Characterization of the structural collapse undergone by an unstable system of ultrasoft particles

The effective repulsion between macromolecules such as polymer chains or dendrimers is everywhere finite, implying that interaction centers can even coincide. If, in addition, the large-distance attraction is sufficiently strong, then the system is driven unstable. An unstable system lacks a conventional thermodynamics since, in the infinite-size limit, it eventually collapses to a finite-size cluster (for instance, a polymer dispersion undergoes irreversible coagulation when increasing the amount of dissolved salt beyond a certain limit). Using a double-Gaussian (DG) potential for demonstration, we study the phase behavior of a system of ultrasoft particles as a function of the attraction strength η. Above a critical threshold ηc, the DG system is unstable but its collective behavior is far from trivial since two separate regions of the thermodynamic plane can be identified, based on the value taken by the average waiting time for collapse: this is finite and small on one side of the boundary, while presumably infinite in the other region. In order to make sense of this evidence, we consider a stable system of particles interacting through a DG potential augmented with a hard core (stabilized DG, or SDG potential). We provide arguments supporting the view that the boundary line of the unstable DG model is the remnant of the spinodal line of a fluid-fluid phase transition occurring in the SDG model when the hard-core diameter is sent to zero.