DCM is my choice solvent as well, It has so many wonderful qualities.
I get most of my DCM how gory dkalz mentioned, via distillation from a hardware store product.
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About the N-chloro-DMT, my take on this reaction, is there is no issue due to its equilibrium .
I'm guessing this reaction reaches equilibrium at the same point it starts. Meaning the compound is formed, but as soon as it forms, within nanoseconds it forms the original reactants.
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Im wondering if you were to put this through a mass spec, the DMT in DCM solution, and get readable results, then see if this compound is noticed in the spectrum.