Efficient Temperature- and Moisture-Compensated Design for Next-Generation Adsorbent-Based Radon Detectors

Abstract

Accurate measurement of low-level radon concentrations in the environment is increasingly important for climate research, radon priority area delineation, and atmospheric studies. Adsorbent-based radon detectors offer high sensitivity but suffer from strong temperature dependence of radon adsorption and rapid degradation under humid conditions, limiting their applicability in long-term environmental monitoring. This work presents a universal design methodology for temperature- and moisture-compensated radon detectors based on hermetically packaged adsorbents enclosed by radon-permeable polymer foils. Analytical models describing the opposing temperature dependences of radon adsorption in adsorbents and radon permeability in polymers are combined to derive a general optimization criterion that minimizes temperature-induced response variations over a defined temperature range. The method is applicable to arbitrary combinations of adsorbent materials and polymer foils, provided their radon adsorption and permeability characteristics are known. The approach is demonstrated using activated carbon fabrics and common polymers (LDPE, HDPE, and polypropylene), for which optimal design parameters are identified. In addition, water vapor permeation through polymer foils is modeled to estimate moisture protection and permissible exposure durations under high humidity. The results demonstrate that appropriately designed compensation modules can significantly reduce temperature sensitivity while extending operational stability in humid environments, enabling next-generation high-sensitivity radon detectors suitable for environmental applications.

1. Introduction

Radon (²²²Rn) research has a history spanning more than a century. It was proposed in the 1920s as a possible cause of lung cancer in underground miners [1], with strong evidence obtained in the second half of the last century [2]. Nowadays, radon is recognized as a carcinogen [3], ranked second after smoking as a cause of lung cancer in the general population, and the leading cause among never-smokers [4,5]. The last several decades have been dominated by research and development of methods and instrumentation for indoor radon measurements, as most exposure occurs indoors [4]. Due to the high temporal variability of radon concentrations, the reference levels set by the European Union for radon in dwellings and workplaces are based on the annual average ²²²Rn activity concentration [6]. The EC Directive [6] requires that national reference levels in EU Member States must not exceed 300 Bq m⁻³. For this reason, most indoor radon measurements are long-term integrated measurements capable of detecting radon concentrations above 10 Bq m⁻³, as virtually all indoor ²²²Rn concentrations exceed 10 Bq m⁻³ [7].

In the last decade, however, interest in measuring low radon concentrations (1–10 Bq m⁻³)—typical of the outdoor environment—has increased significantly [8,9,10]. There are several reasons for this, the main one being the recognized potential of radon as a tracer for greenhouse gas inventory estimates and climate change research [8,9,10], as well as for the delineation of radon priority areas required by the European Directive [6,11]. This has led to new methodological developments. Large active monitors, mostly intended for stationary use, have been developed [12,13,14], and metrological traceability in the 1–10 Bq m⁻³ range has begun to be established [9,10]. However, the challenge of developing miniature and sufficiently sensitive detectors for large-scale environmental applications remains. The sensitivity of currently available commercial passive detectors and active monitors is insufficient to meet this challenge [4,15].

One promising approach, widely investigated in recent years, involves combining efficient radon adsorbents (mostly based on activated carbons) with solid-state nuclear track detectors [16,17,18]. Since the discovery in 1906 [19] of the high radon adsorption capacity of activated carbons, these materials have been widely used for radon measurements [20], including in combination with alpha-particle detectors [21,22,23]. However, two major obstacles have limited their use in long-term measurements, especially under environmental conditions. The first is the strong temperature dependence of radon adsorption in activated carbons [24,25,26,27,28], and the second is the rapid deterioration of adsorption capacity due to atmospheric moisture [29]. Consequently, activated carbons have mostly been used for short-term (a few days) radon sampling, followed by gamma spectrometry or liquid scintillation counting (LSC) measurements [30], sometimes with temperature corrections applied [25]. Meanwhile, new adsorbing materials have been identified [31,32], some of which retain high radon adsorption capacity even when saturated with water [31]. Sensitivity estimates published in 2024 suggest that this approach may improve the sensitivity of radon monitors/detectors by one to two orders of magnitude [33,34] compared to the current state of the art [15,33]. This concept has already been successfully applied in several studies [35,36]. Nevertheless, strong temperature dependence and moisture-induced deterioration remain major barriers to the development of next-generation high-sensitivity radon detectors and monitors based on efficient radon adsorbents.

In 2019–2021, a conceptually new method was invented to mitigate both temperature and humidity effects [37,38]. The key idea is to enclose an adsorbent in a hermetically sealed plastic envelope through which radon can diffuse (Figure 1a,b). The radiation detector may be placed inside the envelope, as shown in Figure 1a, or outside it (Figure 1b), provided that the detected radiation can penetrate the plastic foil. The temperature dependence of radon permeability in plastics (which increases with temperature) is opposite to that of radon adsorption (which decreases with temperature). Therefore, with appropriate design of these “compensating modules,” the temperature influence on detector response may be significantly reduced over a wide temperature range. This was experimentally validated in a pilot study demonstrating the feasibility of the approach [39]. However, that proof-of-concept study [39] achieved temperature compensation using a somewhat “trial-and-error” approach, which cannot easily be generalized to other promising radon adsorbents or various plastic foils. Furthermore, since plastic foils retard moisture penetration, they may provide protection against humidity, potentially allowing longer exposure times before radon adsorption decreases. However, this moisture-retardation effect has not yet been quantitatively evaluated.

In this work, a novel method for the efficient design of compensating modules is developed. The key advantage of this method is that it can be applied to any type of adsorbent material and polymer foil without the need for preliminary trial-and-error procedures. Universal relationships suitable for module design with various materials are derived, and their dependence on the adsorption properties of the adsorbents and the permeability characteristics of the polymers is modeled.

The practical design of compensating modules with walls made of low-density polyethylene (LDPE), high-density polyethylene (HDPE), and polypropylene (PP) is demonstrated. Water penetration through the plastic walls of the compensating modules is also modeled, and estimates of the moisture-retardation factor are obtained.

The method can potentially be applied not only to radon but also to other radioactive noble gas isotopes (e.g., ¹³³Xe).

2. Materials and Methods

2.1. Theoretical Model

The fundamental quantities required for the design of compensating modules are the radon adsorption coefficient, k, of the adsorbent and the radon permeability, P, of the plastic, together with their temperature dependences. The adsorption coefficient k is defined as the ratio of radon specific activity (Bq kg⁻¹) in the adsorbent to the radon activity concentration (Bq m⁻³) in the ambient air (thus k is in units m³/kg = cm³/mg). The following commonly used models describing the temperature dependence of k [24,25,26] and P [40,41,42] were adopted in the present study:

$$k=\gamma exp\left({\displaystyle \frac{Q}{RT}}\right)=k_{0}exp\left({\displaystyle \frac{Q}{RT}}-{\displaystyle \frac{Q}{R{T}_0}}\right)$$

(1)

$$P=\alpha exp\left(-{\displaystyle \frac{E_P}{RT}}\right)=P_{0}exp\left({\displaystyle \frac{E_P}{R{T}_0}}-{\displaystyle \frac{E_P}{RT}}\right),$$

(2)

where Q is the adsorption heat of the adsorbent, and E_P is the apparent activation energy for permeability; R = 8.31441 J mol⁻¹ K⁻¹ is the universal gas constant; T (K) is the absolute temperature; and T₀ is the absolute temperature at which the reference values k₀ and P₀ were determined. The reference temperature T₀ does not need to be 273.15 K; it may, for example, be 294 K (21 °C) or any other temperature at which k and P were accurately determined and adopted as reference values.

Consider a module illustrated in Figure 1 and exposed to radon for a time t_exp. As shown elsewhere [39,43], the ratio ρ of the time-integrated radon activity concentration inside the module (C_in) to that outside the module (C_out) is given by the expression:

$$\rho ={\displaystyle \frac{C_{in}}{C_{out}}}={\displaystyle \frac{1}{1+\lambda \frac{h\left(V+km\right)}{PS}}}\stackrel{V\ll km}{\to }{\displaystyle \frac{1}{1+\lambda \frac{hkm}{PS}}},$$

(3)

where λ is the decay constant of ²²²Rn; h is the thickness of the polymer foil; m is the mass of the adsorbent; V is the air volume inside the module (usually V ≪ km); and S is the total area of the external plastic walls of the module. Due to the increase in P with rising temperature, ρ also increases with temperature, as experimentally demonstrated elsewhere [43,44].

The calibration factor (CF) is defined as the ratio of the signal acquired by the detector during exposure to Cₒᵤₜ. The acquired signal is proportional to the time-integrated specific activity in the adsorbent, i.e., kC_in; therefore, the calibration factor is proportional to the quantity η, given by the following expression:

$$\eta =k\rho = {\displaystyle \frac{k}{1+\lambda \frac{hkm}{PS}}}.$$

(4)

If, by appropriate selection of h, m, and S, the quantity η is made significantly less temperature-dependent than k, the same will apply to the CF, thereby minimizing the influence of temperature variations during exposure on the measurement results.

It is convenient to introduce the following substitution:

$$x={\displaystyle \frac{hm{k}_0}{S{P}_0}}.$$

(5)

Using Equations (1)–(3), the expression for η can be written in the following form:

$$\eta =\eta \left(x,T\right)= {\displaystyle \frac{k_0}{exp\left(\frac{Q}{R{T}_0}-\frac{Q}{RT}\right)+\lambda \frac{hm{k}_0}{S{P}_0}exp\left(\frac{E_P}{RT}-\frac{E_P}{R{T}_0}\right)}}={\displaystyle \frac{k_0}{exp\left(\frac{Q}{R{T}_0}-\frac{Q}{RT}\right)+\lambda xexp\left(\frac{E_P}{RT}-\frac{E_P}{R{T}_0}\right)}}.$$

(6)

The criterion for optimal design is based on minimizing the relative standard deviation (RSD), considered as a function of x, of η over the temperature range of interest (T₁, T₂). The RSD is defined by the following expression:

$$RSD=RSD(x)={\displaystyle \frac{1}{\overline{\eta }}}\sqrt{{\displaystyle \frac{1}{T_2-T_1}}{\int }_{T_1}^{T_2}{\left(\eta -\overline{\eta }\right)}^{2}dT},$$

(7)

where $\overline{\eta }$ is the average value of η = kρ over the temperature interval (T₁, T₂). The RSD values at different x were determined by numerical integration using the η values calculated from Equation (6). In the present modelling, the temperature range of interest was chosen as 5–35 °C; however, other ranges may be applied depending on the expected temperature conditions during exposure. The value of x-“x_opt” at which the RSD reaches its minimum was considered the optimal value for compensating module design.

In the present study, modelling was performed for three different polymers: LDPE, HDPE, and PP. The E_p values for these polymers were determined using experimental data on their radon permeability at different temperatures [43,45]. For Q, experimentally obtained values for various activated carbons [24,25,26,27,28] were used in the modelling. The optimization algorithm based on Equations (6) and (7) can be applied to any adsorbent–polymer pair for which k₀ and P₀ (at reference temperature T₀), as well as Q and E_p, are known.

2.2. Estimation of Water Permeability and Protection Against Humidity

The polymer enclosure (Figure 1) may also reduce water uptake by the adsorbent. Atmospheric humidity is another environmental factor that significantly deteriorates radon adsorption for most adsorbents.

Resistance to water penetration was evaluated for an extreme case, namely exposure to 100% relative humidity (RH). The mass transfer rate (M) of water permeation through the polymer foil was estimated as described in [46]:

$$M=WS{\displaystyle \frac{∆p}{h}},$$

(8)

where W is the water permeability and Δp is the water partial pressure difference across a foil of thickness h. Using the W values reported in the literature [46], the maximum “critical time” (t_crit) during which the module can be exposed without degradation of its performance was estimated using the following expression:

$$t_{crit}={\displaystyle \frac{m_{crit}}{M}},$$

(9)

where m_crit is the maximum mass of water that the adsorbent can take up without affecting its adsorption coefficient.

3. Results

3.1. Estimating E_P and Q Ranges for Modelling

To determine the permeability activation energy, experimental data on radon permeability of LDPE, HDPE, and PP at different temperatures, published in [43,45], were used. The quantity reported in [43] was actually the ρ-value measured experimentally in a hermetic volume V without any adsorbent (m = 0), with one side of the volume covered by a polymer foil through which radon could diffuse into the volume. For this case, Equation (3) can be applied as follows:

$$\rho ={\displaystyle \frac{1}{1+\lambda \frac{hV}{PS}}}.$$

(10)

Accordingly, the corresponding permeability, obtained by solving Equation (10) for P, is as follows:

$$P={\displaystyle \frac{\lambda hV}{S}}{\displaystyle \frac{\rho }{1-\rho }}.$$

(11)

The P values derived from [43] were calculated using experimentally obtained ρ values and Equation (11), whereas the data from [45] reported directly measured P values. The P values were plotted against 1/T in accordance with Equation (2), as shown in Figure 2. As can be seen, they follow an exponential dependence, which appears as a straight line on a semi-logarithmic scale in Figure 2. Statistical analysis of the data shown in Figure 2 was performed using TableCurve 2D, version 5.0. The resulting E_P values for the polymers studied are given in

Table 1. Radon permeability activation energies (E_P) for the examined plastics, determined using data from References [43,45].

	[43]	[45]
LDPE	45.7 ± 8.9 kJ/mol	57.4 ± 3.2
HDPE	41.6 ± 1.4 kJ/mol	43.0 ± 2.9
PP	-	63.9 ± 4.6

, and the reference P₀ values are listed in

Table 2. Reference radon permeability (×10⁻⁷ cm²/s) at 21 °C (294 K), as reported in [43,45,47].

	[43]	[45]	[47] (Room Temperature: 19–23 °C)
LDPE	1.33 ± 0.36	1.13 ± 0.17	1.04 ± 0.12
HDPE	0.307 ± 0.056	0.407 ± 0.041	0.240 ± 0.015
PP		0.0303 ± 0.0044

. The temperature-dependent P values for LDPE and HDPE are illustrated in Figure 3 and Figure 4.

As shown in Table 1 and Table 2 and Figure 3 and Figure 4, the values of P₀ (at 21 °C) and E_P obtained from different data sources are in very good agreement, those from [43,45] falling within the experimental uncertainties.

For the adsorption heat (Q) values, literature data were used, primarily for various activated carbons [24,25,26,27,28]. Reported values range from 18.8 kJ/mol [24] and 20.5 kJ/mol [26] to 25 kJ/mol [25] and approximately 30 kJ/mol [28]. For modelling purposes, a reference value of 25 kJ/mol was adopted, while the effect of varying Q within 18–30 kJ/mol on optimization was also considered.

For the permeability activation energy (E_P), the reference values used were 50 kJ/mol for LDPE, 42 kJ/mol for HDPE, and 64 kJ/mol for PP (see Table 1).

3.2. Optimization

To illustrate how the optimal x value can be applied in practical engineering design, consider the following example: for a given study, 100 mg of activated carbon fabric ACC-5092-10 (Kynol Europe GmbH, Hamburg, Germany) is to be used (k₀ = 11.8 m³/kg = 11.8 mg/cm³ [33]). As reported elsewhere [39], Q = 25 kJ/mol [25] accurately describes the temperature dependence of this adsorbent and is adopted for the modelling here. For P₀, the mean values obtained from the data in [43,45] (see Table 1) were used, as follows:

• LDPE (P₀ = 1.23 × 10⁻⁷ cm²/s, E_P = 50 kJ/mol)
• HDPE (P₀ = 3.57 × 10⁻⁸ cm²/s, E_P = 42.3 kJ/mol)
• PP (P₀ = 3.03 × 10⁻⁹ cm²/s, E_P = 63.9 kJ/mol)

Figure 5 shows the dependence of RSD on x for modules made of LDPE, HDPE, and PP. As can be seen, a clear minimum is observed, with its position varying for different plastics.

The optimal x values (x_opt) for modules using this adsorbent with LDPE, HDPE, and PP are as follows (see Figure 5):

• LDPE: x_opt = 1.7 × 10⁵ s
• HDPE: x_opt = 2.14 × 10⁵ s
• PP: x_opt = 1.12 × 10⁵ s.

Temperature compensation with HDPE is illustrated in Figure 6, which shows the temperature dependencies of k, ρ, and η. The significantly reduced variability of η compared to k and ρ is clearly evident.

Consider a compensating module with thin walls. Based on our experience, the thinnest commercially available foils of LDPE, HDPE, and PP have a thickness of approximately 10 µm (0.01 mm). This thickness is sufficiently small to allow an alpha-particle detector to be positioned outside the module, since the range of alpha particles from ²²²Rn and its progeny in these plastics exceeds 10 µm. Using this information, the total area of the external walls of the plastic envelope that provides optimal temperature compensation over the 5–35 °C range (Figure 1) was estimated as follows:

• LDPE, S = 56 cm². For a square envelope, the area of one side is 28 cm² and the side length is 5.3 cm;
• HDPE, S = 154 cm². For a square envelope, the area of one side is 77 cm² and the side length is 8.8 cm;
• PP, S = 3500 cm². For a square envelope, the area of one side is 1750 cm² and the side length is 42 cm.

As seen, the most compact module is obtained using LDPE, whereas a module made of PP would be considerably larger and likely impractical.

The dependence of x_opt on Q and E_P is shown in Figure 7. At a fixed E_P, x_opt increases with increasing Q, while at a fixed Q, x_opt decreases as E_P increases. Another feature apparent in Figure 5 and Figure 7 is that even when x differs from x_opt by a factor of two or even more, temperature compensation remains satisfactory, with RSD staying below 20%. This indicates that reasonably good temperature compensation can be achieved even if the properties of the adsorbent and plastic are only approximately known.

3.3. Resistance to Humidity

Resistance to humidity was evaluated for polymer foils of LDPE, HDPE, and PP used in the modelling. For engineering calculations, W is typically expressed in units of g·mm·m⁻²·d⁻¹·atm⁻¹ [46]. This indicates that if in Equation (8) the total foil area is in m², thickness in mm, and partial pressure in atmospheres, the resulting mass transfer rate will be in g/day.

We consider 100 mg of ACC-5092-10 fabric. According to [31,48], this adsorbent maintains its adsorption properties until its water content reaches approximately (w/w) 15% (i.e., 15 mg for 100 mg of adsorbent). The permeability data at 25 °C from [46] are as follows:

• LDPE: 0.112 g·mm·m⁻²·d⁻¹·atm⁻¹;
• HDPE: 0.0148 g·mm·m⁻²·d⁻¹·atm⁻¹;
• PP: 0.0575 g·mm·m⁻²·d⁻¹·atm⁻¹.

The partial pressure of water vapor at 100% relative humidity and 25 °C is 0.031 atm. Using these values, the estimated maximum exposure time (t_crit) at 100% RH, during which the detector response remains unaffected at x_opt for each polymer, according to Equations (8) and (9), is as follows:

• LDPE: 8 days;
• HDPE: 22 days;
• PP: 6 h.

These estimates are conservative, assuming 100% RH on the exterior of the foil and 0% RH inside. In real conditions, the critical time may be significantly longer, as environmental RH is rarely 100%, and RH inside the module will gradually increase, reducing the partial pressure difference and the mass transfer rate. Further experiments under realistic environmental conditions would be needed for more precise estimates.

Nevertheless, the modelling clearly shows that HDPE is the best-performing polymer among those studied, offering both effective temperature compensation and humidity protection, while PP is unsuitable for humid environments. The water adsorption of bare ACC-5092-10 at 100% RH was studied elsewhere [31]. As shown in [31], the time needed for this material to reach 15% water content is about 6 h. A retardation factor might be defined as the ratio of t_crit to the time needed for the bare adsorbent to adsorb water content that corresponds to m_crit. This factor for a module with ACC-5092-10 is 32 for walls made of LDPE and 88 for HDPE. This implies, if such extrapolation is reasonable, that if 15% water content of ACC-5092-10 is reached in 2 days under certain humidity conditions, a compensating module made of HDPE could extend this period to nearly 6 months.

4. Discussion

In this work, a novel method for the efficient design of compensating modules for temperature influence compensation and moisture protection of radon adsorbents coupled with radiation detectors is developed. The main advancement and novelty of this method lie in its ability to eliminate the need for trial-and-error procedures used in previous studies [39] and to significantly expand the available design options. The approach is general and can be applied to any type of radon adsorbent and polymer foil, provided that the fundamental parameters of radon adsorption (k₀, Q) and radon permeability (P₀, E_P) are known. Key findings are as follows:

• Validation with common polymers:
  • The method was tested using LDPE, HDPE, and PP.
  • Experimental data from the literature were processed to determine P₀ at 21 °C and the radon permeability activation energies (E_P) for each plastic.
• Temperature compensation:
  • Once the optimal x value (x_opt) is determined, the best temperature compensation is achieved by appropriately linking the adsorbent mass, total area of the plastic envelope, and foil thickness according to Equation (5) for x_opt.
  • Even if the parameter x deviates by a factor of two (or slightly more) from x_opt, temperature compensation remains satisfactory, with the RSD staying below ~20%. This suggests that adequate temperature compensation can be achieved even if the radon adsorption properties of the adsorbent and the radon permeability of the plastic are only approximately known.
• Moisture protection:
  • Compensating modules made of HDPE and LDPE provide effective long-term protection against humidity, retarding water adsorption by a factor of 88 for HDPE and 32 for LDPE.
  • Moisture retarding factor can be further extended by a factor of 2–3 by increasing proportionally the foil thickness (e.g., the x-value, see Equation (5)), although this would slightly reduce the temperature compensation (e.g., the RSD increasing from ~10% to ~15–20%).
  • At lower temperatures, exposure time could be significantly longer due to reduced water permeability and smaller partial pressure differences.

The developed model assumes ideal radon diffusion in polymers and rapid attainment of adsorption equilibrium in the adsorbents. Previous studies of radon diffusion in polymers [45,47] have shown behavior consistent with near-ideal diffusion, within experimental uncertainty, for the plastics investigated. The time required to reach adsorption equilibrium depends on the thickness of the adsorbent; for the activated carbon fabric used in this work, it has been estimated in [39] to be on the order of a few minutes. Based on models detailed elsewhere [20,33], this assumption is valid for activated carbons provided that the adsorbent thickness does not exceed a few tenths of a millimeter. Therefore, the adsorbents used in this method should be sufficiently thin. In practice, thicker adsorbents are not necessary when the detected radiation consists of alpha particles.

Polymers may undergo gradual changes in their properties over time (aging effects). However, such changes are not expected to have a significant impact, as they occur slowly and typically require years to become noticeable. Moreover, temperature compensation remains satisfactory (see Figure 5) even if the parameter x (and thus the polymer permeability, see Equation (5)) varies considerably. Therefore, no substantial effects are anticipated over exposure periods of several months. Additionally, the plastic foil can be replaced after long-term use (e.g., after one year).

In addition to temperature compensation and humidity protection, compensating modules incorporating efficient radon adsorbents offer the potential for high sensitivity, sufficient to address current priorities in measuring low radon concentrations in the environment. Sensitivity estimates depend on the type of detector used and its response function. Such estimates for alpha track detectors are provided in Ref. [34]. For example, for a compensation module of the type studied in the present work (HDPE + ACC-5092-10), a 3-month exposure using Kodak Pathe LR-115/II detectors (Dosirad, Gif-sur-Yvette, France) with a detection area of 1 cm² yields a minimum detectable activity concentration (MDAC) of 1 Bq m⁻³. When large-area track detectors are used (e.g., DVDs) with a detection area of 100 cm², the MDAC can be as low as 0.06 Bq m⁻³. For comparison, the current state of the art in passive radon detection typically provides MDAC values greater than 5 Bq m⁻³ for a 3-month exposure [34].

Compensation modules can be primarily applied in long-term measurements of low concentrations typical of outdoor air, as well as in short-term, high-sensitivity measurements for radon diagnostics [36]. A limitation of modules employing alpha-track detectors at elevated radon levels is measurement bias arising from tracks overlapping at high track densities. In such cases, appropriate corrections for tracks overlapping should be considered [49].

Further research is needed to validate module performance under highly variable temperature and humidity conditions. Exploration of different adsorbents and polymers may further optimize module performance for specific environmental monitoring applications. The method can also be extended to other radioactive noble gases, such as ¹³³Xe. In such cases, only the decay constant and the material properties of the adsorbent and polymer need to be adjusted, while the underlying formalism in Equations (5) and (6) remains valid.

5. Conclusions

In this work, a novel method for the efficient design of compensating modules for temperature compensation and moisture protection of radon adsorbents coupled with radiation detectors was developed. The method is applicable to a wide range of plastics and adsorbents. Its application was demonstrated using low-density polyethylene (LDPE), high-density polyethylene (HDPE), and polypropylene (PP) plastics, together with the activated carbon fabric ACC-5092-10. Among the tested plastics, HDPE exhibited the best overall performance in terms of both temperature compensation and humidity protection. LDPE also performed well, while PP proved less suitable for high-humidity environments. Other polymers may be explored in future studies. With HDPE, exposure times of several months are feasible even under environmental conditions of high humidity.

The developed method shows significant potential for designing compensating modules that enable highly sensitive radon measurements across a wide range of temperatures and humidity levels. Its generality also allows adaptation for other radioactive noble gases (e.g., ¹³³Xe), supporting versatile environmental monitoring applications.

6. Patents

Two patents are related to the compensating modules. The inventor is Dobromir Pressyanov, and the assignee is Sofia University “St. Kliment Ohridski.” The title (the same for both patents) is: COMPENSATION MODULE FOR SENSORS FOR MEASUREMENT OF RADIOACTIVE NOBLE GASES. The patent documents are:

• Patent BG Nr. 67405 (priority 19 March 2019, issued 31 December 2021)
• Patent BG Nr. 67484 (priority 19 August 2020, issued 15 December 2022)