Our injection method is manual (another cheap out), so what I am doing right now is using temperature conditions similar to our pilot process (which may decompose and/or volatilize the analytes), and sampling the headspace. Is this even a proper process? Really, I am just trying everything to learn more and obtain responses to present species. I have had no such luck with this method, but I had broken our gas tight syringe so I was using some cheaper ones. I ordered some more gas tight syringes, so I think we will get better results this way but I will just have to wait and see. The measurements don't need to be super accurate, since these numbers don't need to be reported (it is for our own understanding). I will also be taking some liquid samples, which I am not concerned about determining results.
Would you mind explaining how you know when you are experiencing a matrix effect?
Wow! Its sounds like you've really drawn the short straw here... You have my sympathies and my respect for giving it a damn good go under difficult circumstances!
From what I gather, your pilot process possibly produces some volatile analytes (are you able to share what these might be at all?) which you would like to measure. You've used a method - which sounds very much to me to be a perfectly legitimate form of static headspace sampling - which involves (in your case) withdrawing a syringe worth of headspace into a gas syringe and injecting it into your GC (FID, MS, ECD?). So far you haven't been able to spot any analyte in your headspace samples...
As a start, to give yourself a bit of background knowledge you might like to consider this link as a fair start... I recommend the whole site (LCGC) generally: https://www.chromatographyonline.com/view/static-headspace-sampling
There could be myriad reasons for your results or lack thereof.
It might be that your analytes are not there or have decomposed - Clearly something that you have considered as a possibility. Worth further investigation.
Sample volume/method sensitivity might be another possibility - How much headspace are you recovering? My students do a practical looking at headspace analysis of accelerants (normally a simple mixture of neat Octane and Ethanol seeded in quite high volume onto some burnt debris) and with our old teaching GC-FIDs they sometimes struggle getting decent results even when injecting 1ml of headspace! Sometimes this is down to gas syringes and needles (which love to irreversably ingest septum and block up), but it might also be that FID (if that's what you're using?) doesn't have the sensitivity that you need!
Another factor (assuming that your reaction is liquid phase) is that your analytes are very happy dissolved in your solvent and don't want to partition into headspace. You can change the partition coefficient with heat and you could also try salting-out to force more of the analytes to enter headspace and then sample when at their new more headspace favourable equilibrium. That said, switching to dynamic headspace methods or purge and trap (which are not cheap so are probably not feasible) might be your best bet... With these techniques, if the analyte is there, it's going to come out whether it likes it or not! Failing this, have you considered SPME?
In terms of the matrix effect question, you might find the link below to be useful...https://www.e-b-f.eu/wp-content/uploads/2018/06/fw201709-30.-Benno-Ingelse-Matrix-effect.pdf
From what I can see, this is very much LC focused and GC is a little different (as the number of active sites in the liner does change over time as it degrades), however the principle is broadly the same.
One last point - The use of manual injections (even with liquid injections) almost always requires internal standards (as suggested by BH) as the run to run variability would be too high otherwise. Our GC-MS/MSs with auto-samplers are supposed to have volumetric accuracy; but even with these I always run with IS with my liquid samples, partly because the volumetric accuracy thing is only true in the advertisements and partly to account for changes in MS gain or inlet liner changes. There's nothing more frustrating when after 42 days of stability testing, the technician tells you that they had to clean the MS source and that now the analyte peaks have 120% the area as they did the day before. Not a problem if you use an IS!
In terms of IS the following might be of interest: https://www.chromatographyonline.com/view/when-should-internal-standard-be-used-0
This might help address whether acetone would be a good call or not... I suspect not!