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.

The present understanding of how dipolar forces affect the structure and phase behaviour of classical fluids is reviewed. We focus mainly on the apparent absence of a liquid-vapour phase transition for strongly polar spherical particles, and discuss how the same can be recovered. By concentrating on theoretical and simulation studies of simple models, the roles and interplay of dipolar and Van der Waals interactions and molecular shape can be clearly discerned. Connection is made with experimental work on ferrofluids. Finally, we discuss the theoretical and computational challenges that lie ahead.

We propose a simple statistical mechanical theory for a strongly dipolar fluid at low densities, based on the analogy between a polymer chain and a chain formed by strongly polar particles. The general methods developed in the theory of semiflexible polymers enable one to obtain simple expressions for the energy and conformational entropy of a long dipole chain. We then consider the equilibrium between chains of different lengths and derive a general expression for the free energy as a functional of the chain length distribution. Both steric and dipolar interactions between long chains are shown to be weak and as a result the rarefied fluid of strongly dipolar spheres resembles the ideal gas of noninteracting polydisperse chains. It is shown that the chain length distributions found in simulations are compatible with the assumption of very weak interchain interactions if strong finite-size effects are taken into account. We also investigate whether sufficiently strong attractive van der Waals forces between particles can cause dissociation of the chains. Finally, we discuss the case of a dipolar fluid in an applied field and argue that the coexistence between two aligned phases of chains, as observed by computer simulation, is unlikely to occur in an infinite system.

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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.

Helically twisted fibers can be produced by electrospinning liquid‐crystalline cellulose solutions. Fiber topographies are studied by atomic force microscopy, scanning electron microscopy (see figure) and polarized optical microscopy. The fibers have a nearly universal pitch‐to‐diameter ratio and comprise both right‐ and left‐handed helices.

Abstract:We study a model consisting of particles with dissimilar bonding sites ("patches"), which exhibits self-assembly into chains connected by Y-junctions, and investigate its phase behaviour by both simulations and theory. We show that, as the energy cost epsilon(j) of forming Y-junctions increases, the extent of the liquid-vapour coexistence region at lower temperatures and densities is reduced. The phase diagram thus acquires a characteristic "pinched" shape in which the liquid branch density decreases as the temperature is lowered. To our knowledge, this is the first model in which the predicted topological phase transition between a fluid composed of short chains and a fluid rich in Yjunctions is actually observed. Above a certain threshold for epsilon(j), condensation ceases to exist because the entropy gain of forming Y-junctions can no longer offset their energy cost. We also show that the properties of these phase diagrams can be understood in terms of a temperature-dependent effective valence of the patchy particles.