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

This study demonstrates that the diffusivity of radon progeny $^{210}$Pb and $^{210}$Po in Nylon-6 increases significantly under high relative humidity, reaching values around $4 \times 10^{-13}$ cm$^2$/s at 95% RH, thereby highlighting the critical need to control environmental humidity and radon exposure to prevent internal contamination in ultra-low background physics experiments.

The Gist

The Big Picture: The Invisible Ghost in the Machine

Imagine you are trying to listen to a single, tiny whisper in a room that is supposed to be perfectly silent. This is what scientists do when they search for rare cosmic events like Dark Matter or Neutrinos. Their detectors are so sensitive that even the tiniest bit of natural radioactivity can drown out the "whisper" they are looking for.

One of the biggest troublemakers is Radon, a naturally occurring radioactive gas found in the earth. Radon decays into "children" (progeny), specifically Lead-210 and Polonium-210. These are like tiny, invisible ghosts that stick to surfaces. If they get inside your detector, they start decaying and creating "noise" that looks like the signal you are trying to find.

The Problem: The Nylon "Sponge"

The scientists in this study were worried about Nylon. Nylon is a common plastic used in these experiments to hold things together or store materials. It's like the "duct tape" of the low-background world.

They suspected that Radon's children (Lead-210 and Polonium-210) might not just sit on the surface of the nylon; they might actually soak into it, like water soaking into a sponge. If they soak in, they become part of the detector's "bulk" (the inside), making it impossible to clean them off.

The Experiment: The "Radon Shower"

To test this, the team built a special machine that acts like a Radon Shower:

1. The Source: They used a concentrated Radon source (like a heavy fog machine for radioactive gas).
2. The Electric Field: They turned on a high-voltage electric field. Think of this as a giant magnet that pulls the charged radioactive particles out of the gas and slams them onto a thin sheet of nylon.
3. The Target: A thin sheet of Nylon-6 (50 micrometers thick, about the width of a human hair).
4. The Stress Test: They took this "contaminated" nylon and put it in two different environments:
   • Dry Air (40% Humidity): Like a desert day.
   • Steamy Air (95% Humidity): Like a hot, humid bathroom after a long shower.

The Discovery: The "Wet Sponge" Effect

Here is what they found, using a simple analogy:

• In the Dry Air (40% Humidity): The nylon was like a hard, dry sponge. The radioactive particles stuck to the surface but couldn't get inside. The diffusion (movement into the material) was almost zero.
• In the Steamy Air (95% Humidity): The nylon became like a soft, wet sponge. The moisture made the plastic structure loosen up, allowing the radioactive particles to dive deep into the material.

The Results:

• When the air was humid, the radioactive particles moved into the nylon 1,000 times faster than when the air was dry.
• They measured exactly how fast these particles moved (diffusivity).
  • Lead-210: Moved very slowly in dry air, but sped up significantly in humidity.
  • Polonium-210: Also sped up massively in humidity.

Why Does This Matter? (The "Aha!" Moment)

Think of the nylon as a backpack carrying your sensitive equipment.

• If the backpack is dry, the radioactive dust stays on the outside. You can wipe it off.
• If the backpack gets wet (high humidity), the dust soaks into the fabric. Now, the dust is inside the backpack, and you can never get it out.

For scientists building ultra-sensitive detectors, this is a nightmare. If they store their equipment in a humid room, the nylon parts could become permanently contaminated from the inside out, ruining the experiment's ability to detect rare events.

The Takeaway

1. Humidity is the Enemy: High humidity acts like a key that unlocks the door for radioactive particles to enter plastics like nylon.
2. Control the Environment: To build the world's most sensitive detectors, scientists must not only keep the air clean but also keep the air dry.
3. Future Work: The team plans to test other plastics to see which ones are the "driest sponges" and which ones are the "wettest sponges," helping them choose the best materials for future experiments.

In short: If you want to keep your ultra-sensitive science equipment clean, don't let it get damp. A little bit of humidity can turn a harmless plastic sheet into a radioactive trap.

Technical Summary

1. Problem Statement

Rare-event physics experiments (e.g., dark matter searches, neutrinoless double $\beta$ decay) require extremely low background radiation levels. A persistent source of background is Radon-222 ($^{222}$Rn) and its decay progeny, specifically the long-lived Lead-210 ($^{210}$Pb) and its daughter Polonium-210 ($^{210}$Po).

• The Issue: $^{222}$Rn can diffuse into detector materials. While $^{222}$Rn is a gas, its solid decay products ($^{210}$Pb, $^{210}$Po) can plate out on surfaces and subsequently diffuse into the bulk of the material.
• The Consequence: $^{210}$Pb has a half-life of 22.2 years. If it diffuses into the bulk of detector components (like nylon containers), it acts as a long-term internal source of background radiation. $^{210}$Pb decays to $^{210}$Bi and then to $^{210}$Po, which emits a 5.3 MeV $\alpha$ particle, a significant background for sensitive detectors.
• The Gap: While radon diffusion in polymers is known, the specific diffusion coefficients of $^{210}$Pb and $^{210}$Po in Nylon-6 (a common material in low-background experiments) under varying humidity conditions were not quantitatively established.

2. Methodology

The researchers developed a controlled experimental system to deposit radon progeny onto nylon films and measure their subsequent diffusion.

Experimental Setup

• Deposition Chamber: A vacuum chamber containing a concentrated $^{222}$Rn source (25 kBq). An electric field (3.5 kV) was applied to drift positively charged radon daughters ($^{218}$Po) onto a 50 $\mu$m thick Nylon-6 film (2.5 cm diameter, 1 cm exposed area).
• Humidity Control: Samples were stored in two environments:
  1. Low Humidity: 40% Relative Humidity (RH) in a Class 10,000 clean room.
  2. High Humidity: 95% RH in a controlled humidity chamber.
• Measurement: An Ortec Alpha Duo spectrometer with ULTRA-AS silicon detectors monitored the samples over ~300 days.
  • Technique: The team measured $\alpha$-particle energy spectra. Surface-deposited $^{210}$Po emits full-energy $\alpha$ particles (~5.3 MeV). If $^{210}$Po (or its parent $^{210}$Pb) diffuses into the bulk, the $\alpha$ particles lose energy before exiting the material, resulting in a "degraded" energy spectrum (lower energy peaks).

Data Analysis & Simulation

• Diffusion Model: The film was modeled as a semi-infinite slab. The concentration $C(x,t)$ was solved using the diffusion equation with a surface source boundary condition:
  $$C(x,t) = \frac{Q}{\sqrt{4\pi Dt}} \exp\left(-\frac{x^2}{4Dt}\right)$$
  Where $Q$ is the deposited amount, $D$ is the diffusivity, and $x$ is depth.
• Separation of Isotopes:
  • $^{210}$Po: Measured immediately after humidity exposure (short half-life: 138 days).
  • $^{210}$Pb: Isolated by subtracting the decaying $^{210}$Po contribution from the total signal over time (long half-life: 22.2 years).
• Simulation: Monte Carlo simulations of 5.3 MeV $\alpha$ particles in 50 $\mu$m nylon were used to correlate energy loss with penetration depth.

3. Key Contributions

• First Quantitative Measurement: Provided the first experimental determination of $^{210}$Pb and $^{210}$Po diffusivity in Nylon-6.
• Humidity Dependence: Demonstrated a massive, non-linear dependence of diffusion rates on relative humidity.
• Isotope Differentiation: Developed a method to distinguish between the diffusion of the parent ($^{210}$Pb) and the daughter ($^{210}$Po) by analyzing the time evolution of the $\alpha$ energy spectrum.
• Systematic Uncertainty Analysis: Rigorously quantified uncertainties related to sample positioning, decay during unmonitored periods, energy scale drift, and fitting procedures.

4. Results

The study yielded specific diffusivity coefficients ($D$) under different conditions:

Isotope	Condition	Diffusivity ($D$)
$^{210}$Pb	40% RH	$< 1.14 \times 10^{-15}$ cm$^2$/s (Upper Limit)
$^{210}$Pb	95% RH	$(4.03 \pm 1.01) \times 10^{-13}$ cm$^2$/s
$^{210}$Po	95% RH	$(3.94 \pm 0.98) \times 10^{-13}$ cm$^2$/s

Key Observations:

1. Humidity Effect: There is an approximate 1,000-fold increase in diffusivity when moving from 40% RH to 95% RH.
2. Degraded Spectra: Under 40% RH, degraded $\alpha$ events were minimal (~1%). Under 95% RH, a significant increase in low-energy events was observed, indicating deep penetration of isotopes into the nylon bulk.
3. Mechanism: The authors attribute the high diffusion at 95% RH to the polar structure of nylon and mechanical degradation of the polymer matrix in high humidity, which facilitates ion transport.

5. Significance

• Impact on Experiment Design: The results highlight that environmental humidity control is critical for low-background experiments. Storing detector components (specifically nylon) in high-humidity environments can lead to rapid internal contamination by $^{210}$Pb and $^{210}$Po, creating background levels that exceed experimental tolerances.
• Material Selection: While Nylon-6 is common, its susceptibility to radon daughter diffusion under humid conditions suggests that material handling protocols must be strictly controlled, or alternative materials with lower humidity-dependent diffusivity should be considered.
• Future Work: The authors plan to systematically study other polymers used in rare-event physics to establish a comprehensive database of diffusion coefficients versus humidity, aiding in the design of future ultralow-background detectors.

In conclusion, the paper establishes that humidity is a dominant factor in the diffusion of radon progeny into nylon, potentially compromising the background purity of sensitive physics experiments if not properly managed.