Currently, I work to prepare nano-copper oxide by photolysis methods but why when increasing the polar of solvent causes decrease the size of particles
I am surprised when you say that the use of polar solvents decreases the size of the particles.
I have worked on the precipitation of oxalates in the past and I have observed that the decrease in dielectric constant for the solvent led to a decrease in particle size. It was ascribed to the the decrease in solubility product of the oxalate, which facilitates the formation of homogeneous nuclei at the expense of crystal growth (heterogeneous germination).
The paper below gives an illustration for copper (generally covered by copper oxide) of the low effect of the dielectric constant, when we go from water to ethanol and then to butanol:
Copper Nanoparticles Prepared from Oxalic Precursors Baco et al. ISRN Nanotechnology
Volume 2011 (2011), Article ID 729594.
But I don't know your preparation process. Perhaps a high dielectric constant facilitates the increase in reactants concentration? High reactants concentrations lead to a decrease in particle size for precipitation reactions.
I recommand you to have a look on the classical homogneous nucleation theory (for instance you will find information at https://en.wikipedia.org/wiki/Classical_nucleation_theory). There is an expression of the free energy barrier (delta)G* needed to make an homogeneous nucleus able to growth spontaneously.
This energy is inversely proportional to (delta)g2 and (delta)g is proportional to the ln of the supersaturation S. S is equal to the (ionic product divided by solubility product). So, if you decrease the solubility product of a ionic compound by decreasing the dielectric constant of the solvent, you increase S and finally you make the formation of homogeneous nuclei easier.
At the end of the chemical precipitation you will then obtain a higher number of homogeneous nuclei i.e. a higher number of particles, because of the decrease in the dielectric constant of the solvent. For a given quantity to precipitate, the particles will be then smaller, because this quantity will be divided by a greater number of particles.
I hope my explanation is clear. You have to remember that (delta)g is proportional to S and S increases when the dielectric constant decreases for ionic compounds.
Such an interpretation works quite well for small particles of oxalates, which are more or less single crystals. During the chemical precipitation there are sometimes aggregation phenomena, leading to larger particles or other phenomena. In this case my explanation doesn't work. I am not able to know for instance, the relation between these aggregation phenomena an the dielectric constant.
The principles of Relative super saturation (RRS) provide some useful information on of how to control crystal growth and precipitation size by different concentrations of reagents and the temperature