Method for the determination of polonium-210 in tea samples using response surface methodology (RSM)

NUCLEAR CHEMISTRY, RADIOCHEMISTRY, NUCLEAR MEDICINE

Method for the determination of polonium-210 in tea samples using response surface methodology (RSM)

Sermin Çam Kaynar，

Ümit H. Kaynar

Nuclear Science and Techniques

Vol.30, No.3

Article number 45

Published in print 01 Mar 2019

Available online 13 Feb 2019

DOI：10.1007/s41365-019-0567-5

32500

The method based on solvent parameters (mass, cycle of acidification, and autodeposition time), combined with response surface method (RSM) modelling and optimization, has been developed for maximizing ²¹⁰Po activity in tea samples, as observed by an alpha spectrometer. RSM based on 3-factor and 5-level composite center design (CCD) was used to obtain the optimal combination of solvent conditions. As solvent parameters for ²¹⁰Po activity, different masses (0.5, 0.75, 1, 1.5, and 2 g), different cycles of acidification (2, 3, 4, 5, and 6 times), and different autodeposition times (2, 3, 4, 5, and 6 h) were studied. The 3D response surface plot and the contour plot derived from the mathematical models were used to determine the optimal conditions. According to the obtained results, the experimental value of ²¹⁰Po activity was in good agreement (R² = 0.96) with the value predicted by the model. We found a favorable effect of mass on the ²¹⁰Po activity (p < 0.05).

210Po activityTeaResponse surface methodology.

1 Introduction

Environmental radiation arises from various naturally occurring and man-made sources [1]. The largest contribution to radiation exposure comes from natural sources (approximately ~86%), while man-made sources contribute only ~14%. Doses from other man-made or artificial sources account for less than 1% [2-3]. Among natural radionuclides, ²¹⁰Po (T_1/2, 138.4 d) from the ²³⁸U series, is significant due to its potential internal human radiation exposure. It is an alpha emitter with high linear energy transfer and exists in trace amounts in most plants and foodstuffs [4-5]. It is among the most radiotoxic nuclides to humans [4], and may be a cause of lung cancer [6].

Tea is one of the most widely consumed beverages in the world. It is consumed daily by many countries and is prepared from the Camellia sinensis leaves. Tea leaves are usually characterized by the increased contents radionuclide contaminants like ²¹⁰Pb, ²¹⁰Bi, and ²¹⁰Ро [7] because of the deposition of aerosols containing these radionuclides on tea leaves. There have been several studies related to radionuclides on various teas [2, 7-13]. Determination of the activity concentrations of radionuclides (primarily ²¹⁰Po) in tea remains important; therefore, we chose to determine ²¹⁰Po in tea samples.

This study was aimed to determine the optimum solvent parameters for the activity of ²¹⁰Po in tea samples using response surface methodology (RSM). The mass of the sample, cycle of acidification, and autodeposition time were analyzed using a central composed design (CCD).

2 Material and Method

2.1 Experimental Process

Tea samples were dried to constant weight at room temperature. Different masses (0.5, 0.75, 1, 1.5, and 2 g) were weighed and added to a 250 mL beaker. The concentrated acids (3 mL 65% HNO₃ + 5 mL 35% H₂O₂) were added to the sample and the beaker was covered with a watch glass and allowed to stand overnight at room temperature. Then, the solution was heated on a hotplate at 95 °C and evaporated to near dryness. Then, mixed acids (3 mL HNO₃ and 9 mL 37% HCl) were added to the precipitate followed by re-heating on the hotplate (at 95 °C) and evaporation to near dryness. The acidification process was repeted 2-6 times. After evaporation, 200 mL of 0.5 M HCl was added to the precipitate, and filtered through a filter paper (particle retention 10–15 µm, 125 mm diameter, 84 g m^-2 weight) into a 250 mL beaker. Ascorbic acid (0.5 g) was added to the beaker to reduce Fe³⁺ concentration.

Copper disks of diameter 2.5 cm were cut from a copper plate. They were first wiped with acetone and then left in 1 M HNO₃ for 1-2 m, washed with pure water, and dried at room temperature. The dried copper discs were placed inside a bottle cap with the front face cut out and were compressed with a magnetic bar to prevent it from falling. The prepared copper disks were placed in a 200 mL sample solution so that the magnetic bar portion was below. The autodeposition process was performed on a hotplate. ²¹⁰Po was spontaneously accumulated on the copper disc at the 70 °C (Fig. 1).

Fig. 1.

(Color online) Flow diagram of the entire process.

The activity of ²¹⁰Po was determined by using an alpha spectrometer equipped with A450-20AM PIPS detector. The energy resolution was ≤ 20 keV, the detector efficiency was ≥ 25%, and the background was ≤ 1 count per hour above 3 MeV. System calibration was done by using a ²⁴¹Am point source. The ²¹⁰Po activity concentration of the samples collected onto the copper disc was counted by using the alpha spectrometer based on the alpha particle emission peak with 5.30 MeV energy, and ²⁰⁹Po as the internal tracer. The ²¹⁰Po activity concentration was calculated at different autodeposition times on the copper disc. The chemical efficiency was 37.7% for ²⁰⁹Po. The ²¹⁰Po activity concentration for each sample was corrected for the recovery using the total efficiency.

2.2 Response Surface Methodology (RSM)

RSM is an effective method to solve multivariable problems and provides optimization of many dependent variables in various experiments. It involves mathematical and statistical techniques used to determine the optimum operating conditions in a given system or to determine how it is affected by the independent variables of one or more dependent variables in a region of interest [14-17]. Independent variables (X₁: sample mass, X₂: cycle of acidification, and X₃: autodeposition time) were examined on five levels. These variables and their coded levels of CCD design are given in Table 1.

Independent variables and their coded levels used for optimization.

Factors	Factor code	Range and levels (coded)
		-1.6818	-1	0	1	1.6818
Mass (g)	X₁	0.5	0.75	1	1.5	2
Cycle of acidification (times)	X₂	2	3	4	5	6
Autodeposition time (h)	X₃	2	3	4	5	6

The regression model equation was given as follows;

Y = b_{0} + \sum_{i = 1}^{2} b_{i} x_{i} + \sum_{i = 1}^{2} b_{i i} x_{i}^{2} + \sum_{i = 1}^{1} \sum_{j = i + 1}^{2} b_{i i} x_{i} x_{j} + ε,

(1)

where Y is the response, b₀ is the intercept, b_ij, b_ii, and b_i are the coefficients, n is the number of variables, x_i and x_j are the independent variables, and ε is the error. The optimum data of the chosen variable were found using RSM plots and the regression equation. The correlation coefficient (R²) was found to be high (0.96). The significance of the RSM model was evaluated for the probability value (Prob > F) and F-value. For this calculation, the second-order polynomial equation was as follows:

Y = b_{0} + b_{1} X_{1} + b_{2} X_{2} + b_{3} X_{3} = b_{11} X_{1}^{2} + b_{22} X_{2}^{2} + b_{33} X_{3}^{2} + b_{12} X_{1} X_{2} + b_{13} X_{1} X_{3} + b_{23} X_{2} X_{3}

(2)

The experiments were performed under optimum conditions obtained by RSM (Table 2). Initial studies were conducted to determine to the required mass (X₁: 0.5, 0.75, 1, 1.5, and 2 g), the cycle of acidification (X2: 2, 3, 4, 5 and 6 times), and autodeposition time (X₃: 2, 3, 4, 5, and 6 h). The total design consisted of 20 experimental points. The matrix of the design is listed in Table 2, and six replicates (runs 15-20) were performed at the center of the design.

Experimental design values for tea.

Runorder	X₁	X₂	X₃	Mass(g)	Cycleofacidification(HNO₃:HCl,3:9)	Autodepositiontime(h)	²¹⁰Poactivity(Bq)
							Experimental	Predicted
1	-1	-1	-1	0.75	3	3	0.049	0.049
2	-1	-1	1	0.75	3	5	0.042	0.038
3	-1	1	-1	0.75	5	3	0.050	0.042
4	-1	1	1	0.75	5	5	0.043	0.044
5	1	-1	-1	1.5	3	3	0.103	0.100
6	1	-1	1	1.5	3	5	0.088	0.095
7	1	1	-1	1.5	5	3	0.089	0.091
8	1	1	1	1.5	5	5	0.100	0.099
9	-1.6818	0	0	0.5	4	4	0.026	0.032
10	1.6818	0	0	2	4	4	0.126	0.122
11	0	-1.6818	0	1	2	4	0.071	0.070
12	0	1.6818	0	1	6	4	0.065	0.068
13	0	0	-1.6818	1	4	2	0.060	0.065
14	0	0	1.6818	1	4	6	0.066	0.063
15	0	0	0	1	4	4	0.072	0.069
16	0	0	0	1	4	4	0.076	0.069
17	0	0	0	1	4	4	0.06	0.069
18	0	0	0	1	4	4	0.069	0.069
19	0	0	0	1	4	4	0.069	0.069
20	0	0	0	1	4	4	0.069	0.069

Excel and Minitab 17 were used for graphical analysis and regression analysis of the acquired data. Analysis of variance (ANOVA) was done to obtain the probability and F-value. In addition, the statistical parameters were calculated with RSM, the optimum values were found from the regression equation and the RSM surface/counter plots.

3 Result and discussion

The second-order polynomial equation was obtained by CCD design for elucidating the relationship between the ²¹⁰Po activity and the three independent variables. According to the obtained results, quadratic model equality, giving the activity of ²¹⁰Po, was as follows:

\begin{array}{l} Y = 0.069 + 0.027 Mass(g) \\ -0 .0007 Cycle of acidification \\ -0 .0006 Autodeposition time (h) \\ +0 .003 Mass (g) \times Mass (g) \\ -0 .00094 Cycle of acidification \\ \times Cycle of acidification \\ -0 .002 Autodeposition time (h) \\ \times Autodeposition time (h) - 0 .0005 Mass (g) \\ \times Cycle of acidification + 0 .0013 Mass (g) \\ \times Autodeposition time (h) \\ +0 .0033 Cycle of acidification \\ \times Autodeposition time (h) . \end{array}

(3)

The synergistic and antagonistic influences were described with positive and negative parameters, respectively. For obtaining the statistical explanation of the above equation with t-test, second-order variance analysis of the response surface (ANOVA) was performed (Table 3). Since the obtained F-value was 28.79688, the experimental yields obtained by changing the factor levels were statistically meaningful at the 95% confidence limit. According to the results, the model was compatible where smaller the p-values (< 0.0001) indicated that the model was significant. R² of the second-order model calculated for the ²¹⁰Po activity (Bq) was very close to 1 (0.96), implying that the experimental data agreed with the values predicted by the model. The adjusted determination coefficient (Adj. R² = 0.93) was also close to 1.

Analysis of variance of the regression model for ²¹⁰Po activity.

ANOVA	Df	SS	MS	F	Probability F
Regression	9	0.009996828	0.001111	28.79688	0.00000542
Residual	10	0.000385722	0.0000386
Total	19	0.01038255

Multiple R² = 0.96 Adjusted R² = 0.93

The significance of each coefficient is given in Table 4, with an F-value and a p-value. The larger the F-values and the smaller the p-values, the more significant are the corresponding coefficients. The regression was statistically significant at p-values less than 0.05 and 0.01, as shown in Table 4. Thus, ²¹⁰Po activity was affected significantly by the parameters (X₁, X₁X_1, X₁X_3, and X₂X₃ (p < 0.05); the quadratic parameters (X₂, X₁₁, X_22, and X₁₂) were insignificant (p > 0.05).

Estimated regression coefficients, and the F and p values.

Regression	Coefficients	Standard error	F	p
Intercept	0.069118	0.002533004	27.28693	1.01 E-10*
X₁	0.026666	0.001680587	15.86729	2.03 E-08*
X₂	-0.00074	0.001680587	-0.43966	0.669536
X₃	-0.00058	0.001680587	-0.3446	0.73753
X₁X₁	0.002735	0.001635999	1.671513	0.125571
X₂X₂	-0.000094	0.001635999	-0.05734	0.955403
X₃X₃	-0.00186	0.001635999	-1.13788	0.2817
X₁X₂	-0.0005	0.002195797	-0.22771	0.824462
X₁X₃	0.00125	0.002195797	0.569269	0.581734
X₂X₃	0.00325	0.002195797	1.480101	0.169648

*: Significant (p < 0.05)

The plot of the predicted activity against the experimental ²¹⁰Po activity is given in Fig 2. The experimental activity values were distributed close to the straight line. This showed that the predicted values of the model were in good agreement with the experimental values. This is an evidence of the validity of the regression model. The regression coefficient calculated for the model was R² = 0.96 and it showed the agreement of the values obtained from the model with real values. ²¹⁰Po activity values obtained in this study for different cycles of acidification and different masses were positive.

Fig. 2.

Correlation of experimental and predicted activity of ²¹⁰Po.

Interaction plots for ²¹⁰Po activity are given in Fig. 3 and Fig 4. ²¹⁰Po activity (Bq) is increasing upon increasing the sample mass from 0.5 g to 2 g in Fig. 3 (c,d) and Fig 4. With variations in sample mass, cycle of acidification, and autodeposition time, ²¹⁰Po activity changed as follows: ²¹⁰Po activity increased with increasing sample mass (Fig. 3 (c, e)) and remained constant for different cycles of acidification and autodeposition times (Fig. 3 (a, b)). Fig. 3 (d) shows that with increasing autodeposition time, the ²¹⁰Po activity decreased for 2 cycles of acidification (blue line), remined unchanged for 4 cycles of acidification (red line), and increased for 6 cycles of acidification (green line). In Fig. 3 (d, f), the point of intersection of the lines for cycle of acidification and autodeposition time is 4. In other words, 4 cycles of acidification and 4 h of autodeposition time were found to be optimal for the activity.

Fig. 3

(Color online) Interaction plots for ²¹⁰Po activity. (a) Cycle of acidification and mass, (b) autodeposition time and mass, (c) mass and cycle of acidification, (d) autodeposition time and cycle of acidification, (e) mass and autodeposition time, (f) cycle of acidification and autodeposition time.

Fig. 4.

Main effects plot for ²¹⁰Po activity (Bq).

The combined effect of cycle of acidification and autodeposition time (h) is shown in Fig. 5. The maximum activity of ²¹⁰Po was determined to be 0.87 Bq at a sample mass of 1.25 g.

Fig. 5.

(Color online) Response surface graphs for interactions between investigating parameters (acidification and autodeposition time) of ²¹⁰Po activity.

Contour color map graphs of ²¹⁰Po activity (Fig. 6) showed the effects of the interactions between mass (X₁) and cycle of acidification (X₂) as well as that between mass (X₁) and autodeposition time (X₃) on the ²¹⁰Po activity. An increase in mass from 0.5 g to 2 g improved the activity yield. In addition, increasing the cycle of acidification and autodeposition time leads to a reduction in ²¹⁰Po activity. When more than 4 cycles of acidification were performed and the autodeposition time was more than 4 h, there was a reduction in activity. The maximum activity was obtained for 4 cycles of acidification and autodeposition time of 4 h. Thus, for the maximum activity result of the tea samples, optimal conditions were as follows: 1 g of the sample mass, 4 cycles of acidification, and 4 h of autodeposition time.

Fig. 6.

(Color online) Contour color map graphs for interaction of investigation parameters of ²¹⁰Po activity.

4 Conclusion

In this study, RSM was used to model and optimize the conditions for maximum ²¹⁰Po activity in tea samples. The effect of three independent variables (sample mass, cycle of acidification, and autodeposition time) on ²¹⁰Po activity was obtained by using RSM surface plot and contour plots. The optimal conditions for maximum ²¹⁰Po activity in tea samples were as follows: sample mass of 1 g, 4 cycles of acidification and autodeposition time of 4 h. The experimental activity values and the predicted activity values of ²¹⁰Po agree with each other. In brief, this study provides a new efficient method for determination of ²¹⁰Po activity in tea sample.

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