Criticality of colloids with distinct interaction patches: The limits of linear chains, hyperbranched polymers, and dimers

Abstract

We use a simple model of associating fluids which consists of spherical particles having a hard-core repulsion, complemented by three short-ranged attractive sites on the surface (sticky spots). Two of the spots are of type A and one is of type B; the bonding interactions between each pair of spots have strengths epsilon(AA), epsilon(BB), and epsilon(AB). The theory is applied over the whole range of bonding strengths and the results are interpreted in terms of the equilibrium cluster structures of the phases. In addition to our numerical results, we derive asymptotic expansions for the free energy in the limits for which there is no liquid-vapor critical point: linear chains (epsilon(AA) not equal to 0, epsilon(AB)=epsilon(BB)=0) , hyperbranched polymers (epsilon(AB) not equal to 0, epsilon(AA)=epsilon(B)=0) , and dimers (epsilon(BB) not equal to 0, epsilon(AA)=epsilon(AB)=0) . These expansions also allow us to calculate the structure of the critical fluid by perturbing around the above limits, yielding three different types of condensation: of linear chains (AA clusters connected by a few AB or BB bonds); of hyperbranched polymers (AB clusters connected by AA bonds); or of dimers (BB clusters connected by AA bonds). Interestingly, there is no critical point when in(AA) vanishes despite the fact that AA bonds alone cannot drive condensation.

Fabrication, Assembly, and Application of Patchy Particles

“…Many other models have been developed to describe patchy particle interactions and the main approaches are reviewed in the following section. There are four different categories of models to distinguish based on how the patchy interactions are incorporated in the simulations: i) patchy particle models, involving a pair potential function that depends on the distance and orientation of particles, [108][109][110][111][112][113][114][115][116][117] ii) particle models with distinguishable ''atoms'' belonging to the patch and the core particle, [36,41,42,[118][119][120][121][122] iii) models for interactions between proteins, [123][124][125][126][127][128][129][130] and, iv) a density functional theory (DFT) approach incorporating anisotropic interactions between particles. [38,40] Note that the various theoretical studies involving patchy interactions reviewed in the following are categorized based on the approach and the model involved to address the patchy interactions between particles rather than the type of method used in the simulations.…”

“…Tavares et al [117] investigated the role of dissimilar patches in colloidal interaction to shed light on dipolar fluid behavior. They uses a hard sphere model with three patches located, equidistantly-spaced at the particle equator, of which two are of type A and one is of type B.…”

Patching up dipoles: can dipolar particles be viewed as patchy colloids?

“…By contrast, the entropy of the bonded patches is related to their size and to the properties of the reference system [26,32]. Therefore, when comparing both models with simulation results, better agreement is expected for the patchy model.…”

“…The 2A + 1B model of patchy particles will then consist of HSs of diameter σ, which attract isotropically through the same Yukawa potential as the DYHS fluid, but where the central dipole has been replaced by two patches of type A and one patch of type B, placed on the HS surface [26]. These patches may form AA and AB bonds, which lower the energy by ǫ AA and ǫ AB , respectively.…”

“…In recent work [26], we have established an analogy between Tlusty and Safran's (TS) model [24] and patchy particles with three bonding sites (patches), two of type A and one of type B. In this model, henceforth denoted 2A + 1B model, particles can bind to each other through their patches, thereby forming AA bonds that lower the energy by ǫ AA , and AB bonds that lower the energy by ǫ AB .…”