Ligand-induced incompatible curvatures control ultrathin nanoplatelet polymorphism and chirality.

The ability of thin materials to shape-shift is a common occurrence that leads to dynamic pattern formation and function in natural and man-made structures. However, harnessing this concept to rationally design inorganic structures at the nanoscale has remained far from reach due to a lack of fundamental understanding of the essential physical components. Here, we show that the interaction between organic ligands and the nanocrystal surface is responsible for the full range of chiral shapes seen in colloidal nanoplatelets. The adsorption of ligands results in incompatible curvatures on the top and bottom surfaces of the NPL, causing them to deform into helicoïds, helical ribbons, or tubes depending on the lateral dimensions and crystallographic orientation of the NPL. We demonstrate that nanoplatelets belong to the broad class of geometrically frustrated assemblies and exhibit one of their hallmark features: a transition between helicoïds and helical ribbons at a critical width. The effective curvature [Formula: see text] is the single aggregate parameter that encodes the details of the ligand/surface interaction, determining the nanoplatelets' geometry for a given width and crystallographic orientation. The conceptual framework described here will aid the rational design of dynamic, chiral nanostructures with high fundamental and practical relevance.

Ligand Tail Controls the Conformation of Indium Sulfide Ultrathin Nanoribbons.

We report the conformational control of 2D ultrathin indium sulfide nanoribbons by tuning their amine ligands' alkyl chain. The initial orthorhombic InS nanoribbons bare n-octylamine ligands and display a highly curved geometry with a characteristic figure of eight shapes. Exchanging the native ligand by oleylamine induces their complete unfolding to yield flat board-shaped nanoribbons. Significant strain variations in the InS crystal structure accompany this shape-shifting. By tuning the linear alkyl chain length from 4 to 18 carbon atoms, we show using small-angle X-ray scattering in solution and transmission electron microscopy that the curvature of the nanoribbon subtly depends on the ligand-ligand interactions at the nanoribbon's surface. The curvature decreases gradually as the chain length increases, while carbon unsaturation has an unexpectedly significant effect at constant chain length. These experiments shed light on the critical role of the ligand monolayer on the curvature of ultrathin 2D crystalline nanosheets and demonstrate that weak supramolecular forces within the organic part of colloidal nanocrystals can dramatically impact their shape. This transduction mechanism, in which changes in the organic monolayer impact the shape of a nanocrystal, will help to devise new strategies to design stimuli-responsive systems that take advantage of both the flexibility of organic moieties and the physical properties of the inorganic core.

Brownian dynamics simulations of bottlebrush polymers in dilute solution under simple shear and uniaxial extensional flows.

We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.

Interaction potential for coarse-grained models of bottlebrush polymers.

Bottlebrush polymers are a class of highly branched macromolecules that show promise for applications such as self-assembled photonic materials and tunable elastomers. However, computational studies of bottlebrush polymer solutions and melts remain challenging due to the high computational cost involved in explicitly accounting for the presence of side chains. Here, we consider a coarse-grained molecular model of bottlebrush polymers where the side chains are modeled implicitly, with the aim of expediting simulations by accessing longer length and time scales. The key ingredients of this model are the size of a coarse-grained segment and a suitably coarse-grained interaction potential between the non-bonded segments. Prior studies have not focused on developing explicit forms of such potentials, instead, relying on scaling arguments to model non-bonded interactions. Here, we show how to systematically calculate an interaction potential between the coarse-grained segments of bottlebrush from finer grained explicit side chain models using Monte Carlo and Brownian dynamics and then incorporate it into an implicit side chain model. We compare the predictions from our coarse-grained implicit side chain model with those obtained from models with explicit side chains in terms of the potential of mean force, the osmotic second virial coefficient, and the interpenetration function, highlighting the range of applicability and limitations of the coarse-grained representation. Although presented in the context of homopolymer bottlebrushes in athermal solvents, our proposed method can be extended to other solvent conditions as well as to different monomer chemistries. We expect that our implicit side chain model will prove useful for accelerating large-scale simulations of bottlebrush solutions and assembly.

Dilute solution structure of bottlebrush polymers.

Bottlebrush polymers are a class of macromolecules that have recently found use in a wide variety of materials, ranging from lubricating brushes and nanostructured coatings to elastomeric gels that exhibit structural colors. These polymers are characterized by dense branches extending from a central backbone and thus have properties distinct from linear polymers. It remains a challenge to specifically understand conformational properties of these molecules, due to the wide range of architectural parameters that can be present in a system, and thus there is a need to accurately characterize and model these molecules. In this paper, we use a combination of viscometry, light scattering, and computer simulations to gain insight into the conformational properties of dilute solution bottlebrush polymers. We focus on a series of model bottlebrushes consisting of a poly(norbornene) (PNB) backbone with poly(lactic acid) (PLA) side chains. We demonstrate that intrinsic viscosity and hydrodynamic radius are experimental observations sensitive to molecular architecture, exhibiting distinct differences with different choices of branches and backbone lengths. Informed by the atomistic structure of this PNB-PLA system, we rationalize a coarse-grained simulation model that we evaluate using a combination of Brownian dynamics and Monte Carlo simulations. We show that this exhibits quantitative matching to experimental results, enabling us to characterize the overall shape of the bottlebrush via a number of metrics that can be extended to more general bottlebrush architectures.

Dynamics of Miura-patterned foldable sheets in shear flow.

We study the dynamics of piecewise rigid sheets containing predefined crease lines in shear flow. The crease lines act like hinge joints along which the sheet may fold rigidly, i.e. without bending any other crease line. We choose the crease lines such that they tessellate the sheet into a two-dimensional array of parallelograms. Specifically, we focus on a particular arrangement of crease lines known as a Miura-pattern in the origami community. When all the hinges are fully open the sheet is planar, whereas when all are closed the sheet folds over itself to form a compact flat structure. Due to rigidity constraints, the folded state of a Miura-sheet can be described using a single fold angle. The hinged sheet is modeled using the framework of constrained multibody systems in the absence of inertia. The hydrodynamic drag on each of the rigid panels is calculated based on an inscribed elliptic disk, but intra-panel hydrodynamic interactions are neglected. We find that when the motion of a sheet remains symmetric with respect to the flow-gradient plane, after a sufficiently long time, the sheet either exhibits asymptotically periodic tumbling and breathing, indicating approach to a limit cycle; or it reaches a steady state by completely unfolding, which we show to be a half-stable node in the phase space. In the case of asymmetric motion of the sheet with respect to the flow-gradient plane, we find that the terminal state of motion is one of - (i) steady state with a fully unfolded or fully folded configuration, (ii) asymptotically periodic tumbling, indicating approach to a limit cycle, (iii) cyclic tumbling without repetition, indicating a quasiperiodic orbit, or (iv) cyclic tumbling with repetition after several cycles, indicating a resonant quasiperiodic orbit. No chaotic behavior was found.

Dynamics of polymer adsorption from dilute solution in shear flow near a planar wall.

Adsorption of polymers from dilute solution subject to shear flow near a planar wall is studied using kinetic theory. A dumbbell model consisting of two beads connected by a nonlinear spring is used to describe the polymer molecules, and the beads interact with the wall via a short-range exponential potential. Bead-bead and bead-wall hydrodynamic interactions are also included in the theory. For an initially bare surface, it is found that the quantity of polymer adsorbed decreases with an increase in polymer molecular weight at a given shear rate and point in time. In addition, for a given molecular weight and point in time, the quantity adsorbed decreases with an increase in shear rate. When adsorbed polymer is initially present, similar trends are observed. Furthermore, complete desorption can be achieved at a sufficiently high shear rate. In all cases, the time required to approach a steady value of the adsorbed amount is many orders of magnitude larger than the dumbbell relaxation time. The above findings are in qualitative agreement with experimental measurements reported nearly three decades ago by Lee and Fuller [J. Colloid Interface Sci. 103, 569 (1985)]. Our findings also suggest that the physical mechanism underlying the long-standing observation that shear flow inhibits polymer adsorption and assists polymer desorption is hydrodynamic interaction between stretched polymer molecules and the adsorbing surface.

Adsorption of single polymer molecules in shear flow near a planar wall.

Adsorption of homopolymers from a dilute solution to a planar wall in the presence of shear flow is studied using a bead-spring dumbbell model. The bead-bead and bead-wall interactions are described by generalized Lennard-Jones potentials. A kinetic theory incorporating bead-wall hydrodynamic interaction is developed in order to obtain an analytical expression for the steady-state dumbbell concentration profile. The concentration profile exhibits an exclusion zone in the immediate vicinity of the wall, is followed by a peak, and finally approaches the bulk concentration far away from the wall. Using the analytical expression, the amount adsorbed and the equivalent film thickness are studied as a function of flow strength and the parameters characterizing the bead-wall interaction potential. Shear flow causes migration of the dumbbells due to bead-wall hydrodynamic interaction, which leads to desorption. On increasing the flow strength, the quantity adsorbed and the film thickness decrease until complete desorption occurs. The dependence of the flow strength required for desorption on the model parameters is also studied and a scaling law is derived for the strong-interaction limit. Brownian dynamics simulations are performed to verify the predictions from the kinetic theory. Although the theory makes a number of simplifying assumptions, it captures many of the key features seen in the simulations.

Continuous-time random walk models of DNA electrophoresis in a post array: part II. Mobility and sources of band broadening.

Using the two-state, continuous-time random walk model, we develop expressions for the mobility and the plate height during DNA electrophoresis in an ordered post array that delineate the contributions due to (i) the random distance between collisions and (ii) the random duration of a collision. These contributions are expressed in terms of the means and variances of the underlying stochastic processes, which we evaluate from a large ensemble of Brownian dynamics simulations performed using different electric fields and molecular weights in a hexagonal array of 1 µm posts with a 3 µm center-to-center distance. If we fix the molecular weight, we find that the collision frequency governs the mobility. On the contrary, the average collision duration is the most important factor for predicting the mobility as a function of DNA size at constant Péclet number. The plate height is reasonably well described by a single post rope-over-pulley model, provided that the extension of the molecule is small. Our results only account for dispersion inside the post array and thus represent a theoretical lower bound on the plate height in an actual device.

Shear-Induced Desorption of Isolated Polymer Molecules from a Planar Wall.

We use Brownian dynamics simulations with hydrodynamic interactions to reconcile the apparent contradictions in experiments on the effect of shear flow on desorption of polymers. Our simulations show that desorption is governed by an interplay between chain-wall attraction and wall-induced hydrodynamic repulsion. When adsorption is weak, the chains form large loops and tails that generate stronger hydrodynamic interactions in the presence of the imposed shear flow, causing longer chains to desorb faster than shorter ones. In contrast, when adsorption is strong, the chains adopt a flattened conformation, weakening hydrodynamic interactions and resulting in shorter chains with fewer sticking points desorbing faster than longer ones.