You can use AFM ,SEM and BET measurements to confirm the characterization of your particles surface. Existence of dye molecules onto surface may block active cites and change roughness and other surface properties.

Presumably the dye is incorporated either during fabrication of the beads or using a solution delivery. In the former case, the dye likely segregates differently across the surface. In the latter case, the dye adsorbs preferentially on specific active sites. In both cases, the surface chemistry of the dye-PS beads will be different than the surface chemistry of the bare-PS beads. This is a difference in the NATURE of the bead. Properties that are affected by surface chemistry include zeta potentials and contact angles. Spectroscopic techniques such as FTIR, Raman, UPS, or XPS will characterize the differences in the nature of the surface chemistry.

I would be inclined to say that any changes in surface structure, topography, or roughness (which are measures of the NATURE of a surface not of its properties) due to the dye will have less affect on properties than what is affected by the change in surface chemistry. I doubt that AFM will be feasible to perform on the bead, and BET is sensitive to the chemistry of the absorption site.