Diffusion of $^{210} ext{Pb}$ and $^{210} ext{Po}$ in Nylon

Radon and its progeny constitute a major source of background in rare-event physics experiments, such as those searching for dark matter, neutrinos, and neutrinoless double beta decay, due to their origin as unavoidable decay products of natural uranium. In particular, $^{222}$Rn and its long-lived daughter $^{210}$Pb can diffuse from detector material surfaces, resulting in sustained background contributions. To investigate this process, a system was developed using a controlled radon source, a vacuum chamber with a high electric field, and a thin Nylon-6 film to enable deposition of radon progeny onto the film surface. Nylon-6 was selected for the initial measurement given its history in low-background experiments. We intend to systematically study diffusion in various polymers in the future. Our setup allowed for controlled study of the diffusion behavior of $^{210}$Pb and its daughter $^{210}$Po under varying humidity conditions. Our results show that both $^{210}$Pb and $^{210}$Po diffuse significantly in nylon under high relative humidity, which can potentially lead to internal contamination and increased background in low-background detectors. The diffusivity of $^{210}$Pb was found to be lower than 1.14 $\times$ 10$^{-15}$ cm$^2$/s at 40$%$ relative humidity (RH), and to be (4.03 $\pm$ 1.01) $\times$ 10$^{-13}$ cm$^2$/s at 95$%$ RH. The diffusivity of $^{210}$Po at 95$%$ RH was measured to be (3.94 $\pm$ 0.98) $\times$ 10$^{-13}$ cm$^2$/s. These findings underscore the importance of controlling environmental humidity and material exposure to radon in the design of ultra-low background experiments.

💡 Research Summary

The paper investigates the diffusion of the long‑lived radon progeny 210Pb (t½ = 22.2 y) and its daughter 210Po (t½ = 138 d) into nylon‑6, a polymer commonly used in low‑background experiments as a container or storage material. Because radon (222Rn) is an unavoidable decay product of 238U, its daughters can become a persistent source of α and β background if they migrate from detector surfaces into the bulk.

Experimental method – A controlled radon source (Pylon model 2000A, 25 kBq) was placed in a small acrylic tube filled with nitrogen at ~200 mbar. A high‑voltage (3.5 kV) electric field, generated by a stack of twenty printed‑circuit‑board electrodes, directed positively charged radon daughters (mainly 218Po, 214Pb, 214Bi, 214Po) onto a 50 µm thick nylon‑6 film (2.5 cm diameter). The deposition efficiency, determined from the initial 214Po α rate, was ≈13 Hz, corresponding to about 50 % of the daughters originating from radon decay inside the high‑voltage tube.

After deposition, the film was stored under two humidity conditions: (i) laboratory ambient ≈40 % relative humidity (RH) for ~200 days, and (ii) a controlled humidity chamber at 95 % RH for a short exposure (6 days). Weekly α‑spectra were recorded with an Ortec Alpha Duo system (ULTRA‑AS silicon detector, 15 % detection efficiency at 10 mm distance). The α peaks from 210Po (5304 keV) were monitored over a total period of ~300 days.

Theoretical model – Diffusion was treated as a one‑dimensional process in a semi‑infinite slab. Solving the diffusion equation ∂C/∂t = D∂²C/∂x² with an initial surface delta‑function (C(x,0)=Qδ(x)) and a zero‑flux boundary at the surface yields C(x,t)=Q/(√(4πDt)) exp(−x²/4Dt). The measured fraction of degraded α events (1–5 MeV) relative to the full‑energy peak provides a direct probe of the depth distribution of the emitters, allowing extraction of the diffusion coefficient D.

Results –

• At 40 % RH, no statistically significant degradation of the α peak was observed. An upper limit on the diffusion coefficient of 210Pb was set at D < 1.14 × 10⁻¹⁵ cm² s⁻¹.
• At 95 % RH, both 210Pb and 210Po showed clear diffusion signatures. Fitting the time‑dependent degraded‑event fraction gave D_{Pb} = (4.03 ± 1.01) × 10⁻¹³ cm² s⁻¹ and D_{Po} = (3.94 ± 0.98) × 10⁻¹³ cm² s⁻¹. The total α count decreased by ~2 % after high‑humidity exposure, consistent with a fraction of emitters moving deeper than the detector’s energy threshold or laterally out of the active region.

Uncertainties – The dominant systematic contributions arise from (1) the collection efficiency of charged radon daughters (≈±10 %), (2) the α‑detector efficiency (±5 % at the chosen geometry), (3) humidity control (±2 % RH), and (4) the estimation of the initial surface inventory Q based on the 214Po rate, which carries a statistical uncertainty of ≈15 %.

Implications – The strong humidity dependence demonstrates that even polymers traditionally considered inert can become significant background sources when exposed to moist air. For experiments requiring background levels below 10⁻⁴ cts kg⁻¹ day⁻¹, uncontrolled humidity could lead to internal 210Pb contamination that persists for the entire detector lifetime. Consequently, material handling protocols must include strict humidity control, and the choice of polymer should be guided by quantitative diffusion data.

Future work – The authors plan to extend the methodology to other polymers (e.g., polyethylene, polypropylene, silicone elastomers) and to map diffusion coefficients across a broader RH range (60–80 %). Incorporating temperature dependence and exploring surface treatments (e.g., plasma cleaning, coating) will further inform material selection and storage strategies for next‑generation dark‑matter, neutrinoless double‑beta decay, and neutrino experiments.