Heptatic liquid quasi-crystals by colloidal lithographic pre-assembly

HYPOTHESIS

We hypothesize that pre-assembled lithographic Brownian seven-fold quasi-crystals (QCs) of colloidal tiles at high densities can exhibit a heptatic liquid quasi-crystal (LQC) phase upon release; such heptatic LQCs can undergo heterogeneous dynamics at different length scales, reflecting the underlying symmetry, corrugation, and hierarchy of local sets of tiles.

EXPERIMENTS

We design, fabricate, and release a seven-fold QC composed of three differently shaped rhombic tiles using the method of lithographically pre-assembled monolayers (litho-PAMs). High resolution optical microscopy enables spatio-temporal particle tracking of Brownian fluctuations of many tiles in a large area over a long time. We develop an edge-proximity tessellation method for analyzing nearest neighboring particles that can be applied to assemblies and dense systems of complex shapes.

FINDINGS

A fluctuating heptatic LQC phase is identified at high tile area fractions. Heterogenous dynamics and order at different length scales indicate diverse, hierarchical motif structures. We show that certain motifs can collectively rotate without any cage breaking, leading to alterations of the local tile-structure reminiscent of phason-flips in atomic QCs; this rotation causes a slow decline in the system's spatial order. We anticipate that edge-proximity tessellation will help elucidate phase transitions of other systems made of diverse building blocks having significant geometrical complexity at multiple length scales.

Development of a Self-Viscosity and Temperature-Compensated Technique for Highly Stable and Highly Sensitive Bead-Based Diffusometry

Brownian motion, which is a natural phenomenon, has attracted numerous researchers and received extensive studies over the past decades. The effort contributes to the discovery of optical diffusometry, which is commonly used for micro/nano particle sizing. However, the analysis uncertainty caused by the coupling relationship among particle diameter, temperature, and fluid viscosity usually poses a barrier to precise measurement. Preventing random background noise becomes the key to achieving a high level of accuracy in diffusometry detection. Recently, Janus particles have become known as an ideal tool for resolving the rotational Brownian motion. Followed by our previous study, the rotational Brownian motion and the translational Brownian motion can be separately measured using the Janus particles. Accordingly, a simple self-viscosity and temperature-compensated technique based on the delicate removal of temperature and fluid viscosity variations through particle tracking was first proposed in this study. Consequently, the translational Brownian motion was expressed in terms of particle trajectory, whereas the rotational Brownian motion was expressed in terms of the blinking signal from the Janus particles. The algorithm was verified simulatively and experimentally in temperature (10 °C to 40 °C) and viscosity-controlled (1 mPa·s to 5 mPa·s) fields. In an evaluation of biosensing for a target protein, IFN-γ, the limit of detection of the proposed self-compensated diffusometry reached 0.45 pg/mL, whereas its uncertainties of viscosity and temperature were 96 and 15-fold lower than the pure the rotational Brownian motion counterpart, respectively. The results indicated the low-uncertainty and high-accuracy biosensing capability resulting from the self-viscosity and temperature-compensated technique. This research will provide a potential alternative to future similar bead-based immunosensing, which requires ultra-high stability and sensitivity.

Trace Biomolecule Detection with Functionalized Janus Particles by Rotational Diffusion

Cytokines are small proteins secreted by cells in innate and adaptive immune systems. Abnormal cytokine secretion is often regarded as an early cue of dysregulation of homeostasis due to diseases or infections. Early detection allows early medical intervention. In this study, a natural phenomenon called rotational Brownian motion was characterized by Janus particles and its potential use in detection of trace biomolecules explored. Through the functionalization of the Janus particles with an antibody, the target cytokine, that is, tumor necrosis factor-α, was measured in terms of rotational diffusion. Rotational diffusion is highly sensitive to the particle volume change according to the Stokes-Einstein-Debye relation and can be quantified by blinking signal. Accordingly, 1 μm half-gold and half-fluorescent microbeads were conjugated with 200 nm nanobeads through sandwiched immunocomplexes. The light source, lead time for stabilization, and purification were investigated for optimization. Particle images can be captured with green light at 5 Hz within 300 s. Under such conditions, the functionalized Janus particles eventually achieved a limit of detection of 1 pg/mL. The rotational diffusometry realized by Janus particles was power-free and feasible for ultrasensitive detection, such as early disease detection.

Assembly of colloidal particles in solution

Advances in both top-down and bottom-up syntheses of a wide variety of complex colloidal building blocks and also in methods of controlling their assembly in solution have led to new and interesting forms of highly controlled soft matter. In particular, top-down lithographic methods of producing monodisperse colloids now provide precise human-designed control over their sub-particle features, opening up a wide range of new possibilities for assembly structures that had been previously limited by the range of shapes available through bottom-up methods. Moreover, an increasing level of control over anisotropic interactions between these colloidal building blocks, which can be tailored through local geometries of sub-particle features as well as site-specific surface modifications, is giving rise to new demonstrations of massively parallel off-chip self-assembly of specific target structures with low defect rates. In particular, new experimental realizations of hierarchical self-assembly and control over the chiral purity of resulting assembly structures have been achieved. Increasingly, shape-dependent, shape-complementary, and roughness-controlled depletion attractions between non-spherical colloids are being used in novel ways to create assemblies that go far beyond early examples, such as fractal clusters formed by diffusion-limited and reaction-limited aggregation of spheres. As self-assembly methods have progressed, a wide variety of advanced directed assembly methods have also been developed; approaches based on microfluidic control and applying structured electromagnetic fields are particularly promising.

A Brownian quasi-crystal of pre-assembled colloidal Penrose tiles

Penrose's pentagonal P2 quasi-crystal^1-4 is a beautiful, hierarchically organized multiscale structure in which kite- and dart-shaped tiles are arranged into local motifs, such as pentagonal stars, which are in turn arranged into various close-packed superstructural patterns that become increasingly complex at larger length scales. Although certain types of quasi-periodic structure have been observed in hard and soft matter, such structures are difficult to engineer, especially over large areas, because generating the necessary, highly specific interactions between constituent building blocks is challenging. Previously reported soft-matter quasi-crystals of dendrimers⁵, triblock copolymers⁶, nanoparticles⁷ and polymeric micelles⁸ have been limited to 12- or 18-fold symmetries. Because routes for self-assembling complex colloidal building blocks^9-11 into low-defect dynamic superstructures remain limited¹², alternative methods, such as using optical and directed assembly, are being explored^13,14. Holographic laser tweezers¹⁵ and optical standing waves¹⁶ have been used to hold microspheres in local quasi-crystalline arrangements, and magnetic microspheres of two different sizes have been assembled into local five-fold-symmetric quasi-crystalline arrangements in two dimensions¹⁷. But a Penrose quasi-crystal of mobile colloidal tiles has hitherto not been fabricated over large areas. Here we report such a quasi-crystal in two dimensions, created using a highly parallelizable method of lithographic printing and subsequent release of pre-assembled kite- and dart-shaped tiles into a solution-dispersion containing a depletion agent. After release, the positions and orientations of the tiles within the quasi-crystal can fluctuate, and these tiles undergo random, Brownian motion in the monolayer owing to frequent collisions between neighbouring tiles, even after the system reaches equilibrium. Using optical microscopy, we study both the equilibrium fluctuations of the system at high tile densities and also the 'melting' of the pattern as the tile density is lowered. At high tile densities we find signatures of a five-fold pentatic liquid quasi-crystalline phase, analogous to a six-fold hexatic liquid crystal. Our fabrication approach is applicable to tiles of different sizes and shapes, and with different initial positions and orientations, enabling the creation of two-dimensional quasi-crystalline systems (and other systems that possess multiscale complexity at high tile densities) beyond those of current self- or directed-assembly methods^18-20. We anticipate that our approach for generating lithographically pre-assembled monolayers could be extended to create three-dimensional Brownian systems of fluctuating particles with custom-designed shapes through holographic lithography^21,22 or stereolithography²³.

Local bond order parameters for accurate determination of crystal structures in two and three dimensions

Local order parameters for the characterization of liquid and different two- and three-dimensional crystalline structures are presented.