I think you need to do some more thinking and look into the literature. And if you do look at literature I am pretty positive you will find that no potential exists for what you're trying to do. The problem you are suggesting is multiscale in nature. What's the ratio of the diameters for the sand to
nanoscale filler ratio? 1 mm:100nm? = 10000:1 - now cube that for a volumetric ratio. You're not likely going to be putting physical sand particles and clay particles in the same box.
You'll likely need several methods for the various things you're trying to model. And advice on tackling your entire complex research problem (unless you narrow your scope significantly, e.g. thermal conductivity of some more well-defined clay) is likely out of scope of the LAMMPS list. Heck, depending on what is known about your problem, particle methods may not at all be appropriate.
What you'll do will depend entirely on what you already know, and what you want to know/model.