Our clinic receives samples of this problem only sporadically but when one arrives we still puzzle over the cause. Over the years multiple diagnosticians have looked for a pathogen, mite or insect that may be causing twigs on arborvitae to turn shiny black as in Figure 1. To my knowledge none have found a connection. We have speculated about chemical injury in some cases but most samples involve only one or two twigs randomly scattered in a planting; a distribution that does not point to chemical injury. Likewise if drought or winter injury were the cause we would expect the damage to be more widespread. While the cause remains a mystery the good news is that the problem does not spread to other plants. Figure 2 shows a close-up of an affected twig. What to do? Prune out the black twigs, taking care not to cut any more material than necessary. In general provide normal care for arborvitae: water during hot dry periods, mulch correctly to keep down weeds and conserve moisture and fertilize lightly in the spring to promote new growth.
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Also see this article on Arborvitae problems: