I think that electrostatic forces can affect the surface of the particle and obtain particle agglomerates fastly. The double layer theory explain these effect. It is different when you use carboxilate group or hydrogen in the surface than when you use oxygen for example. All these interactions can affect the stability of the particle (agglomerate) formed.
Well, I think the hydrophobicity is important for the supported catalyst synthesis to some extent if you are in situation of challenging water management (i.e fuel cells). Again, too much hydrophobic support is not necessarily good for the catalyst performance because water activation is necessary for fuel cells.
I investigated the effect of carbon support acid functionlization on the catalyst particle size and found that the crystallite size increased with using the functionalized support. But the functionalization impact is very controversial research topic though many researchers advocate some sort of chemical or physical activation.
The homogeneous formation of the nucleus of a new phase is observed when there are no surfaces in the system on which the formation and growth of the nuclei of a new phase occurs at a sufficient rate.
The heterogeneous formation of the nucleus of a new phase is observed with the introduction of the seed of the substance of the new phase itself or of a substance close to it in structure and properties.
You give an example of a heterogeneous formation of a new phase. Therefore, the surface of the old phase will affect the formation of a new phase. Particles of metals are hydrophilic. Therefore, the hydrophilic old phase will affect their formation. The hydrophobic phase will affect much less. Of course, one cannot exclude another interplay of the chemical structure of both phases.
In a specific case where if i am using two carbon supports having massive difference in surface area ( 250 m2/g to 1250 m2/g) with out any specific treatment for reducing a metal or bimetallic alloy particle ; will the surface feature like hydrophilicity of the high SA carbon help in yielding a much smaller average particle size ? (although the enhanced surface area can definitely help in yielding nanoparticles)
Hydrophilic carbon does not happen. He is always hydrophobic. The substrate with the thermodynamic theory should reduce the Gibbs surface energy or, according to the kinetic theory, the activation energy of the formation of the nucleus of a new phase. I doubt that a hydrophobic substrate with a covalent bond affected the formation of hydrophilic metal nanoparticles with a metal bond.
As Prof. Yuri Mirgorod mentioned carbon is always hydrophobic. The particle size is not likely to increase or decrease with the carbon hydrophobicity but with the synthesis method, operational temperature, and whether it is a monometallic or multimetallic.