I suggest you to do a SEM analysis of your sample using low voltage around 30kV (to prevent sample damage) and do an EDS Mapping. It will give you the distribution of particles based on it's chemical composition across the matrix.
If you have nanoparticles in the gel matrix, TEM would be better than SEM because of its higher resolution. By the way, using the EDS probe in SEM could be difficult with nanoparticles because the probed volume at primary energies in the KeV range or higher would be much, much larger than nanoparticles (you will probe essentially your matrix and the S/N ratio FOR THE NP material would be definitively low).
If you are looking for a "size" dispersion, you may also use UV-Vis-NIR spectrophotometry, just in case you have NPs expected to optically respond in that range of wavelengths (e.g., plasmonic NPs show plasmonic resonances like Ag, Au, whilst metal-oxide NPs may show interband or intraband peaks). Of course, a liquid hydrogel is required in that case.
Yes, that's correct. TEM is much more performing at the NP size level than SEM, even if sample preparation could need some more accuracy and statistics would require more (nominally equivalent) samples. After having obtained clear and well resolved images, you can use typical image processing softwares to extract the size distribution from the pictures.
There might be sample damage of the hydrogels upon exposure to high energy TEM. Additionally, most of these samples might not be electron transparent and so doing TEM might be difficult.
Yes, Anirudha Karati, damage of the gel by TEM beam is possible.Of course, using TEM or also SEM means you are destroying your sample.. it isusually a distructive test.
But the wanted information are obtained in any case. When someone prepare a sample for TEM and sometimes for SEM, he/she knows that sample is sacrificed for measurement.
About electron transparency of the sample, you are correct, it can be so. In that case TEM (and I suppose SEM as well) can not be reliably used. We should just try
I will suggest you to go with TEM at low voltage (around 120 kV) (the gel consist nanoparticle should be trimmed in to a thin section; less than 100 nm). But some times, the burning of sample is observed (it dependes upon the base material property). However, in general, FEG-SEM, cryo-SEM is recommended for biological samples. Apart from that you can also perform normal SEM analysis under back scattered imaging option, which will provide you two different contrasts, each may represent gel and nanoparticle. Apart from that AFM can also be used if the gel matrix is having smooth surface. SAXS (small angle x-ray scattering) is a beautiful tool which will provide your the overall distribution and size of nanoparticles in your gel. The choice is yours depending upon the analysis facility at your place.