Polymer topology influences the structural and dynamic behavior of macromolecules, particularly under non-equilibrium conditions such as shear flow. As a result, conventional Gaussian chain models fail to capture the complex deformation and relaxation dynamics of polymers with branched architectures. In this study, we present a combination of Brownian dynamics simulations with Gram-Charlier (G-C) expansion analysis to quantify non-Gaussian features using two cumulant-based metrics: the standard deviation σ of the one-dimensional projected configurational distribution, where larger values indicate greater deformation, and the normalized fourth cumulant κ4/σ4, where larger values indicate stronger non-Gaussianity. Focusing on linear and star polymers in dilute solution, we systematically investigate how molecular architecture, finite extensibility, and hydrodynamic interactions (HI) influence their deformation and conformational response in shear flow. Our findings reveal that star polymers exhibit constrained global extension but enhanced local stretching near the core, resulting in reduced deviations from Gaussian behavior compared to linear chains. Finite extensibility imposes an upper limit on bond extension, which suppresses configurational deformation at high shear rates and leads to a non-monotonic trend in κ4/σ4. By contrast, hydrodynamic interactions introduce long-range segmental coupling that enhances coordinated motion and amplifies non-Gaussian character, resulting in higher values of κ4/σ4 under strong shear flow. Together, these results establish a robust framework for characterizing the influence of polymer topology on non-equilibrium conformations, offering new insights into the mechanics of branched polymer systems under flow.

Particle-stabilized emulsions offer a strategy for forming mechanically robust microcapsules based on coassembly of silica nanoparticles, polyelectrolytes, and surfactants at oil-water interfaces. Such systems have complicated distributions of inorganic colloidal solids, surfactants, solvents, and ions that influence their compositions and structures over multiple length scales, which have been challenging to characterize and establish. To do so, silica-polyelectrolyte microcapsules were prepared with nearly monodisperse dimensions in the submicron range from water-in-oil (W/O) emulsions that were stabilized by a combination of nonionic surfactants, anionic silica nanoparticles, and cationic polyelectrolyte chains. Nonionic surfactants were used to establish oil as the continuous phase, while silica-polyelectrolyte complexes, self-assembled at the oil-water interfaces, prevented coalescence between droplets and provided mechanical elasticity. Particle charge measurements show that the surface charge density of the silica nanoparticles can be controlled by adjusting the pH conditions or by substituting aluminate ions at their surfaces. These promoted strong electrostatic and hydrogen-bonding interactions with the cationic polyelectrolyte and nonionic surfactant species, direct atomic-scale evidence of which is provided by solid-state two-dimensional (2D) 29Si{1H} NMR. For nanoparticles with higher surface charge densities, strong electrostatic interactions are the basis for particle coassembly with cationic polyelectrolyte species, and the resulting silica-polyelectrolyte complexes adsorb at the oil-water interface, as revealed by cryogenic electron microscopy. Relative to larger spherical nanoparticles, the elongated nanoparticles exhibit more extensive hydrogen bonding with polar organic moieties, which contributes to polyelectrolyte bridging between particles with lower densities of surface negative charges, consistent with interfacial rheology analyses. In addition to interfacial compositions and conditions, noncovalent polyelectrolyte-silica interactions, governed by nanoparticle surface compositions, charge density, and surface area, can be adjusted to control the macroscopic mechanical properties of the microcapsule interfaces.

High-throughput screening and optimization of high-value protein formulations requires intensified measurements to extract a wide range of properties using a small number of measurement techniques, small sample volumes, and short measurement times. We demonstrate how differential dynamic microscopy (DDM) can fill this need by measuring a broad range of key biophysical properties relevant to protein formulations from a single workflow on microliter-scale samples using label-free video optical microscopy. We show that the use of phase contrast imaging dramatically enhances measurement resolution for protein solutions at dilute and semidilute concentrations, enabling measurement of colloidal properties such as protein-protein interactions, protein size, aggregation, and solution viscosity from a single set of measurements. DDM measurements on a representative human immunoglobulin (IgG) system yield estimates for the hydrodynamic radius (R\_h), second osmotic virial coefficient (B\_2), and hydrodynamic interaction (k\_d) that are consistent with independently measured values, validating the ability of DDM to extract these parameters from a single set of measurements. Observed trends in B\_2 with pH and ionic strength are consistent with the antibody's charge and screened electrostatics, demonstrating the ability of DDM to provide insight on protein-protein interactions. To show the utility of DDM as a "multitool" for quantifying multiple formulation properties from a single measurement, we use the results to test a predictive colloidal model for the solution viscosity, which is in fair agreement with measurements obtained using DDM-based microrheology. Combined with low sample requirements and short measurement times, DDM thus offers a high-throughput and efficient route to accelerate protein biophysics and formulation development. ### Competing Interest Statement The authors have declared no competing interest. BASF California Research Alliance, UCB 052673/SA-10916 U.S. National Science Foundation, DMR 2308708, DMR 2445868

Surfactant self-assembly in soft matter formulations spans a complex, multivariate design space, motivating the development of efficient and predictive computational modeling approaches to aid formulation design. However, conventional molecular simulation techniques, including all-atom molecular dynamics and coarse-grained methods, are limited by either accessible time and length scales or predictive accuracy in studying surfactant self-assembly. To address these challenges, we employ a multiscale methodology that uses small-scale all-atom simulations to parameterize statistical field-theoretic models via bottom-up coarse-graining, eliminating the need for experimental input. The resulting molecularly informed field theory is then sampled using self-consistent field theory calculations to efficiently predict self-assembly and phase behavior. We demonstrate this approach by constructing binary phase diagrams for cationic alkyl quaternary-ammonium surfactants (C16TAB, C16TAC, and C10TAB) in water across a range of temperatures, compositions, and salt concentrations. The model successfully captures all experimentally observed surfactant mesophases and reproduces the majority of phase transition orderings de novo. In addition, we show this approach provides a unified framework for predicting equilibrium properties such as mesostructure domain sizes, micelle aggregation numbers, and critical micelle concentrations with qualitative agreement to experimentally observed trends. This multiscale methodology has the potential to be integrated into high-throughput screening workflows for efficient prediction of phase diagrams in novel surfactant formulations.

We report the single-step formation and stability of protocell-like, core-shell coacervate droplets comprising a polyelectrolyte-rich shell and a solvent-rich vacuole core from the poly(allylamine hydrochloride) (PAH) and poly(acrylic acid) (PAA) system. These double emulsion (DE) coacervate droplets coexist with single emulsion (SE) droplets, suggesting a kinetic mechanism of formation. We use high-throughput microscopy and machine learning to classify droplet morphologies across various final compositions (polyelectrolyte ratios and salt concentrations) and processing routes (mixing rate and thermodynamic path). We find that DE droplets form preferentially over SE droplets at a wide range of compositions using a slow injection mixing rate. DE droplet formation is enhanced at lower salt (NaCl) levels and near 1:1 charge stoichiometry, showing a preference for polycation excess. DE droplets are stable to the micron scale and retain their core-shell structure even after coalescence. Nevertheless, they are metastable; direct observations of various coarsening phenomena suggest that they are primarily stabilized by the viscoelasticity and high viscosity of the polymer-rich shell. Overall, the scalable, simple mixing process used herein offers a novel mechanism to produce multiphase coacervate droplets that is orthogonal to existing routes, which require either dropwise synthesis or thermodynamic tuning.

There has been significant interest in the engineering of polymer topology to control rheology and mechanical stability in dilute solutions for applications involving extreme shear rate flows. However, methods to experimentally probe properties at relevant shear rates (≈ 104-106 s-1) have remained ex situ, obscuring access to measures of polymer deformation and rheology that would otherwise provide mechanistic insight into the topology-dependent properties that control their behavior in extreme shear flows. In this study, we used novel in situ small angle neutron scattering measurements in a capillary rheometer (capillary rheo-SANS) to simultaneously measure solution viscosities and polymer deformations in high shear on a series of chemically homologous topology-defined polymers including linear, randomly branched, and star-shaped molecules. We demonstrate that differences in the onset of chain stretching and shear thinning of these polymers in dilute solution are controlled primarily by differences in their molecular relaxation time. These differences correlate with differences in chain scission inferred from ex situ measurements at more extreme shear rates. Together, the results demonstrate a direct coupling between chain deformation and scission, and suggest that the dominant effect of branching as a means to impart resilience against mechanical degradation is through differences in relaxation dynamics due to branching. We anticipate that these results will provide key insights to engineer topology-controlled polymers for rheological modification, mechanical stability, and controlled mechano-chemistry.

Differential isotope effects are an emerging tool for discovering possible nontrivial quantum mechanical effects within biological systems. However, it is often nearly impossible to elucidate the exact mechanisms by which a biological isotope effect manifests due to the complexity of these systems. As such, one proposed in vitro system of study for a quantum isotope effect is calcium phosphate aggregation, where symmetric calcium phosphate molecular species, known as Posner molecules, have been theorized to have phosphorus nuclear spin-dependent self-binding rates, which could be differently modulated by doping with stable lithium isotopes. Here, we present in vitro evidence for such a differential lithium isotope effect on the formation and aggregation of amorphous calcium phosphate from solution under certain conditions. Experiments confirm that lithium incorporates into amorphous calcium phosphate, with 7Li found to promote a greater abundance of observable calcium phosphate particles than 6Li under identical solution preparations. These in vitro results offer a potential explanation for in vivo biological studies that have shown differential lithium isotope effects. Given the importance of calcium phosphate in biological systems-ranging from mitochondrial signaling pathways to key biomineralization processes, as well as the proposed role of Posner molecules as a "neural qutrit"-these results present an important step in understanding calcium phosphate nucleation as well as the potential role of calcium phosphate for quantum biology and processing.

Chemical upcycling of polyethylene (PE) to long-chain alkylaromatics through tandem hydrocracking/aromatization has potential to provide value-added chemicals. However, the liquid product is a complex mixture of alkanes, alkylbenzenes, and polyaromatics, limiting its direct usability. The most valuable component of the product mixture is the alkylbenzenes because of their potential as precursors to anionic surfactants. In this study, a one-pot reactive separation is described. Sulfonating the product mixture from PE upcycling with silica sulfuric acid followed by neutralization with sodium hydroxide yields sodium alkylbenzenesulfonates (up to 93 mol % selectivity), along with a separate phase of lubricant-range hydrocarbons as a coproduct. Compared to petroleum-based sodium dodecylbenzenesulfonates, the reported PE-derived surfactant molecules show competitive physicochemical properties, including surface tension and interfacial tension. According to life cycle assessment, the described reaction strategy demonstrates 20% lower greenhouse gas emissions, when considering uses for the coproducts of PE upcycling, compared to conventional linear alkylbenzenesulfonates (LAS) manufacturing directly from petrochemical feedstocks.

Theories of interpreting polymer physics and rheology at the molecular level from experiments, including small-angle scattering, typically rely on the assumption that polymer chains possess a Gaussian configuration distribution. This assumption frequently fails to describe features of real polymer molecules both at equilibrium (when polymers have nonlinear topology or heterogeneous chemistry) and out of equilibrium (when they are subjected to nonlinear deformations). To better describe non-Gaussian polymer conformation distributions, we propose a moments analysis based on the Gram-Charlier expansion as a natural framework for describing structure and scattering from non-Gaussian polymers. The expansion describes the conformation distribution in terms of cumulants (equivalent to moments of the distribution) of the underlying segment density distribution function, providing low-dimensional descriptors that can be inferred directly from measured scattering in a way that is agnostic to a polymer's topology, chemistry, or state of deformation. We use this framework to show that cumulants can be used to "fingerprint" non-Gaussian conformation distributions of polymers either at equilibrium (applied to sequence-defined heteropolymers) or out of equilibrium (applied to polymers experiencing nonlinear deformation due to flow). We anticipate that this new analysis method will provide a general framework for examining nonideal polymer configurations and the properties that arise from them.

Fast and programmable transport of droplets on a substrate is desirable in microfluidic, thermal, biomedical, and energy devices. Photoresponsive surfactants are promising candidates to manipulate droplet motion due to their ability to modify interfacial tension and generate "photo-Marangoni" flow under light stimuli. Previous works have demonstrated photo-Marangoni droplet migration in liquid media; however, migration on other substrates, including solid and liquid-infused surfaces (LIS), remains an outstanding challenge. Moreover, models of photo-Marangoni migration are still needed to identify optimal photoswitches and assess the feasibility of new applications. In this work, we demonstrate 2D droplet motion on liquid surfaces and on LIS, as well as rectilinear motion in solid capillary tubes. We synthesize photoswitches based on spiropyran and merocyanine, capable of tension changes of up to 5.5 mN/m across time scales as short as 1.7 s. A millimeter-sized droplet migrates at up to 5.5 mm/s on a liquid, and 0.25 mm/s on LIS. We observe an optimal droplet size for fast migration, which we explain by developing a scaling model. The model also predicts that faster migration is enabled by surfactants that maximize the ratio between the tension change and the photoswitching time. To better understand migration on LIS, we visualize the droplet flow using tracer particles, and we develop corresponding numerical simulations, finding reasonable agreement. The methods and insights demonstrated in this study enable advances for manipulation of droplets for microfluidic, thermal and water harvesting devices.

Bioinspired hydroxypyridinone (HOPO)functionalized materials are shown to display a remarkable capacity for stability and for chelating a wide array of metal ions. This allows for the synthesis of multifunctional networks with diverse physical properties when compared to traditional catechol systems. In the present study, we report a facile, one-pot synthesis of an amino HOPO ligand and simple, scalable incorporation into PEG-acrylate based networks via active ester chemistry. This modular network approach allows for fabrication of patterned HOPO containing networks which can chelate a range of metal ions, such as transition metals (Fe3+) and lanthanides (Ho3+, Tb3+), leading to modulation of mechanical, magnetic, and fluorescent properties. Moreover, networks with tailored, heterogeneous properties can be prepared through localization of metal ion incorporation in 3-dimensions via masking techniques, creating distinctly soft, hard, magnetic, and fluorescent domains.

The measured force during a puncture test is found to increase when the needle tip is near to the vial walls. An experimental method for quantifying this increase in stiffness is developed.

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.

High-throughput microrheology and simple viscosity modeling can be used to continuously monitor the kinetic evolution of polymer molecular weight during controlled polymerizations.

Fast and programmable transport of liquid droplets on a solid substrate is desirable in microfluidic, thermal, biomedical, and energy devices. Past research has focused on designing substrates with asymmetric structures or gradient wettability where droplet behaviors are passively controlled, or by applying external electric, thermal, magnetic, or acoustic stimuli that either require the fabrication of electrodes or a strong applied field. In this work, we demonstrate tunable and programmable droplet motion on liquid-infused surfaces (LIS) and inside solid-surface capillary channels using low-intensity light and photo-responsive surfactants. When illuminated by the light of appropriate wavelengths, the surfactants can reversibly change their molecular conformation thereby tuning interfacial tensions in a multi-phase fluid system. This generates a Marangoni flow that drives droplet motions. With two novel surfactants that we synthesized, we demonstrate fast linear and complex 2D movements of droplets on liquid surfaces, on LIS, and inside microchannels. We also visualized the internal flow pattern using tracer particles and developed simple scaling arguments to explain droplet-size-dependent velocity. The method demonstrated in this study serves as a simple and exciting new approach for the dynamic manipulation of droplets for microfluidic, thermal, and water harvesting devices.

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.

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 β-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 β-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.

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 β-sheet forming domain is synthesized with varying side chains and block lengths. By changing the β-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 β-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.

Bioinspired iron-catechol cross-links have shown remarkable success in increasing the mechanical properties of polymer networks, in part due to clustering of Fe3+-catechol domains which act as secondary network reinforcing sites. We report a versatile synthetic procedure to prepare modular PEG-acrylate networks with independently tunable covalent bis(acrylate) and supramolecular Fe3+-catechol cross-linking. Initial control of network structure is achieved through radical polymerization and cross-linking, followed by postpolymerization incorporation of catechol units via quantitative active ester chemistry and subsequent complexation with iron salts. By tuning the ratio of each building block, dual cross-linked networks reinforced by clustered iron-catechol domains are prepared and exhibit a wide range of properties (Young's moduli up to ∼245 MPa), well beyond the values achieved through purely covalent cross-linking. This stepwise approach to mixed covalent and metal-ligand cross-linked networks also permits local patterning of PEG-based films through masking techniques forming distinct hard, soft, and gradient regions.

Shear banding in entangled polymer solutions is an elusive phenomenon in polymer rheology. One recently proposed mechanism for the existence of banded velocity profiles in entangled polymer solutions stems from a coupling of the flow to banded concentration profiles. Recent work [Burroughs et al., Phys. Rev. Lett. 126, 207801 (2021)] provided experimental evidence for the development of large gradients in concentration across the fluid. Here, a more systematic investigation is reported of the transient and steady-state banded velocity and concentration profiles of entangled polybutadiene in dioctyl phthalate solutions as a function of temperature (T), number of entanglements (Z), and applied shear rate (Wiapp), which control the susceptibility of the fluid to unstable flow-concentration coupling. The results are compared to a two-fluid model that accounts for coupling between elastic and osmotic polymer stresses, and a strong agreement is found between model predictions and measured concentration profiles. The interface locations and widths of the time-averaged, steady-state velocity profiles are quantified from high-order numerical derivatives of the data. At high levels of entanglement and large Wiapp, a significant wall slip is observed at both inner and outer surfaces of the flow geometry but is not a necessary criterion for a nonhomogeneous flow. Furthermore, the transient evolution of flow profiles for large Z indicate transitions from curved to “stair-stepped” and, ultimately, a banded steady state. These observed transitions provide detailed evidence for shear-induced demixing as a mechanism of shear banding in polymer solutions.