Good question. There is no simple answer.
I would not recommend eliminating the data. The fact that NPs did not form under those conditions is important information.
If I understand correctly, your measured response is particle size. Obviously you don't have a particle size for runs where no particles were formed.
For those runs you could put a very small number for particle size (no particle is the same as infinitely small particles!). This is a bit of a cheat but it could still help to build a useful model.
You could also have a separate column with a binary response: particles yes/no. You could use this to build a separate model. You should know that binary response contain less information than continuous responses.
If you have JMP Pro you could define the response with a "limit of detection". That is, a particle size limit below which you can't detect particles. Your no-synthesis runs would be below this limit of detection. And you can build a model that takes this information into account. I think this will probably be the most useful solution.
(You should also know that if you choose your native language in JMP Community you can post in that language and it will auto-translate into the chosen language of other community users.)
I hope that helps,
Phil