Na+ and K+ content in plant tissues is usually determined by the freeze-thaw method (Cuin TA, Tian Y, Betts SA, Chalmandrier R, Shabala S: Ionic relations and osmotic adjustment in durum and bread wheat under saline conditions.Funct Plant Biol 2009, 36(12):1110-1119.) in tissue frozen at -20oC. If you keep your samples in closed bags -80oC will not affect the results.
Once leaf samples are removed from the plant, the elements in them won't leave the tissue unless leaf sap is coming out, or something degrades the tissue (fungus, insects etc). If frozen at -80C, the leaf samples are fine untill defrosted. If oven dried at +80C they will be suitable once they reach constant weight (ie no more water left in tissue).
To prepare samples for flame photometry, I would suggest oven drying (+80C), grinding to a homogenous powder and acid digesting (or at least dissolving/leaching in acid eg 4% HNO3). As well as calibration solutions (ie. more than one), prepare blanks and a solution of known concentration and if possible, a reference material of known Na and K concentration as well. Test the known concentration solution regularly through the run. A colleague of mine once spent months working with a flame photometer that had drift issues of 10-20% over several hours of use, and a distinctly non-linear response. Eventually he got it working well, but it had provided much data for many previous studies that we have severe doubts about now.
Yes I do: Wheal, Fowles and Palmer 2011. There are three methods described.
You may find leaching in hot (95deg) dilute (4%) nitric acid also works, see Wheal and Palmer 2010. This may not extract quite as much K from your samples, which is why a reference material is important to include in each batch of samples. I think it was fairly effective on Na from leaf material, it will depend on what sort of leaves: hard sclerophyll leaves will be difficult to penetrate, while high water content leaves like lettuce and spinach will be a lot easier.
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