well, the increasing of particle size might be the agglomeration of adsorbent particle after adsorption. if you want to make sure that the metal is adsorbed on adsorbent surface you need to characterize it by elemental analysis (EDS). IR could be employed also (the occurrence of new spectra ot shifted initial spectra. But it doesnt mean that the increasing of particle do not relay to the metal have adsorbed.
I suggest particularly for metal adsorption SEM can be done, in which bright spots of metal adsorbed on material can be viewed. Best would be to carry before and after analysis of samples. The particles size increases can give no direct clue of adsorption its directly related to agglomeration
it depends upon whether metal ion is chemisorbed/ physisorbed on the surface modified adsobents or plain surface having neutral surface functional groups. with sufficient mobility the metal ions migrate to form aggregates/aggelomerates with changing parameters. You need to find out the avarage particle size distribution prior and after you alter the parameters. if you work with porous adsorbents you may observe the change in the pore size distributions/ pore volume as well.
whenever adsorption experiments are carried out under uncontrolled pH conditions, initially the pH of the solution rises, due to which metal may get precipitated and may get attach to the adsorbent particle (which can be removed by just washing with water). As it is well known that adsorption is the phenomenon which takes place in micro levels, even though adsorbent adsorbs all metal ions present in solution,the increase particle size cannot be recognized so easily. but one simple approach is that, by measuring the weight of the adsorbent before and after the experimentation (quantitative).
I do not know about the chemical composition of your bare samples but if they are differ from the deposited metal ions. They must be differentiable through a HR-TEM image. Actually the thickness may be measurable in that sense. Furthermore if the expected size increase is huge enough they may be separeted from each other with membranes and that will be an absolute proof with an elemental analysis. But if you don't have any of these possibilities then you should find and imaging technique with an elemental analysis detector. There are such systems like EDX detector attached FESEM instruments for this type of analysis.
Agglomeration is a problem, so use SEM / TEM depending on the size of the particles which will show you exactly whether the sample is agglomerated or the particles are free. Also examine effect of pH on the adsorption of an entity as well as kinetic studies using batch method.