Structure and phase behavior of polymer-linked colloidal gels

Illuminating Disorder: Optical Properties of Complex Plasmonic Assemblies

The optical properties of disordered plasmonic nanoparticle assemblies can be continuously tuned through the structural organization and composition of their colloidal building blocks. However, progress in the design and experimental realization of these materials has been limited by challenges associated with controlling and characterizing disordered assemblies and predicting their optical properties. This Perspective discusses integrated studies of experimental assembly of disordered optical materials, such as doped metal oxide nanocrystal gels and metasurfaces, with electromagnetic computations on large-scale simulated structures. The simulations prove vital for connecting experimental parameters to disordered structural motifs and optical properties, revealing structure-property relations that inform design choices. Opportunities are identified for optimizing optical property designs for disordered materials using computational inverse methods and tools from machine learning.

Hydrophobic deep eutectic solvent-based eutectogels for underwater sensing

Eutectogels derived from deep eutectic solvents (DESs) exhibit great potential for the fabrication of flexible sensors. However, the hygroscopicity of eutectogels hinders their applications in underwater sensing. In this work, a hydrophobic eutectogel with exceptional long-term underwater stability is produced through one-step polymerization of lauryl methacrylate and glycidyl methacrylate in a hydrophobic DES. The hydrophobic gel network and hydrophobic DES fulfill the eutectogel with outstanding water resistance (water contact angle > 110°) and excellent mechanical properties in an aqueous environment, thus leading to extraordinary durability (over 1000 testing cycles). Additionally, based on this eutectogel, underwater strain and pressure sensors with high sensitivity, rapid responsiveness, and superior durability were fabricated for accurate real-time monitoring of human activity. Furthermore, it has been demonstrated that the eutectogel sensor can transmit information through Morse code, performing as a wearable underwater communicator. This research provides an exemplary way for a demonstration method of hydrophobic eutectogel for durable underwater applications.

Predicting the size and morphology of nanoparticle clusters driven by biomolecular recognition

Nanoparticle aggregation is a driving principle of innovative materials and biosensing methodologies, improving transduction capabilities displayed by optical, electrical or magnetic measurements. This aggregation can be driven by the biomolecular recognition between target biomolecules (analytes) and receptors bound onto nanoparticle surface. Despite theoretical advances on modelling the entropic interaction in similar systems, predictions of the fractal morphologies of the nanoclusters of bioconjugated nanoparticles are lacking. The morphology of resulting nanoclusters is sensitive to the location, size, flexibility, average number of receptors per particle f̄, and the analyte-particle concentration ratio. Here we considered bioconjugated iron oxide nanoparticles (IONPs) where bonds are mediated by a divalent protein that binds two receptors attached onto different IONPs. We developed a protocol combining analytical expressions for receptors and linker distributions, and Brownian dynamics simulations for bond formation, and validated it against experiments. As more bonds become available (e.g., by adding analytes), the aggregation deviates from the ideal Bethe's lattice scenario due to multivalence, loop formation, and steric hindrance. Generalizing Bethe's lattice theory with a (not-integer) effective functionality feff leads to analytical expressions for the cluster size distributions in excellent agreement with simulations. At high analyte concentration steric impediment imposes an accessible limit value facc to feff, which is bounded by facc < feff < f̄. A transition to gel phase, is correctly captured by the derived theory. Our findings offer new insights into quantifying analyte amounts by assessing nanocluster size, and predicting nanoassembly morphologies accurately is a first step towards understanding variations of physical properties in clusters formed after biomolecular recognition.

Structural Control of Plasmon Resonance in Molecularly Linked Metal Oxide Nanocrystal Gel Assemblies

Nanocrystal gels exhibit collective optical phenomena based on interactions among their constituent building blocks. However, their inherently disordered structures have made it challenging to understand, predict, or design properties such as optical absorption spectra that are sensitive to the coupling between the plasmon resonances of the individual nanocrystals. Here, we bring indium tin oxide nanocrystal gels under chemical control and show that their infrared absorption can be predicted and systematically tuned by selecting the nanocrystal sizes and compositions and molecular structures of the link-mediating surface ligands. Thermoreversible assemblies with metal-terpyridine links form reproducible gel architectures, enabling us to derive a plasmon ruler that governs the spectral shifts upon gelation, predicated on the nanocrystal and ligand compositions. This empirical guide is validated using large-scale, many-bodied simulations to compute the optical spectra of gels with varied structural parameters. Based on the derived plasmon ruler, we design and demonstrate a nanocrystal mixture whose spectrum exhibits distinctive line narrowing upon assembly.

Design, characterization and applications of nanocolloidal hydrogels

Nanocolloidal gels (NCGs) are an emerging class of soft matter, in which nanoparticles act as building blocks of the colloidal network. Chemical or physical crosslinking enables NCG synthesis and assembly from a broad range of nanoparticles, polymers, and low-molecular weight molecules. The synergistic properties of NCGs are governed by nanoparticle composition, dimensions and shape, the mechanism of nanoparticle bonding, and the NCG architecture, as well as the nature of molecular crosslinkers. Nanocolloidal gels find applications in soft robotics, bioengineering, optically active coatings and sensors, optoelectronic devices, and absorbents. This review summarizes currently scattered aspects of NCG formation, properties, characterization, and applications. We describe the diversity of NCG building blocks, discuss the mechanisms of NCG formation, review characterization techniques, outline NCG fabrication and processing methods, and highlight most common NCG applications. The review is concluded with the discussion of perspectives in the design and development of NCGs.

Effects of linker length on phase separation: lessons from the Rubisco-EPYC1 system of the algal pyrenoid

Biomolecular condensates are membraneless organelles formed via phase separation of macromolecules, typically consisting of bond-forming "stickers" connected by flexible "linkers". Linkers have diverse roles, such as occupying space and facilitating interactions. To understand how linker length relative to other lengths affects condensation, we focus on the pyrenoid, which enhances photosynthesis in green algae. Specifically, we apply coarse-grained simulations and analytical theory to the pyrenoid proteins of Chlamydomonas reinhardtii: the rigid holoenzyme Rubisco and its flexible partner EPYC1. Remarkably, halving EPYC1 linker lengths decreases critical concentrations by ten-fold. We attribute this difference to the molecular "fit" between EPYC1 and Rubisco. Varying Rubisco sticker locations reveals that the native sites yield the poorest fit, thus optimizing phase separation. Surprisingly, shorter linkers mediate a transition to a gas of rods as Rubisco stickers approach the poles. These findings illustrate how intrinsically disordered proteins affect phase separation through the interplay of molecular length scales.

Modular mixing in plasmonic metal oxide nanocrystal gels with thermoreversible links

Gelation offers a powerful strategy to assemble plasmonic nanocrystal networks incorporating both the distinctive optical properties of constituent building blocks and customizable collective properties. Beyond what a single-component assembly can offer, the characteristics of nanocrystal networks can be tuned in a broader range when two or more components are intimately combined. Here, we demonstrate mixed nanocrystal gel networks using thermoresponsive metal-terpyridine links that enable rapid gel assembly and disassembly with thermal cycling. Plasmonic indium oxide nanocrystals with different sizes, doping concentrations, and shapes are reliably intermixed in linked gel assemblies, exhibiting collective infrared absorption that reflects the contributions of each component while also deviating systematically from a linear combination of the spectra for single-component gels. We extend a many-bodied, mutual polarization method to simulate the optical response of mixed nanocrystal gels, reproducing the experimental trends with no free parameters and revealing that spectral deviations originate from cross-coupling between nanocrystals with distinct plasmonic properties. Our thermoreversible linking strategy directs the assembly of mixed nanocrystal gels with continuously tunable far- and near-field optical properties that are distinct from those of the building blocks or mixed close-packed structures.

Comparative Study of Covalent and van der Waals CdS Quantum Dot Assemblies from Many-Body Perturbation Theory

Quantum dot (QD) assemblies are nanostructured networks made from aggregates of QDs and feature improved charge and energy transfer efficiencies compared to discrete QDs. Using first-principles many-body perturbation theory, we systematically compare the electronic and optical properties of two types of CdS QD assemblies that have been experimentally investigated: (i) QD gels, where individual QDs are covalently connected via di- or polysulfide bonds, and (ii) QD nanocrystals, where individual QDs are bound via van der Waals interactions. Our work illustrates how the electronic and optical properties evolve when discrete QDs are assembled into 1D, 2D, and 3D gels and nanocrystals, as well as how the one-body and many-body interactions in these systems impact the trends as the dimensionality of the assembly increases. Furthermore, our work reveals the crucial role of the di- or polysulfide covalent bonds in the localization of the excitons, which highlights the difference between QD gels and QD nanocrystals.

Colorimetric quantification of linking in thermoreversible nanocrystal gel assemblies

Nanocrystal gels can be responsive, tunable materials, but designing their structure and properties is challenging. By using reversibly bonded molecular linkers, gelation can be realized under conditions predicted by thermodynamics. However, simulations have offered the only microscopic insights, with no experimental means to monitor linking leading to gelation. We introduce a metal coordination linkage with a distinct optical signature allowing us to quantify linking in situ and establish structural and thermodynamic bases for assembly. Because of coupling between linked indium tin oxide nanocrystals, their infrared absorption shifts abruptly at a chemically tunable gelation temperature. We quantify bonding spectroscopically and use molecular simulation to understand temperature-dependent bonding motifs, revealing that gel formation is governed by reaching a critical number of effective links that extend the nanocrystal network. Microscopic insights from our colorimetric linking chemistry enable switchable gels based on thermodynamic principles, opening the door to rational design of programmable nanocrystal networks.

Spatially uniform dynamics in equilibrium colloidal gels

Gels of DNA nanostars, besides providing a compatible scaffold for biomedical applications, are ideal model systems for testing the physics of equilibrium colloidal gels. Here, using dynamic light scattering and photon correlation imaging (a recent technique that, by blending light scattering and imaging, provides space-resolved quantification of the dynamics), we follow the process of gel formation over 10 orders of magnitude in time in a model system of tetravalent DNA nanostars in solution, a realization of limited-valence colloids. Such a system, depending on the nanostar concentration, can form either equilibrium or phase separation gels. In stark contrast to the heterogeneity of concentration and dynamics displayed by the phase separation gel, the equilibrium gel shows absence of aging and a remarkable spatially uniform dynamics.

Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.

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.

Sol/gel transition of oil/water microemulsions controlled by surface grafted triblock copolymer dodecyl-PEO227-dodecyl: molecular dynamics simulations with experimentally validated interaction potential

We studied a large range of identical spherical oil/water microemulsion (O/W-MI) volume fractions. The O/W-MIs are stabilized by cetylpyridinium chloride ionic surfactant (CpCl) and octanol cosurfactant and dispersed in salt water. We grafted different numbers of dodecyl-(polyEthylene oxide)227-dodecyl triblock copolymer that we note (n(D-PEO227-D)), where n varies from 0 to 12. We accomplished the grafting process by replacing a small amount of CpCl and octanol with the appropriate n(D-PEO227-D). The aim is to determine the interaction/structure relationship of the covered microemulsions. Precisely, we are interested in a quantitative investigation of the influence of volume fraction Φ, temperature (T), and n(D-PEO227-D) on the microemulsion sol/gel transition. To this end, we first study the uncoated microemulsion structure depending only on Φ. Second, we determine the coated microemulsions structure as a function of n(D-PEO227-D) for different Φ. Third, we examine the effect of temperature on the uncoated and coated microemulsion. We show that the sol/gel transition is controlled by the three main parameters, Φ, T, and n(D-PEO227-D). Accordingly, the uncoated microemulsion sol/gel transition, at ambient temperature, occurred for Φ ≃ 33.65%. By increasing Φ, the O/W-MIs show a glass state, which occurs, along with the gel state, at Φ ≃ 37% and arises clearly at Φ ≃ 60%. The coated O/W-MI sol/gel transition is found to be linearly dependent on n(D-PEO227-D) and takes place for Φ ≃ 26.5% for n(D-PEO227-D) = 12. Ordinarily, the decrease in temperature leads to gel formation of microemulsions for low Φ. Additionally, in this work, we found that the gelation temperature increases linearly with n(D-PEO227-D). Thus, the parameter n(D-PEO227-D) can control the sol/gel transition of the O/W-MIs at ambient temperature and moderate Φ.

Colloidal Nanocrystal Gels from Thermodynamic Principles

Gels assembled from solvent-dispersed nanocrystals are of interest for functional materials because they promise the opportunity to retain distinctive properties of individual nanocrystals combined with tunable, structure-dependent collective behavior. By incorporating stimuli-responsive components, these materials could also be dynamically reconfigured between structurally distinct states. However, nanocrystal gels have so far been formed mostly through irreversible aggregation, which has limited the realization of these possibilities. Meanwhile, gelation strategies for larger colloidal microparticles have been developed using reversible physical or chemical interactions. These approaches have enabled the experimental navigation of theoretically predicted phase diagrams, helping to establish an understanding of how thermodynamic behavior can guide gel formation in these materials. However, the translation of these principles to the nanoscale poses both practical and fundamental challenges. The molecules guiding assembly can no longer be safely assumed to be vanishingly small compared to the particles nor large compared to the solvent.In this Account, we discuss recent progress toward the assembly of tunable nanocrystal gels using two strategies guided by equilibrium considerations: (1) reversible chemical bonding between functionalized nanocrystals and difunctional linker molecules and (2) nonspecific, polymer-induced depletion attractions. The effective nanocrystal attractions, mediated in both approaches by a secondary molecule, compete against stabilizing repulsions to promote reversible assembly. The structure and properties of the nanocrystal gels are controlled microscopically by the design of the secondary molecule and macroscopically by its concentration. This mode of control is compelling because it largely decouples nanocrystal synthesis and functionalization from the design of interactions that drive assembly. Statistical thermodynamic theory and computer simulation have been applied to simple models that describe the bonding motifs in these assembling systems, furnish predictions for conditions under which gelation is likely to occur, and suggest strategies for tuning and disassembling the gel networks. Insights from these models have guided experimental realizations of reversible gels with optical properties in the infrared range that are sensitive to the gel structure. This process avoids time-consuming and costly trial-and-error experimental investigations to accelerate the development of nanocrystal gel assemblies.These advances highlight the need to better understand interactions between nanocrystals, how interactions give rise to gel structure, and properties that emerge. Such an understanding could suggest new approaches for creating stimuli-responsive and dissipative assembled materials whose properties are tunable on demand through directed reconfiguration of the underlying gel microstructure. It may also make nanocrystal gels amenable to computationally guided design using inverse methods to rapidly optimize experimental parameters for targeted functionalities.

Smoluchowski equations for linker-mediated irreversible aggregation

We developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.

Universal Gelation of Metal Oxide Nanocrystals via Depletion Attractions

Nanocrystal gelation provides a powerful framework to translate nanoscale properties into bulk materials and to engineer emergent properties through the assembled microstructure. However, many established gelation strategies rely on chemical reactions and specific interactions, e.g., stabilizing ligands or ions on the nanocrystals' surfaces, and are therefore not easily transferable. Here, we report a general gelation strategy via nonspecific and purely entropic depletion attractions applied to three types of metal oxide nanocrystals. The gelation thresholds of two compositionally distinct spherical nanocrystals agree quantitatively, demonstrating the adaptability of the approach for different chemistries. Consistent with theoretical phase behavior predictions, nanocrystal cubes form gels at a lower polymer concentration than nanocrystal spheres, allowing shape to serve as a handle to control gelation. These results suggest that the fundamental underpinnings of depletion-driven assembly, traditionally associated with larger colloidal particles, are also applicable at the nanoscale.

Surveying the free energy landscape of clusters of attractive colloidal spheres

Controlling the assembly of colloidal particles into specific structures has been a long-term goal of the soft materials community. Much can be learned about the process of self-assembly by examining the early stage assembly into clusters. For the simple case of hard spheres with short-range attractions, the rigid clusters of N particles (where N is small) have been enumerated theoretically and tested experimentally. Less is known, however, about how the free energy landscapes are altered when the inter-particle potential is long-ranged. In this work, we demonstrate how adaptive biasing in molecular simulations may be used to pinpoint shifts in the stability of colloidal clusters as the inter-particle potential is varied. We also discuss the generality of our techniques and strategies for application to related molecular systems.

Using Patchy Particles to Prevent Local Rearrangements in Models of Non-equilibrium Colloidal Gels

Simple models based on isotropic interparticle attractions often fail to capture experimentally observed structures of colloidal gels formed through spinodal decomposition and subsequent arrest: the resulting gels are typically denser and less branched than their experimental counterparts. Here, we simulate gels formed from soft particles with directional attractions ("patchy particles"), designed to inhibit lateral particle rearrangement after aggregation. We directly compare simulated structures with experimental colloidal gels made using soft attractive microgel particles, by employing a "skeletonization" method that reconstructs the three-dimensional backbone from experiment or simulation. We show that including directional attractions with sufficient valency leads to strongly branched structures compared to isotropic models. Furthermore, combining isotropic and directional attractions provides additional control over aggregation kinetics and gel structure. Our results show that the inhibition of lateral particle rearrangements strongly affects the gel topology and is an important effect to consider in computational models of colloidal gels.