Reentrant Phase Diagram of Network Fluids

Abstract

Abstract:We introduce a microscopic model for particles with dissimilar patches which displays an unconventional "pinched'' phase diagram, similar to the one predicted by Tlusty and Safran in the context of dipolar fluids [Science 290, 1328[Science 290, (2000]. The model-based on two types of patch interactions, which account, respectively, for chaining and branching of the self-assembled networks-is studied both numerically via Monte Carlo simulations and theoretically via first-order perturbation theory. The dense phase is rich in junctions, while the less-dense phase is rich in chain ends. The model provides a reference system for a deep understanding of the competition between condensation and self-assembly into equilibrium-polymer chains.

Self-Assembly in Chains, Rings, and Branches: A Single Component System with Two Critical Points

“…Two recent investigations have provided insights particularly relevant for this work: (i) a numerical study of Janus colloids in which a gas-liquid critical point and a self-assembly process are simultaneously observed [15,16]. In this model, the formation of energetically stable vesicles stabilizes at low temperature T the gas-phase; (ii) a study of particles with dissimilar patches [17][18][19], promoting respectively chaining and branching, specifically designed to reproduce a mean-field model introduced by Safran and Tlustly [20] to describe the phase behavior of dipolar fluids. Here branching produces a gas-liquid critical point, but on cooling the formation of energetically favored chains stabilizes, this time, the liquid-phase.…”

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

“…1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 A more interesting consequence of using the 2A+1B patchy model is that, if our mapping is valid, then the phase diagram of DYHSs should be rentrant, or 'pinched' in the ǫ * Y → 0 limit: for T * < ∼ (2/3)T * c , the density difference between the coexisting liquid and vapour phases decreases as the temperature is further lowered. This is in stark contrast to the behaviour of most fluids, but has actually been confirmned by simulation of 2A + 9B patchy colloids [31].…”

“…As ǫ * Y → 0 and the DHS limit is approached, the phase diagram develops a 'pinch', or re-entrance, at low temperatures: the densities of the coexisting liquid and vapour phases become more similar, rather than more different, as is the norm in most fluids. This is a consequence of the fact that 1/3 ≤ ǫ AB ≤ 1/2, and was previously observed in a Monte Carlo simulation of a variant of our patchy fluid with two A and nine B patches [31]. In the present model this pinching only appears at the smallerst ǫ Y , for which the chaining/branching competition dominates over the effect of isotropic interactions.…”

“…The energy cost of this Y-junction is thus −ǫ AB + ǫ AA /2. Moreover, it was also shown that Wertheim's first order perturbation theory [27][28][29][30], as applied to the patchy model predicts the same phase behaviour as TS: a critical point can only exist if ǫ AB > ǫ AA /3 (which is equivalent to ǫ j > ǫ e /3 in the TS model); coexistence, when present, is between a low-density phase with few AA and AB bonds, and a high-density phase rich in AB and AA bonds; and pinching is also observed [31].…”

“…In fact, both configurations seem reasonable for Y-arrangements of dipoles: (a) results from slightly bending one chain and attaching another chain at the bend; (b) is a highly symmetric (ring-like) configuration that corresponds to the lowest possible energy. Choosing (a) or (b) has completely different consequences for the phase behaviour [26,33]: (a) corresponds to ǫ AB /ǫ AA ≈ 0.105 (i.e., ǫ AB /ǫ AA < 1/3) and thus to the absence of a critical point, whereas (b) corresponds to ǫ AB /ǫ AA = 0.875 (i.e., ǫ AB /ǫ AA > 1/2) and thus to the existence of a critical point that is not of the TS type, since the ground state is not a gas of long chains [31]. In order to avoid this somewhat arbitrary (and possibly biased) choice, we will let u 3 (or, equivalently, ǫ AB ) be a free parameter of the patchy model, and determine it by fitting the DYHS thermodynamics as determined by simulations [13] to that of our 2A + 1B model.…”