I am not sure if On-Mark Bob is quite correct. I think the main cause of black smoke in jet engines is the way the air and fuel was mixed and burnt in the primary combustrion zone where an over rich mixture was easier to light off and sustain (less chance of flameouts) but resulted in the formation of particulates (soot) like a diesel under load. The JT8D in the DC9, 737 and 727 was originally a filthy smoker, but to meet the anti pollution requirements P & W came up with a smokeless burner can which greatly reduced the amount of smoke to what you see today. Back in the 70's it was quite common to see aircraft flying with what appeared engines inoperative when in reality they were fitted with a mix of modified (smokeless) and original burner cans JT8D's. I don't think there was any measureable efficiency gain with smokeless burner cans.
Hey barit 1, you are right about the Convair 880. After a full power run up there was a layer of soot all over the ramp behind each engine in which noticeable footprints were left if anyone walked over it. GE did come up with a smokeless can for the CJ805 but they fell apart with thermal distress in a fairly short time during in service trials so the operator I was involved with abandoned them.