Long-lived radon daughters are a critical background source in experiments searching for low-energy rare events. Originating from radon in ambient air, radioactive polonium, bismuth and lead isotopes plate-out on materials that are later employed in the experiment. In this paper, we examine cleaning procedures for their capability to remove radon daughters from PTFE surfaces, a material often used in liquid xenon TPCs. We found a large difference between the removal efficiency obtained for the decay chains of $^{222}$Rn and $^{220}$Rn, respectively. This indicates that the plate-out mechanism has an effect on the cleaning success. While the long-lived $^{222}$Rn daughters could be reduced by a factor of ~2, the removal of $^{220}$Rn daughters was up to 10 times more efficient depending on the treatment. Furthermore, the impact of a nitric acid based PTFE cleaning on the liquid xenon purity is investigated in a small-scale liquid xenon TPC.
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