Concentration-induced shape transition of nano-aggregates in solution

Monomer-concentration-induced shape formation and transition are found to be very common in varieties of self-assembled soft matter nano-systems. In this paper, we present a theory, based on our previous studies, to explain the concentration-induced shape transition of multilamellar nano-aggregates in solution. We regard self-assembly (aggregation) as layer growth process which is controlled by monomer concentration due to the chemical equilibrium with the monomer solution. By considering mechanical balance between three sources of energy of the layer, the surface energy, the curvature elastic energy, and the internal cohesion energy gained in the aggregation process, we are able to relate the monomer concentration to shape transition of the layer by a simple equation. From this equation, we predict there is a critical monomer concentration (CTVC) below which the tube-to-vesicle shape transition could occur. Our theory are strongly supported by the fact that some parameters of the model are estimated to locate within the reasonable range of soft materials.