Influence of the Water Temperature on Direct

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2012 IEEE Nuclear Science Symposium and Medical Imaging Conference Record (NSS/MIC)

N39-5

Influence of the Water Temperature on Measurements of Rn-222 in Water by Liquid Scintillation Counting of Polycarbonates I. Dimitrova, S. Georgiev, K. Mitev, Member, IEEE, D. Pressyanov

Abstract—An approach for measurement of 222 Rn in water has been recently proposed, in which polycarbonate specimens are exposed in the water and are afterwards measured by either gamma-spectrometry, gross beta-counting or liquid scintillation counting (LSC) or etched for alpha tracks. One of the advantages of this approach is that the specimens could be exposed directly in the water source. However, the signal is influenced by the temperature of the water. This work presents results that demonstrate this temperature influence for the case of LSC measurement of the exposed polycarbonates. In addition, results for the values of the partition coefficient K (quantifying the solubility of 222 Rn from water to polycarbonate) and the diffusion length LD of radon in polycarbonate at temperatures which are typical for natural water sources are presented. Based on experimental results, polynomial functions are given that allow to estimate the values of K and LD for temperatures covering most of the range met in practice. These values could further be used to apply temperature corrections to the measurement signal for any of the above measurement techniques.

I. I NTRODUCTION EASUREMENTS of 222 Rn (radon) in water sources are part of the radiation protection of the public, since radon in water is one of the potential sources of radon in buildings. Taking into account the health threat that radon exposure poses, the Commission of the European Communities recommends monitoring radon activity concentration in water sources [1]. In addition, radon-in-water measurements are widely applied in hydrological studies of water basins, in which 222 Rn is used as environmental tracer [2]. A novel approach for measurement of 222 Rn in water has been recently proposed [3], in which polycarbonate samples (of Makrolon or equivalent material) are exposed in the water. Since these polycarbonates have a high absorption ability to radon, the activity absorbed inside them could be registered and used to determine 222 Rn activity concentration in the water. Different measurement techniques could be employed to register the activity in the exposed polycarbonates - gammaspectrometry or gross beta-counting [3], alpha-track etching [4] or liquid scintillation counting (LSC) [5]. The principles of this method for measurement of 222 Rn in water is illustrated in (Fig.1). The method could be applied either by exposure of polycarbonates in water samples or directly in the water

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Manuscript received November 16, 2012. This work is supported by the Bulgarian National Science Fund under grant DMU 03/14 (12.12.2011) ”NEMO”. I. Dimitrova, S. Georgiev, K. Mitev and D. Pressyanov are with the Sofia Univeristy ”St. Kliment Ohridski”, Faculty of Physics, Sofia 1164, Bulgaria (Tel.: ++ 359 2 8687009, e-mail: [email protected]fia.bg)

978-1-4673-2030-6/12/$31.00 ©2012 IEEE

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basin. Direct exposure of polycarbonates in the basin saves the need to take and transport water samples while avoiding radon losses and the need to bring specialized equipment on site. Another advantage is that polycarbonates could be used to monitor many points or depths in the basin simultaneously.

Fig. 1. Principle scheme of measurement of 222 Rn in water by polycarbonates. During exposure 222 Rn is absorbed in the specimen. The absorbed activity could be registered by gamma-spectrometry or gross beta-counting [3], etching for alpha tracks [4] and liquid scintillation counting (LSC) [5] of the exposed polycarbonates.

In our practice we have come to natural water basins and water sources with a wide range of temperatures (from a few to over 70◦ C). Both experiment and theoretical modeling have shown that the activity absorbed in the polycarbonate specimens during exposure is influenced by the temperature [6]. Therefore, the signal obtained when the specimens are measured is also influenced by the water temperature and it should be corrected to account for the different temperature. The aim of this work is to determine the values of the partition coefficient K (quantifying the solubility of 222 Rn from water to polycarbonate) and the diffusion length LD of radon in polycarbonate at different temperatures. These values could further be used to account for the temperature influence on the signal in a wide range of temperatures. II. M ETHOD AND M ATERIALS A theoretical model that describes the processes of sorption and desorption of radon in polycarbonates has been recently developed [6]. As shown in [6], the absorbed 222 Rn activity in a thin polycarbonate plate with thickness L and surface P , exposed for time texp in water with constant activity concentration CA is given by: A(t) = KCA L2D

∞ 8λP X 1 − e−λ2k+1 texp , L λ2k+1 k=0

(1)

constant of 222 Rn, λ2k+1 where λ is the  decay  2 (2k+1)πLD λ 1+ . The partition coefficient L

=

C

is defined as the ratio between the activity conK = pc(x=0+) CA centration of 222 Rn at the polycarbonate surface (Cpc(x=0+) ) p and in the water (CA ). The diffusion length LD = D/λ is defined as the average distance that radon atoms travel in the polycarbonate before they decay and is determined by the diffusion coefficient of radon in the polycarbonate D. Both K and LD depend on the temperature. In a previous work [7] values of the diffusion length of radon in polycarbonate LD were determined for temperatures in the range 5 - 38◦ C. To determine the value of LD at a temperature in the upper range of temperatures typical for water sources, dedicated experiment was conducted. Identical polycarbonate plates with thickness 290 µm were exposed at a temperature of 63◦ C in 2 L bottles to water with the same activity concentration of 222 Rn. The activity concentration of 222 Rn in the water was determined by gamma-spectrometry with HPGe detector and by LSC measurement. All plates were exposed for about 67 h, so that the absorbed activity is close to its maximum [5]. After the exposure they were left in air at 59◦ C and were measured by LSC. The LSC measurements were carried out by placing the polycarbonate piece inside the scintillation cocktail (ULTIMA GOLD LTT by Perkin Elmer) and using the total counting rate (alpha+beta). The measurement duration was less than 10 minutes in all cases. It has been shown that polycarbonate pieces are highly transparent to the cocktail light and that this approach allows fast and sensitive measurements [5]. The LSC measurements of the different polycarbonate plates were made at different moments in the first 72 hours after the exposure. Since all plates were the same, the measurements at different moments represent a follow-up of the signal after the exposure. As shown in [6], the 222 Rn activity in a thin polycarbonate plate at a moment t after the end of exposure, which lasted for time texp and was carried out in water with initial activity concentration CA that decays with time, is given by:

L =290µm were exposed at different temperatures T of 7.4 ◦ C, 17.1 ◦ C, 43.5 ◦ C and 63◦ C in water with known activity concentration of 222 Rn. After the end of exposure the plates were measured by LS counting in the way described above and the activity of the radon absorbed in them was determined. Then, for each plate exposed at one of the three lower temperatures, the found activity was divided by the activity absorbed in the plate exposed at 63◦ C. As it follows from Eq.2, the obtained activity ratios could be written as: K(T = Ti ) f (L, Ti ) A(Ti ) = , A(T63 ) K(T = T63 ) f (L, T63 )

(3)

where the function f (L, T ) = P∞ λtexp −e−λ2k+1 texp −λ2k+1 t L2D (T ) k=0 e e describes the λ2k+1 −λ distribution of the activity inside the plate. The value of f (L, T ) for each temperature was calculated by a computer code [9] based on the developed theoretical model using the values of the diffusion length LD at this temperature. Since the activities A(T ) were measured, the values of f (L, T ) were calculated and the value of K at T = 63◦ C was found in the previous experiment, the values of K at the other three temperatures could be found as: K(T = Ti ) = K(T = T63 )

A(Ti ) f (L, T63 ) . A(T63 ) f (L, Ti )

(4)

In the same experiment groups of polycarbonate plates with different thicknesses (250µm, 495µm, 580µm and 700µm) were also exposed and measured by LSC. Applying the approach described above to each group gave independent estimates for the values of K for each of the three temperatures (of 7.4 ◦ C, 17.1 ◦ C and 43.5 ◦ C). In this way, five values of K were found using plates with the five different thicknesses. There was a very good agreement (within 5 per cent) between the independent estimates of K for each of the three temperatures. Therefore, average values were used as final estimates of the partition coefficients of 222 Rn from water to polycarbonate for the above temperatures. III. R ESULTS

∞ X eλtexp − e−λ2k+1 texp −λ2k+1 t 2 8λP e . A(t) = KCA LD L λ2k+1 − λ k=0 (2) An algorithm developed in [8] allows to determine the values of K and LD by fitting the results for the activity in polycarbonate plates as a function of the time after the exposure with a function obtained from Eq.2 with a finite number of terms. In this way, the value of K for the temperature during the exposure and the value of LD for the temperature after the exposure could be determined. The algorithm was applied to the results of the LSC measurements of the exposed 290 µmthick plates and thus the values of K for 63◦ C and of LD for 59◦ C were determined. To determine the values of the partition coefficient K of 222 Rn from water to polycarbonate for other temperatures in the range met in practice, additional exposure experiment was conducted. Four polycarbonate plates with thickness

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The obtained value for the diffusion length of radon in polycarbonate at 59 ◦ C is LD =205.6±1.8µm (including only uncertainty due to the fit). In Fig.2 this result along with results for LD obtained in a previous work [7] are fitted with a second order polynomial function. The polynomial equation could be used to estimate LD for a given temperature in the range from 5◦ C to 59◦ C by interpolation. The obtained values of the partition coefficient K are given in Table I. In Fig.3 these values are fitted with a second order polynomial function, which could be used to estimate the values of K for the given temperature interval (from 7.4◦ C to 63◦ C) by interpolation. To test if the interpolation gives adequate results, the value of K for 25◦ C was calculated using the polynomial equation shown in Fig.3. The obtained value was K(T25 )=101 ± 27, while the partition coefficient determined for this temperature in a previous experiment was 100 ± 15 [10].

7.4◦ C 102.5 ± 9.6

K at temperature: 17.1◦ C 43.5◦ C 117.7 ± 10.5 80.7 ± 7.0

63◦ C 49.3 ± 3.4

120

T=25, K=101+/-16

110

TABLE I PARTITION COEFFICIENT K OF RADON FROM WATER TO POLYCARBONATE . T HE UNCERTAINTIES ARE GIVEN AT THE LEVEL OF 1σ.

100 90 80

K

70 60 50

Y =105.1+0.2860 X-0.0187 X

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Fig. 3. Polynomial fit of the experimentally determined values of K for different temperatures. The blue point marks a values obtained in an independent experiment [10], not included in the fit. The shown equation (for X = T and Y = K) could be used to interpolate and find K for a given temperature in the studied range.

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The polynomials shown in Fig.2 and Fig.3 could be used to estimate the values of the partition coefficient K and the diffusion lenght LD for most of the temperature range typical for natural water sources. Using these values, the absorbed 222 Rn activity inside a polycarbonate plate exposed directly in the water source could be estimated using the developed theoretical model [6] (see Eq.1). Moreover, the theoretical model allows to obtain the profile of the distribution of the 222 Rn activity inside the polycarbonate. Examples of activity distribution inside 290µm-thick polycarbonate plates exposed at the temperatures used in the conducted experiments are shown in Fig.4. As can be seen, for exposures at the two lower temperatures, at which LD is smaller, the activity is concentrated near the edges of the plate. In contrast, for exposures at the two higher temperatures the activity is more homogeneously distributed. However, the activity concentration at the borders of the polycarbonate is somewhat smaller for the higher temperatures, which is due to the smaller solubility. The calculation of the absorbed activity and its distribution could further be used to correct the signal obtained when the polycarbonate is measured by a specified method after the exposure. The correction should account for differences due to difference between the temperature of exposure in the water source and the temperature of exposure during the calibration. For some of the measurement techniques that could be applied, the measurement signal depends only on the activity inside the polycarbonate and not on its distribution (for example, gamma-spectrometry). However, for other techniques

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(like gross beta-counting and alpha-track etching) the signal depends on the activity distribution. Therefore, to apply a temperature correction for these techniques detailed profiles of the activity (like those shown in Fig.4) should be calculated. The algorithm used to calculate these profiles is described in Ref.[9].

5.00E-008

Activity per 1micron, Bq/ m

Fig. 2. Polynomial fit of the values of LD for different temperatures - all values except this at 59◦ C are determined in a previous work [7]. The shown equation (for X = T and Y = LD ) could be used to interpolate and find LD for a given temperature in the studied range.

T=63 oC (L D =232 m)

T=43.5 oC(L D =122 m)

T=18 oC (L D =49.5 m)

T=7.4 oC(L D =42.4 m)

4.00E-008

3.00E-008

2.00E-008

1.00E-008

0.00E+000 0

50

100

150

200

250

d (depth), m

Fig. 4. Profiles of the activity of 222 Rn absorbed inside a 290µm-thick polycarbonate plate, exposed to water with 1 Bq/l activity concentration of 222 Rn. The profiles at different temperatures are obtained by a computer code [9] using the experimental values of K and LD . The profiles allow to apply temperature corrections to measurements of222 Rn in water by polycarbonates exposed directly in the source.

For the case of LSC measurement of the polycarbonates, the influence of the signal on the temperature to which the polycarbonates are exposed in the water could be seen, if the sensitivities S of the LSC measurement are compared. For measurement of 222 Rn in water by LSC of polycarbonates

sensitivity S is defined as [5]:

[2]

n , (5) CA where n is the net counting rate and CA is the activity concentration of 222 Rn in the water at the beginning of exposure. In Table II the obtained sensitivities S for plates with thickness 250 µm and 700 µm are given. The values are determined for the moment of placing the polycarbonates in the vial with LS cocktail - for a given later moment t, S could be found by multiplying by e−λ222 t . As shown in Ref.[5] and confirmed by this experiment, the measurement efficiency (alpha+beta) stays constant with time and therefore the total counting rate changes only due to 222 Rn decay (not shown). The given sensitivities are valid for exposure in 2 L bottles at decaying ambient activity of 222 Rn and for the particular LS counter used. As seen in Table II, S is strongly dependent on the temperature of exposure and this should be accounted for, in order to obtain correct measurement results. S=

PC thickness 250 µm 700 µm

S (cpm/Bq.l−1 ) at temperature: 7.4◦ C 17.1◦ C 43.5◦ C 63◦ C 0.62 0.78 1.23 1.02 0.62 0.83 1.41 1.63

TABLE II S ENSITIVITIES OF MEASUREMENTS OF 222 R N IN WATER BY LSC OF POLYCARBONATES . T HE RELATIVE UNCERTAINTY OF S IS ABOUT 5% ( AT 1σ LEVEL ), DUE MAINLY TO THE UNCERTAINTY OF THE ACTIVITY w. CONCENTRATION OF 222 R N IN THE WATER CA

IV. C ONCLUSIONS Values of the partition coefficient K of 222 Rn from water to polycarbonate for temperatures in the range 7 - 63◦ C are determined. The value of the diffusion length LD of 222 Rn in polycarbonate for temperature of 59◦ C is also determined. Polynomial functions are given, which could be used to estimate K and LD for most of the water sources’ temperatures met in practice. The values of K and LD could further be used to apply temperature corrections to measurements of 222 Rn in water by exposure of polycarbonates directly in the water basin. Corrections could be derived for measurements of the exposed polycarbonates by LSC, gamma-spectrometry, gross-beta counting and alpha-track etching of the exposed polycarbonates. ACKNOWLEDGMENT I. Dimitrova and S. Georgiev thank to 2012 NSS MIC Conference Committee for the ”Valentin T. Jordanov Radiation Instrumentation Travel Grant” and the ”Trainee Grant” awarded. R EFERENCES [1]

Commission of the European Communities, Document number C(2001) 4580, OJ L 344, 28.12.2001, 85

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C. G. Smith, P. W. Swarzenski, N. T. Dimova, J. Zhang, in Handbook of Environmental Isotope Geochemistry, Advances of Isotope Geochemistry Part 2, Springer-Verlag (2011) 345 [3] D. Pressyanov, I. Dimitrova, S. Georgiev, E. Hristova, K. Mitev, Nucl. Instr. and Meth. A, 574 (2007) 202 [4] I. Dimitrova, K. Mitev, D. Pressyanov, S. Georgiev, T. Boshkova Radiat. Meas., 46 (2011) 119 [5] K. Mitev, I. Dimitrova, V. Zhivkova, S. Georgiev, G. Gerganov, D. Pressyanov, T. Boshkova, Nucl. Instr. and Meth. A, 677 (2012) 31 [6] D. Pressyanov, K. Mitev, S. Georgiev, I. Dimitrova, Nucl. Instr. and Meth. A, 598 (2009) 620 [7] D. Pressyanov, Health Phys., 97(6) (2009) 604 [8] D. Pressyanov, S. Georgiev, I. Dimitrova, K. Mitev, T. Boshkova, Radiat. Prot. Dosim., 145(2-3) (2011) 123 [9] S. Georgiev, K. Mitev, D. Pressyanov, I. Dimitrova, T. Boshkova, Radiat. Meas., 47 (2012) 303 [10] D. Pressyanov, K. Mitev, I. Dimitrova, S. Georgiev, Nucl. Instr. and Meth. A, 629 (2011) 323