Multivalent Patchy Colloids for Quantitative 3D Self-Assembly Studies

Spearheading a new era in complex colloid synthesis with TPM and other silanes

Colloid science has recently grown substantially owing to the innovative use of silane coupling agents (SCAs), especially 3-trimethoxysilylpropyl methacrylate (TPM). SCAs were previously used mainly as modifying agents, but their ability to form droplets and condense onto pre-existing structures has enabled their use as a versatile and powerful tool to create novel anisotropic colloids with increasing complexity. In this Review, we highlight the advances in complex colloid synthesis facilitated by the use of TPM and show how this has driven remarkable new applications. The focus is on TPM as the current state-of-the-art in colloid science, but we also discuss other silanes and their potential to make an impact. We outline the remarkable properties of TPM colloids and their synthesis strategies, and discuss areas of soft matter science that have benefited from TPM and other SCAs.

Porous Self-Assemblies Mediated by Dumbbell Particles as Cross-Linking Agents

Self-assembly of colloidal particles is emerging as a promising approach for producing novel materials. These colloidal particles can be synthesized with protrusions (lobes) on their surfaces that allow the formation of porous structures with a wide range of applications. Using Langevin dynamics simulations, we studied self-assembly in the binary mixtures of lobed colloidal particles with variations in their lobe sizes to investigate the feasibility of using dumbbell particles (with two lobes) as cross-linkers to increase the porosity in self-assembled morphologies. Each binary system was formed by mixing the dumbbell particles with one of the following types of particles: trigonal planar (three lobes), tetrahedral (four lobes), trigonal bipyramidal (five lobes), and octahedral (six lobes). We observed that the lobe size on each particle can be tuned to favor the formation of random aggregates and spherical aggregates when the lobes are larger and well-ordered crystalline structures when the lobes are smaller. We also observed that these polydisperse systems form self-assembled structures characterized by porosities higher than those of the structures formed by the monodisperse systems. These results indicate that the lobe size is an important design feature that can be optimized to achieve desired structures with distinct morphologies and porosities, and the dumbbell particles are effective cross-linking agents to enhance the porosity in self-assembled structures.

Polymer Brushes and Surface Nanostructures: Molecular Design, Precise Synthesis, and Self-Assembly

For over two decades, polymer brushes have found wide applications in industry and scientific research. Now, polymer brush research has been a significant research focus in the community of polymer science. In this review paper, we give an introduction to the synthesis, self-assembly, and applications of one-dimensional (1D) polymer brushes on polymer backbones, two-dimensional (2D) polymer brushes on flat surfaces, and three-dimensional (3D) polymer brushes on spherical particles. Examples of the synthesis of polymer brushes on different substrates are provided. Studies on the formation of the surface nanostructures on solid surfaces are also reviewed in this article. Multicomponent polymer brushes on solid surfaces are able to self-assemble into surface micelles (s-micelles). If the s-micelles are linked to the substrates through cleavable linkages, the s-micelles can be cleaved from the substrates, and the cleaved s-micelles are able to self-assemble into hierarchical structures. The formation of the surface nanostructures by coassembly of polymer brushes and "free" polymer chains (coassembly approach) or polymerization-induced surface self-assembly approach, is discussed. The applications of the polymer brushes in colloid and biomedical science are summarized. Finally, perspectives on the development of polymer brushes are offered in this article.

Polymer brush-based nanostructures: from surface self-assembly to surface co-assembly

Surface structures play an important role in the practical applications of materials. The synthesis of polymer brushes on a solid surface has emerged as an effective tool for tuning surface properties. The fabrication of polymer brush-based surface nanostructures has greatly facilitated the development of materials with unique surface properties. In this review article, synthetic methods used in the synthesis of polymer brushes, and self-assembly approaches applied in the fabrication of surface nanostructures including self-assembly of polymer brushes, co-assembly of polymer brushes and "free" block copolymer chains, and polymerization induced surface self-assembly, are reviewed. It is demonstrated that polymer brush-based surface nanostructures, including spherical surface micelles, wormlike surface structures, layered structures and surface vesicles, can be fabricated. Meanwhile, the challenges in the synthesis and applications of the surface nanostructures are discussed. This review is expected to be helpful for understanding the principles, methods and applications of polymer brush-based surface nanostructures.

Modeling the assembly of oppositely charged multi-indented lock- and key-colloids

The interactions between oppositely charged multi-indented lock- and spherical key-particles are investigated by means of Monte Carlo simulations at low volume fractions. The specificity of the interactions is initially investigated in an excess of either lock- or key-particles, and we find ordered clusters with highly directional bonds. This suggests electrostatics alone to be capable of inducing the assembly of specifically bound clusters. Considering different numbers of indentations and number ratios corresponding to perfect lattices (cubic/hexagonal/diamond), we however only find gel-like structures with no tendency to form dense ordered aggregates or lattices. We conjecture that the high entropic cost that comes with specific binding of several keys to a single lock impedes the spontaneous formation of defined lattices at low volume fractions and "lock" the assembly into disordered gel-like structures.

Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding

The assembly of functional biomolecular condensates often involves liquid-liquid phase separation (LLPS) of proteins with multiple modular domains, which can be folded or conformationally disordered to various degrees. To understand the LLPS-driving domain-domain interactions, a fundamental question is how readily the interactions in the condensed phase can be inferred from interdomain interactions in dilute solutions. In particular, are the interactions leading to LLPS exclusively those underlying the formation of discrete interdomain complexes in homogeneous solutions? We address this question by developing a mean-field LLPS theory of two stoichiometrically constrained solute species. The theory is applied to the neuronal proteins SynGAP and PSD-95, whose complex coacervate serves as a rudimentary model for neuronal postsynaptic densities (PSDs). The predicted phase behaviors are compared with experiments. Previously, a three SynGAP/two PSD-95 ratio was determined for SynGAP/PSD-95 complexes in dilute solutions. However, when this 3:2 stoichiometry is uniformly imposed in our theory encompassing both dilute and condensed phases, the tie-line pattern of the predicted SynGAP/PSD-95 phase diagram differs drastically from that obtained experimentally. In contrast, theories embodying alternate scenarios postulating auxiliary SynGAP-PSD-95 as well as SynGAP-SynGAP and PSD-95-PSD-95 interactions, in addition to those responsible for stoichiometric SynGAP/PSD-95 complexes, produce tie-line patterns consistent with experiment. Hence, our combined theoretical-experimental analysis indicates that weaker interactions or higher-order complexes beyond the 3:2 stoichiometry, but not yet documented, are involved in the formation of SynGAP/PSD-95 condensates, imploring future efforts to ascertain the nature of these auxiliary interactions in PSD-like LLPS and underscoring a likely general synergy between stoichiometric, structurally specific binding and stochastic, multivalent "fuzzy" interactions in the assembly of functional biomolecular condensates.

Clusters formed by dumbbell-like one-patch particles confined in thin systems

Performing isothermal-isochoric Monte Carlo simulations, I examine the types of clusters that dumbbell-like one–patch particles form in thin space between two parallel walls, assuming that each particle is synthesized through the merging of two particles, one non-attracting and the other attracting for which, for example, the inter-particle interaction is approximated by the DLVO model . The shape of these dumbbell-like particles is controlled by the ratio of the diameters q of the two spherical particles and by the dimensionless distance l between these centers. Using a modified Kern–Frenkel potential, I examine the dependence of the cluster shape on l and q. Large island-like clusters are created when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q<1$$\end{document}q<1. With increasing q, the clusters become chain-like . When q increases further, elongated clusters and regular polygonal clusters are created. In the simulations, the cluster shape becomes three-dimensional with increasing l because the thickness of the thin system increases proportionally to l.

Phase behavior of a binary mixture of patchy colloids: Effect of particle size and gravity

We study theoretically the effect of size difference and that of gravity in the phase behavior of a binary mixture of patchy particles. The species, 2A and 3B, have two A and three B patches, respectively, and only bonds between patches A and B (AB bonds) are allowed. This model describes colloidal systems where the aggregation of particles (3B) is mediated and controlled by a second species, the linkers (2A) to which they bind strongly. Thermodynamic calculations are performed using Wertheim's perturbation theory with a hard sphere reference term that accounts for the difference in the size of the two species. Percolation lines are determined employing a generalized Flory-Stockmayer theory, and the effects of gravity are included through a local density approximation. The bulk phase diagrams are calculated, and all the stacking sequences generated in the presence of gravity are determined and classified in a stacking diagram. The relative size of the particles can be used to control the phase behavior of the mixture. An increase in the size of particles 3B, relative to the size of the linkers 2A, is found to promote mixing while keeping the percolating structures and, in certain cases, leads to changes in the stacking sequence under gravity.

Effect of the Interaction Length on Clusters Formed by Spherical One-Patch Particles on Flat Planes

Considering that one-patch particles rotate three-dimensionally and translate on a two-dimensional flat plane, I performed isothermal-isochoric Monte Carlo simulations to study how two-dimensional self-assemblies formed by spherical patchy particles depending on the interaction length and patch area. As the interaction potential between one-patch particles, the Kern-Frenkel (KF) potential is used in the simulations. With increasing patch area, the shape of the most numerous clusters changes from dimers to island-like clusters with a square lattice via triangular trimers, square tetramers, and chain-like clusters when the interaction length is as long as the particle radius. With a longer interaction length, other shapes of polygonal clusters such as another type of square tetramers, two types of pentagonal pentamers, hexagonal hexamers, and hexagonal heptamers also form.

Inverse Design of Self-Assembling Diamond Photonic Lattices from Anisotropic Colloidal Clusters

Colloidal nanoparticles with anisotropic interactions are promising building blocks for the fabrication of complex functional materials. A challenge in the self-assembly of colloidal particles is the rational design of geometry and chemistry to program the formation of a desired target structure. We report an inverse design procedure integrating Langevin dynamics simulations and evolutionary algorithms to engineer anisotropic patchy colloidal clusters to spontaneously assemble into a cubic diamond lattice possessing a complete photonic band gap. The combination of a tetrahedral cluster geometry and optimized placement of a single type of anisotropic interaction patch results in a colloidal building block predicted to assemble a cubic diamond lattice with more than 82% yield. This design represents an experimentally viable colloidal building block capable of high-fidelity assembly of a cubic diamond lattice.