We understand that if we have more than one particle of each type with equal populations, the portion of the total excluded volume that locates outside of the box is larger when large particles are positioned adjacent to the wall. To quantitatively measure the entropy, we used excess entropy (s ex = ss id ) expression derived from Carnahan-Starling equation of state for hard spheres (described in Methods) . We developed a model containing a binary mixture of hard spheres in a three-dimensional (3D) box with dimensions of 100 Å. For the sake of simplicity, we assumed the excluded volume of particles does not overlap with each other. With this assumption, the occupied volume is calculated by the following equation: