Dynamics of a self-interacting sheet in shear flow.

Solution processing of 2D materials such as graphene is important for applications thereof, yet a complete fundamental understanding of how 2D materials behave dynamically in solution is lacking. Here, we extend previous work by Silmore et al., Soft Matter, 2021, 17(18), 4707-4718 by adding short-ranged Lennard-Jones interactions to 2D sheets in shear flow. We find that the addition of these interactions allows for a rich landscape of conformations which depend on the balance between shear strength, bending rigidity, and interaction strength as well as the initial configuration of the sheet. We explore this conformational space and classify sheets as flat, tumbling, 1D folded, or 2D folded based on their conformational properties. We use kinetic and energetic arguments to explain why sheets adopt certain conformations within the folded regime. Finally, we calculate the stresslet and find that, even in the absence of thermal fluctuations and multiple sheet interactions, shear-thinning followed by shear-thickening behavior can appear.

Enumerating Stable Nanopores in Graphene and Their Geometrical Properties Using the Combinatorics of Hexagonal Lattices.

Nanopores in two-dimensional (2D) materials, including graphene, can be used for a variety of applications, such as gas separations, water desalination, and DNA sequencing. So far, however, all plausible isomeric shapes of graphene nanopores have not been enumerated. Instead, a probabilistic approach has been followed to predict nanopore shapes in 2D materials, due to the exponential increase in the number of nanopores as the size of the vacancy increases. For example, there are 12 possible isomers when N = 6 atoms are removed, a number that theoretically increases to 11.7 million when N = 20 atoms are removed from the graphene lattice. In this regard, the development of a smaller, exhaustive data set of stable nanopore shapes can help future experimental and theoretical studies focused on using nanoporous 2D materials in various applications. In this work, we use the theory of 2D triangular "lattice animals" to create a library of all stable graphene nanopore shapes based on a modification of a well-known algorithm in the mathematical combinatorics of polyforms known as Redelmeier's algorithm. We show that there exists a correspondence between graphene nanopores and triangular polyforms (called polyiamonds) as well as hexagonal polyforms (called polyhexes). We develop the concept of a polyiamond ID to identify unique nanopore isomers. We also use concepts from polyiamond and polyhex geometries to eliminate unstable nanopores containing dangling atoms, bonds, and moieties. We verify using density functional theory calculations that such pores are indeed unstable. The exclusion of these unstable nanopores leads to a remarkable reduction in the possible nanopores from 11.7 million for N = 20 to only 0.184 million nanopores, thereby indicating that the number of stable nanopores is almost 2 orders of magnitude lower and is much more tractable. Not only that, by extracting the polyhex outline, our algorithm allows searching for nanopores with dimensions and shape factors in a specified range, thus aiding the design of the geometrical properties of nanopores for specific applications. We also provide the coordinate files of the stable nanopores as a library to facilitate future theoretical studies of these nanopores.

Discretized hexagonal boron nitride quantum emitters and their chemical interconversion.

Quantum emitters in two-dimensional hexagonal boron nitride (hBN) are of significant interest because of their unique photophysical properties, such as single-photon emission at room temperature, and promising applications in quantum computing and communications. The photoemission from hBN defects covers a wide range of emission energies but identifying and modulating the properties of specific emitters remain challenging due to uncontrolled formation of hBN defects. In this study, more than 2000 spectra are collected consisting of single, isolated zero-phonon lines (ZPLs) between 1.59 and 2.25 eV from diverse sample types. Most of ZPLs are organized into seven discretized emission energies. All emitters exhibit a range of lifetimes from 1 to 6 ns, and phonon sidebands offset by the dominant lattice phonon in hBN near 1370 cm-1. Two chemical processing schemes are developed based on water and boric acid etching that generate or preferentially interconvert specific emitters, respectively. The identification and chemical interconversion of these discretized emitters should significantly advance the understanding of solid-state chemistry and photophysics of hBN quantum emission.

Thermally fluctuating, semiflexible sheets in simple shear flow.

We perform Brownian dynamics simulations of semiflexible colloidal sheets with hydrodynamic interactions and thermal fluctuations in shear flow. As a function of the ratio of bending rigidity to shear energy (a dimensionless quantity we denote S) and the ratio of bending rigidity to thermal energy, we observe a dynamical transition from stochastic flipping to crumpling and continuous tumbling. This dynamical transition is broadened by thermal fluctuations, and the value of S at which it occurs is consistent with the onset of chaotic dynamics found for athermal sheets. The effects of different dynamical conformations on rheological properties such as viscosity and normal stress differences are also quantified. Namely, the viscosity in a dilute dispersion of sheets is found to decrease with increasing shear rate (shear-thinning) up until the dynamical crumpling transition, at which point it increases again (shear-thickening), and non-zero first normal stress differences are found that exhibit a local maximum with respect to temperature at large S (small shear rate). These results shed light on the dynamical behavior of fluctuating 2D materials dispersed in fluids and should greatly inform the design of associated solution processing methods.

A theory of mechanical stress-induced H2O2 signaling waveforms in Planta.

Recent progress in nanotechnology-enabled sensors that can be placed inside of living plants has shown that it is possible to relay and record real-time chemical signaling stimulated by various abiotic and biotic stresses. The mathematical form of the resulting local reactive oxygen species (ROS) wave released upon mechanical perturbation of plant leaves appears to be conserved across a large number of species, and produces a distinct waveform from other stresses including light, heat and pathogen-associated molecular pattern (PAMP)-induced stresses. Herein, we develop a quantitative theory of the local ROS signaling waveform resulting from mechanical stress in planta. We show that nonlinear, autocatalytic production and Fickian diffusion of H2O2 followed by first order decay well describes the spatial and temporal properties of the waveform. The reaction-diffusion system is analyzed in terms of a new approximate solution that we introduce for such problems based on a single term logistic function ansatz. The theory is able to describe experimental ROS waveforms and degradation dynamics such that species-dependent dimensionless wave velocities are revealed, corresponding to subtle changes in higher moments of the waveform through an apparently conserved signaling mechanism overall. This theory has utility in potentially decoding other stress signaling waveforms for light, heat and PAMP-induced stresses that are similarly under investigation. The approximate solution may also find use in applied agricultural sensing, facilitating the connection between measured waveform and plant physiology.

Buckling, crumpling, and tumbling of semiflexible sheets in simple shear flow.

As 2D materials such as graphene, transition metal dichalcogenides, and 2D polymers become more prevalent, solution processing and colloidal-state properties are being exploited to create advanced and functional materials. However, our understanding of the fundamental behavior of 2D sheets and membranes in fluid flow is still lacking. In this work, we perform numerical simulations of athermal semiflexible sheets with hydrodynamic interactions in shear flow. For sheets initially oriented near the flow-vorticity plane, we find buckling instabilities of different mode numbers that vary with bending stiffness and can be understood with a quasi-static model of elasticity. For different initial orientations, chaotic tumbling trajectories are observed. Notably, we find that sheets fold or crumple before tumbling but do not stretch again upon applying greater shear.

Dynamics of a single polyampholyte chain.

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples-random charge densities and periodic charge densities-with different scaling properties. Under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

Addressing the isomer cataloguing problem for nanopores in two-dimensional materials.

The presence of extended defects or nanopores in two-dimensional (2D) materials can change the electronic, magnetic and barrier membrane properties of the materials. However, the large number of possible lattice isomers of nanopores makes their quantitative study a seemingly intractable problem, confounding the interpretation of experimental and simulated data. Here we formulate a solution to this isomer cataloguing problem (ICP), combining electronic-structure calculations, kinetic Monte Carlo simulations, and chemical graph theory, to generate a catalogue of unique, most-probable isomers of 2D lattice nanopores. The results demonstrate remarkable agreement with precise nanopore shapes observed experimentally in graphene and show that the thermodynamic stability of a nanopore is distinct from its kinetic stability. Triangular nanopores prevalent in hexagonal boron nitride are also predicted, extending this approach to other 2D lattices. The proposed method should accelerate the application of nanoporous 2D materials by establishing specific links between experiment and theory/simulations, and by providing a much-needed connection between molecular design and fabrication.

Collective mode Brownian dynamics: A method for fast relaxation of statistical ensembles.

Sampling equilibrium configurations of correlated systems of particles with long relaxation times (e.g., polymeric solutions) using conventional molecular dynamics and Monte Carlo methods can be challenging. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics simulations that can reduce the computational time it takes to reach equilibrium and draw decorrelated samples. Importantly, the method is completely agnostic to the particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in O(N) time. Particle motion in this scheme is computed by integrating the overdamped Langevin equation with an Euler-Maruyama scheme, in which Brownian displacements are drawn efficiently using a low-rank representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter and release a massively parallel implementation of the code as a plugin for the open-source package HOOMD-blue [J. A. Anderson et al., J. Comput. Phys. 227, 5342 (2008) and J. Glaser et al., Comput. Phys. Commun. 192, 97 (2015)] which runs on graphics processing units.

Measuring the Accessible Surface Area within the Nanoparticle Corona Using Molecular Probe Adsorption.

The corona phase-the adsorbed layer of polymer, surfactant, or stabilizer molecules around a nanoparticle-is typically utilized to disperse nanoparticles into a solution or solid phase. However, this phase also controls molecular access to the nanoparticle surface, a property important for catalytic activity and sensor applications. Unfortunately, few methods can directly probe the structure of this corona phase, which is subcategorized as either a hard, immobile corona or a soft, transient corona in exchange with components in the bulk solution. In this work, we introduce a molecular probe adsorption (MPA) method for measuring the accessible nanoparticle surface area using a titration of a quenchable fluorescent molecule. For example, riboflavin is utilized to measure the surface area of gold nanoparticle standards, as well as corona phases on dispersed single-walled carbon nanotubes and graphene sheets. A material balance on the titration yields certain surface coverage parameters, including the ratio of the surface area to dissociation constant of the fluorophore, q/KD, as well as KD itself. Uncertainty, precision, and the correlation of these parameters across different experimental systems, preparations, and modalities are all discussed. Using MPA across a series of corona phases, we find that the Gibbs free energy of probe binding scales inversely with the cube root of surface area, q. In this way, MPA is the only technique to date capable of discerning critical structure-property relationships for such nanoparticle surface phases. Hence, MPA is a rapid quantitative technique that should prove useful for elucidating corona structure for nanoparticles across different systems.

Single-Particle Tracking for Understanding Polydisperse Nanoparticle Dispersions.

Colloidal dispersions of nanomaterials are often polydisperse in size, significantly complicating their characterization. This is particularly true for materials early in their historical development due to synthetic control, dispersion efficiency, and instability during storage. Because a wide range of system properties and technological applications depend on particle dimensions, it remains an important problem in nanotechnology to identify a method for the routine characterization of polydispersity in nanoparticle samples, especially changes over time. Commonly employed methods such as dynamic light scattering or analytical ultracentrifugation (AUC) accurately estimate only the first moment of the distribution or are not routine. In this work, the use of single-particle tracking (SPT) to probe size distributions of common nanoparticle dispersions, including polystyrene nanoparticles, single-walled carbon nanotubes, graphene oxide, chitosan-tripolyphosphate, acrylate, hexagonal boron nitride, and poly(lactic-co-glycolic acid), is proposed and explored. The analysis of particle tracks is conducted using a newly developed Bayesian algorithm that is called Maximum A posteriori Nanoparticle Tracking Analysis. By combining SPT and AUC techniques, it is shown that it is possible to independently estimate the mean aspect ratio of anisotropic particles, an important characterization property. It is concluded that SPT provides a facile, rapid analytical method for routine nanomaterials characterization.

Short and Soft: Multidomain Organization, Tunable Dynamics, and Jamming in Suspensions of Grafted Colloidal Cylinders with a Small Aspect Ratio.

The yet virtually unexplored class of soft colloidal rods with a small aspect ratio is investigated and shown to exhibit a very rich phase and dynamic behavior, spanning from liquid to nearly melt state. Instead of the nematic order, these short and soft nanocylinders alter their organization with increasing concentration from isotropic liquid with random orientation to small domains with preferred local orientation and eventually a multidomain arrangement with a local orientational order. The latter gives rise to a kinetically suppressed state akin to structural glass with detectable terminal relaxation, which, on further increasing concentration, reveals features of hexagonally packed order as in ordered block copolymers. The respective dynamic response comprises four regimes, all above the overlapping concentration of 0.02 g/mL:(I) from 0.03 to 0.1 g/mol, the system undergoes a liquid-to-solidlike transition with a structural relaxation time that grows by 4 orders of magnitude. (II) From 0.1 to 0.2 g/mL, a dramatic slowing-down is observed and is accompanied by an evolution from isotropic to a multidomain structure. (III) Between 0.2 and 0.6 g/mol, the suspensions exhibit signatures of shell interpenetration and jamming, with the colloidal plateau modulus depending linearly on concentration. (IV) At 0.74 g/mL, in the densely jammed state, the viscoelastic signature of hexagonally packed cylinders from microphase-separated block copolymers is detected. These properties set short and soft nanocylinders apart from long colloidal rods (with a large aspect ratio) and provide insights for fundamentally understanding the physics in this intermediate soft colloidal regime and for tailoring the flow properties of nonspherical soft colloids.

Capacitance of thin films containing polymerized ionic liquids.

Electrode-polymer interfaces dictate many of the properties of thin films such as capacitance, the electric field experienced by polymers, and charge transport. However, structure and dynamics of charged polymers near electrodes remain poorly understood, especially in the high concentration limit representative of the melts. To develop an understanding of electric field-induced transformations of electrode-polymer interfaces, we have studied electrified interfaces of an imidazolium-based polymerized ionic liquid (PolyIL) using combinations of broadband dielectric spectroscopy, specular neutron reflectivity, and simulations based on the Rayleigh's dissipation function formalism. Overall, we obtained the camel-shaped dependence of the capacitance on applied voltage, which originated from the responses of an adsorbed polymer layer to applied voltages. This work provides additional insights related to the effects of molecular weight in affecting structure and properties of electrode-polymer interfaces, which are essential for designing next-generation energy storage and harvesting devices.

Implantable Nanosensors for Human Steroid Hormone Sensing In Vivo Using a Self-Templating Corona Phase Molecular Recognition.

Dynamic measurements of steroid hormones in vivo are critical, but steroid sensing is currently limited by the availability of specific molecular recognition elements due to the chemical similarity of these hormones. In this work, a new, self-templating synthetic approach is applied using corona phase molecular recognition (CoPhMoRe) targeting the steroid family of molecules to produce near infrared fluorescent, implantable sensors. A key limitation of CoPhMoRe has been its reliance on library generation for sensor screening. This problem is addressed with a self-templating strategy of polymer design, using the examples of progesterone and cortisol sensing based on a styrene and acrylic acid copolymer library augmented with an acrylated steroid. The pendant steroid attached to the corona backbone is shown to self-template the phase, providing a unique CoPhMoRE design strategy with high efficacy. The resulting sensors exhibit excellent stability and reversibility upon repeated analyte cycling. It is shown that molecular recognition using such constructs is viable even in vivo after sensor implantation into a murine model by employing a poly (ethylene glycol) diacrylate (PEGDA) hydrogel and porous cellulose interface to limit nonspecific absorption. The results demonstrate that CoPhMoRe templating is sufficiently robust to enable a new class of continuous, in vivo biosensors.

Real-time detection of wound-induced H2O2 signalling waves in plants with optical nanosensors.

Decoding wound signalling in plants is critical for understanding various aspects of plant sciences, from pest resistance to secondary metabolite and phytohormone biosynthesis. The plant defence responses are known to primarily involve NADPH-oxidase-mediated H2O2 and Ca2+ signalling pathways, which propagate across long distances through the plant vasculature and tissues. Using non-destructive optical nanosensors, we find that the H2O2 concentration profile post-wounding follows a logistic waveform for six plant species: lettuce (Lactuca sativa), arugula (Eruca sativa), spinach (Spinacia oleracea), strawberry blite (Blitum capitatum), sorrel (Rumex acetosa) and Arabidopsis thaliana, ranked in order of wave speed from 0.44 to 3.10 cm min-1. The H2O2 wave tracks the concomitant surface potential wave measured electrochemically. We show that the plant RbohD glutamate-receptor-like channels (GLR3.3 and GLR3.6) are all critical to the propagation of the wound-induced H2O2 wave. Our findings highlight the utility of a new type of nanosensor probe that is species-independent and capable of real-time, spatial and temporal biochemical measurements in plants.

High-Resolution Nanoparticle Sizing with Maximum A Posteriori Nanoparticle Tracking Analysis.

The rapid and efficient characterization of polydisperse nanoparticle dispersions remains a challenge within nanotechnology and biopharmaceuticals. Current methods for particle sizing, such as dynamic light scattering, analytical ultracentrifugation, and field-flow fractionation, can suffer from a combination of statistical biases, difficult sample preparation, insufficient sampling, and ill-posed data analysis. As an alternative, we introduce a Bayesian method that we call maximum a posteriori nanoparticle tracking analysis (MApNTA) for estimating the size distributions of nanoparticle samples from high-throughput single-particle tracking experiments. We derive unbiased statistical models for two observable quantities in a typical nanoparticle trajectory-the mean square displacement and the trajectory length-as a function of the particle size and calculate size distributions using maximum a posteriori (MAP) estimation with cross validation to mildly regularize solutions. We show that this approach infers nanoparticle size distributions with high resolution by performing extensive Brownian dynamics simulations and experiments with mono- and polydisperse solutions of gold nanoparticles as well as single-walled carbon nanotubes. We further demonstrate particular utility for characterizing minority components and impurity populations and highlight this ability with the identification of an impurity in a commercially produced gold nanoparticle sample. Modern algorithms such as MApNTA should find widespread use in the routine characterization of complex nanoparticle dispersions, allowing for significant advances in nanoparticle synthesis, separation, and functionalization.

Tunable Pickering emulsions with polymer-grafted lignin nanoparticles (PGLNs).

Lignin is an abundant biopolymer that has native interfacial functions but aggregates strongly in aqueous media. Polyacrylamide was grafted onto kraft lignin nanoparticles using reversible addition-fragmentation chain transfer (RAFT) chemistry to form polymer-grafted lignin nanoparticles (PGLNs) that tune aggregation strength while retaining interfacial activities in forming Pickering emulsions. Polymer graft density on the particle surface, ionic strength, and initial water and cyclohexane volume fractions were varied and found to have profound effects on emulsion characteristics, including emulsion volume fraction, droplet size, and particle interfacial concentration that were attributed to changes in lignin aggregation and hydrophobic interactions. In particular, salt concentration was found to have a significant effect on aggregation, zeta potential, and interfacial tension, which was attributed to changes in solubility of both the kraft lignin and the polyacrylamide grafts. Dynamic light scattering, UV-vis spectroscopy, optical microscopy, and tensiometry were used to quantify emulsion properties and nanoparticle behavior. Under all conditions, the emulsions exhibited relatively fast creaming but were stable against coalescence and Ostwald ripening for a period of months. All emulsions were also oil-in-water (o/w) emulsions, as predicted by the Bancroft rule, and no catastrophic phase inversions were observed for any nanoparticle compositions. We conclude that lower grafting density of polyacrylamide on a lignin core resulted in high levels of interfacial activity, as characterized by higher concentration at the water-cyclohexane interface with a corresponding decrease in interfacial tension. These results indicate that the interfacial properties of polymer-grafted lignin nanoparticles are primarily due to the native hydrophobic interactions of the lignin core. These results suggest that the forces that drive aggregation are also correlated with interfacial activities, and polymer-nanoparticle interactions are critical for optimizing interfacial activities. Controlled radical polymerization is a powerful tool for polymer grafting that can leverage the intrinsic interfacial functions of lignin for the formation of Pickering emulsions.