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

Sermin ?am Kaynar·ümit H.Kaynar

Abstract The method based on solvent parameters(mass,cycle of acidification,and autodeposition time),combined with response surface methodology(RSM)modeling 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 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).

Keywords 210Po activity·Tea·Response 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(T1/2,138.4 d)from the238U 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 of radionuclide contaminants like210Pb,210Bi,and210Po[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(primarily210Po)in tea remains important;therefore,we chose to determine210Po in tea samples.

This study was aimed to determine the optimum solvent parameters for the activity of210Po 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 hot plate at 95°C and evaporated to near dryness.Then,mixed acids(3 mL HNO3and 9 mL 37%HCl)were added to the precipitate followed by re-heating on the hot plate(at 95°C)and evaporation to near dryness.The acidification process was repeated 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-2weight)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 HNO3for 1–2 m,washed with pure water,and dried at room temperature.The dried copper disks 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 hot plate.210Po was spontaneously accumulated on the copper disk at the 70°C(Fig.1).

The activity of210Po was determined by using an alpha spectrometer equipped with a 450-20 AM 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 a241Am point source.The210Po activity concentration of the samples collected onto the copper disk was counted by using the alpha spectrometer based on the alpha-particle emission peak with 5.30 MeV energy,and209Po as the internal tracer.The210Po activity concentration was calculated at different autodeposition times on the copper disk.The chemical efficiency was 37.7%for209Po.The210Po 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 acidi fication,and X3:autodeposition time)were examined on five levels.These variables and their coded levels of CCD design are given in Table 1.

The regression model equation was given as follows:

where Y is the response,b0is the intercept,bij,bii,and biare the coefficients,n is the number of variables,xiand xjare 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 signi ficance 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:

Fig.1(Color online)Flow diagram of the entire process

Table 1 Independent variables and their coded levels used for optimization

The experiments were performed under optimum conditions obtained by RSM(Table 2).Initial studies were conducted to determine 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.

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 Results and discussion

The second-order polynomial equation was obtained by CCD design for elucidating the relationship between the210Po activity and the three independent variables.According to the obtained results,quadratic model equality,given the activity of210Po,was as follows:

Table 2 Experimental design values for tea

Table 3 Analysis of variance of the regression model for 210Po activity

Table 4 Estimated regression coefficients and the F and p values

The synergistic and antagonistic in fluences 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 the smaller p values(＜0.0001)indicated that the model was signi ficant.R2of the second-order model calculated for the210Po activity(Bq)was very close to 1(0.96),implying that the experimental data agreed with the values predicted by themodel.The adjusted determination coefficient(Adj.R2=0.93)was also close to 1.

Fig.2 Correlation of experimental and predicted activity of 210Po

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 acidi fication and autodeposition time

Fig.4 Main effects plot for 210Po activity(Bq)

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,X1X1,X1X3,and X2X3(p＜0.05);the quadratic parameters(X2,X11,X22,and X12)were insignificant(p＞0.05).

Fig.5(Color online)Response surface graphs for interactions between investigating parameters(acidification and autodeposition time)of 210Po activity

The plot of the predicted activity against the experimental210Po activity is shown 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.6(Color online)Contour color map graphs for the interaction of investigation parameters of 210Po activity

Interaction plots for210Po activity are shown in Figs.3 and 4.210Po activity(Bq)increased upon increasing the sample mass from 0.5 to 2 g as shown in Figs.3c,d and 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.3c,e)and remained constant for different cycles of acidification and autodeposition times(Fig.3a,b).Figure 3d shows that with increasing autodeposition time,the210Po activity decreased for 2 cycles of acidification(blue line),remained unchanged for 4 cycles of acidification(red line),and increased for 6 cycles of acidification(green line).In Fig.3d,f,the point of intersection of the lines for the 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.

The combined effect of cycle of acidification and autodeposition time(h)is shown in Fig.5.The maximum activity of210Po was determined to be 0.87 Bq at a sample mass of 1.25 g.

Contour color map graphs of210Po 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 the210Po activity.An increase in mass from 0.5 to 2 g improved the activity yield.In addition,increasing the cycle of acidification and autodeposition time leads to a reduction in210Po 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.

4 Conclusion

In this study,RSM was used to model and optimize the conditions for maximum210Po activity in tea samples.The effect of three independent variables(sample mass,cycle of acidification,and autodeposition time)on210Po activity was obtained by using RSM surface plot and contour plots.The optimal conditions for maximum210Po 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 of210Po agree with each other.In brief,this study provides a new efficient method for the determination of210Po activity in tea sample.