If you really want silence at the end, then the last beat should be a dotted eighth followed by a small rest. In addition, as a string player, I would need more specific instructions for the articulated quarter notes. By the way, why are they articulated? Because it's slow, and I would run out of bow if it were one long (tied) note?
In short, each quarter note should have a starting and ending dynamic indicated, with an individual decrescendo. Otherwise, the performer might give you a terraced effect.
Note that unless the performer knows you really want a note to fade to nothing, then even a triple p will be interpreted as needing to be audible to the audience. (Composers' dynamic markings tend to be interpreted as intentions more than actual reality.)
By the way if what you want is four sighing sounds, each successive one softer than the previous one, then you would start each quarter note a little louder than the previous one ended.
But let's say you decide you don't need the articulation and you decide to go with a dotted half tied to a dotted eighth followed by a tiny rest. We kind of need to know what comes next so we can recommend appropriate bowing.