Diffusion of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mmultiscripts> <mml:mrow> <mml:mi>Pb</mml:mi> </mml:mrow> <mml:mprescripts/> <mml:none/> <mml:mrow> <mml:mn>210</mml:mn> </mml:mrow> </mml:mmultis

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>β</a:mi> </a:math> decay, due to their origin as unavoidable decay products of natural uranium. In particular, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:mmultiscripts> <c:mrow> <c:mi>Rn</c:mi> </c:mrow> <c:mprescripts/> <c:none/> <c:mrow> <c:mn>222</c:mn> </c:mrow> </c:mmultiscripts> </c:mrow> </c:math> and its long-lived daughter <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:mmultiscripts> <e:mrow> <e:mi>Pb</e:mi> </e:mrow> <e:mprescripts/> <e:none/> <e:mrow> <e:mn>210</e:mn> </e:mrow> </e:mmultiscripts> </e:mrow> </e:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:mmultiscripts> <g:mrow> <g:mi>Pb</g:mi> </g:mrow> <g:mprescripts/> <g:none/> <g:mrow> <g:mn>210</g:mn> </g:mrow> </g:mmultiscripts> </g:mrow> </g:math> and its daughter <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mrow> <i:mmultiscripts> <i:mrow> <i:mi>Po</i:mi> </i:mrow> <i:mprescripts/> <i:none/> <i:mrow> <i:mn>210</i:mn> </i:mrow> </i:mmultiscripts> </i:mrow> </i:math> under varying humidity conditions. Our results show that both <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"> <k:mrow> <k:mmultiscripts> <k:mrow> <k:mi>Pb</k:mi> </k:mrow> <k:mprescripts/> <k:none/> <k:mrow> <k:mn>210</k:mn> </k:mrow> </k:mmultiscripts> </k:mrow> </k:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:mmultiscripts> <m:mrow> <m:mi>Po</m:mi> </m:mrow> <m:mprescripts/> <m:none/> <m:mrow> <m:mn>210</m:mn> </m:mrow> </m:mmultiscripts> </m:mrow> </m:math> 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 <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mmultiscripts> <o:mrow> <o:mi>Pb</o:mi> </o:mrow> <o:mprescripts/> <o:none/> <o:mrow> <o:mn>210</o:mn> </o:mrow> </o:mmultiscripts> </o:mrow> </o:math> was found to be lower than <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mn>1.14</q:mn> <q:mo>×</q:mo> <q:mrow> <q:msup> <q:mrow> <q:mn>10</q:mn> </q:mrow> <q:mrow> <q:mo>−</q:mo> <q:mn>15</q:mn> </q:mrow> </q:msup> <q:mtext> </q:mtext> <q:mtext> </q:mtext> <q:msup> <q:mrow> <q:mi>cm</q:mi> </q:mrow> <q:mn>2</q:mn> </q:msup> <q:mo>/</q:mo> <q:mi mathvariant="normal">s</q:mi> </q:mrow> </q:math> at 40% relative humidity (RH) and to be <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"> <t:mrow> <t:mo stretchy="false">(</t:mo> <t:mn>4.03</t:mn> <t:mo>±</t:mo> <t:mn>1.01</t:mn> <t:mo stretchy="false">)</t:mo> <t:mo>×</t:mo> <t:msup> <t:mrow> <t:mn>10</t:mn> </t:mrow> <t:mrow> <t:mo>−</t:mo> <t:mn>13</t:mn> </t:mrow> </t:msup> <t:mtext> </t:mtext> <t:mtext> </t:mtext> <t:msup> <t:mrow> <t:mi>cm</t:mi> </t:mrow> <t:mrow> <t:mn>2</t:mn> </t:mrow> </t:msup> <t:mo>/</t:mo> <t:mi mathvariant="normal">s</t:mi> </t:mrow> </t:math> at 95% RH. The diffusivity of <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:mrow> <y:mmultiscripts> <y:mrow> <y:mi>Po</y:mi> </y:mrow> <y:mprescripts/> <y:none/> <y:mrow> <y:mn>210</y:mn> </y:mrow> </y:mmultiscripts> </y:mrow> </y:math> at 95% RH was measured to be <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mrow> <ab:mo stretchy="false">(</ab:mo> <ab:mn>3.94</ab:mn> <ab:mo>±</ab:mo> <ab:mn>0.98</ab:mn> <ab:mo stretchy="false">)</ab:mo> <ab:mo>×</ab:mo> <ab:msup> <ab:mrow> <ab:mn>10</ab:mn> </ab:mrow> <ab:mrow> <ab:mo>−</ab:mo> <ab:mn>13</ab:mn> </ab:mrow> </ab:msup> <ab:mtext> </ab:mtext> <ab:mtext> </ab:mtext> <ab:msup> <ab:mrow> <ab:mi>cm</ab:mi> </ab:mrow> <ab:mrow> <ab:mn>2</ab:mn> </ab:mrow> </ab:msup> <ab:mo>/</ab:mo> <ab:mi mathvariant="normal">s</ab:mi> </ab:mrow> </ab:math> . These findings underscore the importance of controlling environmental