SHS. Even on the size-dependence of $\tau _{ij}^{-1}$ some possible support of the proposed forms may be argued [@Fantoni06; @Gazzillo06].

Conclusions
===========

In this work we have summarized recent advances in predicting theoretically the phase diagram for polydisperse suspensions of colloidal particles with surface adhesion, within the simple description of Baxter’s model. Emphasis was put on the crucial – unsolved – step required to get the multi-component SHS-PY solution, and the proposed recipies to deal with this problem. This first one is based on a simplification of the closure. It has the advantage of allowing a complete analytical analysis on the effects of polydispersity, including fractionation, but has the disadvantage of a very questionable accuracy. The second one is based on a perturbative method, starting from the energy PY one-component solution, which is known to provide an accurate description of the phase diagram. The drawback of this scheme is that it works for mild polydispersity, and that cannot describe the changes of the critical point region. Notwithstanding these limitations, this novel approach is expected to find practical application in the interpretation of all those phenomena where Baxter’s model and polydispersity both play a privileged role.

**Ackowledgments**\
Part of the work 