utilized for experimentation were analytical-grade reagents, were used without further purification and were purchased from Tianjin Fengchuan Chemical Reagent Co., Ltd. (China), including barium chloride dihydrate (BaCl₂·2H₂O), sodium hydroxide (NaOH), carbamide ([NH₂]₂CO), ethylene diamine tetra acetic acid (EDTA), sodium triphosphate and citric acid. The analytical-grade reagents were also analyzed for quality by the method in accordance with the recommended methods of the National Standard of the People’s Republic of China (GB/T).

2.2 Instrumentation

The experiments were carried out in the homogeneous precipitation experimental devices, which are shown in Figure 1. A typical homogeneous precipitation experimental device consists of iron support, a thermostatic water bath, a condensation pipe, stirring equipment, a two-neck flask and a stirring speed control device.

Figure 1:

Schematic diagram of homogeneous precipitation experimental device.

1-Iron support; 2-Thermostatic water bath; 3-Condensation pipe; 4-Stirring equipment; 5-Two-neck flask; 6-Stirring speed control device.

2.3 Characterization

The phase composition of the BaCO₃ powders which were prepared by the homogeneous precipitation method was characterized by X-ray diffraction (XRD). XRD (D/Max2200, Rigaku, Japan) measurements were performed using CuKα radiation (λ=1.5406 Å) and a Ni filter, in the 2θ range 5–100° with a scanning rate of 0.25°/min. The structure and morphology of BaCO₃ powders were observed using a scanning electron microscope (XL30ESEM-TMPG-TMP, Philips, Holland).

2.4 Method for determination of yield

The yield of ultra-fine barium carbonate powders could be obtained theoretically after the chemical reaction, and were prepared by homogeneous precipitation method, which was used titration to determine such as following processing, measuring accurately the reaction solution of certain volume (v) by suction pipet after the reaction, then filtrating and cleaning, making pH of the filtrate fix at 10 or 11, adding 2 to 3 drops of thyme phenolphthalein indicator, the solution was blue, and make the solution colorless with titrant of 0.1 mol/l EDTA prepared as an end.

The Ba²⁺ concentration was calculated by equation:

where v is the volume of the reaction solution, and v₁ is the volume of consumption for the EDTA standard titration solution.

The yield of the product was calculated based on the following equation:

where c₀ is the concentration of Ba²⁺ of the initial reaction solution.

2.5 Experimental design

In this study, three operating factors, namely the Ba²⁺ concentration (χ₁), reaction temperature (χ₂) and reaction time (χ₃), were chosen as independent variables, each at five levels coded -1.682, -1, 0, +1 and +1.682 and the dependent variable was the yield of product (Y). The molar quantity of urea is six and NaOH 2.5. The range and levels of the variables investigated are listed in Table 1. Generally, a 2ⁿ factorial runs with 2n axial runs and n_c center runs (six replicates) for three independent variables (n=3) at two levels (low [-] and high [+]) was employed. A total of 20 experimental runs were performed, according to Table 2, to optimize the parameters, as calculated from Eq. (3):

where N is the total number of experimental runs and n is the number of factors.

For statistical calculations, the relation between the coded values and actual values are described in the following Eq. (4):

where χ_i is a coded value of the variable, A_i is the actual value of the variable, A₀ is the actual value of the A_i at the center point and ΔA is the step change of variable.

However, preparations of barium carbonate by the homogeneous precipitation method were often considered to possess a nonlinear relationship between independent variables and dependent variables. Consequently, the general form of the second-degree polynomial is applied to fit the data into the equation by the nonlinear regression procedure. The model equation used for the analysis is given by Eq. (5):

where Y is the predicted response, β₀ is the constant coefficient, β_i is the linear coefficient, β_ii is the quadratic coefficient, β_ij is the interaction coefficient, k is the number of factors studied and optimized in the experiment, χ_i, χ_j are the coded values of independent variables, and the terms χ_iχ_j and χi2 represent the interaction and quadratic terms, respectively.

2.6 Procedure

To carry out the RSM approach, “Design Expert” software (version 7.1.5, STAT-EASE Inc., Minneapolis, MN, USA) was used for regression and graphical analyses, from which the data was obtained. The maximum values of the yield of product were taken as the responses of the design experiment. Statistical analysis of the model was performed to carry out the ANOVA. The optimum experimental conditions for preparing ultra-fine barium carbonate powders by the homogeneous precipitation method were determined using RSM and CCD. The desirable response is influenced by several independent variables and the objective is to optimize this response, and then obtain the superfine high-purity barium carbonate powder after filtering, cleaning and drying.

3.1 Response surface analysis for the optimization of three factors

Searching for the optimum conditions for the preparation of ultra-fine barium carbonate powders, the optimized experimental independent variables and the corresponding yield of ultra-fine barium carbonate powders are also shown in Table 2. CCD is used to calculate the correlation between the experiment variables of prepared barium carbonate and the yield of barium carbonate. The yield of barium carbonate is found to range from 39.06% to 55.69%. Runs 15–20 at the center point are used to determine the experimental error. According to the least squares method, the models are selected based on the highest order polynomials, while the additional significant terms are also put into account and the models were not aliased. The final empirical model in terms of coded factors after excluding the insignificant terms for the yield of barium carbonate (Y) is shown in Eq. (6):

The results of the second-order response surface model fitting in the form of ANOVA are given in Table 3. The value of the determination coefficient (R²=0.9679) indicates that the sample variation of 96.79% for yield of barium carbonate is attributed to independent variables and only 3.21% of the total variations cannot be explained by the model. The value of the adjusted determination coefficient (adj.R²=0.9390) is also very high to advocate for a high significance of the model. The statistical analysis of the coefficients of the model revealed that linear and quadratic terms were significant, while the interaction coefficients were nonsignificant. This indicated that independent variables individually affected the dependent variable. The coefficient of variation (CV) indicates the degree of precision with which the experiments are compared. The lower reliability of the experiment is usually indicated with a high value of CV. In the present case, a low CV (2.59%) indicated that the experiments performed were more precise and highly reliable.

The ANOVA of the quadratic model for the yield of barium carbonate is listed in Table 4. From the ANOVA of response surface quadratic model for yield of barium carbonate, the Model F-value of 33.48 implied that the model is significant as well. The significance of each coefficient is determined by the p value. The smaller the p value (p<0.05) is, the more significant the corresponding coefficient will be. In this case, χ₁, χ₂, χ₃, χ12, χ22 and χ32 are significant model terms. The statistical results obtained show that the above models are adequate to predict the yield of barium carbonate within the range of error.

The satisfactory correlation between observed values and predicted ones is shown in Figure 2. It can be seen that the predicted values obtained are quite close to the observed values, and the deviation between the observed and predicted ones is less. The fitted regression equation shows the fitting is good.

Figure 2:

Relationship between the observed and predicted values.

Figure 3 shows the effect of Ba²⁺ concentration and reaction temperature on the yield of carbonate powders. Ba²⁺ concentration and reaction temperature has a positive linear effect on the yield of carbonate powders. This is most likely due to the improvement of efficiency resulting from the increased kinetics of reaction with the rise of Ba²⁺ concentration and reaction temperature. Figure 4 shows the effect of Ba²⁺ concentration and reaction time on the yield of carbonate powders. How Ba²⁺ concentration affects the yield of carbonate powders is described in Figure 3. Reaction time has a positive linear effect on the yield of carbonate powders for most of the time. For a very long time, however, the negative quadratic effect also became significant. Figure 5 shows the effect of reaction temperature and reaction time on the yield of carbonate powders. How the reaction temperature and reaction time affect the yield of carbonate powders is described in Figures 3 and 4, respectively. There is a linear significant interaction between the reaction temperature and reaction time.

Figure 3:

Response surface for effect of Ba²⁺ concentration and reaction temperature on yield.

Figure 4:

Response surface for effect of Ba²⁺ concentration and reaction time on yield.

Figure 5:

Response surface for effect of reaction temperature and reaction time on yield.

3.2 The best experimental conditions

The optimum preparation conditions for yield of carbonate powders are a Ba²⁺ concentration of 0.8 mol/l, reaction temperature of 85°C and reaction time of 4 h. The validation of the model is carried out under predicted conditions. The predicted yield of prepared barium carbonate powders is 55.23%, while the experimental yield is 54.98%. As a result, the model from RSM is considered to be accurate and reliable for predicting the yield of carbonate powders. The XRD patterns of BaCO₃ particles which were prepared by the homogeneous precipitation method are shown in Figure 6. This shows that the data of the diffraction peak obtained remain the same with the diffraction data of the orthorhombic structure of BaCO₃ (JCPDS card No. 05-0378), which illustrates that the product of barium carbonate prepared was a typical orthorhombic structure of BaCO₃.

Figure 6:

X-ray diffractionn (XRD) pattern of BaCO₃ particles prepared by the homogeneous precipitation method.