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The photonic post-processing of suspended carbon nanotube (CNT) ribbons made by floating catalyst chemical vapor deposition (FC-CVD) results in selective sorting of the carbon nanotubes present. Defective, thermally non-conductive or unconnected CNTs are burned away, in some cases leaving behind a highly crystalline (as indicated by the Raman G:D ratio), highly conductive network. However, the improvement in crystallinity does not always occur but is dependent on sample composition. Here, we report on fundamental features, which are observed for all samples. Pulse irradiation (not only by laser but also white light camera flashes, as well as thermal processes such as Joule heating) lead to (1) the sweating-out of catalyst nanoparticles resulting in molten catalyst beads of up to several hundreds of nanometres in diameter on the textile surface and (2) a significant improvement in CNT bundle alignment. The behavior of the catalyst beads is material dependent. Here, we show the underlying mechanisms of the photonic post-treatment by modelling the macro- and microstructural changes of the CNT network and show that it is mainly the amount of residual catalyst which determines how much energy these materials can withstand before their complete decomposition.