Stochastic Yield Catastrophes and Robustness in Self-Assembly

A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. Here, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield

Recent advances in the formation of phase inversion membranes made from amorphous or semi-crystalline polymers

Structural characteristics in membranes formed by diffusion induced phase separation processes are discussed. Established theories on membrane formation from ternary systems can be extended to describe the effects of high or low molecular weight additives. A mechanism for the formation of nodular structures in the top layer of ultrafiltration membranes is presented. In the last part structures arising from polymer crystallization during immersion precipitation are discussed

Tunable Assembly of Gold Nanorods in Polymer Solutions to Generate Controlled Nanostructured Materials

Gold nanorods grafted with short chain polymers are assembled into controlled open structures using polymer-induced depletion interactions and structurally characterized using small angle x-ray scattering. When the nanorod diameter is smaller than the radius of gyration of the depletant polymer, the depletion interaction depends solely on the correlation length of the polymer solution and not directly on the polymer molecular weight. As the polymer concentration increases, the stronger depletion interactions increasingly compress the grafted chains and push the gold nanorods closer together. By contrast, other structural characteristics such as the number of nearest neighbors and fractal dimension exhibit a non-monotonic dependence on polymer concentration. These parameters are maximal at intermediate concentrations, which are attributed to a crossover from reaction-limited to diffusion-limited aggregation. The control over structural properties of anisotropic nanoscale building blocks demonstrated here will be beneficial to designing and producing materials \emph{in situ} with specific direction-dependent nanoscale properties and provides a crucial route for advances in additive manufacturing

Phase separation processes in polymer solutions in relation to membrane formation

This review covers new experimental and theoretical physical research related to the formation of polymeric membranes by phase separation of a polymer solution, and to the morphology of these membranes. Two main phase separation processes for polymeric membrane formation are discussed: thermally induced phase separation and immersion precipitation. Special attention is paid to phase transitions like liquid-liquid demixing, crystallization, gelation, and vitrification, and their relation to membrane morphology. In addition, the mass transfer processes involved in immersion precipitation, and their influence on membrane morphology are discussed

Manipulating Self-Assembly in Silver(I) Complexes of 1,3-Di-\u3cem\u3eN\u3c/em\u3e-pyrazolylorganyls

Three di-N-pyrazolylorganyls with different conformational flexibilities in the three-atom organyl spacers have been prepared, and the self-assembly properties with AgBF4 have been studied both in solution and in the solid state. All ligands give low-coordinate silver(I) centers that are capable of participating in multiple noncovalent interactions, but only the rigid 1,8-dipyrazolylnaphthalene ligand promotes very short Ag−Ag contacts