  In this work, we report on the fabrication of continuous transparent and
flexible supercapacitors by depositing a CNT network onto a polymer electrolyte
membrane directly from an aerogel of ultra-long CNTs produced floating in the
gas phase. The supercapacitors combine record power density of $1370 kW
kg^{-1}$ at high transmittance ($ca. 70%$), high electrochemical stability
during extended cycling ($>94%$ capacitance retention over $20 000 cycles$) as
well as against repeated $180{\deg}$ flexural deformation. They represent a
significant enhancement of 1-3 orders of magnitude compared to the prior-art
transparent supercapacitors based on graphene, CNTs, and rGO. These features
mainly arise from the exceptionally long length of the CNTs, which makes the
material behave as a bulk conductor instead of an aspect ratio-limited
percolating network, even for electrodes with $>90%$ transparency. The
electrical and capacitive figures-of-merit for the transparent conductor are
$FoMe = 2.7$, and $FoMc = 0.46 F S^{-1} cm^{-2}$ respectively
