The hydrolysis reaction of APTES is self catalyzed since the presence of amine groups offers this task for both hydrolysis and condensation reactions for the same kinetics that offered by acid or base-catalyst which is often used as potent catalyst in stöber method with the single alkoxides that free of amine groups.
Yes dear Vijay Chavan , I have looked at the yellow highlighted paragraphs of the attached paper. I am afraid that you missed the route as you not concentrate on your question goal. Please make only the section "1.3. Organic Solvent Deposition" as your road map as this method is convenient for use in silica particle modification and as can see it is in full agreement with my answer.
Dear Mohammed Hussein j. H. Al'Atia, I had tried that method but I don't know why it is not working.
The following attachment is the IR spectra of Fe3O4@SiO2 and Fe3O4@SiO2@APTMS please see it's not showing a predominant peak of -CH2 group of APTMS, Even I had tried with APTES but the result is same.
Yes dear Vijay Chavan I have quick looked on the result you got in Fe3O4SiO2APTMS.pdf. It seem to me that you did well to get the modification coating by the APTES as I see two peaks area within the band in the region 2850-2950 cm-1. This region is often assigned to symmetric vibration of the C-H group, therefore such function indicates the intensity of the organic substitution in the obtained modified silica. Now, if you look at the results in Fe3O4SiO2.pdf,you never got such peaks which mean that there are not any sign for any amine modification coating.