Optimized design of block copolymers with covarying properties for nanolithography.

The ability to impart multiple covarying properties into a single material represents a grand challenge in manufacturing. In the design of block copolymers (BCPs) for directed self-assembly and nanolithography, materials often balance orthogonal properties to meet constraints related to processing, structure and defectivity. Although iterative synthesis strategies deliver BCPs with attractive properties, identifying materials with all the required attributes has been difficult. Here we report a high-throughput synthesis and characterization platform for the discovery and optimization of BCPs with A-block-(B-random-C) architectures for lithographic patterning in semiconductor manufacturing. Starting from a parent BCP and using thiol-epoxy 'click' chemistry, we synthesize a library of BCPs that cover a large and complex parameter space. This allows us to readily identify feature-size-dependent BCP chemistries for 8-20-nm-pitch patterns. These blocks have similar surface energies for directed self-assembly, and control over the segregation strength to optimize the structure (favoured at higher segregation strengths) and defectivity (favoured at lower segregation strengths).

Strongly Chiral Liquid Crystals in Nanoemulsions.

Liquid crystal (LC) emulsions represent a class of confined soft matter that exhibit exotic internal organizations and size-dependent properties, including responses to chemical and physical stimuli. Past studies have explored micrometer-scale LC emulsion droplets but little is known about LC ordering within submicrometer-sized droplets. This paper reports experiments and simulations that unmask the consequences of confinement in nanoemulsions on strongly chiral LCs that form bulk cholesteric and blue phases (BPs). A method based on light scattering is developed to characterize phase transitions of LCs within the nanodroplets. For droplets with a radius to the pitch ratio (Rv /p0 ) as small as 2/3, the BP-to-cholesteric transition is substantially suppressed, leading to a threefold increase of the BP temperature interval relative to bulk behavior. Complementary simulations align with experimental findings and reveal the dominant role of chiral elastic energy. For Rv /p0  ≈ 1/3, a single LC phase forms below the clearing point, with simulations revealing the new configuration to contain a τ-1/2 disclination that extends across the nanodroplet. These findings are discussed in the context of mechanisms by which polymer networks stabilize BPs and, more broadly, for the design of nanoconfined soft matter.

Interplay of structure, elasticity, and dynamics in actin-based nematic materials.

Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can be manipulated over a relatively wide range of elastic moduli. Specifically, thin films of actin filaments are assembled at an oil-water interface. At sufficiently high concentrations, one observes the formation of a nematic phase riddled with [Formula: see text] topological defects, characteristic of a two-dimensional nematic system. As the average filament length increases, the defect morphology transitions from a U shape into a V shape, indicating the relative increase of the material's bend over splay modulus. Furthermore, through the sparse addition of rigid microtubule filaments, one can gain additional control over the liquid crystal's elasticity. We show how the material's bend constant can be raised linearly as a function of microtubule filament density, and present a simple means to extract absolute values of the elastic moduli from purely optical observations. Finally, we demonstrate that it is possible to predict not only the static structure of the material, including its topological defects, but also the evolution of the system into dynamically arrested states. Despite the nonequilibrium nature of the system, our continuum model, which couples structure and hydrodynamics, is able to capture the annihilation and movement of defects over long time scales. Thus, we have experimentally realized a lyotropic liquid crystal system that can be truly engineered, with tunable mechanical properties, and a theoretical framework to capture its structure, mechanics, and dynamics.

Defect removal in the course of directed self-assembly is facilitated in the vicinity of the order-disorder transition.

The stability of prototypical defect morphologies in thin films of symmetric diblock copolymers on chemically patterned substrates is investigated by self-consistent field theory. The excess free energy of defects and barriers of defect-removal mechanisms are obtained by computing the minimum free-energy path. Distinct defect-removal mechanisms are illustrated demonstrating that (i) defects will become unstable at a characteristic value of incompatibility χN* above the order-disorder transition and (ii) the kinetics is accelerated at weak segregation. Numerical findings are placed in the context of physical mechanisms, and implications for directed self-assembly are discussed.

Molecular modeling of vapor-deposited polymer glasses.

We have investigated the properties of vapor-deposited glasses prepared from short polymer chains using molecular dynamics simulations. Vapor-deposited polymer glasses are found to have higher density and higher kinetic stability than ordinary glasses prepared by gradual cooling of the corresponding equilibrium liquid. In contrast to results for binary Lennard-Jones glasses, the deposition rate is found to play an important role in the stability of polymer vapor-deposited glasses. Glasses deposited at the slowest deposition rate and at the optimal substrate temperature are found to correspond to the ordinary glasses that one could hypothetically prepare by cooling the liquid at rates that are 4-5 orders of magnitude slower than those accessible in the current simulations. For intermediate-length polymer chains, the resulting vapor-deposited glasses are found to be highly anisotropic. For short chains, however, the glasses are isotropic, showing that structural anisotropy is not a necessary condition for formation of stable glasses by physical vapor deposition.

Coarse-grained simulations of macromolecules: from DNA to nanocomposites.

This review discusses multiscale modeling and simulations of macromolecules and macromolecular systems in the context of two specific examples. In the first, recent attempts to develop coarse-grained representations of DNA are reviewed, and a discussion of recent predictions of such models is presented, particularly in the context of DNA melting and rehybridization. The second example considers polymer nanocomposites; a review of recent simulations is presented, with an emphasis on the description of entanglements in such systems and new methods for the study of the segregation of nanoparticles that arises in copolymers, in which composition heterogeneity can be used to control nanoparticle position and develop an increased understanding of nanoparticle-polymer interactions.

An immersed boundary method for Brownian dynamics simulation of polymers in complex geometries: application to DNA flowing through a nanoslit with embedded nanopits.

This work presents an immersed boundary method that allows fast Brownian dynamics simulation of solutions of polymer chains and other Brownian objects in complex geometries with fluctuating hydrodynamics. The approach is based on the general geometry Ewald-like method, which solves the Stokes equation with distributed regularized point forces in O(N) or O(NlogN) operations, where N is the number of point forces in the system. Time-integration is performed using a midpoint algorithm and Chebyshev polynomial approximation proposed by Fixman. This approach is applied to the dynamics of a genomic DNA molecule driven by flow through a nanofluidic slit with an array of nanopits on one wall of the slit. The dynamics of the DNA molecule was studied as a function of the Péclet number and chain length (the base case being λ-DNA). The transport characteristics of the hopping dynamics in this device differ at low and high Péclet number, and for long DNA, relative to the pit size, the dynamics is governed by the segments residing in the pit. By comparing with results that neglect them, hydrodynamic interactions are shown to play an important quantitative role in the hopping dynamics.

Coarse-Grained Simulation of Bottlebrush: From Single-Chain Properties to Self-Assembly.

Bottlebrush polymers consist of a linear backbone with densely grafted side chains. They are known to have a range of properties of interest, such as enhanced mechanical strength and rapid self-assembly into large domains, and have attracted attention as promising candidates for applications in photonics, lithography, energy storage, organic optoelectronics, and drug delivery. Here, we present a coarse-grained model of bottlebrush polymers that is able to reproduce their experimentally observed persistence lengths and chain conformations in the melt. The model is then used to investigate the morphologies of this class of materials for various chain architectures and grafting densities.

Graphoepitaxial assembly of asymmetric ternary blends of block copolymers and homopolymers.

Ternary blends of cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers and polystyrene and poly(methyl methacrylate) homopolymers were assembled in trench features of constant width. Increasing the fraction of homopolymer in the blend increased the spacing and size of block copolymer domains, which were oriented perpendicular to the substrate to form a hexagonal lattice within the trench. The number of rows of cylinders within the trench was controlled by the blend composition. Depending on the domain size and spacing, the hexagonal lattice was stretched or compressed perpendicular to the trench walls but not perturbed parallel to the walls, indicating a decoupling of the perturbation in the perpendicular and parallel directions. The row spacing was uniform across the trench as a function of position from the trench wall. The results are compared with an analytical model and with Monte Carlo simulations.

Hydrodynamic effects on the translocation rate of a polymer through a pore.

The translocation of large DNA molecules through narrow pores has been examined in the context of multiscale simulations that include a full coupling of fluctuating hydrodynamic interactions, boundary effects, and molecular conformation. The actual rate constants for this process are determined for the first time, and it is shown that hydrodynamic interactions can lead to translocation rates that vary by multiple orders of magnitude when molecular weights are only changed by a factor of 10, in stark contrast to predictions from widely used free draining calculations.

Tethered DNA dynamics in shear flow.

We study the cyclic dynamics of a single polymer tethered to a hard wall in shear flow using Brownian dynamics, the lattice Boltzmann method, and a recent stochastic event-driven molecular dynamics algorithm. We focus on the dynamics of the free end (last bead) of the tethered chain and we examine the cross-correlation function and power spectral density of the chain extensions in the flow and gradient directions as a function of chain length N and dimensionless shear rate Wi. Extensive simulation results suggest a classical fluctuation-dissipation stochastic process and question the existence of periodicity of the cyclic dynamics, as previously claimed. We support our numerical findings with a simple analytical calculation for a harmonic dimer in shear flow.

A pH-Triggered, Self-Assembled, and Bioprintable Hybrid Hydrogel Scaffold for Mesenchymal Stem Cell Based Bone Tissue Engineering.

Effective bone tissue engineering can restore bone and skeletal functions that are impaired by traumas and/or certain medical conditions. Bone is a complex tissue and functions through orchestrated interactions between cells, biomechanical forces, and biofactors. To identify ideal scaffold materials for effective mesenchymal stem cell (MSC)-based bone tissue regeneration, here we develop and characterize a composite nanoparticle hydrogel by combining carboxymethyl chitosan (CMCh) and amorphous calcium phosphate (ACP) (designated as CMCh-ACP hydrogel). We demonstrate that the CMCh-ACP hydrogel is readily prepared by incorporating glucono δ-lactone (GDL) into an aqueous dispersion or rehydrating the acidic freeze-dried nanoparticles in a pH-triggered controlled-assembly fashion. The CMCh-ACP hydrogel exhibits excellent biocompatibility and effectively supports MSC proliferation and cell adhesion. Moreover, while augmenting BMP9-induced osteogenic differentiation, the CMCh-ACP hydrogel itself is osteoinductive and induces the expression of osteoblastic regulators and bone markers in MSCs in vitro. The CMCh-ACP scaffold markedly enhances the efficiency and maturity of BMP9-induced bone formation in vivo, while suppressing bone resorption occurred in long-term ectopic osteogenesis. Thus, these results suggest that the pH-responsive self-assembled CMCh-ACP injectable and bioprintable hydrogel may be further exploited as a novel scaffold for osteoprogenitor-cell-based bone tissue regeneration.

Molecular simulation of the swelling of polyelectrolyte gels by monovalent and divalent counterions.

Permanently crosslinked polyelectrolyte gels are known to undergo discontinuous first-order volume phase transitions, the onset of which may be caused by a number of factors. In this study we examine the volumetric properties of such polyelectrolyte gels in relation to the progressive substitution of monovalent counterions by divalent counterions as the gels are equilibrated in solvents of different dielectric qualities. We compare the results of coarse-grained molecular dynamics simulations of polyelectrolyte gels with previous experimental measurements by others on polyacrylate gels. The simulations show that under equilibrium conditions there is an approximate cancellation between the electrostatic contribution and the counterion excluded-volume contribution to the osmotic pressure in the gel-solvent system; these two contributions to the osmotic pressure have, respectively, energetic and entropic origins. The finding of such a cancellation between the two contributions to the osmotic pressure of the gel-solvent system is consistent with experimental observations that the swelling behavior of polyelectrolyte gels can be described by equations of state for neutral gels. Based on these results, we show and explain that a modified form of the Flory-Huggins model for nonionic polymer solutions, which accounts for neither electrostatic effects nor counterion excluded-volume effects, fits both experimental and simulated data for polyelectrolyte gels. The Flory-Huggins interaction parameters obtained from regression to the simulation data are characteristic of ideal polymer solutions, whereas the experimentally obtained interaction parameters, particularly that associated with the third virial coefficient, exhibit a significant departure from ideality, leading us to conclude that further enhancements to the simulation model, such as the inclusion of excess salt, the allowance for size asymmetric electrolytes, or the use of a distance-dependent solvent dielectricity model, may be required. Molecular simulations also reveal that the condensation of divalent counterions onto the polyelectrolyte network backbone occurs preferentially over that of monovalent counterions.

3-D microwell culture of human embryonic stem cells.

Human embryonic stem cells (hESCs) have the ability to proliferate indefinitely and differentiate into each of the embryonic cell lineages. Great care is required to maintain undifferentiated hESC cultures since spontaneous differentiation often occurs in culture, presumably resulting from soluble factors, cell-cell contact, and/or cell-matrix signaling. hESC differentiation is typically stimulated via generation of embryoid bodies (EBs) and lineage commitment of individual cells depends upon numerous cues throughout the EB environment, including EB shape and size. Common EB formation protocols, however, produce a very heterogeneous size distribution, perhaps reducing efficiency of directed differentiation. We have developed a 3-D microwell-based method to maintain undifferentiated hESC cultures for weeks without passaging using physical and extracellular matrix patterning constraints to limit colony growth. Over 90% of hESCs cultured in microwells for 2-3 weeks were viable and expressed the hESC transcription marker Oct-4. Upon passaging to Matrigel-coated tissue culture-treated polystyrene dishes (TCPS), microwell cultured hESCs maintained undifferentiated proliferation. Microwell culture also permits formation of hESC colonies with a defined size, which can then be used to form monodisperse EBs. When cultured in this system, hESCs retained pluripotency and self-renewal, and were able to be passaged to standard unconstrained culture conditions.

Controlled deformation of vesicles by flexible structured media.

Liquid crystalline (LC) materials, such as actin or tubulin networks, are known to be capable of deforming the shape of cells. Here, elements of that behavior are reproduced in a synthetic system, namely, a giant vesicle suspended in a LC, which we view as a first step toward the preparation of active, anisotropic hybrid systems that mimic some of the functionality encountered in biological systems. To that end, we rely on a coupled particle-continuum representation of deformable networks in a nematic LC represented at the level of a Landau-de Gennes free energy functional. Our results indicate that, depending on its elastic properties, the LC is indeed able to deform the vesicle until it reaches an equilibrium, anisotropic shape. The magnitude of the deformation is determined by a balance of elastic and surface forces. For perpendicular anchoring at the vesicle, a Saturn ring defect forms along the equatorial plane, and the vesicle adopts a pancake-like, oblate shape. For degenerate planar anchoring at the vesicle, two boojum defects are formed at the poles of the vesicle, which adopts an elongated, spheroidal shape. During the deformation, the volume of the topological defects in the LC shrinks considerably as the curvature of the vesicle increases. These predictions are confirmed by our experimental observations of spindle-like shapes in experiments with giant unilamellar vesicles with planar anchoring. We find that the tension of the vesicle suppresses vesicle deformation, whereas anchoring strength and large elastic constants promote shape anisotropy.

Modulating membrane properties: the effect of trehalose and cholesterol on a phospholipid bilayer.

The protective properties of trehalose on cholesterol-containing lipid dipalmitoylphosphatidylcholine (DPPC) bilayers are studied through molecular simulations. The ability of the disaccharide to interact with the phospholipid headgroups and stabilize the membrane persists even at high cholesterol concentrations and restricts some of the changes to the structure that would otherwise be imposed by cholesterol molecules. Predictions of bilayer properties such as area per lipid, tail ordering, and chain conformation support the notion that the disaccharide decreases the main melting transition in these multicomponent model membranes, which correspond more closely to common biological systems than pure bilayers. Molecular simulations indicate that the membrane dynamics are slowed considerably by the presence of trehalose, indicating that high sugar concentrations would serve to avert possible phase separations that could arise in mixed phospholipid systems. Various time correlation functions suggest that the character of the modifications in lipid dynamics induced by trehalose and cholesterol is different in the hydrophilic and hydrophobic regions of the membrane.

Chirality-selected phase behaviour in ionic polypeptide complexes.

Polyelectrolyte complexes present new opportunities for self-assembled soft matter. Factors determining whether the phase of the complex is solid or liquid remain unclear. Ionic polypeptides enable examination of the effects of stereochemistry on complex formation. Here we demonstrate that chirality determines the state of polyelectrolyte complexes, formed from mixing dilute solutions of oppositely charged polypeptides, via a combination of electrostatic and hydrogen-bonding interactions. Fluid complexes occur when at least one of the polypeptides in the mixture is racemic, which disrupts backbone hydrogen-bonding networks. Pairs of purely chiral polypeptides, of any sense, form compact, fibrillar solids with a ß-sheet structure. Analogous behaviour occurs in micelles formed from polypeptide block copolymers with polyethylene oxide, where assembly into aggregates with either solid or fluid cores, and eventually into ordered phases at high concentrations, is possible. Chirality is an exploitable tool for manipulating material properties in polyelectrolyte complexation.

Modeling the polydomain-monodomain transition of liquid crystal elastomers.

We study the mechanism of the polydomain-monodomain transition in liquid crystalline elastomers at the molecular scale. A coarse-grained model is proposed in which mesogens are described as ellipsoidal particles. Molecular dynamics simulations are used to examine the transition from a polydomain state to a monodomain state in the presence of uniaxial strain. Our model demonstrates soft elasticity, similar to that exhibited by side-chain elastomers in the literature. By analyzing the growth dynamics of nematic domains during uniaxial extension, we provide direct evidence that at a molecular level the polydomain-monodomain transition proceeds through cluster rotation and domain growth.

Directed assembly of non-equilibrium ABA triblock copolymer morphologies on nanopatterned substrates.

The majority of past work on directed assembly of block copolymers on chemically nanopatterned surfaces (or chemical patterns) has focused on AB diblock copolymers, and the resulting morphologies have generally corresponded to equilibrium states. Here we report a study on directed assembly of ABA triblock copolymers. Directed assembly of thin films of symmetric poly(methyl methacrylate-b-styrene-b-methyl methacrylate) (PMMA-b-PS-b-PMMA) triblock copolymers is shown to be capable of achieving a high degree of perfection, registration, and accuracy on striped patterns having periods, L(s), commensurate with the bulk period of the copolymer, L(o). When L(s) is incommensurate with L(o), the triblock copolymer domains can reach dimensions up to 55% larger or 13% smaller than L(o). The range over which triblock copolymers tolerate departures from a commensurate L(s) is significantly larger than that accessible with the corresponding diblock copolymer material on analogous directed assembly systems. The assembly kinetics of the triblock copolymer is approximately 3 orders of magnitude slower than observed in the diblock system. Theoretically informed simulations are used to interpret our experimental observations; a thermodynamic analysis reveals that triblocks can form highly ordered, non-equilibrium metastable structures that do not arise in the diblock.

Pattern dimensions and feature shapes of ternary blends of block copolymer and low molecular weight homopolymers directed to assemble on chemically nanopatterned surfaces.

Ternary blends of cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) and low molecular weight PS and PMMA were directed to assemble on chemically patterned surfaces with hexagonal symmetry. The chemical patterns consisted of strongly PMMA preferential spots, patterned by electron-beam lithography, in a matrix of PS. The spot-to-spot spacing of the chemical patterns (L(s)) was varied between 0.9L(0) and 1.1L(0), where L(0) is the cylinder-to-cylinder spacing of the pure block copolymer in bulk. The homopolymer volume fraction of the blends (ϕ(H)) was varied between 0 and 0.3. In addition, chemical patterns were formed with selected spots missing from the perfect hexagonal array, such that the interpolation of domains between patterned spots could be examined on patterns where the polymer/pattern feature density ranged from 1:1 to 4:1. The assemblies were analyzed with top-down SEM, from which orientational order parameter (OP(o)) values were determined. The SEM analysis was complemented by Monte Carlo simulations, which offered insights into the shapes of the assembled cylindrical domains. It was found that, in comparison to pure block copolymer, adding homopolymer increased the range of L(s) values over which assemblies with high OP(o) values could be achieved for 1:1 assemblies. However, the corresponding simulations showed that in the 1:1 assemblies the shape of the cylinders was more uniform for pure block copolymer than for blends. In the case of the 4:1 assemblies, the range of L(s) values over which assemblies with high OP(o) values could be achieved was the same for all values of ϕ(H) tested, but the domains of the pure block copolymer had a more uniform shape. Overall, the results provided insights into the blend composition to be used to meet technological requirements for directed assembly with density multiplication.