Minimal conditions for solidification and thermal processing of colloidal gels.

Colloidal gelation is used to form processable soft solids from a wide range of functional materials. Although multiple gelation routes are known to create gels of different types, the microscopic processes during gelation that differentiate them remain murky. A fundamental question is how the thermodynamic quench influences the microscopic driving forces of gelation, and determines the threshold or minimal conditions where gels form. We present a method that predicts these conditions on a colloidal phase diagram, and mechanistically connects the quench path of attractive and thermal forces to the emergence of gelled states. Our method employs systematically varied quenches of a colloidal fluid over a range of volume fractions to identify minimal conditions for gel solidification. The method is applied to experimental and simulated systems to test its generality toward attractions with varied shapes. Using structural and rheological characterization, we show that all gels incorporate elements of percolation, phase separation, and glassy arrest, where the quench path sets their interplay and determines the shape of the gelation boundary. We find that the slope of the gelation boundary corresponds to the dominant gelation mechanism, and its location approximately scales with the equilibrium fluid critical point. These results are insensitive to potential shape, suggesting that this interplay of mechanisms is applicable to a wide range of colloidal systems. By resolving regions of the phase diagram where this interplay evolves in time, we elucidate how programmed quenches to the gelled state could be used to effectively tailor gel structure and mechanics.

Phosphates form spectroscopically dark state assemblies in common aqueous solutions.

Phosphates and polyphosphates play ubiquitous roles in biology as integral structural components of cell membranes and bone, or as vehicles of energy storage via adenosine triphosphate and phosphocreatine. The solution phase space of phosphate species appears more complex than previously known. We present nuclear magnetic resonance (NMR) and cryogenic transmission electron microscopy (cryo-TEM) experiments that suggest phosphate species including orthophosphates, pyrophosphates, and adenosine phosphates associate into dynamic assemblies in dilute solutions that are spectroscopically "dark." Cryo-TEM provides visual evidence of the formation of spherical assemblies tens of nanometers in size, while NMR indicates that a majority population of phosphates remain as unassociated ions in exchange with spectroscopically invisible assemblies. The formation of these assemblies is reversibly and entropically driven by the partial dehydration of phosphate groups, as verified by diffusion-ordered spectroscopy (DOSY), indicating a thermodynamic state of assembly held together by multivalent interactions between the phosphates. Molecular dynamics simulations further corroborate that orthophosphates readily cluster in aqueous solutions. This study presents the surprising discovery that phosphate-containing molecules, ubiquitously present in the biological milieu, can readily form dynamic assemblies under a wide range of commonly used solution conditions, highlighting a hitherto unreported property of phosphate's native state in biological solutions.

A colloidal model for the equilibrium assembly and liquid-liquid phase separation of the reflectin A1 protein.

Reflectin is an intrinsically disordered protein known for its ability to modulate the biophotonic camouflage of cephalopods based on its assembly-induced osmotic properties. Its reversible self-assembly into discrete, size-controlled clusters and condensed droplets are known to depend sensitively on the net protein charge, making reflectin stimuli-responsive to pH, phosphorylation, and electric fields. Despite considerable efforts to characterize this behavior, the detailed physical mechanisms of reflectin's assembly are not yet fully understood. Here, we pursue a coarse-grained molecular understanding of reflectin assembly using a combination of experiments and simulations. We hypothesize that reflectin assembly and phase behavior can be explained from a remarkably simple colloidal model whereby individual protein monomers effectively interact via a short-range attractive and long-range repulsive (SA-LR) pair potential. We parameterize a coarse-grained SA-LR interaction potential for reflectin A1 from small-angle x-ray scattering measurements, and then extend it to a range of pH values using Gouy-Chapman theory to model monomer-monomer electrostatic interactions. The pH-dependent SA-LR interaction is then used in molecular dynamics simulations of reflectin assembly, which successfully capture a number of qualitative features of reflectin, including pH-dependent formation of discrete-sized nanoclusters and liquid-liquid phase separation at high pH, resulting in a putative phase diagram for reflectin. Importantly, we find that at low pH size-controlled reflectin clusters are equilibrium assemblies, which dynamically exchange protein monomers to maintain an equilibrium size distribution. These findings provide a mechanistic understanding of the equilibrium assembly of reflectin, and suggest that colloidal-scale models capture key driving forces and interactions to explain thermodynamic aspects of native reflectin behavior. Furthermore, the success of SA-LR interactions presented in this study demonstrates the potential of a colloidal interpretation of interactions and phenomena in a range of intrinsically disordered proteins.

Experimental observation of near-wall effects during the puncture of soft solids.

Performing conventional mechanical characterization techniques on soft materials can be challenging due to issues such as limited sample volumes and clamping difficulties. Deep indentation and puncture is a promising alternative as it is an information-rich measurement with the potential to be performed in a high-throughput manner. Despite its promise, the method lacks standardized protocols, and open questions remain about its possible limitations. Addressing these shortcomings is vital to ensure consistent methodology, measurements, and interpretation across samples and labs. To fill this gap, we examine the role of finite sample dimensions (and by extension, volume) on measured forces to determine the sample geometry needed to perform and unambiguously interpret puncture tests. Through measurements of puncture on a well-characterized elastomer using systematically varied sample dimensions, we show that the apparent mechanical response of a material is in fact sensitive to near-wall effects, and that additional properties, such as the sliding friction coefficient, can only be extracted in the larger dimension case where such effects are negligible.

Tailoring Writability and Performance of Star Block Copolypeptides Hydrogels through Side-Chain Design.

Shear-recoverable hydrogels based on block copolypeptides with rapid self-recovery hold potential in extrudable and injectable 3D-printing applications. In this work, a series of 3-arm star-shaped block copolypeptides composed of an inner hydrophilic poly(l-glutamate) domain and an outer ß-sheet forming domain is synthesized with varying side chains and block lengths. By changing the ß-sheet forming domains, hydrogels with diverse microstructures and mechanical properties are prepared and structure-function relationships are determined using scattering and rheological techniques. Differences in the properties of these materials are amplified during direct-ink writing with a strong correlation observed between printability and material chemistry. Significantly, it is observed that non-canonical ß-sheet blocks based on phenyl glycine form more stable networks with superior mechanical properties and writability compared to widely used natural amino acid counterparts. The versatile design available through block copolypeptide materials provides a robust platform to access tunable material properties based solely on molecular design. These systems can be exploited in extrusion-based applications such as 3D-printing without the need for additives.

Competition between ß-Sheet and Coacervate Domains Yields Diverse Morphologies in Mixtures of Oppositely Charged Homochiral Polypeptides.

Biomolecular assembly processes involving competition between specific intermolecular interactions and thermodynamic phase instability have been implicated in a number of pathological states and technological applications of biomaterials. As a model for such processes, aqueous mixtures of oppositely charged homochiral polypeptides such as poly-l-lysine and poly-l-glutamic acid have been reported to form either ß-sheet-rich solid-like precipitates or liquid-like coacervate droplets depending on competing hydrogen bonding interactions. Herein, we report studies of polypeptide mixtures that reveal unexpectedly diverse morphologies ranging from partially coalescing and aggregated droplets to bulk precipitates, as well as a previously unreported re-entrant liquid-liquid phase separation at high polypeptide concentration and ionic strength. Combining our experimental results with all-atom molecular dynamics simulations of folded polypeptide complexes reveals a concentration dependence of ß-sheet-rich secondary structure, whose relative composition correlates with the observed macroscale morphologies of the mixtures. These results elucidate a crucial balance of interactions that are important for controlling morphology during coacervation in these and potentially similar biologically relevant systems.

Coacervate or precipitate? Formation of non-equilibrium microstructures in coacervate emulsions.

Non-equilibrium processing of aqueous polyelectrolyte complex (PEC) coacervates is critical to many applications. In particular, many coacervate-forming systems are known to become trapped in out-of-equilibrium states (e.g., precipitation). The mechanism and conditions under which these states form, and whether they age, is not clearly understood. Here, we elucidate the influence of processing on the PEC coarsening mechanism as it varies with flow during mixing for a model system of poly(allylamine hydrochloride) and poly(acrylic acid sodium salt) in water. We demonstrate that flow conditions can be used to toggle the formation of rough, precipitate-like aggregates of micron-scale PEC structures. These structures form at compositions with viscous-dominant equilibrium rheology, and observations of their formation via optical microscopy suggest that they comprise colloidal aggregates of PEC coacervate droplets. We further show that these aggregates exhibit micron-scale coarsening, with a mixing time-dependent characteristic aging time scale. The results show that the formation of precipitate-like structures is not solely determined by composition, but is instead highly sensitive to mass transport and colloidal instability effects. Our observations suggest that the details of mixing flow can provide non-equilibrium structural control of a broad range of PEC coacervate materials orthogonally to structure-property inspired polymeric design. We anticipate that these findings will open the door for future studies on the control of non-equilibrium PEC formation and structure.

Strength of fluid-filled soft composites across the elastofracture length.

Materials that utilize heterogeneous microstructures to control macroscopic mechanical response are ubiquitous in nature. Yet, translating nature's lessons to create synthetic soft solids has remained challenging. This is largely due to the limited synthetic routes available for creating soft composites, particularly with submicron features, as well as uncertainty surrounding the role of such a microstructured secondary phase in determining material behavior. This work leverages recent advances in the development of photocrosslinkable thermogelling nanoemulsions to produce composite hydrogels with a secondary phase assembled at well controlled length scales ranging from tens of nm to tens of µm. Through analysis of the mechanical response of these fluid-filled composite hydrogels, it is found that the size scale of the secondary phase has a profound impact on the strength when at or above the elastofracture length. Moreover, this work shows that mechanical integrity of fluid-filled soft solids can be sensitive to the size scale of the secondary phase.

High-throughput microscopy to determine morphology, microrheology, and phase boundaries applied to phase separating coacervates.

Evolution of composition, rheology, and morphology during phase separation in complex fluids is highly coupled to rheological and mass transport processes within the emerging phases, and understanding this coupling is critical for materials design of multiphase complex fluids. Characterizing these dependencies typically requires careful measurement of a large number of equilibrium and transport properties that are difficult to measure in situ as phase separation proceeds. Here, we propose and demonstrate a high-throughput microscopy platform to achieve simultaneous, in situ mapping of time-evolving morphology and microrheology in phase separating complex fluids over a large compositional space. The method was applied to a canonical example of polyelectrolyte complex coacervation, whereby mixing of oppositely charged species leads to liquid-liquid phase separation into distinct solute-dense and dilute phases. Morphology and rheology were measured simultaneously and kinetically after mixing to track the progression of phase separation. Once equilibrated, the dense phase viscosity was determined to high compositional accuracy using passive probe microrheology, and the results were used to derive empirical relationships between the composition and viscosity. These relationships were inverted to reconstruct the dense phase boundary itself, and further extended to other mixture compositions. The resulting predictions were validated by independent equilibrium compositional measurements. This platform paves the way for rapid screening and formulation of complex fluids and (bio)macromolecular materials, and serves as a critical link between formulation and rheology for multi-phase material discovery.

Modeling colloidal interactions that predict equilibrium and non-equilibrium states.

Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium "arrested states," such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation.

Flow-Induced Concentration Nonuniformity and Shear Banding in Entangled Polymer Solutions.

Recent models have predicted entangled polymer solutions could shear band due to unstable flow-induced demixing. This work provides the first experimental probe of the in situ concentration profile of entangled polymer solutions under shear. At shear rates above a critical value, we show that the concentration and velocity profiles can develop bands, in quantitative agreement with steady-state model predictions. These findings highlight the critical importance of flow-concentration coupling in entangled polymer solutions.

Influence of Polarity Change and Photophysical Effects on Photosurfactant-Driven Wetting.

Photosurfactants have shown considerable promise for enabling stimuli-responsive control of the properties and motion of fluid interfaces. Recently, a number of photoswitch chemistries have emerged to tailor the photoresponsive properties of photosurfactants. However, systematic studies investigating how photoresponsive surfactant behavior depends on the photochemical and photophysical properties of the switch remain scarce. In this work, we develop synthetic schemes and surfactant designs to produce a well-controlled library of photosurfactants to comparatively assess the behavior of photoswitch chemistry on interfacial behavior. We employ photoinduced spreading of droplets at fluid interfaces as a model for such studies. We show that although photosurfactant response is largely guided by expected trends with changes in polarity of the photoswitch, interfacial behavior also depends nontrivially and sometimes counter-intuitively on the kinetics and mechanisms of photoswitching, particularly at the interface of two solvents, as well as on complex interactions with other surfactants. Understanding these complexities enables the design of new photosurfactant systems and their optimization toward responsive functions including triggered spreading, dewetting, and destabilization of droplets on solid and fluid surfaces.

Soluto-inertial phenomena: Designing long-range, long-lasting, surface-specific interactions in suspensions.

Equilibrium interactions between particles in aqueous suspensions are limited to distances less than 1 µm. Here, we describe a versatile concept to design and engineer nonequilibrium interactions whose magnitude and direction depends on the surface chemistry of the suspended particles, and whose range may extend over hundreds of microns and last thousands of seconds. The mechanism described here relies on diffusiophoresis, in which suspended particles migrate in response to gradients in solution. Three ingredients are involved: a soluto-inertial "beacon" designed to emit a steady flux of solute over long time scales; suspended particles that migrate in response to the solute flux; and the solute itself, which mediates the interaction. We demonstrate soluto-inertial interactions that extend for nearly half a millimeter and last for tens of minutes, and which are attractive or repulsive, depending on the surface chemistry of the suspended particles. Experiments agree quantitatively with scaling arguments and numerical computations, confirming the basic phenomenon, revealing design strategies, and suggesting a broad set of new possibilities for the manipulation and control of suspended particles.

Controlling Complex Nanoemulsion Morphology Using Asymmetric Cosurfactants for the Preparation of Polymer Nanocapsules.

Complex nanoemulsions, comprising multiphase nanoscale droplets, hold considerable potential advantages as vehicles for encapsulation and delivery as well as templates for nanoparticle synthesis. Although methods exist to controllably produce complex emulsions on the microscale, very few methods exist to produce them on the nanoscale. Here, we examine a recently developed method involving a combination of high-energy emulsification with conventional cosurfactants to produce oil-water-oil (O/W/O) complex nanoemulsions. Specifically, we study in detail how the composition of conventional ethoxylated cosurfactants Span80 and Tween20 influences the morphology and structure of the resulting complex nanoemulsions in the water-cyclohexane system. Using a combination of small-angle neutron scattering and cryo-electron microscopy, we find that the cosurfactant composition controls the generation of complex droplet morphologies including core-shell and multicore-shell O/W/O nanodroplets, resulting in an effective state diagram for the selection of nanoemulsion morphology. Additionally, the cosurfactant composition can be used to control the thickness of the water shell contained within the complex nanodroplets. We hypothesize that this degree of control, despite the highly nonequilibrium nature of the nanoemulsions, is ultimately determined by a competition between the opposing spontaneous curvature of the two cosurfactants, which strongly influences the interfacial curvature of the nanodroplets as a result of their ultralow interfacial tension. This is supported by a correlation between cosurfactant compositions that produces complex nanoemulsions and those that produce homogeneous mixed micelles in equilibrium surfactant-cyclohexane solutions. Ultimately, we show that the formation of complex O/W/O nanoemulsions is weakly perturbed upon the addition of hydrophilic polymer precursors, facilitating their use as templates for the formation of polymer nanocapsules.

Synthesis of Oil-Laden Poly(ethylene glycol) Diacrylate Hydrogel Nanocapsules from Double Nanoemulsions.

Multiple emulsions have received great interest due to their ability to be used as templates for the production of multicompartment particles for a variety of applications. However, scaling these complex droplets to nanoscale dimensions has been a challenge due to limitations on their fabrication methods. Here, we report the development of oil-in-water-in-oil (O1/W/O2) double nanoemulsions via a two-step high-energy method and their use as templates for complex nanogels comprised of inner oil droplets encapsulated within a hydrogel matrix. Using a combination of characterization methods, we determine how the properties of the nanogels are controlled by the size, stability, internal morphology, and chemical composition of the nanoemulsion templates from which they are formed. This allows for identification of compositional and emulsification parameters that can be used to optimize the size and oil encapsulation efficiency of the nanogels. Our templating method produces oil-laden nanogels with high oil encapsulation efficiencies and average diameters of 200-300 nm. In addition, we demonstrate the versatility of the system by varying the types of inner oil, the hydrogel chemistry, the amount of inner oil, and the hydrogel network cross-link density. These nontoxic oil-laden nanogels have potential applications in food, pharmaceutical, and cosmetic formulations.

Oil-in-Water-in-Oil Multinanoemulsions for Templating Complex Nanoparticles.

Complex nanoemulsions involving nanodroplets with a defined inner structure have great potential for encapsulation and templating applications. We report a method to form novel complex oil-in-water-in-oil nanoemulsions using a combination of high-energy processing with mixed nonionic surfactants that simultaneously achieve ultralow interfacial tension and frustrated curvature of the water-oil interface. The method produces multinanoemulsions possessing morphologies resembling water-swollen reverse vesicles with core-shell and multicore-shell morphologies of water in cyclohexane. A combination of macroscopic and microscopic characterization conclusively verifies and quantifies the complex morphologies, which vary systematically and reproducibly with water content for water volume fractions between 0.01 and 0.10. The complex morphologies are stable tens of hours, providing a route for their use as liquid templates for internally structured nanoparticles. As a demonstration, we test the complex nanoemulsions' ability to template complex polymer nanogels.

Dark-field differential dynamic microscopy.

Differential dynamic microscopy (DDM) is an emerging technique to measure the ensemble dynamics of colloidal and complex fluid motion using optical microscopy in systems that would otherwise be difficult to measure using other methods. To date, DDM has successfully been applied to linear space invariant imaging modes including bright-field, fluorescence, confocal, polarised, and phase-contrast microscopy to study diverse dynamic phenomena. In this work, we show for the first time how DDM analysis can be extended to dark-field imaging, i.e. a linear space variant (LSV) imaging mode. Specifically, we present a particle-based framework for describing dynamic image correlations in DDM, and use it to derive a correction to the image structure function obtained by DDM that accounts for scatterers with non-homogeneous intensity distributions as they move within the imaging plane. To validate the analysis, we study the Brownian motion of gold nanoparticles, whose plasmonic structure allows for nanometer-scale particles to be imaged under dark-field illumination, in Newtonian liquids. We find that diffusion coefficients of the nanoparticles can be reliably measured by dark-field DDM, even under optically dense concentrations where analysis via multiple-particle tracking microrheology fails. These results demonstrate the potential for DDM analysis to be applied to linear space variant forms of microscopy, providing access to experimental systems unavailable to other imaging modes.

Microdynamics and arrest of coarsening during spinodal decomposition in thermoreversible colloidal gels.

Coarsening and kinetic arrest of colloidal systems undergoing spinodal decomposition (SD) is a conserved motif for forming hierarchical, bicontinuous structures. Although the thermodynamic origins of SD in colloids are widely known, the microstructural processes responsible for its coarsening and associated dynamics en route to arrest remain elusive. To better elucidate the underlying large-scale microdynamical processes, we study a colloidal system with moderate-range attractions which displays characteristic features of arrested SD, and study its dynamics during coarsening through a combination of differential dynamic microscopy and real-space tracking. Using these recently developed imaging techniques, we reveal directly that the coarsening arises from collective dynamics of dense domains, which undergo slow, intermittent, and ballistic motion. These collective motions indicate interfacial effects to be the driving force of coarsening. The nature of the gelation enables control of the arrested length scale of coarsening by the depths of quenching into the spinodal regime, which we demonstrate to provide an effective means to control the elasticity of colloidal gels.

Texture analysis microscopy: quantifying structure in low-fidelity images of dense fluids.

Optical images are often corrupted by noise, low contrast, uneven illumination and artefacts, which may pose significant challenges to image analysis, particularly for dense fluids. Traditionally, noise removal and contrast enhancement are achieved by global arithmetic operations on the image as a whole, and/or by image convolution with various kernels. However, these methods work under very limited conditions and can compromise detail within the image. Here, we develop a new technique, texture analysis microscopy (TAM), to overcome these challenges based on the method of image correlation. TAM recasts an image by the statistical similarities between a raw image and a template feature (e.g. a Gaussian) that best approximates features in the image. We demonstrate the superiority of TAM by applying it to low-fidelity images under conditions where traditional methods fail or have deteriorative performance, for analyses including structural correlations, particle identification and sizing.

Homogeneous percolation versus arrested phase separation in attractively-driven nanoemulsion colloidal gels.

We elucidate mechanisms for colloidal gelation of attractive nanoemulsions depending on the volume fraction (ϕ) of the colloid. Combining detailed neutron scattering, cryo-transmission electron microscopy and rheological measurements, we demonstrate that gelation proceeds by either of two distinct pathways. For ϕ sufficiently lower than 0.23, gels exhibit homogeneous fractal microstructure, with a broad gel transition resulting from the formation and subsequent percolation of droplet-droplet clusters. In these cases, the gel point measured by rheology corresponds precisely to arrest of the fractal microstructure, and the nonlinear rheology of the gel is characterized by a single yielding process. By contrast, gelation for ϕ sufficiently higher than 0.23 is characterized by an abrupt transition from dispersed droplets to dense clusters with significant long-range correlations well-described by a model for phase separation. The latter phenomenon manifests itself as micron-scale "pores" within the droplet network, and the nonlinear rheology is characterized by a broad yielding transition. Our studies reinforce the similarity of nanoemulsions to solid particulates, and identify important qualitative differences between the microstructure and viscoelastic properties of colloidal gels formed by homogeneous percolation and those formed by phase separation.