If we consider the distribution of spherical shape particles in a polymer matrix, what would be the criteria for saying that the distribution of these particles is homogeneous into this matrix ?
You can confirm the homogeneous dispersion of the particle in the polymer matrix by electrical percolation or rheology percolation method. However, it depends on the particle to be used in the matrix.
I was wondering which parameter would describe the best, of a homogenous distribution, like (mean) interparticular distance,... For exemple, if you have a SEM picture of the particle/matrix blend how can say if the distribution is homogenous.
Coming to your answer, is it possible to characterize the homogeneity when the composition is far below the percolation threshold?
The electrical and rheology percolation method denotes that the filler is homogeneously dispersed below that percolation (particular wt. % of filler) beyond which the dispersion is not uniform agglomeration may happen.
You can do TEM or SEM. Then you have to use the proper software-image analysis to calculate both: the size distribution and interparticle distane. The problem in image analysis is in case the paarticles touch each other-the analysis is longer.
In the beginning you can just look at the iamge and estimate visually the homogeneity of the particles and even measure witha ruler some parameters.
Regardless of previous methods mentioned by Prof. Janik and Mr. Arun, there is another method which is a little bit difficult but precise as follows:
Find a solvent for your matrix which is a non-solvent for the particles. (for example toluene for PVA dispersed in PS matrix...) then, wash the matrix with the solvent. Now, we have particles dispersed in the nonsolvent (medium) ..., Use Dynamic Light Scattering (DLS) or Static light scattering in order to measure particle size and its distribution.
Despite the fact that image analysis softwares are useful, they are not as precise as DLS and SLS since your SEM and/or TEM images are not representative of whole sample and all the partciles !!!
I agree with Hossein Adelnia: this method I used as well for some polymer blends. You can modify the final step and instead to use DLS you can put the particles to SEM or TEM-it depends what you have in your lab; DLS or TEM/SEM.
The method proposed by Hossein is very interesting. But how to know the initial position of each particle when the polymes is dissolved. If I have a 3D sample, when the polymer is dissolved, the particles don't keep their initial position. This phenomenum is more problematic if I have the nanoparticles. I understood that the particle size distribution can be determined by DLS but is it possible to use DLS for particle distribution (not size distribution)?
Concerning the method proposed by Helena, that is what I would like to use even a SEM/TEM picture doesn't represent the whole sample. After measuring the size and interparticular distance (ID), how to say the distribution is homogenous? Do I calculate the mean ID and compare each distance by the ID and plot the ID distribution?
Which software are you using? I know that ImageJ is frequenty used free software.
As it was mentioned, the sample should be immersed in a solvent which is a non solvent for particles. as an example I mentioned to Poly vinyl alcohol diapered in Polystyrene matrix. if toluene is used. it is ok. it is a non solvent for PVA. So, the PVA particles dimension will remain intact. nothing changes. and it does not matter whether its nanoparticles or micropatilces you have. DLS will give you precise results. Be sure that non solvent does not change the particles dimension. because particle dimension in solid state is equivalent to when it is dispersed in a non solvent.
another important point: for sample preparation try to prepare a low solid content dispersion in order to avoid from any coagulation !!!!
Let me add this that this method does not give you interparicle distance !!!
it will give you precise particle size and particle size distribution ...
should you need any other information, please feel free to ask
Fundamentally depends on the aggregation state of the sample. But if it´s a solid CT Scan I think is the best choice. Furthermore is a non destructive technique.