A. G. Zilman

Thermodynamics and structure of self-assembled networks.

We study a generic model of self-assembling chains that can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micelles, dipolar fluids, and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. As for the calculation of thermodynamic properties as well as the scattering structure factor, the mapping rigorously accounts for all possible cluster configurations, except for closed rings. The model is solved in the mean-field approximation. It is found that despite the absence of any specific interaction between the chains, the presence of the junctions induces an effective attraction between the monomers, which in the case of threefold junctions leads to a first-order reentrant phase separation between a dilute phase consisting mainly of single chains, and a dense network, or two network phases. The model is then modified to predict the structural properties at the mean-field level. Independent of the phase separation, we predict a percolation (connectivity) transition at which an infinite network is formed. The percolation transition partially overlaps with the first-order transition, and is a continuous, nonthermodynamic transition that describes a change in the topology of the system. Our treatment that predicts both the thermodynamic phase equilibria as well as the spatial correlations in the system allows us to treat both the phase separation and the percolation threshold within the same framework. The density-density correlation has the usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying the onset of medium-range order in the system. Implications of the results for different physical systems are discussed.

Role of cross-links in bundle formation, phase separation and gelation of long filaments

We predict the thermodynamic and structural behavior of solutions of self-assembling chains, cross-links and end-cap molecules. We find that at the mean-field level, the entropy of self-assembled junctions induces an effective attraction that can result in equilibrium between a sol phase and a connected network. A connected network can also be formed in a non-thermodynamic transition upon increase of the monomer or cross-link density, or with decreasing temperature. For rigid rods, at low temperatures, we predict a transition from an isotropic network to anisotropic bundles of rods linked by cross-links, that is triggered by the interplay between the configurational entropy of the cross-link distribution, and the rotational and translational entropy of the rods.

Entropic Phase Separation in Polymer-Microemulsion Networks

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase separation mechanism of the system is extremely robust and does not depend on the particlular physical realization of the network. The discussed model applies as well to other polymer linked particle aggregates, such as nano-particles connected with short DNA linkers.

Entropic networks in colloidal, polymeric and amphiphilic systems

Self-assembly in soft-matter systems often results in the formation of locally cylindrical or chain-like structures. We review the theory of these systems whose large-scale structure and properties depend on whether the chains are finite, with end-caps or join to form junctions that result in networks. Physical examples discussed here include physical gels, wormlike micelles, dipolar fluids and microemulsions. In all these cases, the competition between end-caps and junctions results in an entropic phase separation into junction-rich and junction-poor phases, as recently observed by electron microscopy and seen in computer simulations. A simple model that accounts for these phenomena is reviewed. Extensions of these ideas can be applied to treat network formation and phase separation in a system of telechelic (hydrophobically tipped, hydrophilic) polymers and oil-in-water microemulsions, as observed in recent experiments.

Dynamics of Sol-Gel Clusters and Branched Polymers

We study the dynamics of sol-gel clusters. We find that the dynamic structure factor decays in time as a stretched exponential, and the viscoelastic modulus is an algebraic function of time. The difference beween screened and non-screened systems in the context of cluster dynamics is discussed.