Dimitrios Nikolopoulos^{1*}, Sofia Kottou^{2}, Ermioni Petraki^{1,3}, Efstratios Vogiannis^{4} and Panayiotis H.Yannakopoulos^{1}  
^{1}Department of Electronic Computer Systems Engineering, TEI of Piraeus, Greece, Petrou Ralli & Thivon 250, GR122 44, Aigaleo, Greece  
^{2}Medical Physics Department, Medical School, University of Athes, Mikras Asias 75, GR11527, Goudi, Greece  
^{3}Department of Engineering and Design, Brunel University, Kingston Lane, Uxbridge, Middlesex UB8 3PH, London, UK  
^{4}Evangeliki Model School of Smyrna, Lesvou 4, GR17123, Greece  
Corresponding Author :  Dimitrios Nikolopoulos Department of Electronic Computer Systems Engineering TEI of Piraeus, Greece, Petrou Ralli & Thivon 250 GR122 44, Aigaleo, Greece Tel: +00302105381560 Mobile: +00306977208318 Fax: +00302105381436 Email: [email protected]; [email protected] 
Received March 29, 2014; Accepted May 22, 2014; Published May 24, 2014  
Citation: Nikolopoulos D, Kottou S, Petraki E, Vogiannis E, Yannakopoulos PH. (2014) Response of CR39 Polymer RadonSensors via MonteCarlo Modelling and Measurements. J Phys Chem Biophys 4:144. doi:10.4172/21610398.1000144  
Copyright: © 2014 Nikolopoulos D, et al. This is an openaccess article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. 
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International studies of radon indoors and in workplaces have shown significant radiation dose burden of the general population due to inhalation of radon (222Rn) and its shortlived progeny (218Po,214Pb, 214Bi, 214Po). As far as atmospheric radon concerns, 222Rn, is not necessarily in equilibrium with its shortlived progeny. For this reason, radon’s equilibrium factor F was solved graphically as a function of the track density ratio R=TB/TR, namely of the ratio between the recordings of cuptype and bare CR39 detectors. TB was computed through special MonteCarlo codes which were implemented for the calculation of the efficiency of bare CR39 polymers, regarding their ability in sensing the alpha particles emitted by the decay of radon and its shortlived progeny. For a realistic approach, MonteCarlo inputs were adjusted according to actual experimental concentration measurements of radon, decay products and F of Greek apartment dwellings. Concentration measurements were further utilized for the calculation of the unattached fraction, fp, in terms of Potential Alpha Energy Concentration (PAEC, defined as the sum of the initial  per volume  energies of all alpha particles emitted due to the decay of radon and its shortlived progeny that are present within a certain amount of air). This was employed for the calculation of F in terms of ratio (A4/A0), where Ai represents the activity concentration of radon (i=0) and 214Po (i=4) respectively. Measured and calculated values of F were plotted versus R. The results were fitted and checked with model’s predictions.
Introduction 
Radon (^{222}Rn) is a naturally occurring radioactive gas generated by the decay of radium (^{226}Ra) which is present in soil, rocks, building materials and waters [1]. Following the decay of radium, a fraction of radon emanates and migrates through diffusion and convection. After migrating, part of radon escapes to the atmosphere and waters, and, disintegrates to a series of shortlived decay products (progeny) (^{218}Po, ^{214}Bi, ^{214}Pb and ^{214}Po). Outdoor concentrations of radon and progeny are low (in the order of 10 Bq.m^{3}). On the other hand, indoor concentrations are accumulated, as a result of geological and meteorological parameters, ventilation, heating, water use and building materials [1]. Due to indoor accumulation, radon and progeny are recognised as the most significant natural source of human radiation exposure [1] and the most important cause of lung cancer incidence except for smoking [1]. 
Radon and its shortlived progeny disintegrate through a and bdecay. In specific ^{222}Rn undergoes adecay with λ0=2.093x10^{6} s^{1}, ^{218}Po adecay with λ_{1}=3,788x10^{3} s^{1}, ^{214}Pb bdecay with λ_{2}=4.234x10^{3} s^{1}, ^{214}Bi bdecay constant with λ_{3}=5.864x10^{4} s^{1} and ^{214}Po adecay with λ_{4}=4,234x10^{3} s^{1} [1,2]. In indoor environments ^{222}Rn, is not necessarily in equilibrium with its shortlived progeny and for this reason the equilibrium factor F serves as a fare compromise for identifying the status of equilibrium between parent ^{222}Rn and remaining shortlived progeny [1,2]. Continuous measurement of F is timeconsuming and requires active instruments. Hence the timeintegration of F prerequisites special apparatus and may not be easily employed in largescale surveys. For this reason, several researchers investigated combined uses of bare and cupenclosed Solid State Nuclear Track Detectors (SSNTDs) for longterm estimation of F [28]. This paper reviews the theoretical aspects of the topic and formulates an new approximation based MonteCarlo simulation, actual measurements and related published data. The paper addresses issues of relating recordings of bare CR39 SSNTDs with those of calibrated cuptype dosimeters 
Theoretical aspects 
Radon’s equilibrium factor, F, is defined as the ratio of the equilibrium equivalent concentration of radon (A_{e}) over the actual activity concentration of radon in air (A_{0}), namely [1]: 
(1) 
Equilibrium equivalent concentration is determined by the following equation [1,914] 
(2) 
and hence 
(3) 
Superscripts a and u distinguish the contribution of each one of the two states of radon progeny (attached, unattached), subscripts 1,2 and 3 correspond to ^{218}Po, ^{214}Pb and ^{214}Bi and A_{0}, (x=a,u and i=1,2,3) (Bq.m^{3}) represent measured concentrations of radon and progeny respectively. 
Assuming radioactive disintegration, ventilation and deposition as the sole processes of removal of radon progeny in ambient air, (x=a,u and i=1,2,3) can be calculated as [2,3]: 
(4) 
Parameter d_{j} reported by Faj and Planninic [3] can be expressed as 
(5) 
Where λ_{v} represents the ventilation rate, λ_{i}^{d,x} (x=a,u and i=1,2,3) is the deposition rate constant of attached and unattached progeny and 
(6) 
is the attached fraction of progeny i. Neglecting the attachment of ^{214}Pb,^{214}Bi and ^{214}Po nuclei, F may be calculated as: 
(7) 
Faj and Planninic [3] calculated dj as a function of λ_{v} employing the Carnado’s formula. The solution enabled calculation of F as a function of λ_{v}, namely F = F (λ_{v}). Similar approach has been followed previously as well [3,7,12,13,16,17]. 
In actual conditions, however, attachment of unattached progeny to aerosol and humidity particles may differ and this affects progeny concentrations (x=a,u and i=1,2,3). According to recent publications [9,10], the deposition and attachment rate constants of attached and unattached progeny differentiate in highhumidity environments due to peaking of water droplets and for this reason, symbolisation λ_{i}^{d,x} (x=a,u and i=1,2,3) was adopted. Presuming however only typical lowhumidity ambient room environments under a Jacobian [12,13,15] steadystate with complete mixing, λ_{i}^{d,u} and λ_{i}^{d,a} 
can be considered approximately constant for indoor room conditions [3,4,79,11]. In such conditions attachment and deposition rates are equal between unattached and attached nuclei and hence, symbolisation λ^{d,x} (x=a,u) could be employed. According to Porstendorfer et al. [13] in typical rooms no differences are usually addressed between ambient electrical charged and neutral progeny clusters in attaching to aerosols and and depositing to surfaces. Under this perspective, the deposition rates of attached and unattached progeny to surfaces are equal. Employing symbolisation of Porstendorfer et al. [13] the term of equation (5) represents the deposition rate of attached nuclei, namely 
(8) 
Where q^{a} is the symbol for the deposition rate of all attached progeny. Symbolising q^{u} the deposition rate of all unattached progeny it follows from (9) that 
(9) 
Assuming a steadystate Jacobian model and complete mixing, concentrations of attached and unattached nuclei can be calculated then as [13] 
(10) 
and 
(11) 
Where R_{i} is the recoil fraction of progeny i, X is the attachment rate to aerosols and i =1,2,3. R_{1} =0.8 while R_{2}=R_{3}=0 [1]. Employing (10) and (11) in (3), F can be calculated as a function of λ_{v}, λ^{d,u}, λ^{da} and X, namely F = F (λ_{v}, λ^{d,u}, λ^{da}, X). The latter approximation was employed by Eappen et al. [7] upper and lower bounds for F as well as average modelled values and related uncertainties. 
It is very important that both approaches for the calculation of A^{x} (x=a,u and i=1,2,3), namely equation (4) for Faj and Planninic and equations (10),(11) for Eappen et al. [2,3,7] yield to similar final approximations for the most probable relation of modelled values of 
F versus measured progeny concentrations (x=a,u and i=1,2,3). This relationship can be employed for the determination of F versus the recording efficiency between bare and cuptype SSNTDs (R). According to Faj and Planninic (1991) [4] this relationship follows the exponential law 
(12) 
where 
(13) 
And T_{B} , T_{R} are the recorded track density values of bare and cupenclosed SSNTDs. Similar were also the results reported by other investigators [3,4,7,14] Figure 1 presents the best approximations of F versus R according to the model of Faj and Planninic and according to the model of Eappen et al. [7] (Jacobi’s model). Excellent coincidence is observed for all values of R. 
Theoretical and Experimental Techniques 
Theoretical approach 
Let’s assume a twin CR39 detector system, namely a bare CR39 SSNTD and another enclosed in a cup. The detector inside the cup records tracks attributable to time integrated ^{222}Rn concentration and the detector outside records tracks due to both ^{222}Rn and its progeny. While radon’s concentration is unequivocally estimated, it is not so direct to estimate the progeny’s equilibrium factor and PAEC from the track density of bare detectors. When the environment predominantly consists of radon and its progeny, a unique relationship as the one of equation (12) can be established between equilibrium factor values and the ratio of the cup to bare detector track densities [37,14,1621]. 
Lets symbolise by T_{R} and T_{B} the track density values recorded on CR39 by cuptype and bare detectors respectively. For calibrated CR 39 cuptype dosimeters, T_{R} will relate linearly to the concentration A_{O} of ^{222}Rn outside the cup. On the other hand, the track density TB of bare CR39’s will be proportional to the ambient concentration of all aemitting nuclei, namely to A_{O} of ^{222}Rn, A_{1} of ^{218}Po and A_{4} of ^{214}Po. If K_{R} and K_{B} are the sensitivity factors tracks.cm^{2} perBq.m^{3} of cuptype and bare CR39 respectively, then 
(14) 
and 
(15) 
Since A_{3} = A_{4}. Equation (13), according to (14) and (15) can be written as 
(16) 
where 
(17) 
is the sensitivity factor ratio, and Importantly, equation (17) calculates R from the concentration ratios r_{1}and r_{3}. According to equations (3), (16) and (17), if the concentrations (x=a,u and i=1,2,3) are known from measurements, equilibrium factor can be calculated from measurement as well as from and . If additionally the sensitivity factors k_{B} and k_{R} are known then k can be determined, and hence R. In this manner, the relationship between F and R can be established. 
Experimental approach 
In the framework of the NRSF Thalis Project of TEI of Piraeus, Greece, several active radon and progeny measurements have been conducted in Greek dwellings. Numerous measurements were performed with EQF3023 (EQF) of Sarad Instruments Gbhm. This instrument allows continuous 2hour cycle measurement of radon and progeny nuclei, the latter discriminated for their attached or unattached mode. Radon’s concentration is measured through ionisations produced within a chamber installed inside EQF by the alpha particles emitted during the decay of a radon’s amount that is collected at the beginning of each cycle via 10minute pumping. Progeny concentration is measured by two semiconductor detectors at two stages. First, during the first hour of the 2hour cycle, all alpha activity is collected by the first semiconductor either if this corresponds to unattached or attached progeny. Simultaneously, the second detector collects the unattached progeny nuclei that manage to transmit through a meshgrid of 50 nm. Then, during the second cycle, the semiconductor detectors are interchanged, while, at this stage, the first remains in contact with a paper filter on which all plated out progeny are also measured. Through alphaspectrographic techniques and proper mathematical analysis, as stated by the manufacturer’s manual, all activities are determined. From the active database, several actual values of A_{0} and (x=a,u, i=1,2,3) were employed. From these additional value sets were calculated as averages at the 95% confidence interval, under the constraint of employing only partial values of a certain dwelling measurementset during each calculation. From these actual (x=a,u, i=1,2,3) measurement sets, equilibrium factor F values were calculated according to (3). Additionally, to this type of calculation, F was also derived from calculated values of the unattached fraction, f_{p}, in terms of PAEC as where (x=a,u, i=1,2,3). This was employed for the calculation of F in terms of ratio according to Doerschel and Piesch [14] where Ai represents the activity concentration of radon (i=0) and ^{214}Po (i=4) respectively. 
Passive radon measurements within the Thalis Project are being conducted with a cuptype CR39 dosimeter which was calibrated previously [15]. This cuptype dosimeter has wellestablished linear response to radon exposure. The sensitivity factor of this dosimeter has been experimentally defined and found equal to k_{r} = (4.62 ± 0.33) (tracks.cm^{2} perBq.m^{3}.h). From the actual measurements of A_{0}, T_{R} was calculated according to (14). 
Track density of bare CR39 detectors was calculated by means of combining the real measurements of EQF with results derived via MonteCarlo methods. More specifically, A_{1} and A_{3} were calculated from EQF measurements considering that i = 1,3. From these and the corresponding A_{0} values, the concentration ratios were calculated as and . Since kB is not easily measurable, MonteCarlo methods were employed for its determination. The following steps were followed: 
1. The distance l travelled by alpha particles prior to hitting CR39 was calculated versus alpha energy through SRIM2013 for the whole alphaparticle energy range of radon’s decay chain. The relationship 
(18) 
was employed where R_{max} =4.09cm for alphaparticles originating from ^{222}Rn, R_{max} =4.67cm for alphaparticles originating from ^{218}Po and R_{max} =6.78cm for alphaparticles originating from ^{214}Po. 
2. Random emission points of ^{222}Rn, ^{218}Po and ^{214}Po were generated around CR39 and their travelling direction vectors were calculated. 
3. From the direction vectors of (2), the hit data (l,θ_{h},φ_{h}) were calculated. 
4. For alphaparticles with l inside an effective volume, incident energy E_{h} was calculated from the reciprocal of (18) under the constraint θ_{h} ≤ θ_{cr}. 
5. From hit data (E_{h},θ_{h},φ_{h}) the range and end points in CR39 were calculated. 
6. Steps (1)(5) were iterated for N_{0} particles of ^{222}Rn, ^{218}Po and ^{214}Po. 
7. From steps (1)(6) the number of recorded particles of ^{222}Rn, N_{0}^{rec} , of ^{218}Po, N_{1}^{rec} and and of ^{214}Po , N_{4}^{rec} were calculated To estimate realistic values of N0 for ^{222}Rn, ^{218}Po and ^{214}Po (denoted as N0,i) the following equation was employed 
(19) 
where V_{i} is the sensitive volume’s dimensions, t_{exp} is an assumed value for the exposure time (30 days) and i=0,1,4. From (19) and the MonteCarlo output the recorded particles N_{i}^{rec}, i=0,1,4 were calculated. From N_{i}^{rec} the track density of bare CR39 detectors was calculated as 
(20) 
Where S is the area of the employed CR39 detectors, namely 1 cm^{2}. 
From (20) the total sensitivity factor k_{B} of bare CR39 detectors was calculated as 
(21) 
Outcomes and Discussion 
Table 1 presents characteristic sets F, R according to the methodology already described. It may be recalled that the F values were calculated from experimental EQF measurements and that the R values were calculated from measurements and calculations. 
The relationship between F and R has similarities to that of Figure 2. For this reason the data of Table 1 were fitted to the exponential model (12), namely to F = a.e^{b.R} Fitting gave a = 0.1663, b= 0.5165 with r^{2}=0.91. These data are in accordance to the published results of Faj and Planninic, Eappen et al. [3,4,7]. It is noted that the latter publication represents a critical review of the subject together with other results. Differences are due to differences in the sensitivity factor of the employed cuptype dosimeters of this study and those of the other studies. Indeed different geometries of cuptype dosimeters induce differentiations in detection efficiency due to alterations (a) in the field that the detectors face; (b) in the distribution of energies and incidence angles of alpha particles that hit the detector’s surface or surfaces; (c) in radon’s entrance properties e.g., diffusion, permeability etc.; (d) other reasons. The relationship between calculated values of F and R indicated non good fit to the exponential model (12) with r^{2}=0.51. This finding strengthens the integrity of the approximation followed in this paper, namely the “semiempirical” modelling, viz., MonteCarlo modelling fed with experimental measurements. Accounting the criticism of the method of Doerschel and Piesch [13] from several researchers [5,7,1621] the fit result of calculated F values verified, more or less, this criticism. No other F calculation approaches [6,7.14,18,21] were attempted, despite that some of these could provide better estimation of F values. Nevertheless, the approach of this paper outweighs in one fact; the actual measurements of F. In addition, the overall Monte Carlo modelling constitutes a new approach to previous simulations [16,1826], most importantly, by taking into account the latest version of SRIM software, namely SRIM 2013. Apart from the work of Rezaie and Rezaie, et al. [22,23] which also used SRIM, all previous modelling for use of nuclear track detectors in long term estimation of F, followed completely other approximations [17,18] or mathematicalanalytical models [16,24,25]. However, despite the different approximations, the findings of this paper could be useful for alternative longterm estimation of F or MonteCarlo modelling of cuptype, bare detectors or other detector installations. This latter view, namely longterm estimation of F, was the final outcome of this work. Accounting the findings of this work, longterm measurements with CR39 polymers will be implemented. Further work will simulate LR115 polymers under similar semiempirical modelling approach, expecting to implement a multisensor assembly of cupenclosed and bare CR39 and LR115 polymers for longterm radon progeny measurements. 
From the data of Table 1, sensitivity factors of bare CR39 SSNTDs were calculated according to (21). Average kB of this study was found equal to k_{B} = (4.6 ± 0.6)(tracks.cm^{2} perBq.m^{3}.h). This value does not differ significantly from the value of k_{R}. The latter implies from equation (17) that k k ≈1. This finding is very important. Indeed, Faj and Planninic [3,4] assumed equal values for k_{B} and k_{R}. The present study verifies this result. Similar was also the outcomes of Eappen et al. [9]. Related publications gave also comparable results [5,6]. All these findings could be explained by the fact that CR39 registers alpha particles from radon and progeny identical either if enclosed in a cup or bare. Observed track density differences are attributable only to the fact that cup type CR39 dosimeters are proportional to radon concentration only, while bare CR39 SSNTDs register proportional to the concentrations of all alphaemitters. Future work will employ other expressions of F namely those that take into account the the unattached fraction in terms of PAEC. 
Conclusion 
This study reported a newly developed MonteCarlo simulation tool for modelling the CR39 SSNTDs efficiency. Simulation combined MonteCarlo techniques, experimental data and the latest version of SRIM (SRIM2013) software program group. This “semiempirical” simulation perspective constitutes a completely new approach in SSNTD modelling. Modelling rendered calculation of sensitivity of CR39 detectors based on energy and angular distributions of alphaparticles emitted by the decay of radon and progeny. The relationship between equilibrium factor F and recorded track density values ratio (of bare and cupenclosed SSNTDs respectively), R, was additionally calculated through measurements and calculations. The sensitivity of bare CR39 detectors was calculated equal to k_{B} = (4.6 ± 0.6)(tracks.cm^{2} perBq.m^{ 3}.h). This value is not significantly different from the corresponding sensitivity factor k_{R} of the cuptype dosimeters employed in this work. The ratio of for k_{B} and k_{R} was found approximately one, namely k ≈1 . This finding is considered as very important since it is verifies the results the similar studies. In addition, it also verifies the integrity of MonteCarlo simulation and the overall mathematical approximations. 
Acknowledgements 
This research has been co‐financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) ‐ Research Funding Program: THALES Investing in knowledge society through the European Social Fund. 
References 

Table 1 
Figure 1  Figure 2 