Thermodynamics and structure of self-assembled networks

We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, 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. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the junctions induces an effective attraction between the monomers, which in the case of three-fold 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. Independent of the phase separation, we predict the percolation (connectivity) transition at which an infinite network is formed that partially overlaps with the first-order transition. The percolation transition is a continuous, non thermodynamic transition that describes a change in the topology of the system. Our treatment which 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 correlation has a usual Ornstein-Zernicke form at low monomer densities. At higher densities, a peak emerges in the structure factor, signifying an onset of medium-range order in the system. Implications of the results for different physical systems are discussed.Comment: Submitted to Phys. Rev.

Rheological behaviour of wormlike micelles : effect of salt content

We study the effect of salt content on the rheological properties of wormlike micelles formed from hexadecyltrimethylammonium bromide (CTAB) in presence of potassium bromide (KBr) and of cetylpyridinium chlorate (CPClO3) in presence of sodium chlorate (ClO3Na). Upon increasing the salt concentration, at fixed surfactant concentration, we observe for both systems a maximum of the zero-shear viscosity η0. For salt concentrations less than that corresponding to the maximum of [MATH], the variation of η0 with the surfactant concentration C can be described by a reptation model. Beyond the maximum, the scaling laws obtained for η0(C) are characterized by values of the exponent much smaller than those predicted by the existing theoretical models. The results are qualitatively interpreted by a description based on a structural evolution upon increasing salt content from a system of entangled linear micelles to a multiconnected network. Measurements of the plateau modulus of CTAB solutions, as a function of KBr, give results supporting the above hypothesis.Nous présentons une étude de l'influence de la teneur en sel sur les propriétés rhéologiques de solutions de micelles cylindriques formées à partir de bromure d'hexadecyltrimethylammonium (CTAB) en présence de bromure de potassium (KBr) et de chlorate de cetylpyridinium (CPClO3) en présence de chlorate de sodium (ClO3Na). Lorsqu'on fait varier la concentration en sel, à concentration en tensioactif constante, on observe pour les deux systèmes un maximum de la viscosité à gradient nul η0. Pour des concentrations en sel inférieures à celle correspondant au maximum de [MATH] la variation de η0 avec la concentration en tensioactif C peut être décrite par un modèle de reptation. Au-delà du maximum les lois d'échelles obtenues pour η0(C) sont caractérisées par des valeurs de l'exposant beaucoup plus faibles que celles prédites par les modèles théoriques existants. Les résultats sont interprétés qualitativement à partir d'une description fondée sur l'évolution de la structure micellaire lorsqu'on augmente la teneur en sel, d'un système de micelles linéaires enchevêtrées vers un réseau interconnecté. Les mesures du plateau du module de cisaillement en fonction de la concentration en KBr pour des solutions de CTAB donnent des résultats étayant cette hypothèse

Static and dynamic properties of a network of wormlike surfactant micelles (cetylpyridinium chlorate in sodium chlorate brine)

The structure of solutions of cetylpyridinium chlorate micelles is studied by light scattering and found to be analogous to that of polymer solutions in good solvent and in the semi dilute range. In contrast the micellar solutions are found here to be very fluid and their measured rheological properties are strikingly different from that of polymer solutions. These rheological properties are not accounted for by the recently developed model for semi dilute solutions of equilibrium polymers which described well the properties of other similar wormlike micellar systems. We suggest that the existence of crosslinks rather than entanglement points in the network of wormlike micelles could be responsible for these unexpected properties

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 endcaps 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