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.

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.

Physics of Directional Polymer Crystallization.

It has been proposed that the nonisothermal directional crystallization of a polymer driven by a moving sink has an exact analogy to an equivalent isothermal crystallization protocol. We show that this is substantially true because polymers are poor thermal conductors; thus, polymer crystallization occurs over a relatively narrow spatial regime, while the thermal gradients created by this freezing occur over a much broader scale. This separation of scales allows us to replace the crystallization process, which is spatially distributed, with an equivalent step. The temperature at this step, which corresponds to the desired equivalent isothermal crystallization temperature, scales linearly with sink velocity. However, a few metrics, such as the Avrami exponent characterizing the kinetics of crystallization are very different in the two cases. These findings provide new insights into the physics of these spatially varying crystallization protocols and should inspire new experiments to probe the underlying equivalences more deeply.

Understanding Gas Transport in Polymer-Grafted Nanoparticle Assemblies.

We rationalize the unusual gas transport behavior of polymer-grafted nanoparticle (GNP) membranes. While gas permeabilities depend specifically on the chemistry of the polymers considered, we focus here on permeabilities relative to the corresponding pure polymer which show interesting, "universal" behavior. For a given NP radius, Rc, and for large enough areal grafting densities, σ, to be in the dense brush regime we find that gas permeability enhancements display a maximum as a function of the graft chain molecular weight, Mn. Based on a recently proposed theory for the structure of a spherical brush in a melt of GNPs, we conjecture that this peak permeability occurs when the densely grafted polymer brush has the highest, packing-induced extension free energy per chain. The corresponding brush thickness is predicted to be h max = 3 R c , independent of chain chemistry and σ, i.e., at an apparently universal value of the NP volume fraction (or loading), ϕNP, ϕNP,max = [Rc/(Rc + hmax)]3 ≈ 0.049. Motivated by this conclusion, we measured CO-2 and CH4 permeability enhancements across a variety of Rc, Mn and σ, and find that they behave in a similar manner when considered as a function of ϕNP, with a peak in the near vicinity of the predicted ϕNP,max. Thus, the chain length dependent extension free energy appears to be the critical variable in determining the gas permeability for these hybrid materials. The emerging picture is that these curved polymer brushes, at high enough σ behave akin to a two-layer transport medium - the region in the near vicinity of the NP surface is comprised of extended polymer chains which speed-up gas transport relative to the unperturbed melt. The chain extension free energy increases with increasing chain length, up to a maximum, and apparently leads to an increasing gas permeability. For long enough grafts, there is an outer region of chain segments that is akin to an unperturbed melt with slow gas transport. The permeability maximum and decreasing permeability with increasing chain length then follow naturally.

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.

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.

Gas Transport in Interacting Planar Brushes.

Recent experiments on melts of spherical nanoparticles (NPs) densely grafted with polymer chains show enhanced gas transport relative to the neat polymer (without NPs). As a means of understanding this unexpected behavior, we consider here the simpler case of two interacting planar brushes, under conditions representing a polymer melt far below its critical point (i.e., where the "free volume" or holes act akin to a poor solvent). Computer simulations illustrate, in agreement with mean-field ideas, that the density profile far away from the walls is flat but with a value that is marginally larger than the corresponding polymer melt under identical state conditions. We find that tracer particles, which represent the gas of interest, segregate preferentially to the grafting surface, with this result being relatively insensitive to the nature of polymer-surface interactions. These brush layers therefore correspond to heterogeneous transport media: the gas molecules near the grafting surface have accelerated dynamics (presumably parallel to the wall) relative to the corresponding polymer melt, but they have slower dynamics in the central region of the brush. We therefore find that gas molecules perform hop-like motions - they spend a significant part of their time in the regions of fast transport, separated by motions where they "hop" from one surface to the other. These phenomena in combination lead to an overall speedup in gas dynamics in these brush layers relative to a polymer melt, in good agreement with the experimental data.

Theory of statistics of ties, loops, and tails in semicrystalline polymers.

Polymer crystals grown from melts consist of alternating lamellar crystalline regions and amorphous regions. We study the statistics of ties: chains which bridge the adjacent lamellae, loops: chains which come out of one lamella and enter back into the same lamella before reaching the other lamellae, and tails: chains which end in an amorphous region. We develop a theory to calculate the probabilities of formation of ties, loops, and tails with consideration of finite chain length and cooperative incorporation of a chain into multiple lamellae. The results of our numerical calculations based on a field-theoretic formalism show that the fraction of ties increases with increasing chain length, and it decreases with increasing interlamellar separation. In the limiting case of an infinite chain confined between only two walls, we recover the classical results of the gambler's ruin model. We show that the density anomaly encountered in previous theories is avoided naturally in the present theory without forcing the majority of stems to form tight loops. The derived results on the probability of tie chains in the amorphous regions are pertinent to the mechanical properties of semicrystalline polymers.

Lower Critical Solution Temperature Behavior in Polyelectrolyte Complex Coacervates.

In light of recent experimental observations of lower critical solution temperature (LCST) in polyelectrolyte complex coacervates (Ali, S. et al. ACS Macro Lett. 2019, 8, 289-293), we explore its possible mechanisms on the basis of a slight modification of our theory (Adhikari, S. et al. J. Chem. Phys. 2018, 149, 163308). We explore the consequences of the temperature dependence of the solvent dielectric constant (ε) and the solvent-polymer interaction parameter (χ) on the complex coacervates' phase behavior. The results show that the temperature dependence of the solvent dielectric constant and solvent-polymer interaction parameter can result in a complex phase behavior involving two disjoint unstable regions on the temperature (T)-polyelectrolyte concentration (ϕ p) plane. Comparison of phase diagrams constructed for different possible temperature dependencies of ε and χ shows that the experimentally observed LCST behavior is obtained only if the solvent dielectric constant decreases and the solvent-polymer interaction parameter increases with increasing temperature. Preferential partitioning of salt into the polyelectrolyte poor phase is predicted for all possible combinations of temperature dependencies of χ and ε considered in this work.

Polyelectrolyte complex coacervation by electrostatic dipolar interactions.

We address complex coacervation, the liquid-liquid phase separation of a solution of oppositely charged polyelectrolyte chains into a polyelectrolyte rich complex coacervate phase and a dilute aqueous phase, based on the general premise of spontaneous formation of polycation-polyanion complexes even in the homogeneous phase. The complexes are treated as flexible chains made of dipolar segments and uniformly charged segments. Using a mean field theory that accounts for the entropy of all dissociated ions in the system, electrostatic interactions among dipolar and charged segments of complexes and uncomplexed polyelectrolytes, and polymer-solvent hydrophobicity, we have computed coacervate phase diagrams in terms of polyelectrolyte composition, added salt concentration, and temperature. For moderately hydrophobic polyelectrolytes in water at room temperature, neither hydrophobicity nor electrostatics alone is strong enough to cause phase separation, but their combined effect results in phase separation, arising from the enhancement of effective hydrophobicity by dipolar attractions. The computed phase diagrams capture key experimental observations including the suppression of complex coacervation due to increases in salt concentration, temperature, and polycation-polyanion composition asymmetry, and its promotion by increasing the chain length, and the preferential partitioning of salt into the polyelectrolyte dilute phase. We also provide new predictions such as the emergence of loops of instability with two critical points.