A simple theory for entropic interaction induced between large spheres in a binary mixture of small and medium spheres

We develop a simple theory for the entropic interaction between large spheres immersed in a binary mixture of small and medium spheres. In the context of the Asakura-Oosawa-type theory, the densities of small and medium spheres were assumed to be uniform except within the excluded volumes generated by the large spheres. In this study, two essential terms are newly formulated as correction terms for the uniform density approximation employed in the theory. The first part represents the entropic gain arising from the holding of a medium sphere which accompanies an increase in the total volume available to the translational displacement of small spheres and the other medium spheres. The second one accounts for the entropic loss caused by the restriction of translational freedom of the medium sphere held. It is important to incorporate both of the two parts in the theory. The resulting theory, which gives us semiquantitatively correct results for the dimerization free energy of large spheres (the difference from the result calculated by the integral equation theory is only ∼20% at usual total packing fractions), enables us to provide a new mechanism of the association of macromolecules arising from the addition of crowding agents.