Modeling response of radon track detectors with solid absorbers as radiators

Radiation Measurements 46 (2011) 357e361

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Modeling response of radon track detectors with solid absorbers as radiators Dobromir S. Pressyanov* Faculty of Physics, St. Kliment Ohridski University of Sofia, 5 James Bourchier Blvd., 1164 Sofia, Bulgaria

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 July 2010 Received in revised form 11 January 2011 Accepted 16 January 2011

Recently, a new radon monitor, based on the combination of plastic radon absorber/radiator and an alpha-track detector, has been proposed. In this report a theoretical model of its response is described. The modeling is performed for two widely used track detectors: CR-39 and Kodak Pathe LR-115 type II. Theoretical estimates of the response for various designs of such monitors are obtained and comparison with available experimental data is made. The results demonstrate the feasibility of this approach for practical applications. Ó 2011 Elsevier Ltd. All rights reserved.

Keywords: 222 Rn Plastic absorbers Alpha-tracks Theoretical model Track detector

1. Introduction A new direction in radon detection methodology was introduced in the last decade. It employs radon absorption in proper plastic materials. In the first successful developments the high radon absorption ability of bisphenol-A polycarbonates (trade names Makrolon,1 Makrofol,1 Lexan,2 etc.) was combined with their track etch properties (Pressyanov et al., 1999, 2000). On this basis a method for retrospective measurements based on home stored CDs/DVDs has been proposed (Pressyanov et al., 2001), studied (Pressyanov et al., 2003) and applied (Pressyanov et al., 2010). An alternative design of absorption-based radon monitors has been proposed recently (Tommasino et al., 2009). In this approach the plastic absorber serves as a radiator and is coupled in contact with an external alpha-track detector. This design can complement both the traditional track-detector-based radon monitors and the above mentioned polycarbonate method. However, substantial experimental and theoretical work will be necessary to study the properties and prospective applications of this new approach. Recently, a theoretical model that describes the properties of conventional polycarbonate detectors e (e.g. CDs/DVDs) has been developed (Pressyanov, 2009). A similar approach can be used to model the response of monitors proposed by Tommasino et al. * Tel./fax: þ359 2 8687009. E-mail address: [email protected]fia.bg. 1 Makrofol and Makrolon are trademarks of Bayer; Makrofol is the brand name for thermoplastic films made from the polycarbonate Makrolon. 2 Lexan is a trademark of ‘SABIC Innovative Plastics’. 1350-4487/$ e see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.radmeas.2011.01.007

(2009) in which the radon absorber (Tommasino and Tommasino, 2008) serves as a radiator for an external alpha-track detector. Such model can be helpful to study the characteristics and/or limitations of this radon detection mode. In this report a theoretical model of the response of these monitors is described. Results for two ‘source geometries’ and for two of the most widely used alphatrack detectors: CR-39 and Kodak Pathe LR-115 type II are presented. Theoretical estimates are compared with experimental data published by Tommasino et al. (2009) and potential applications are discussed. 2. Theoretical model 2.1. Source geometry Once radon atom is catched by a surface trap it further diffuses through the absorber volume. In the present report we consider gas penetration from the both sides of the plate plastic radiator. This case can be considered as common, as the detector is in not hermetic contact with the absorber and radon penetrates freely through the small gap between the detector and absorber. As previously shown (Pressyanov, 2009) the equilibrium profile in plate absorber for such case is given by the expression:

c1 ðxÞ ¼ Kc½Aexpðx=LD Þ þ Bexpðx=LD Þ;

(1)

pffiffiffiffiffiffiffiffiffi where x is the depth beneath the surface, LD ¼ D=l is the diffusion length of 222Rn in the absorber material, c1 is atom concentration of 222Rn in the absorber material, c is its ambient

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Therefore, in modeling we have approximated this profile with ‘homogenious radon distribution’. The model was applied for the two source geometries that correspond to M-absorber and Cabsorber concentration profiles. 2.2. Detector response

Fig. 1. Concentration profile of the absorbed 222Rn in a plate bisphenol-A polycarbonate M-absorber of thickness 80 mm. The concentration profile is shown at 3 different temperatures: 5  C, 23  C and 38  C.

concentration. The solubility is represented by the partition coefficient K (dimensionless), defined as the ratio of the concentrations in the polycarbonate at its surface and the ambient concentration. The constants A and B are (Pressyanov, 2009):

A ¼

expðL=LD Þ  1 ; expðL=LD Þ  expðL=LD Þ

B ¼

1  expðL=LD Þ ; expðL=LD Þ  expðL=LD Þ

(2)

where L is the thickness of the absorber. This concentration profile is valid for ‘monolithic absorber’ (M-absorber) (Fig. 1). However, Tommasino et al. (2009) have proposed also use of composite absorbers (C-absorbers): a stack of several thin (20 mm) absorber foils stuck together but so that radon can diffuse freely between them. In this case the concentration profile in a single sheet is given by Eqn. (1) but the resultant profile in a C-absorber is stuck by individual profiles as shown in Fig. 2. For 80 mm C-absorber of 4  20 mm thick absorber foils the maximum deviation of the real concentration profile from the homogenious one was within 3%.

Fig. 2. Concentration profile of the absorbed 4  20 mm polycarbonate foils at 23  C.

222

Rn in a plate C-absorber e a stack of

Detection properties of an alpha-track detector are described by the ‘response function’ of the detector. The response function QðE; qÞ is 1 e if alpha-tracks appear for alphas of energy E and incident angle q, and 0 e otherwise. The modeling was performed for two kind of detectors: Kodak Pathe LR-115/II and CR-39. The detectors LR-115 are routinely used in the laboratory of the author, and the response function obtained in our past research (Ginev, 1996) was used. For modeling response of CR-39 the response function described by Barillon (1994) was used. Alpha-tracks related to 222Rn are formed by 3 alpha emitting isotopes: 222Rn, 218Po and 214Po (always in equilibrium with 214Bi). The concentration profile of 218Po and 214Po is the same as that of 222 Rn as decay atoms stay immobilized in the solid matrix. The detection geometry e absorber þ detector in contact with its surface is shown in Fig. 3. In the present model we will assume that tracks are formed only by alpha particles that originate from the interior of the absorber. This corresponds to the physical reality when: (1) The absorber is sufficiently thick, so the alphas from the front space and from the radon progeny plate-out on the front surface cannot create tracks. For example with LR-115/II detectors this is ensured by 50 mm thick polycarbonate absorber and with CR-39 by 80 mm. (2) The gap between the detector and the back surface of the absorber (Fig. 3) is very small (e.g. of the order of micrometers) so the plate-out on the surfaces there can be neglected. The number of alpha particles emitted in a small volume DV that hit a small spot of area DS of the detector surface per unit time is:

dN_ i ¼

DScosq li ci dV; 4pr 2

(3)

where li are the decay constants, ci are the atom concentrations of 222 Rn and 222Rn progeny in the absorber material, and i ¼ 1,2,3 refer to 222Rn, 218Po and 214Po, respectively. However, the tracks are

Fig. 3. Geometry of the irradiation by alpha particles of a detection spot DS. The critical angle qc is the maximum incident angle at which etched tracks can be revealed.

D.S. Pressyanov / Radiation Measurements 46 (2011) 357e361

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etched only for these E, q for which Q ¼ 1. Therefore, the partial track-density rate is:

cosq ai QðE; qÞdV; 4pr 2

dn_ i ¼

(4)

where ai ¼ li ci is the activity concentration of the i-th isotope. Under radioactive equilibrium a1 ¼ a2 ¼ a3 . Taking into account Eqn. (1) with M-absorber, the partial track density for exposure time Texp is:

ZTexp Z

cosq ai QðE; qÞdVdt 4pr 2

ni ¼ V

0

Z

¼ KI0 fr;qg

cosq ½Aexpðx=LD Þ þ Bexpðx=LD ÞdV; 4pr 2

(5)

where fr; qg is the partial volume from which the alpha particles can hit the detection spot so the etched track will be revealed and RT I0 ¼ 0 exp a dt is the integrated ambient 222Rn activity concentration. To take the integral note that the air gap between the detector and the absorber is considered as negligible and x ¼ rcosq:

Fig. 4. Lower RL and upper RU threshold ranges as dependent on the incident angle q for detector Kodak Pathe LR-115/II. At any q the detection window is between RL and RU.

    Zqc rZ2 ðqÞ  rcosq rcosq Aexp  þ Bexp LD LD

For the case of absorber with homogeneous concentration profile (suitable for C-absorber) one can obtain by analogous procedure:

1 ni ¼ KI0 2

r1 ðqÞ

0

 sinqcosq dqdr:

ð6Þ

Physically, the meaning of the distances r1, r2 is that the alpha particle of energy Ei, emitted from a distance in the interval (r1, r2) arrives at the detection point with energy within the detection window, e.g. within the interval (EL, EU). Let RU(q) and RL(q) are the alpha particles ranges corresponding to the energy at the upper (EU(q)) and lower (EL(q)) energy threshold for detection at this angle q. For detectors Kodak Pathe LR-115/II always RU ðqÞ  Ri , where Ri is the range of alpha particles from the i-th isotope. In such case r2 ðqÞ ¼ Ri  RL ðqÞ and r1 ðqÞ ¼ Ri  RU ðqÞ. However, for CR-39 detectors there are angles (q < qi) for which RU ðqÞ > Ri . In this case r1 ¼ 0. The range-energy dependence of (ICRU, 1993) has been used, along with the response function for the corresponding detector to obtain the functions RL ðqÞ and RU ðqÞ. For illustration, RL ðqÞ and RU ðqÞ for Kodak Pathe LR-115/II and absorber of Makrofol are shown in Fig. 4. Response to radon is described in terms of ‘calibration factor’ (CF, CF ¼ net track density/integrated 222Rn activity concentration). According to the above model, the CF is given as follows: CF ¼ CF1 þ CF2 þ CF3 , where, for the case of M-absorber:

1 CFi ¼ K 2

Zqc rZ2 ðqÞ  0

r1 ðqÞ

    rcosq rcosq Aexp  þ Bexp LD LD

 sinqcosq dqdr ¼

1 KL J ; 2 Di

ð7Þ

where:

1 CFi ¼ K 2

Zqc rZ2 ðqÞ r1 ðqÞ

0

¼

1 K 2

drsinqcosqdq ¼

Zqc

1 KH 2 i

½r2 ðqÞ  r1 ðqÞ sinqcosq dq

0 8 > Zqc Zqi < 1 ¼ K ½Ri  RL ðqÞsinqcosq dq þ ½RU ðqÞ 2 > : 0

9 > =  RL ðqÞsinqcosq dq : > ;

qi

ð9Þ

The Eqns. (8) and (9) are presented in a general form, suited for CR-39. To use them for modeling LR-115/II response, one should substitute qi h 0. The values of Ji (dimensionless) and Hi (dimension of length) have been numerically calculated for the corresponding detectors. This way, the CF for M-absorber was: CF ¼ KLD J=2, where ðJ ¼ J1 þ J2 þ J3 Þ and for C-absorber: CF ¼ KH=2, where ðH ¼ H1 þ H2 þ H3 Þ. The obtained CF is in units of length (e.g. mm if LD or H are expressed in mm). To obtain it in more common units, say cm2 kBq1 h1 m3 one can use the expression:

  CFðmmÞ CF cm2 kBq1 h1 m3 ¼ : 2778

(10)

        Zqi   Zqc  Ri  RL ðqÞ Ri  RL ðqÞ R  RU A 1  exp  þ B exp sinq dq þ Ji ¼ cosq cosq  1 A exp  i cosq LD LD LD qi

0

  exp 

    Zqc  R  RL R  RU sinq dq þ sinq dq: B exp i cosq  exp i cosq LD LD



Ri  RL cosq LD

qi

ð8Þ

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D.S. Pressyanov / Radiation Measurements 46 (2011) 357e361

3. Results and discussion The model needs values of the input parameters K and LD for the material of the absorber. The material for which these quantities were studied in more detail is bisphenol-A type of polycarbonate (Pressyanov, 2009). Therefore, the response of detectors with this material as an absorber has been modeled. We have modeled CF both for M- and C-absorbers at different temperatures, using the data for K and LD provided elsewhere (Pressyanov, 2009). Fig. 5 illustrates the obtained results for M-absorber (80 mm) and Fig. 6 for C-absorber (4  20 mm). The response of radon monitors that employ radon absorption in proper materials depends on the temperature (Pressyanov et al., 2004). The temperature dependence is via K and LD for M-absorber, but only via K for C-absorber with homogenious concentration profile. As seen in Figs. 5 and 6 the temperature influence is more pronounced with CR-39 detectors. If the detectors are used close to the room temperature (e.g. 20  5  C), the temperature bias is less than 10%. Regarding other environmental factors (e.g. pressure, humidity, dust and cigarette smoke), provisionally we may transfer the conclusions from the elaborate studies of their influence to the conventional polycarbonate method (Pressyanov et al., 2003, 2004) and to suppose minor effect. The value of K for the studied polycarbonate material at room temperature (20  C) is about 25 (Pressyanov, 2009). The sensitivity can be improved by using materials with higher K. In their report Tommasino et al. (2009) have announced use of material with K ¼ 40. For (4  20 mm) C-absorber the authors have reported experimental CF ¼ 0.40  0.05 cm2 kBq1 h1 m3 (for illustration: this corresponds to net track density of 86 cm2 for 3 mo exposure at 100 Bq m3). For this K our model estimate is CF ¼ 0.33  0.04 cm2 kBq1 h1 m3. We consider this as a reasonable agreement, taking into account that the used in our report CR-39 response function and track-counting mode can be somewhat different from that in experiments presented in (Tommasino et al., 2009). This is the first comparison between theory and experiment. The results suggest that the model provides feasible results. Another modeled dependence was that of the sensitivity with M-absorber on the thickness of the absorber. The results are shown in Fig. 7. It is interesting to note that, at thickness 300 mm the sensitivity becomes practically constant.

Specific feature in applications of the polycarbonate method is that after the end of exposure to radon, the detectors should be left for some time to degas. With absorbers of thickness 300 mm more than a week is needed. This is essential for short exposure times (e.g. days) and may hamper applications with short esposures. The radon monitors that are modeled in the present report give an opportunity for flexible design. The time for desorption depends on the thickness of a single sheet of the absorber e e.g. the desorption from 4  20 mm C-absorber will be much faster than from 80 mm Mabsorber. To model this process we have used the theoretical model of the desorption process, described elsewhere (Pressyanov et al., 2009). As an estimate for the time necessary for the effectively full desorption, we have used the time T0.01 for which the absorbed activity decreases 100 times, due to the combined effect of decay and out-gasing. The dependence of T0.01 on the thickness of the polycarbonate foils at different temperatures is shown in Fig. 8. As an example: at 23  C this time for 80 mm M-absorber is about 4

Fig. 5. Calibration factor for CR-39 and LR-115/II detector with M-absorber of thickness 80 mm at different temperatures.

Fig. 7. Calibration factors for the studied detectors as dependent on the thickness of M-absorber.

Fig. 6. Calibration factor for CR-39 and LR-115/II detector with C-absorber of thickness 80 mm at different temperatures.

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4. Conclusion In this report a theoretical model is developed and used to study the detection characteristics of recently proposed radon film badges in which solid radon absorbers/radiators are combined with an external alpha-track detector. The analytical scheme of the model is presented in abstract form suitable for the general case, but numerical results are obtained for polycarbonate radiators and detectors CR-39 and Kodak Pathe LR-115/II. The sensitivity and response at different temperatures, as well as the dependence of the response on the absorber thickness were modeled. The possibility for flexible design in respect to the time needed for desorption is demonstrated. Comparison with experimental results for CR-39 detector (Tommasino et al., 2009) shows a good agreement. We conclude that the proposed model can be useful for design of a new generation of radon monitors - film badges with solid radiators, and for interpretation of their results. Acknowledgments Fig. 8. The time for decrease (decay þ desorption) of the absorbed activity to 1% of its initial value, as dependent on the absorber thickness at 3 different temperatures.

This work was supported by the Scientific Research Fund of St. Kliment Ohridski University of Sofia.

days, while for 4  20 mm C-absorber is about 7 h. If the arrangement is 8  10 mm this time will be less than 2 h e e.g. comparable to the time necessary the short-lived 222Rn progeny plate-outed on the surface or generated by the absorbed 222Rn to decay. At this step one can only speculate about the possible applications of these new techniques. As pointed out by Tommasino et al. (2009) the radon film badges, consisting of absorber/radiator þ alpha-track detector present the opportunity to create new generation of radon monitors. They offer sensitivity that is between the sensitivity of the traditional diffusion chambers and the convential version of the polycarbonate method. The CF with this kind of monitors, obtained by modeling and experiments is in the range 0.03e0.4 cm2 kBq1 h1 m3. For comparison with CDs at 80 mm depth we have obtained CF of about 0.02 cm2 kBq1 h1 m3 (Pressyanov, 2009) and with diffusion chambers used by the author, with LR-115/II detectors, CF ¼ 1.97 cm2kBq1h1m3 (Picolo et al., 2000). We feel that 222Rn monitors with external absorber/ radiator can complement successfully the conventional polycarbonate method and the traditional diffusion chambers. Although less sensitive than some diffusion chambers, they offer many useful qualities e e.g. unique compactness, desired response sensitivity, possibility to use in hostile environment etc. However, to reveal the potential for applications a great deal of research and development work will be required. The results in the present report demonstrate the feasibility of the proposed theoretical model. Such modeling can be useful in the forthcoming new developments both on the stage of design of radon monitors and optimization of their characteristics, and at the stage of interpretation of the obtained results.

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