Abelardo Ramírez-Hernández

Molecular pathways for defect annihilation in directed self-assembly

Significance A molecular model is used to calculate the free energy of formation of ordered and disordered copolymer morphologies. We rely on advanced methodologies to identify the minimum free energy pathways that connect such states of the material. Our predictions for defect formation and annealing are compared with experimental observations. Our results provide a detailed molecular view of isolated block copolymer defects, which measure approximately 5 nm and represent isolated events in large areas. They are true “needles in the hay stack” that can only be studied by concerted molecular simulations and dedicated access to production-level fabrication tools. We show that defect annealing is an activated process, where defects are eliminated by operating near the order−disorder transition. Over the last few years, the directed self-assembly of block copolymers by surface patterns has transitioned from academic curiosity to viable contender for commercial fabrication of next-generation nanocircuits by lithography. Recently, it has become apparent that kinetics, and not only thermodynamics, plays a key role for the ability of a polymeric material to self-assemble into a perfect, defect-free ordered state. Perfection, in this context, implies not more than one defect, with characteristic dimensions on the order of 5 nm, over a sample area as large as 100 cm2. In this work, we identify the key pathways and the corresponding free energy barriers for eliminating defects, and we demonstrate that an extraordinarily large thermodynamic driving force is not necessarily sufficient for their removal. By adopting a concerted computational and experimental approach, we explain the molecular origins of these barriers and how they depend on material characteristics, and we propose strategies designed to overcome them. The validity of our conclusions for industrially relevant patterning processes is established by relying on instruments and assembly lines that are only available at state-of-the-art fabrication facilities, and, through this confluence of fundamental and applied research, we are able to discern the evolution of morphology at the smallest relevant length scales—a handful of nanometers—and present a view of defect annihilation in directed self-assembly at an unprecedented level of detail.

Block copolymer assembly on nanoscale patterns of polymer brushes formed by electrohydrodynamic jet printing.

Fundamental understanding of the self-assembly of domains in block copolymers (BCPs) and capabilities in control of these processes are important for their use as nanoscale templates in various applications. This paper focuses on the self-assembly of spin-cast and printed poly(styrene-block-methyl methacrylate) BCPs on patterned surface wetting layers formed by electrohydrodynamic jet printing of random copolymer brushes. Here, end-grafted brushes that present groups of styrene and methyl methacrylate in geometries with nanoscale resolution deterministically define the morphologies of BCP nanostructures. The materials and methods can also be integrated with lithographically defined templates for directed self-assembly of BCPs at multiple length scales. The results provide not only engineering routes to controlled formation of complex patterns but also vehicles for experimental and simulation studies of the effects of chemical transitions on the processes of self-assembly. In particular, we show that the methodology developed here provides the means to explore exotic phenomena displayed by the wetting behavior of BCPs, where 3-D soft confinement, chain elasticity, interfacial energies, and substrates surface energy cooperate to yield nonclassical wetting behavior.

Liquid crystal nanodroplets, and the balance between bulk and interfacial interactions

Molecular dynamics simulations of a coarse grain model are used to explore the morphology of thermotropic liquid crystal nanodroplets. The characteristic length of the droplets is such that different contributions to the energy, including interfacial and bulk-like terms, have comparable magnitudes. Depending on the relative strength of such contributions, a wide variety of mesophases can be identified. These range from a completely disordered isotropic phase at elevated temperatures, to ordered radial and smectic phases at low temperatures. Bipolar, uniaxial and axial phases are also observed. Our results suggest that according to the ratio between perpendicular and planar anchoring strengths, an isotropic–radial transition may occur through several intermediate phases. In contrast, a direct bipolar–radial transition is never observed. Our results are summarized in the form of a generic phase diagram for spherical nanodroplets as a function of anchoring strength. The diagram exhibits a number of common features with phase transitions that have been observed in experiments with larger, micron-sized droplets. Perhaps more importantly, it serves to emphasize the balance that exists in nanodroplets between surface and bulk interactions, droplet size and temperature, and how that balance influences the behavior of the system.

A multichain polymer slip-spring model with fluctuating number of entanglements for linear and nonlinear rheology

A theoretically informed entangled polymer simulation approach is presented for description of the linear and non-linear rheology of entangled polymer melts. The approach relies on a many-chain representation and introduces the topological effects that arise from the non-crossability of molecules through effective fluctuating interactions, mediated by slip-springs, between neighboring pairs of macromolecules. The total number of slip-springs is not preserved but, instead, it is controlled through a chemical potential that determines the average molecular weight between entanglements. The behavior of the model is discussed in the context of a recent theory for description of homogeneous materials, and its relevance is established by comparing its predictions to experimental linear and non-linear rheology data for a series of well-characterized linear polyisoprene melts. The results are shown to be in quantitative agreement with experiment and suggest that the proposed formalism may also be used to describe the dynamics of inhomogeneous systems, such as composites and copolymers. Importantly, the fundamental connection made here between our many-chain model and the well-established, thermodynamically consistent single-chain mean-field models provides a path to systematic coarse-graining for prediction of polymer rheology in structurally homogeneous and heterogeneous materials.

Numerical simulation of Gaussian chains near hard surfaces.

We present a coarse grain representation for Gaussian chains in the presence of hard surfaces. Whereas a Gaussian chain in the bulk can be represented by a bead-spring model with a quadratic potential between adjacent beads, the presence of a surface reduces the number of allowed chain configurations and modifies the effective potential between the beads. We derive the corrected potentials for several surface geometries: a single wall, two parallel walls (slit), and a spherical or cylindrical object (nanoparticle). Those potentials can be used in any model that includes a Gaussian chain, regardless of the simulation method. As an illustration, we consider a coarse grain model of a polymeric melt and, using Monte Carlo simulations, we compute the density profiles for (i) a melt confined in a slit and (ii) a melt in the vicinity of a nanoparticle. The case of a polymeric solution confined within a slit is also addressed, and the proposed approach is shown to yield results in qualitative agreement with those obtained with field-theoretic simulations.

Theoretically informed entangled polymer simulations: linear and non-linear rheology of melts

In recent years, there has been a resurgence in developing models and theories for the non-equilibrium behavior of polymeric liquids. The so-called “tube” models, gradually refined over decades of research, can now provide a description of the linear and non-linear rheology of entangled polymers that is qualitatively consistent with experiments. Such approaches, however, have been limited to homopolymers. Here we present a general formalism that relies on the concept of slip links to describe the dynamics of high polymers. In this work, it is shown to be capable of describing quantitatively the linear response of pure homopolymers and blends, the non-linear rheology of highly entangled systems, and the dynamics of diblock copolymers.

Directly Observing Micelle Fusion and Growth in Solution by Liquid-Cell Transmission Electron Microscopy

Amphiphilic small molecules and polymers form commonplace nanoscale macromolecular compartments and bilayers, and as such are truly essential components in all cells and in many cellular processes. The nature of these architectures, including their formation, phase changes, and stimuli-response behaviors, is necessary for the most basic functions of life, and over the past half-century, these natural micellar structures have inspired a vast diversity of industrial products, from biomedicines to detergents, lubricants, and coatings. The importance of these materials and their ubiquity have made them the subject of intense investigation regarding their nanoscale dynamics with increasing interest in obtaining sufficient temporal and spatial resolution to directly observe nanoscale processes. However, the vast majority of experimental methods involve either bulk-averaging techniques including light, neutron, and X-ray scattering, or are static in nature including even the most advanced cryogenic transmission electron microscopy techniques. Here, we employ in situ liquid-cell transmission electron microscopy (LCTEM) to directly observe the evolution of individual amphiphilic block copolymer micellar nanoparticles in solution, in real time with nanometer spatial resolution. These observations, made on a proof-of-concept bioconjugate polymer amphiphile, revealed growth and evolution occurring by unimer addition processes and by particle-particle collision-and-fusion events. The experimental approach, combining direct LCTEM observation, quantitative analysis of LCTEM data, and correlated in silico simulations, provides a unique view of solvated soft matter nanoassemblies as they morph and evolve in time and space, enabling us to capture these phenomena in solution.

A multi-chain polymer slip-spring model with fluctuating number of entanglements: Density fluctuations, confinement, and phase separation

Coarse grained simulation approaches provide powerful tools for the prediction of the equilibrium properties of polymeric systems. Recent efforts have sought to develop coarse-graining strategies capable of predicting the non-equilibrium behavior of entangled polymeric materials. Slip-link and slip-spring models, in particular, have been shown to be capable of reproducing several key aspects of the linear response and rheology of polymer melts. In this work, we extend a previously proposed multi-chain slip-spring model in a way that correctly incorporates the effects of the fluctuating environment in which polymer segments are immersed. The model is used to obtain the equation of state associated with the slip-springs, and the results are compared to those of related numerical approaches and an approximate analytical expression. The model is also used to examine a polymer melt confined into a thin film, where an inhomogeneous distribution of polymer segments is observed, and the corresponding inhomogeneities associated with density fluctuations are reflected on the spatial slip-spring distribution.

Investigation of cross-linking poly(methyl methacrylate) as a guiding material in block copolymer directed self-assembly

Directed self-assembly (DDSA) of block copolymers ((BCP) is attracting a growing amount of interest as a techhnique to expand traditional lithography beyond its current limits. It has reecently been demonstrated that chemoepitaxy can be used to successfully ddirect BCP assembly to form large arrays off high-density features. The imec DSA LiNe flow uses lithography and trim-etch to produce a “prepattern” of cross-linked polystyrene (PS) stripes, which in turn guide the formation of assembled BCPP structures. Thhe entire process is predicated on the preferential interaction of the respective BCP domains with particular regionss of the underlying prepattern. The use of polystyrene as the guiding material is not uniquely required, however, and in fact may not even be preferable. This study investigates an alternate chemistry –– crosslinked poly(methyl methacrylate), X-PMMA, –– as the underlying polymer mat, providing a route to higher auto-affinity and therefore a stronger guiding ability. In addition to tthe advantages of the chemistry under investigation, this study explores the broader theme of extending BCP DSA to other materials.

Mesoscale martensitic transformation in single crystals of topological defects

Significance The processes that mediate crystal nucleation and growth, and the transformation between crystal structures having different lattice symmetries, are of fundamental importance to a wide range of scientific disciplines. Here, we use single crystals of liquid-crystal blue phases with a controlled orientation to study the liquid analog of a crystal–crystal transformation. In contrast to traditional atomic crystals, the transitions that arise in blue phases take place over submicron length scales. They do, however, occur in a diffusionless manner, with characteristics that are reminiscent of traditional martensitic transformations in atomic crystals. Liquid-crystal blue phases (BPs) are highly ordered at two levels. Molecules exhibit orientational order at nanometer length scales, while chirality leads to ordered arrays of double-twisted cylinders over micrometer scales. Past studies of polycrystalline BPs were challenged by the existence of grain boundaries between randomly oriented crystalline nanodomains. Here, the nucleation of BPs is controlled with precision by relying on chemically nanopatterned surfaces, leading to macroscopic single-crystal BP specimens where the dynamics of mesocrystal formation can be directly observed. Theory and experiments show that transitions between two BPs having a different network structure proceed through local reorganization of the crystalline array, without diffusion of the double-twisted cylinders. In solid crystals, martensitic transformations between crystal structures involve the concerted motion of a few atoms, without diffusion. The transformation between BPs, where crystal features arise in the submicron regime, is found to be martensitic in nature when one considers the collective behavior of the double-twist cylinders. Single-crystal BPs are shown to offer fertile grounds for the study of directed crystal nucleation and the controlled growth of soft matter.