Quantitative Metrics for Assessing Positional and Orientational Order in Colloidal Crystals

Topological phases in nanoparticle monolayers: can crystalline, hexatic, and isotropic-fluid phases coexist in the same monolayer?

Topological phases are stable configurations of matter in 2-dimensions (2D) formed via spontaneous symmetry breaking. These play a crucial role in determining the system properties. Though a number of fundamental studies on topological phase transitions and topological defect dynamics have been conducted with model colloidal systems (typically microns in size), the same is lacking on nanoparticle monolayers (NPMLs, typically made of ligand-coated sub-ten nanometer particles). Here, we show that in an evaporation-driven self-assembly process, the three topological phases, namely crystalline, hexatic, and isotropic-fluid phases, can coexist within the same NPML. We associate this coexistence with the local variation in particle size, which can be described by a unique frequency parameter (p25), quantifying the fraction of NPs that has size deviation greater than or equal to 25% of the mean size (where the deviation,ζ is defined as ζ = ((|Size-mean|)/mean)). The p25-values for the three phases are distinctly different: crystalline arrangement occurs when p25 < ∼0.02, while a hexatic phase exists for 0.02 ≤ p25 ≤ 0.1. For p25 ≥ 0.1, the isotropic-fluid phase occurs. Following KTHNY-theory, we further numerically extrapolate the occurrence of each phase to the accumulated excess planar strain in the NPML due to the presence of various topological defects in the structures.

Controlling disorder in self-assembled colloidal monolayers via evaporative processes

Monolayers of assembled nano-objects with a controlled degree of disorder hold interest in many optical applications, including photovoltaics, light emission, sensing, and structural coloration. Controlled disorder can be achieved through either top-down or bottom-up approaches, but the latter is more suited to large-scale, low-cost fabrication. Disordered colloidal monolayers can be assembled through evaporatively driven convective assembly, a bottom-up process with a wide range of parameters impacting particle placement. Motivated by the photonic applications of such monolayers, in this review we discuss the quantification of monolayer disorder, and the assembly methods that have been used to produce them. We review the impact of particle and solvent properties, as well as the use of substrate patterning, to create the desired spatial distributions of particles.

Quantifying patterns in optical micrographs of one- and two-dimensional ellipsoidal particle assemblies

Current developments in colloidal science include the assembly of anisotropic colloids with broad geometric diversity. As the complexity of particle assemblies increases, the need for ubiquitous algorithms that quantitatively analyze images of the assemblies to deliver key information such as quantification of crystal structures becomes more urgent. This contribution describes algorithms capable of image analysis for classifying colloidal structures based on abstracted interparticle relationship information and quantitatively analyzing the abundance of each structure in mixed pattern assemblies. The algorithm parameters can be adjusted, allowing for the algorithms to be adapted for different image analyses. Three different ellipsoidal particle assembly images are presented to demonstrate the effectiveness of the algorithms: a one-dimensional (1D) particle chain assembly and two two-dimensional (2D) polymorphic crystals each consisting of assemblies of two distinct plane symmetry groups. Angle relationships between neighbouring particles are calculated and neighbour counts of each particle are determined. Combining these two parameters as rules for classification criteria allows for the labeling and quantification of each particle into a defined symmetry class within an assembly. The algorithms provide a labelled image comprising classification results and particle counts of each defined class. For multiple images or individual frames from a video, the script can be looped to achieve automatic processing. The yielded classification data allow for more in-depth image analysis of mixed pattern particle assemblies. We envision that these algorithms will have utility in quantitative analysis of images comprising ellipsoidal colloidal materials, nanoparticles, or biological matter.

Pattern detection in colloidal assembly: A mosaic of analysis techniques

Characterization of the morphology, identification of patterns and quantification of order encountered in colloidal assemblies is essential for several reasons. First of all, it is useful to compare different self-assembly methods and assess the influence of different process parameters on the final colloidal pattern. In addition, casting light on the structures formed by colloidal particles can help to get better insight into colloidal interactions and understand phase transitions. Finally, the growing interest in colloidal assemblies in materials science for practical applications going from optoelectronics to biosensing imposes a thorough characterization of the morphology of colloidal assemblies because of the intimate relationship between morphology and physical properties (e.g. optical and mechanical) of a material. Several image analysis techniques developed to investigate images (acquired via scanning electron microscopy, digital video microscopy and other imaging methods) provide variegated and complementary information on the colloidal structures under scrutiny. However, understanding how to use such image analysis tools to get information on the characteristics of the colloidal assemblies may represent a non-trivial task, because it requires the combination of approaches drawn from diverse disciplines such as image processing, computational geometry and computational topology and their application to a primarily physico-chemical process. Moreover, the lack of a systematic description of such analysis tools makes it difficult to select the ones more suitable for the features of the colloidal assembly under examination. In this review we provide a methodical and extensive description of real-space image analysis tools by explaining their principles and their application to the investigation of two-dimensional colloidal assemblies with different morphological characteristics.

Nematic colloids at liquid crystal-air interfaces via photopolymerization

We demonstrate the preparation of colloidal crystals at nematic liquid crystal-air interfaces by simultaneous photopolymerization and assembly. Polymer colloids are produced by polymerization-induced phase separation of 2-hydroxyethyl methacrylate in the non-reactive liquid crystal (LC) 4-cyano-4'-pentylbiphenyl (5CB) using an open-cell setup. Colloids adsorbed to the nematic 5CB-air interface form non-close-packed hexagonal crystals that cover the entire interface area. We examine the mechanism of growth and assembly for the preparation of LC-templated interfacial colloidal superstructures.

Pattern Formation in Binary Colloidal Assemblies: Hidden Symmetries in a Kaleidoscope of Structures

In this study, we present a detailed investigation of the morphology of binary colloidal structures formed by self-assembly at air/water interface of particles of two different sizes, with a size ratio such that the larger particles do not retain a hexagonal arrangement in the binary assembly. While the structure and symmetry of binary mixtures in which such hexagonal order is preserved has been thoroughly scrutinized, binary colloids in the regime of nonpreservation of the hexagonal order have not been examined with the same level of detail due also to the difficulty in finding analysis tools suitable to recognize hidden symmetries in seemingly amorphous and disordered arrangements. For this purpose, we resorted to a combination of different analysis tools based on computational geometry and computational topology to get a comprehensive picture of the morphology of the assemblies. By carrying out an extensive investigation of binary assemblies in this regime with variable concentration of smaller particles with respect to larger particles, we identify the main patterns that coexist in the apparently disordered assemblies and detect transitions in the symmetries upon increase in the number of small particles. As the concentration of small particles increases, large particle arrangements become more dilute and a transition from hexagonal to rhombic and square symmetries occurs, accompanied also by an increase in clusters of small particles; the relative weight of each specific symmetry can be controlled by varying the composition of the assemblies. The demonstration of the possibility to control the morphology of apparently disordered binary colloidal assemblies by varying experimental conditions and the definition of a route for the investigation of disordered assemblies are important for future studies of complex colloidal patterns to understand self-assembly mechanisms and to tailor the physical properties of colloidal assemblies.

Tunable hydrodynamics: a field-frequency phase diagram of a non-equilibrium order-to-disorder transition

We present experiments on a model system consisting of dielectric (silicone oil) drops in a "leaky dielectric" (castor oil) carrier fluid that exhibits dynamic non-equilibrium phases as a function of the amplitude and frequency of an external AC electric field. At high frequencies, the dielectric drops are pinned to a periodic lattice by dielectrophoretic forces induced by a patterned bottom electrode. Beginning with this state of imposed order, we examine the processes that take this system from order to disorder, with decreasing frequency corresponding to an increase in the range of the hydrodynamic forces. We find two kinds of disorder, shape- and translational disorder, that occur in frequency-amplitude space. We also find regimes where drop breakup is dominant, and where order/disorder of large drops can be probed without significant drop breakup. With decreasing frequency (i.e., increasing hydrodynamic coupling between drops) and on timescales from seconds to minutes, the drops exhibit motion that resembles Brownian motion of particles in a crystal, with an effective temperature that increases with the strength of the electrohydrodynamic driving force. In this limit, the system behaves like a thermal system and the lattice is seen to melt at an effective Lindemann parameter of L_eff ∼ 0.08. This non-equilibrium thermodynamics, probed on timescales from seconds to minutes, likely arises from the pseudo-random velocity fields in the carrier fluid, as evidenced by the fractional, t^3/2, super-diffusive tracer dynamics at shorter timescales.

Approaches to self-assembly of colloidal monolayers: A guide for nanotechnologists

Self-assembly of quasi-spherical colloidal particles in two-dimensional (2D) arrangements is essential for a wide range of applications from optoelectronics to surface engineering, from chemical and biological sensing to light harvesting and environmental remediation. Several self-assembly approaches have flourished throughout the years, with specific features in terms of complexity of the implementation, sensitivity to process parameters, characteristics of the final colloidal assembly. Selecting the proper method for a given application amidst the vast literature in this field can be a challenging task. In this review, we present an extensive classification and comparison of the different techniques adopted for 2D self-assembly in order to provide useful guidelines for scientists approaching this field. After an overview of the main applications of 2D colloidal assemblies, we describe the main mechanisms underlying their formation and introduce the mathematical tools commonly used to analyse their final morphology. Subsequently, we examine in detail each class of self-assembly techniques, with an explanation of the physical processes intervening in crystallization and a thorough investigation of the technical peculiarities of the different practical implementations. We point out the specific characteristics of the set-ups and apparatuses developed for self-assembly in terms of complexity, requirements, reproducibility, robustness, sensitivity to process parameters and morphology of the final colloidal pattern. Such an analysis will help the reader to individuate more easily the approach more suitable for a given application and will draw the attention towards the importance of the details of each implementation for the final results.

Quantifying disorder in colloidal films spin-coated onto patterned substrates

Polycrystals of thin colloidal deposits, with thickness controlled by spin-coating speed, exhibit axial symmetry with local 4-fold and 6-fold symmetric structures, termed orientationally correlated polycrystals (OCPs). While spin-coating is a very facile technique for producing large-area colloidal deposits, the axial symmetry prevents us from achieving true long-range order. To obtain true long-range order, we break this axial symmetry by introducing a patterned surface topography and thus eliminate the OCP character. We then examine symmetry-independent methods to quantify order in these disordered colloidal deposits. We find that all the information in the bond-orientational order parameters is well captured by persistent homology analysis methods that only use the centers of the particles as input data. It is expected that these methods will prove useful in characterizing other disordered structures.

Self-Assembly of Single-Sized and Binary Colloidal Particles at Air/Water Interface by Surface Confinement and Water Discharge

We present an innovative apparatus allowing self-assembly at air/water interface in a smooth and reproducible way. The combination of water discharge and surface confinement of the area over which self-assembly takes place allows transfer of the assembled monolayer without any risk of damage to the colloidal crystal. As we demonstrate, the designed approach offers remarkable advantages in terms of cost and robustness compared to state-of-the art methods and is suitable for the fabrication of highly ordered monolayers even for more challenging assembly experiments such as transfer on rough substrates or assembly of binary colloids. Hence, our apparatus represents a significant headway toward high scale production of large area colloidal crystals. For the binary colloid assembly experiments, we also report the first experimental demonstration of a morphology based on the alternation of three and four small particles in the interstices between large particles.

Large-area 2D microgel colloidal crystals fabricated via benzophenone-based photochemical reaction

Large area, high quality 2D microgel CCs were fabricated by first assembling the microgel spheres into highly ordered 3D CCs, followed by fixing the first 111 plane of the 3D CC onto the substrate via a benzophenone-based photochemical reaction.