Dynamic crosslinking compatibilizes immiscible mixed plastics.

The global plastics problem is a trifecta, greatly affecting environment, energy and climate1-4. Many innovative closed/open-loop plastics recycling or upcycling strategies have been proposed or developed5-16, addressing various aspects of the issues underpinning the achievement of a circular economy17-19. In this context, reusing mixed-plastics waste presents a particular challenge with no current effective closed-loop solution20. This is because such mixed plastics, especially polar/apolar polymer mixtures, are typically incompatible and phase separate, leading to materials with substantially inferior properties. To address this key barrier, here we introduce a new compatibilization strategy that installs dynamic crosslinkers into several classes of binary, ternary and postconsumer immiscible polymer mixtures in situ. Our combined experimental and modelling studies show that specifically designed classes of dynamic crosslinker can reactivate mixed-plastics chains, represented here by apolar polyolefins and polar polyesters, by compatibilizing them via dynamic formation of graft multiblock copolymers. The resulting in-situ-generated dynamic thermosets exhibit intrinsic reprocessability and enhanced tensile strength and creep resistance relative to virgin plastics. This approach avoids the need for de/reconstruction and thus potentially provides an alternative, facile route towards the recovery of the endowed energy and materials value of individual plastics.

Controlling the Self-Assembly of DNA Origami Octahedra via Manipulation of Inter-Vertex Interactions.

Recent studies have demonstrated novel strategies for the organization of nanomaterials into three-dimensional (3D) ordered arrays with prescribed lattice symmetries using DNA-based self-assembly strategies. In one approach, the nanomaterial is sequestered into DNA origami frames or "material voxels" and then coordinated into ordered arrays based on the voxel geometry and the corresponding directional interactions based on its valency. While the lattice symmetry is defined by the valency of the bonds, a larger-scale morphological development is affected by assembly processes and differences in energies of anisotropic bonds. To facilely model this assembly process, we investigate the self-assembly behavior of hard particles with six interacting vertices via theory and Monte Carlo simulations and exploration of corresponding experimental systems. We demonstrate that assemblies with different 3D crystalline morphologies but the same lattice symmetry can be formed depending on the relative strength of vertex-to-vertex interactions in orthogonal directions. We observed three distinct assembly morphologies for such systems: cube-like, sheet-like, and cylinder-like. A simple analytical theory inspired by well-established ideas in the areas of protein crystallization, based on calculating the second virial coefficient of patchy hard spheres, captures the simulation results and thus represents a straightforward means of modeling this self-assembly process. To complement the theory and simulations, experimental studies were performed to investigate the assembly of octahedral DNA origami frames with varying binding energies at their vertices. X-ray scattering confirms the robustness of the formed nanoscale lattices for different binding energies, while both optical and electron microscopy imaging validated the theoretical predictions on the dependence of the distinct morphologies of assembled state on the interaction strengths in the three orthogonal directions.

Directional polymer crystallisation with a fast-moving sink.

It has previously been shown that non-isothermal directional polymer crystallisation driven by local melting (Zone Annealing), has a close analogy with an equivalent isothermal crystallisation protocol. This surprising analogy is due to the low thermal conductivity of polymers-because they are poor thermal conductors, crystallisation occurs over a relatively narrow spatial domain while the thermal gradient spans a much wider scale. This separation of scales, which occurs in the limit of small sink velocity, allows replacing the crystallinity profile with a step and the temperature at the step acts as an effective isothermal crystallisation temperature. In this paper, we study directional polymer crystallisation under faster moving sinks using both numerical simulations and analytical theory. While, only partial crystallisation occurs, regardless, a steady state exists. At large velocity, the sink quickly moves ahead of a region that is still crystallizing; since polymers are poor thermal conductors, the latent heat dissipation to the sink becomes inefficient, eventually resulting in the temperature increasing back to the melting point thereby resulting in incomplete crystallization. This transition occurs when the two length scales measuring the sink-interface distance and the width of the crystallizing interface become comparable. For steady state and in the limit of large sink velocity, regular perturbation solutions of the differential equations governing heat transport and crystallization in the region between the heat sink and the solid-melt interface are in good agreement with numerical results.

Unusual High-Frequency Mechanical Properties of Polymer-Grafted Nanoparticle Melts.

Brillouin light spectroscopy is used to measure the elastic moduli of spherical polymer-grafted nanoparticle (GNP) melts as a function of chain length at fixed grafting density (0.47 chains/nm^{2}) and nanoparticle radius (8 nm). While the moduli follow a rule of mixtures (Wood's law) for long chains, they display enhanced elasticity and anomalous dissipation for graft chains <100 kDa. GNP melts with long polymers at high σ have a dry zone near the GNP core, surrounded by a region where the grafts can interpenetrate with chain fragments from adjacent GNPs. We propose that the departures from Wood's law for short chains are due to the effectively larger silica volume fraction in the region where sound propagates-this is caused by the short, interpenetrated chain fragments being pushed out of the way. We thus conclude that transport mechanisms (of gas, ions, sound, thermal phonons) in GNP melts are radically different if interpenetrated chain segments can be "pushed out of the way" or not. This provides a facile new means for manipulating the properties of these materials.

Controlling toughness of polymer-grafted nanoparticle composites for impact mitigation.

Toughness in an entangled polymer network is typically controlled by the number of load-bearing topological constraints per unit volume. In this work, we demonstrate a new paradigm for controlling toughness at high deformation rates in a polymer-grafted nanoparticle composite system where the entanglement density increases with the molecular mass of the graft. An unexpected peak in the toughness is observed right before the system reaches full entanglement that cannot be described through the entanglement concept alone. Quasi-elastic neutron scattering reveals enhanced segmental fluctuations of the grafts on the picosecond time scale, which propagate out to nanoparticle fluctuations on the time scale 100s of seconds as evidenced by X-ray photon correlation spectroscopy. This surprising multi-scale dissipation process suggests a nanoparticle jamming-unjamming transition. The realization that segmental dynamics can be coupled with the entanglement concept for enhanced toughness at high rates of deformation is a novel insight with relevance to the design of composite materials.

Ordered three-dimensional nanomaterials using DNA-prescribed and valence-controlled material voxels.

The ability to organize nanoscale objects into well-defined three-dimensional (3D) arrays can translate advances in nanoscale synthesis into targeted material fabrication. Despite successes in nanoparticle assembly, most extant methods are system specific and not fully compatible with biomolecules. Here, we report a platform for creating distinct 3D ordered arrays from different nanomaterials using DNA-prescribed and valence-controlled material voxels. These material voxels consist of 3D DNA frames that integrate nano-objects within their scaffold, thus enabling the object's valence and coordination to be determined by the frame's vertices, which can bind to each other through hybridization. Such DNA material voxels define the lattice symmetry through the spatially prescribed valence decoupling the 3D assembly process from the nature of the nanocomponents, such as their intrinsic properties and shapes. We show this by assembling metallic and semiconductor nanoparticles and also protein superlattices. We support the technological potential of such an assembly approach by fabricating light-emitting 3D arrays with diffraction-limited spectral purity and 3D enzymatic arrays with increased activity.

Colloidal assembly by directional ice templating.

We investigate directional ice templating of dilute aqueous colloidal particle dispersions and examine the nature of the assemblies that result. We coat micron-size polystyrene colloids with cross-linkable polymer (polyethyleneimine, PEI), add cross-linker, and subject this dispersion to unidirectional freezing. We work at sufficiently low colloid concentrations, such that the particles do not percolate on freezing. When the aqueous dispersion freezes, ice crystals force polymer-coated particles and cross-linker into close proximity. This results in the formation of cross-linked clusters of particles at ice crystal boundaries. We vary the particle volume fraction from φ ∼ 2.5 × 10-3 to φ ∼ 5.0 × 10-2 and observe that there is a transition from isolated single particles to increasingly large sized clusters. Most of the clusters formed under these conditions are either linear, two-particle wide chains, or sheet-like aggregates. The probability (Pn) of clusters containing n particles (n > 2) obeys a power law Pn ∼ n-η, where η strongly depends on the particle concentration in the dispersion, varying from 2.10 (for φ ∼ 5.0 × 10-2) to 3.03 (for φ ∼ 2.5 × 10-3). This change in η is qualitatively different from the case of isotropic freezing, where η is particle concentration-independent and depends only on the ice nucleation density. To understand the differences between isotropic and directional ice templating, we performed lattice simulations of a highly simplified model, where ice crystals grow at a constant rate to force clustering. We ignore hydrodynamic interactions and ice growth instabilities. Despite ignoring these experimental details, the simulations capture the experimental results, nearly quantitatively. As the ice crystals grow and the space available to the colloids "closes up" so that the particles cluster to form aggregates, crystallization protocol-induced differences in the geometry of these "closed up" spaces determine the scaling behaviour of Pn.

Modeling polymer crystallisation induced by a moving heat sink.

Recent experimental work has shown that polymer crystallisation can be used to "move" and organize nanoparticles (NP). As a first effort at modeling this situation, we consider the classical Stefan problem but with the modification that polymer crystallisation does not occur at a single temperature. Rather, the rate of crystallisation is proportional to its subcooling, and here we employ a form inspired by the classical Avrami model to describe this functional form. Our results for the movement of the polymer crystallisation front, as defined as the point where the crystallinity is 50%, closely track the results of the classical Stefan problem. Thus, at this level of approximation, the crystallisation kinetics of the polymer do not cause qualitative changes to the physics of this situation. Inspired by this fact we study the more interesting situation where the directional recrystallisation of a polymer melt is considered, e.g., through the application of a moving heat sink over an initially molten polymer, reminiscent of a processing technique termed zone annealing. The polymer crystallisation shows that a steady state exists for a range of sink velocities. The solid-melt interface moves slightly ahead of the sink but at the same velocity. The steady-state distance between the sink and the interface decreases with increasing sink velocity - this is a consequence of the excess cooling provided by the sink over what is required to crystallise the melt. The most interesting new result is that the temperature of the crystal-melt interface decreases with increasing sink velocity. This is in line with the ansatz of Lovinger and Gryte who suggested that larger zone annealing velocities correspond to progressively larger effective undercoolings at which polymer crystallisation occurs.

Boundary layer description of directional polymer crystallisation.

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger-Gryte ansatz.

Engineering Organization of DNA Nano-Chambers through Dimensionally Controlled and Multi-Sequence Encoded Differentiated Bonds.

Engineering the assembly of nanoscale objects into complex and prescribed structures requires control over their binding properties. Such control might benefit from a well-defined bond directionality, the ability to designate their engagements through specific encodings, and the capability to coordinate local orientations. Although much progress has been achieved in our ability to design complex nano-objects, the challenges in creating such nano-objects with fully controlled binding modes and understanding their fundamental properties are still outstanding. Here, we report a facile strategy for creating a DNA nanochamber (DNC), a hollow cuboid nano-object, whose bonds can be fully prescribed and complexly encoded along its three orthogonal axes, giving rise to addressable and differentiated bonds. The DNC can host nanoscale cargoes, which allows for the integration with functional nano-objects and their organization in larger-scale systems. We explore the relationship between the design of differentiated bonds and a formation of one-(1D), two-(2D), and three-(3D) dimensional organized arrays. Through the realization of different binding modes, we demonstrate sequence encoded nanoscale heteropolymers, helical polymers, 2D lattices, and mesoscale 3D nanostructures with internal order, and show that this assembly strategy can be applied for the organization of nanoparticles. We combine experimental investigations with computational simulation to understand the mechanism of structural formation for different types of ordered arrays, and to correlate the bonds design with assembly processes.

Accelerated Local Dynamics in Matrix-Free Polymer Grafted Nanoparticles.

The tracer diffusion coefficient of six different permanent gases in polymer-grafted nanoparticle (GNP) membranes, i.e., neat GNP constructs with no solvent, show a maximum as a function of the grafted chain length at fixed grafting density. This trend is reproduced for two different NP sizes and three different polymer chemistries. We postulate that nonmonotonic changes in local, segmental friction as a function of graft chain length (at fixed grafting density) must underpin these effects, and use quasielastic neutron scattering to probe the self-motions of polymer chains at the relevant segmental scale (i.e., sampling local friction or viscosity). These data, when interpreted with a jump diffusion model, show that, in addition to the speeding-up in local chain dynamics, the elementary distance over which segments hop is strongly dependent on graft chain length. We therefore conclude that transport modifications in these GNP layers, which are underpinned by a structural transition from a concentrated brush to semidilute polymer brush, are a consequence of both spatial and temporal changes, both of which are likely driven by the lower polymer densities of the GNPs relative to the neat polymer.

Modeling gas transport in polymer-grafted nanoparticle membranes.

We use coarse-grained molecular dynamics simulations to study gas diffusion within nanocomposites consisting of matrix-free polymer-grafted nanoparticles. We compare the transport of gas penetrants in systems using polymer models with and without an angle potential and show that gas diffusion enhancement occurs in nanocomposite systems only with the angle potential. This enhancement is related to the free volume in the system, but the cage size experienced by the gas penetrant seems to be a more relevant indicator of gas diffusion enhancement. The enhancement seen in our simulations is smaller than that observed in experiments.

Diminishing Interfacial Effects with Decreasing Nanoparticle Size in Polymer-Nanoparticle Composites.

Using molecular simulations on model polymer nanocomposites at fixed filler loading, we show that interfacial polymer dynamics are affected less with decreasing nanoparticle (NP) size. However, the glass transition temperature T_{g} changes substantially more for an extremely small NP. The reason for this apparent contradiction is that the mean NP spacing decreases with decreasing particle size. Thus, all polymers are effectively interfacial for sufficiently small NPs, resulting in relatively large T_{g} shifts, even though the interfacial effects are smaller. For larger NPs, interfacial relaxations are substantially slower than the matrix for favorable NP-polymer interactions. The minority "bound" polymer dynamically decouples from the polymer matrix, and we only find small changes in T_{g} relative to that of the bulk polymer for large NPs. These results are used to organize a large body of relevant experimental data, and we propose an apparent universal dependence on the ratio of the face-to-face distance between the NPs and the chain radius of gyration.

Defining the optimal criterion for separating gases using polymeric membranes.

Polymeric membranes are efficient in separating gas mixtures, typically by exploiting the sieving mechanism. What controls the sieve size of a given polymer matrix is unclear, although one line of thought implies that the local cage size, defined by the dynamic motions of the glassy polymer matrix, is the relevant metric. Here, we use coarse-grained molecular dynamics simulations and show that the sieve size is defined by a static cavity size controlled by polymer chain stiffness (a packing-driven metric) combined with the local cage-like motions of the polymer host. The best separation performance for a pair of gases is when this combined metric is roughly half way between the diameters of the gases in question, with the static and dynamic quantities contributing roughly equally. For the various models simulated we find the existence of an upper bound correlation which passes through this optimal point and has a slope expected from the Freeman model, namely , where the d's correspond to the kinetic diameters of the gases in question. Our results thus demonstrate that the relevant free volume size that affects gas transport in these condensed phases is defined by both static and dynamic measures.

Accurate estimation of the polymer coverage of hairy nanoparticles.

Understanding and predicting the mechanisms underpinning the self-assembly of polymer-grafted nanoparticles (PGNPs) are important for controlling the engineering applications of these novel materials. The self-assembly of these materials is driven by their surfactancy, i.e., by the fact that the (inorganic) nanoparticles energetically dislike the (organic) polymer tethers. In previous work we developed a model in which a grafted polymer chain was treated as a rigid equivalent sphere (ES) which was impenetrable to the NPs, but completely penetrable to other ESs. This description, along with a geometric analogy with patchy particles, allowed us to facilely explain the self-assembly of PGNPs. However, since we model an ES as being completely penetrable to other ESs but impenetrable to the NPs the physical correspondence between a "real" grafted polymer and an ES is not clear. The application of the ES model to experiments and to computer simulations has therefore seen limited success, and only qualitative agreement has been obtained. In this paper, we develop a more realistic description, termed the modified ES (mES) model, based on the work of Daoud and Cotton on curved polymer brushes, which takes the impenetrability of the individual chain monomers into account. While this approach increases the complexity of our formalism, we find that the resulting mES model quantitatively captures computer simulation results on the structure of the PGNPs and also quantitatively explains their self-assembly over a broad range of conditions.

Size-dependent penetrant diffusion in polymer glasses.

Molecular Dynamics simulations are used to understand the underpinning basis of the transport of gas-like solutes in deeply quenched polymeric glasses. As found in previous work, small solutes, with sizes smaller than 0.15 times the chain monomer size, move as might be expected in a medium with large pores. In contrast, the motion of larger solutes is activated and is strongly facilitated by matrix motion. In particular, solute motion is coupled to the local elastic fluctuations of the matrix as characterized by the Debye-Waller factor. While similar ideas have been previously proposed for the viscosity of supercooled liquids above their glass transition, to our knowledge, this is the first illustration of this concept in the context of solute mass transport in deeply quenched polymer glasses.

Coarse-grained molecular dynamics simulation of activated penetrant transport in glassy polymers.

Membrane separations of gas mixtures strive to maximize the permeability of a desired species while keeping out undesired ones. Permeability vs. selectivity data from many polymer membranes for a given gas pair with diameters dA and dB are typically collected in a "Robeson plot"', and are bound from above by a line with a slope λ = (dB/dA)2 - 1. A microscopic understanding of this relationship, especially λ, is still missing. We perform molecular dynamics simulations of penetrant diffusion using three different coarse-grained polymer models over a wide range of penetrant sizes, temperatures, and monomer densities. The empirically relevant λ = (dB/dA)2 - 1 is only found for polymers that are either supercooled liquids with caged segmental dynamics or glasses and when the penetrant size is approximately half the Kuhn length of the chains, for which the penetrant diffusion is an activated process.

Stoichiometric control of DNA-grafted colloid self-assembly.

There has been considerable interest in understanding the self-assembly of DNA-grafted nanoparticles into different crystal structures, e.g., CsCl, AlB2, and Cr3Si. Although there are important exceptions, a generally accepted view is that the right stoichiometry of the two building block colloids needs to be mixed to form the desired crystal structure. To incisively probe this issue, we combine experiments and theory on a series of DNA-grafted nanoparticles at varying stoichiometries, including noninteger values. We show that stoichiometry can couple with the geometries of the building blocks to tune the resulting equilibrium crystal morphology. As a concrete example, a stoichiometric ratio of 3:1 typically results in the Cr3Si structure. However, AlB2 can form when appropriate building blocks are used so that the AlB2 standard-state free energy is low enough to overcome the entropic preference for Cr3Si. These situations can also lead to an undesirable phase coexistence between crystal polymorphs. Thus, whereas stoichiometry can be a powerful handle for direct control of lattice formation, care must be taken in its design and selection to avoid polymorph coexistence.

Unexpected thermal annealing effects on the viscosity of polymer nanocomposites.

The effects of thermal annealing, 12-50 K above the glass transition temperature, on the zero-shear viscosity, η, of polymer nanocomposites (PNCs) and the corresponding host polymers were studied. For all specimens, including neat and 4 wt% dioctyl phthalate (DOP)-plasticized polystyrene (PS), neat poly(methyl methacrylate) (PMMA), and PNCs containing bare and grafted silica nanoparticles in neat and DOP-plasticized PS, the η increased with time initially, and only asymptotically approached a steady-state value after thermal annealing for ∼100 to ∼200 h. We found that this phenomenon occurred regardless of the solvent used to prepare the sample although the fractional changes in η (δη/η) are visibly bigger for tetrahydrofuran (THF). Moreover, the PNCs not plasticized by DOP showed bigger δη/η than their host polymers while the plasticized ones behave essentially the same as the neat hosts. Interestingly, some unplasticized PNCs prepared from THF exhibited smaller viscosities than the host polymer, but this anomaly disappeared on thermal annealing. By correlating the viscosity measurements with the evolution of the solvent content, average NP aggregate size and the amount of adsorbed PS on silica for samples prepared from different solvents, we infer that the temporal viscosity evolution originates from out-of-equilibrium chain conformations produced during sample preparation. Because these relaxations are limited by the rearrangement of the polymer chains adsorbed on the NP or sample substrate surface, the timescales over which η changes can be much longer than the polymer reptation time, as observed.

Freezing transitions in a system of two-dimensional octupolar multipoles.

We have investigated the fluid-solid freezing transitions in a system of axially symmetric particles confined to a two-dimensional plane and interacting via purely repulsive octupolar interaction potential varying as the seventh power of the inverse interparticle separation. Both the one-component and two-component cases have been considered. The classical density functional theory of freezing has been employed to study the relative stability of the triangular solid phase of the system with respect to the fluid phase of the system using the structural inputs calculated by solving the Rogers-Young integral equation theory. Considering the freezing of the fluid into substitutionally disordered solid, in the case of binary mixtures, we observe that the temperature-composition phase diagram is a spindle for moderate particle asymmetries in the range 0.90-0.75. Further increasing the asymmetry to 0.70 results in the coexistence of the fluid phases of two different compositions.