Programmable Anisotropy and Percolation in Supramolecular Patchy Particle Gels

Tuning Colloidal Gel Properties: The Influence of Central and Noncentral Forces

Colloidal gels, ubiquitous in industrial applications, can undergo reversible solid-to-liquid transitions. Recent work demonstrates that adding surface roughness to primary particles enhances the toughness and influences the self-healing properties of colloidal gels. In the present work, we first use colloidal probe atomic force microscopy (CP-AFM) to assess the quantitative changes in adhesive and frictional forces between thermoresponsive particles as a function of their roughness. The presence of static friction, generated by interparticle adhesion results in noncentral forces, leading to network structures that are more readily constrained in their nodes. Systems with higher friction exhibited increased sedimentation stability, a decrease in percolation threshold and a more abrupt elastic to plastic transition, but an enhanced capacity in storing elastic energy until fluidification. Additional experiments with geometrically smooth but "chemically rough" (patchy) particles further emphasized the importance of static interparticle friction in the macroscopic yielding and recovery behavior of colloidal gels.

Neuromorphic Computing Primitives Using Polymer-Networked Nanoparticles

Nanoparticle networks have potential applications in brain-like computing yet their ability to adopt different states remains unexplored. In this work, we reveal the dynamics of the attachment of polyelectrolytes onto gold nanoparticles (AuNPs), using a bottom-up two-bead-monomer dissipative particle dynamics (TBM-DPD) model to show the heterogeneity of polymer coverage. We found that the use of one polyelectrolyte homopolymer limits the complexity of the possible engineered nanoparticle networks (ENPNs) that can be built. In addressing this challenge, we first found the commensurability rules between the numbers of AuNPs and poly(allylamine hydrochloride)s (PAHs). This gives rise to a well-defined valency of a AuNP which is the maximum number of PAHs that it can accommodate. We further use an engineered block copolymer, which has a conductive middle block to mediate the distance between a dimer of AuNP. We argue that by controlling the length of conductive block that is connecting the AuNPs and their respective topology, we can have ENPNs potentially adopt multiple states necessary for primitive neuromorphic computing.

Bacteriorhodopsin of purple membrane reverses anisotropy outside the pH range of proton pumping based on logic gate realization

The bacteriorhodopsin of purple membrane is the first discovered light-sensing protein among ion transporting microbial rhodopsins, some of which (e.g. Archaerhodopsin 3) could be broadly used as tools in optogenetics having wide potential of medical applications. Since its discovery as early as in 1971, bacteriorhodopsin has attracted wide interests in nano-biotechnology, particularly in optoelectronics devices. Therefore, the present work has been motivated due to two topics; firstly, anisotropy demand became indispensible in bioelectronics; secondly, the stationary level of electric response in bacteriorhodopsin within the pH range of proton pumping (pH 3 - pH 10) implies, in turn, raising here a question about whether the electric anisotropy is implicated for reducing (or switching off) such level beyond such pH range. Noteworthy is that the purple membrane converts to blue form upon acidification, while to reddish purple form upon alkalization. In the present study, the acidic and alkaline forms of bacteriorhodopsin have exhibited most probable state of reversal for the dielectric anisotropy around pH 2.5 and pH 10.5, respectively. This is underscored by proposing a correlation seemingly found between disassembly of the crystalline structure of bacteriorhodopsin and the reversal of dielectric anisotropy, at such acidic and alkaline reversal pH's, in terms of the essence of the crystalline lattice. Most importantly, the results have substantiated dual frequency characteristics and logic gate-based dielectric anisotropy reversal to bacteriorhodopsin, which may implicate it for potential applications in bioelectronics.

Nonuniversal Dynamics of Hyperbranched Metallo-Supramolecular Polymer Networks by the Spontaneous Formation of Nanoparticles

Various transient and permanent bonds are commonly combined in increasingly complex hierarchical structures to achieve biomimetic functions, along with high mechanical properties. However, there is a traditional trade-off between mechanical strength and biological functions like self-healing. To fill this gap, we develop a metallo-supramolecular polymer hydrogel based on the hyperbranched poly(ethylene imine) (PEI) backbone and phenanthroline ligands, which have unexpectedly high plateau modulus at low concentrations. Rheological measurements demonstrate nonuniversal metal-ion-specific dynamics, with significantly larger plateau moduli, longer relaxation times, and stronger temperature dependencies, compared to equivalent networks based on model-type telechelic precursors, which cannot be explained by the theory of linear viscoelasticity. TEM images reveal the in situ mineralization of metal ions, which nucleate by the ligand complexation and grow thanks to the spontaneous reducing effect of the PEI backbone. Evidently, the complex lifetime works against Ostwald ripening, resulting in the formation of thermodynamically stable smaller particles. This trend is followed by time-dependent network buildup measurements and is confirmed by a kinetic model for particle formation and aggregation. The spontaneous formation of particles with complex lifetime-dependent sizes can explain the nonuniversal dynamics through the interaction of polymer segments and particles at the nanoscale. This work describes how the polymer backbone can affect the strength and stability of supramolecular bonds, promising for combining high mechanical properties and self-healing comparable to natural tissues.

Bottlebrush Midblocks Promote Colloidal Bridging of Telechelic Polymers

Telechelic polymers are effective rheological modifiers that bridge between associative constituents to form elastic networks. The performance of linear telechelic chains, however, is controlled by entropic forces and thus suffers from an upper limit on bridge formation. This work overcomes this limitation by utilizing telechelic triblock copolymers containing bottlebrush midblocks. By comparing the rheological properties of emulsions linked by telechelic bottlebrush polymers to those containing linear chains, we determined that telechelic polymers with bottlebrush midblocks form elastic networks more efficiently. These enhanced rheological properties arise from the high stiffness of the bottlebrush midblocks, which offsets the entropic stretching penalty for bridge formation, enabling them to more readily form networks. This molecular-level control over polymer conformation in complex fluids opens avenues for designing highly elastic networks with minimal polymeric additives.

A logic-activated nanoswitch for killing cancer cells according to assessment of drug-resistance

A logic-activated nanoswitch that could diagnose the differences between drug-resistant and non-drug-resistant cancer cells and control the release of drugs was developed for enhanced chemo-gene therapy using a standalone system. Compared to traditional treatments, the nanoswitch displayed improved anti-tumor efficiency in vitro.

Percolation thresholds of disks with random nonoverlapping patches on four regular two-dimensional lattices

In percolation of patchy disks on lattices, each site is occupied by a disk, and neighboring disks are regarded as connected when their patches contact. Clusters of connected disks become larger as the patchy coverage of each disk χ increases. At the percolation threshold χ_{c}, an incipient cluster begins to span the whole lattice. For systems of disks with n symmetric patches on Archimedean lattices, a recent work [Wang et al., Phys. Rev. E 105, 034118 (2022)2470-004510.1103/PhysRevE.105.034118] found symmetric properties of χ_{c}(n), which are due to the coupling of the patches' symmetry and the lattice geometry. How does χ_{c} behave with increasing n if the patches are randomly distributed on the disks? We consider two typical random distributions of the patches, i.e., the equilibrium distribution and a distribution from random sequential adsorption. Combining Monte Carlo simulations and the critical polynomial method, we numerically determine χ_{c} for 106 models of different n on the square, honeycomb, triangular, and kagome lattices. The rules governing χ_{c}(n) are investigated in detail. They are quite different from those for disks with symmetric patches and could be useful for understanding similar systems.

Valence can control the nonexponential viscoelastic relaxation of multivalent reversible gels

Gels made of telechelic polymers connected by reversible cross-linkers are a versatile design platform for biocompatible viscoelastic materials. Their linear response to a step strain displays a fast, near-exponential relaxation when using low-valence cross-linkers, while larger supramolecular cross-linkers bring about much slower dynamics involving a wide distribution of timescales whose physical origin is still debated. Here, we propose a model where the relaxation of polymer gels in the dilute regime originates from elementary events in which the bonds connecting two neighboring cross-linkers all disconnect. Larger cross-linkers allow for a greater average number of bonds connecting them but also generate more heterogeneity. We characterize the resulting distribution of relaxation timescales analytically and accurately reproduce stress relaxation measurements on metal-coordinated hydrogels with a variety of cross-linker sizes including ions, metal-organic cages, and nanoparticles. Our approach is simple enough to be extended to any cross-linker size and could thus be harnessed for the rational design of complex viscoelastic materials.

Recent advances in synchrotron scattering methods for probing the structure and dynamics of colloids

Recent progress in synchrotron based X-ray scattering methods applied to colloid science is reviewed. An important figure of merit of these techniques is that they enable in situ investigations of colloidal systems under the desired thermophysical and rheological conditions. An ensemble averaged simultaneous structural and dynamical information can be derived albeit in reciprocal space. Significant improvements in X-ray source brilliance and advances in detector technology have overcome some of the limitations in the past. Notably coherent X-ray scattering techniques have become more competitive and they provide complementary information to laboratory based real space methods. For a system with sufficient scattering contrast, size ranges from nm to several μm and time scales down to μs are now amenable to X-ray scattering investigations. A wide variety of sample environments can be combined with scattering experiments further enriching the science that could be pursued by means of advanced X-ray scattering instruments. Some of these recent progresses are illustrated via representative examples. To derive quantitative information from the scattering data, rigorous data analysis or modeling is required. Development of powerful computational tools including the use of artificial intelligence have become the emerging trend.

Soft Viscoelastic Magnetic Hydrogels from the In Situ Mineralization of Iron Oxide in Metal-Coordinate Polymer Networks

The design of soft magnetic hydrogels with high concentrations of magnetic particles is complicated by weak retention of the iron oxide particles in the hydrogel scaffold. Here, we propose a design strategy that circumvents this problem through the in situ mineralization of iron oxide nanoparticles within polymer hydrogels functionalized with strongly iron-coordinating nitrocatechol groups. The mineralization process facilitates the synthesis of a high concentration of large iron oxide nanoparticles (up to 57 wt % dry mass per single cycle) in a simple one-step process under ambient conditions. The resulting hydrogels are soft (kPa range) and viscoelastic and exhibit strong magnetic actuation. This strategy offers a pathway for the energy-efficient design of soft, mechanically robust, and magneto-responsive hydrogels for biomedical applications.

Non-Maxwellian viscoelastic stress relaxations in soft matter

Viscoelastic stress relaxation is a basic characteristic of soft matter systems such as colloids, gels, and biological networks. Although the Maxwell model of linear viscoelasticity provides a classical description of stress relaxation, it is often not sufficient for capturing the complex relaxation dynamics of soft matter. In this Tutorial, we introduce and discuss the physics of non-Maxwellian linear stress relaxation as observed in soft materials, the ascribed origins of this effect in different systems, and appropriate models that can be used to capture this relaxation behavior. We provide a basic toolkit that can assist the understanding and modeling of the mechanical relaxation of soft materials for diverse applications.

Scientific machine learning for modeling and simulating complex fluids

The formulation of rheological constitutive equations-models that relate internal stresses and deformations in complex fluids-is a critical step in the engineering of systems involving soft materials. While data-driven models provide accessible alternatives to expensive first-principles models and less accurate empirical models in many engineering disciplines, the development of similar models for complex fluids has lagged. The diversity of techniques for characterizing non-Newtonian fluid dynamics creates a challenge for classical machine learning approaches, which require uniformly structured training data. Consequently, early machine-learning based constitutive equations have not been portable between different deformation protocols or mechanical observables. Here, we present a data-driven framework that resolves such issues, allowing rheologists to construct learnable models that incorporate essential physical information, while remaining agnostic to details regarding particular experimental protocols or flow kinematics. These scientific machine learning models incorporate a universal approximator within a materially objective tensorial constitutive framework. By construction, these models respect physical constraints, such as frame-invariance and tensor symmetry, required by continuum mechanics. We demonstrate that this framework facilitates the rapid discovery of accurate constitutive equations from limited data and that the learned models may be used to describe more kinematically complex flows. This inherent flexibility admits the application of these "digital fluid twins" to a range of material systems and engineering problems. We illustrate this flexibility by deploying a trained model within a multidimensional computational fluid dynamics simulation-a task that is not achievable using any previously developed data-driven rheological equation of state.

The Role of Receptor Uniformity in Multivalent Binding

Multivalency is prevalent in various biological systems and applications due to the superselectivity that arises from the cooperativity of multivalent binding. Traditionally, it was thought that weaker individual binding would improve the selectivity in multivalent targeting. Here, using analytical mean field theory and Monte Carlo simulations, we discover that, for receptors that are highly uniformly distributed, the highest selectivity occurs at an intermediate binding energy and can be significantly greater than the weak binding limit. This is caused by an exponential relationship between the bound fraction and receptor concentration, which is influenced by both the strength and combinatorial entropy of binding. Our findings not only provide new guidelines for the rational design of biosensors using multivalent nanoparticles but also introduce a new perspective in understanding biological processes involving multivalency.

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.

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

Percolation thresholds of randomly rotating patchy particles on Archimedean lattices

We study the percolation of randomly rotating patchy particles on 11 Archimedean lattices in two dimensions. Each vertex of the lattice is occupied by a particle, and in each model the patch size and number are monodisperse. When there are more than one patches on the surface of a particle, they are symmetrically decorated. As the proportion χ of the particle surface covered by the patches increases, the clusters connected by the patches grow and the system percolates at the threshold χ_{c}. We combine Monte Carlo simulations and the critical polynomial method to give precise estimates of χ_{c} for disks with one to six patches and spheres with one to two patches on the 11 lattices. For one-patch particles, we find that the order of χ_{c} values for particles on different lattices is the same as that of threshold values p_{c} for site percolation on these lattices, which implies that χ_{c} for one-patch particles mainly depends on the geometry of lattices. For particles with more patches, symmetry becomes very important in determining χ_{c}. With the estimates of χ_{c} for disks with one to six patches, using analyses related to symmetry, we are able to give precise values of χ_{c} for disks with an arbitrary number of patches on all 11 lattices. The following rules are found for patchy disks on each of these lattices: (1) as the number of patches n increases, values of χ_{c} repeat in a periodic way, with the period n_{0} determined by the symmetry of the lattice; (2) when mod(n,n_{0})=0, the minimum threshold value χ_{min} appears, and the model is equivalent to site percolation with χ_{min}=p_{c}; and (3) disks with mod(n,n_{0})=m and n_{0}-m (m<n_{0}/2) share the same χ_{c} value. The results can be useful references for studying the connectivity of patchy particles on two-dimensional lattices at finite temperatures.

Assembling Inorganic Nanocrystal Gels

Inorganic nanocrystal gels retain distinct properties of individual nanocrystals while offering tunable, network-structure-dependent characteristics. We review different mechanisms for assembling gels from colloidal nanocrystals including (1) controlled destabilization, (2) direct bridging, (3) depletion, as well as linking mediated by (4) coordination bonding or (5) dynamic covalent bonding, and we highlight how each impacts gel properties. These approaches use nanocrystal surface chemistry or the addition of small molecules to mediate inter-nanocrystal attractions. Each method offers advantages in terms of gel stability, reversibility, or tunability and presents new opportunities for the design of reconfigurable materials and fueled assemblies.

Structural, mechanical, and vibrational properties of particulate physical gels

Our lives are surrounded by a rich assortment of disordered materials. In particular, glasses are well known as dense, amorphous materials, whereas gels exist in low-density, disordered states. Recent progress has provided a significant step forward in understanding the material properties of glasses, such as mechanical, vibrational, and transport properties. In contrast, our understanding of particulate physical gels is still highly limited. Here, using molecular dynamics simulations, we study a simple model of particulate physical gels, the Lennard-Jones (LJ) gels, and provide a comprehensive understanding of their structural, mechanical, and vibrational properties, all of which are markedly different from those of LJ glasses. First, the LJ gels show sparse, heterogeneous structures, and the length scale ξ_s of the structures grows as the density is lowered. Second, the LJ gels are extremely soft, with both shear G and bulk K moduli being orders of magnitude smaller than those of LJ glasses. Third, many low-frequency vibrational modes are excited, which form a characteristic plateau with the onset frequency ω_* in the vibrational density of states. Structural, mechanical, and vibrational properties, characterized by ξ_s, G, K, and ω_*, respectively, show power-law scaling behaviors with the density, which establishes a close relationship between them. Throughout this work, we also reveal that LJ gels are multiscale, solid-state materials: (i) homogeneous elastic bodies at long lengths, (ii) heterogeneous elastic bodies with fractal structures at intermediate lengths, and (iii) amorphous structural bodies at short lengths.

Building blocks for autonomous computing materials: Dimers, trimers, and tetramers

Autonomous computing materials for data storage and computing offer an opportunity for next generation of computing devices. Patchy nanoparticle networks, for example, have been suggested as potential candidates for emulating neuronal networks and performing brain-like computing. Here, we use molecular dynamics (MD) simulations to show that stable dimers, trimers, and tetramers can be built from citrate capped gold nanoparticles (cit-AuNPs) linked by poly(allylamine hydrochloride) (PAH) chains. We use different lengths of PAHs to build polymer-networked nanoparticle assemblies that can emulate a complex neuronal network linked by axons of varying lengths. We find that the tetramer structure can accommodate up to 11 different states when the AuNP pairs are connected by either of two polymer linkers, PAH₂₀₀ and PAH₃₀₀. We find that the heavy AuNPs contribute to the assembly's structure stability. To further illustrate the stability, the AuNP-AuNP distances in dimer, trimer, and tetramer structures are reduced by steering the cit-AuNPs closer to each other. At different distances, these steered structures are all locally stable in a 10 ns MD simulation time scale because of their connection to the AuNPs. We also find that the global potential energy minimum is at short AuNP-AuNP distances where AuNPs collapse because the -NH₃ ⁺ and -COO^- attraction reduces the potential energy. The stability and application of these fundamental structures remain to be further improved through the use of alternative polymer linkers and nanoparticles.