In this paper, we develop a thermodynamic perturbation theory to describe theself-assembly of patchy colloids which exhibit both patch-patch attractions aswell as patch / non-patch attractions. That is, patches attract other patchesas well as the no patch region. In general these attractions operate ondifferent energy scales, which allows for controlled self-assembly as well asanomalous phase behavior. As an application we apply the model to the study ofliquid water.
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