Molecular dynamics study of the role of the free surface on block copolymer thin film morphology and alignment

Directed Self-Assembly by Sparsely Prepatterned Substrates with Self-Responsive Polymer Brushes

The guiding pattern in the chemoepitaxially directed self-assembly (DSA) of block copolymers is often fabricated by periodically functionalizing homogeneously random copolymer brushes tethered on a substrate. The prepatterned copolymer brushes constitute a soft penetrable surface, and their two components can in principle locally segregate in response to the overlying self-assembly process of block copolymers. To reveal how the self-responsive behavior of the copolymer brushes affects the directing effect, we develop a dissipative particle dynamics model to explicitly include the prepatterned polymer brushes and implement it to simulate the DSA of a cylinder-forming diblock copolymer melt on the sparse pattern of polymer brushes. Through large-scale dynamic simulations, we identify the windows of the content of the random copolymer, the film thickness, and the diameter of the patterned spot, for the formation of perfectly ordered hexagonal patterns composed of perpendicular cylinders. Our dynamic simulations reveal that the random copolymer brushes grafted on the unpatterned area exhibit a remarkable self-responsive ability with respect to the self-assembly of the diblock copolymers overlying them, which may widen the effective window of the content of the random copolymer. Within the processing windows of these key parameters, defect-free patterns are successfully achieved both in simulations and in experiments with sizes as large as a few micrometers for 4-fold density multiplications. This work demonstrates that highly efficient computer simulations based on an effective model can provide helpful guidance for experiments to optimize the critical parameters and even may promote the application of DSA.

Deposition patterns formed by the evaporation of linear diblock copolymer solution nanodroplets on solid surfaces

The evaporation-induced deposition pattern of the linear diblock copolymer solution has attracted attention in recent years. Given its critical applications, we study deposition patterns of the linear diblock copolymer solution nanodroplet on a solid surface (the wall) by molecular dynamics simulations. This study focuses on the influence of the nonbonded interaction strength, including the interaction between the wall and polymer blocks (ɛAW and ɛBW), the interaction between the solvent and the wall (ɛSW), and the interaction between polymer blocks (ɛAB). Conditions leading to diverse deposition patterns are explored, including the coffee-ring and the volcano-like structures. The formation of the coffee-ring structure is attributed to receding interfaces, the heterogeneity inside the droplet, and the self-assembly of polymer chains. This study contributes to the establishment of guidelines for designing deposition patterns of the linear diblock copolymer solution nanodroplet, which facilitates practical applications such as inkjet printing.

Mechanochemistry in Block Copolymers: New Scission Site due to Dynamic Phase Separation

Mechanochemistry can lead to the degradation of the properties of covalent macromolecules. In recent years, numerous functional materials have been developed based on block copolymers (BCPs), however, like homopolymers, their chains could undergo mechanochemical damage during processing, which could have crucial impact on their performance. To investigate the mechanochemical response of BCPs, multiple polymers comprising different ratios of butyl acrylate and methyl methacrylate were prepared with similar degree of polymerization and stressed in solution via ultrasonication. Interestingly, all BCPs, regardless of the amount of the methacrylate monomer, presented a mechanochemistry rate constant similar to that of the methacrylate homopolymer, while a random copolymer reacted like the acrylate homopolymer. Size-exclusion chromatography showed that, in addition to the typical main peak shift towards higher retention times, a different daughter fragment was produced indicating a secondary selective scission site, situated around the covalent connection between the two blocks. Molecular dynamics modeling using acrylate and methacrylate oligomers were carried out and indicated that dynamic phase separation occurs even in a good solvent. Such non-random conformations can explain the faster polymer mechanochemistry. Moreover, the dynamic model for end-to-end chain overstretching supports bond scission which is not necessarily chain-centered.

Surface enrichment dictates block copolymer orientation

Orientation of block copolymer (BCP) morphology in thin films is critical to applications as nanostructured coatings. Despite being well-studied, the ability to control BCP orientation across all possible block constituents remains challenging. Here, we deploy coarse-grained molecular dynamics simulations to study diblock copolymer ordering in thin films, focusing on chain makeup, substrate surface energy, and surface tension disparity between the two constituent blocks. We explore the multi-dimensional parameter space of ordering using a machine-learning approach, where an autonomous loop using a Gaussian process (GP) control algorithm iteratively selects high-value simulations to compute. The GP kernel was engineered to capture known symmetries. The trained GP model serves as both a complete map of system response, and a robust means of extracting material knowledge. We demonstrate that the vertical orientation of BCP phases depends on several counter-balancing energetic contributions, including entropic and enthalpic material enrichment at interfaces, distortion of morphological objects through the film depth, and of course interfacial energies. BCP lamellae are found more resistant to these effects, and thus more robustly form vertical orientations across a broad range of conditions; while BCP cylinders are found to be highly sensitive to surface tension disparity.

Autonomous discovery of emergent morphologies in directed self-assembly of block copolymer blends

The directed self-assembly (DSA) of block copolymers (BCPs) is a powerful approach to fabricate complex nanostructure arrays, but finding morphologies that emerge with changes in polymer architecture, composition, or assembly constraints remains daunting because of the increased dimensionality of the DSA design space. Here, we demonstrate machine-guided discovery of emergent morphologies from a cylinder/lamellae BCP blend directed by a chemical grating template, conducted without direct human intervention on a synchrotron x-ray scattering beamline. This approach maps the morphology-template phase space in a fraction of the time required by manual characterization and highlights regions deserving more detailed investigation. These studies reveal localized, template-directed partitioning of coexisting lamella- and cylinder-like subdomains at the template period length scale, manifesting as previously unknown morphologies such as aligned alternating subdomains, bilayers, or a "ladder" morphology. This work underscores the pivotal role that autonomous characterization can play in advancing the paradigm of DSA.

Priming self-assembly pathways by stacking block copolymers

Block copolymers spontaneously self-assemble into well-defined nanoscale morphologies. Yet equilibrium assembly gives rise to a limited set of structures. Non-equilibrium strategies can, in principle, expand diversity by exploiting self-assembly's responsive nature. In this vein, we developed a pathway priming strategy combining control of thin film initial configurations and ordering history. We sequentially coat distinct materials to form prescribed initial states, and use thermal annealing to evolve these manifestly non-equilibrium states through the assembly landscape, traversing normally inaccessible transient structures. We explore the enormous associated hyperspace, spanning processing (annealing temperature and time), material (composition and molecular weight), and layering (thickness and order) dimensions. We demonstrate a library of exotic non-native morphologies, including vertically-oriented perforated lamellae, aqueduct structures (vertical lamellar walls with substrate-pinned perforations), parapets (crenellated lamellae), and networks of crisscrossing lamellae. This enhanced structural control can be used to modify functional properties, including accessing regimes that surpass their equilibrium analogs.

Chain Redistribution Stabilizes Coexistence Phases in Block Copolymer Blends

The nanoscale morphologies of block copolymer (BCP) thin films are determined by chain architecture. Experimental studies of thin film blends of different BCP chain types have demonstrated that blending can stabilize new motifs, such as coexistence phases. Here, we deploy coarse-grained molecular dynamics (MD) simulations in order to better understand the self-assembly behavior of BCP blend thin films. We consider blends of lamella- and cylinder-forming BCP chains, studying their morphological makeup, the chain distribution within the morphology, and the underlying polymer chain conformations. Our simulations show that there are local concentration deviations at the scale of the morphological objects that dictate the local structure, and that BCP chains redistribute within the morphology so as to stabilize the structure. Underlying these effects are measurable distortions in the BCP chain conformations. The conformational freedom afforded by BCP blending stabilizes defects and allows coexistence phases to appear, while also leading to kinetic trapping effects. These results highlight the power of blending in designing the morphology that forms.

Molecular Simulations of Laser Spike Annealing of Block Copolymer Lamellar Thin-Films

We use molecular dynamics simulations to study the phase behavior of a coarse-grained lamella-forming A-b-B diblock copolymer under thin-film soft confinement for different heating cycle lengths, film thicknesses, and substrate-polymer affinities. This model describes the effect on thin-film morphology with a free surface (air-polymer interface) and a solid substrate. Our simulation results were first validated by showing that they capture changes for the order-disorder transition temperature with annealing conditions consistent with those found in laser spike annealing experiments, when the vertical lamella phase formed on neutral substrates. In addition, simulations with a substrate selective for a particular block revealed the formation of other phases, including a mixed vertical-horizontal lamella and a metastable island phase having horizontal but incomplete lamella layers. The nanoscale roughness features of this island phase, and hence its surface wettability, can be tuned with suitable choices of chemistry and annealing conditions.

Pathway-engineering for highly-aligned block copolymer arrays

While the ultimate driving force in self-assembly is energy minimization and the corresponding evolution towards equilibrium, kinetic effects can also play a very strong role. These kinetic effects, such as trapping in metastable states, slow coarsening kinetics, and pathway-dependent assembly, are often viewed as complications to be overcome. Here, we instead exploit these effects to engineer a desired final nano-structure in a block copolymer thin film, by selecting a particular ordering pathway through the self-assembly energy landscape. In particular, we combine photothermal shearing with high-temperature annealing to yield hexagonal arrays of block copolymer cylinders that are aligned in a single prescribed direction over macroscopic sample dimensions. Photothermal shearing is first used to generate a highly-aligned horizontal cylinder state, with subsequent thermal processing used to reorient the morphology to the vertical cylinder state in a templated manner. Finally, we demonstrate the successful transfer of engineered morphologies into inorganic replicas.

Through-Thickness Vertically Ordered Lamellar Block Copolymer Thin Films on Unmodified Quartz with Cold Zone Annealing

Template-free directed self-assembly of ultrathin (approximately tens of nanometers) lamellar block copolymer (l-BCP) films into vertically oriented nanodomains holds much technological relevance for the fabrication of next-generation devices from nanoelectronics to nanomembranes due to domain interconnectivity and high interfacial area. We report for the first time the formation of full through-thickness vertically oriented lamellar domains in 100 nm thin polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) films on quartz substrate, achieved without any PMMA-block wetting layer formation, quartz surface modification (templating chemical, topographical) or system modifications (added surfactant, top-layer coat). Vertical ordering of l-BCPs results from the coupling between a molecular and a macroscopic phenomenon. A molecular relaxation induced vertical l-BCP ordering occurs under a transient macroscopic vertical strain field, imposed by a high film thermal expansion rate under sharp thermal gradient cold zone annealing (CZA-S). The parametric window for vertical ordering is quantified via a coupling constant, C (= v∇T), whose range is established in terms of a thermal gradient (∇T) above a threshold value, and an optimal dynamic sample sweep rate (v ∼ d/τ), where τ is the l-BCP's longest molecular relaxation time and d is the T_g,heat - T_g,cool distance. Real-time CZA-S morphology evolution of vertically oriented l-BCP tracked along ∇T using in situ grazing incidence small angle X-ray scattering (GISAXS) exhibited an initial formation phase of vertical lamellae, a polygrain structure formation stage, and a grain coarsening phase to fully vertically ordered l-BCP morphology development. CZA-S is a roll-to-roll manufacturing method, rendering this template-free through-thickness vertical ordering of l-BCP films highly attractive and industrially relevant.

Thickness-dependence of block copolymer coarsening kinetics

Despite active research, many fundamental aspects of block copolymer ordering remain unresolved. We studied the thickness-dependence of block copolymer grain coarsening kinetics, and find that thinner films order more rapidly than thicker films. Bilayer films, or monolayers with partial layers of islands, order more slowly than monolayers because of the greater amount of material that must rearrange in a coordinated fashion. Sub-monolayer films order much more rapidly than monolayers, exhibiting considerably smaller activation energies, as well as larger exponents for the time-growth power-law. Using molecular dynamics simulations, we directly study the motion of defects in these film regimes. We attribute the enhanced grain growth in sub-monolayers to the film boundaries, where defects can be spontaneously eliminated. The boundaries thus act as efficient sinks for morphological defects, pointing towards methods for engineering rapid ordering of self-assembling thin films.

Non-native three-dimensional block copolymer morphologies

Self-assembly is a powerful paradigm, wherein molecules spontaneously form ordered phases exhibiting well-defined nanoscale periodicity and shapes. However, the inherent energy-minimization aspect of self-assembly yields a very limited set of morphologies, such as lamellae or hexagonally packed cylinders. Here, we show how soft self-assembling materials-block copolymer thin films-can be manipulated to form a diverse library of previously unreported morphologies. In this iterative assembly process, each polymer layer acts as both a structural component of the final morphology and a template for directing the order of subsequent layers. Specifically, block copolymer films are immobilized on surfaces, and template successive layers through subtle surface topography. This strategy generates an enormous variety of three-dimensional morphologies that are absent in the native block copolymer phase diagram.

Rapid ordering of block copolymer thin films

Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.

Reordering transitions during annealing of block copolymer cylinder phases

While equilibrium block-copolymer morphologies are dictated by energy-minimization effects, the semi-ordered states observed experimentally often depend on the details of ordering pathways and kinetics. Here, we explore reordering transitions in thin films of block-copolymer cylinder-forming polystyrene-block-poly(methyl methacrylate). We observe several transient states as films order towards horizontally-aligned cylinders. In particular, there is an early-stage reorganization from randomly-packed cylinders into hexagonally-packed vertically-aligned cylinders; followed by a reorientation transition from vertical to horizontal cylinder states. These transitions are thermally activated. The growth of horizontal grains within an otherwise vertical morphology proceeds anisotropically, resulting in anisotropic grains in the final horizontal state. The size, shape, and anisotropy of grains are influenced by ordering history; for instance, faster heating rates reduce grain anisotropy. These results help elucidate aspects of pathway-dependent ordering in block-copolymer thin films.

Latent Alignment in Pathway-Dependent Ordering of Block Copolymer Thin Films

Block copolymers spontaneously form well-defined nanoscale morphologies during thermal annealing. Yet, the structures one obtains can be influenced by nonequilibrium effects, including processing history or pathway-dependent assembly. Here, we explore various pathways for ordering of block copolymer thin films, using oven-annealing, as well as newly disclosed methods for rapid photothermal annealing and photothermal shearing. We report the discovery of an efficient pathway for ordering self-assembled films: ultrarapid shearing of as-cast films induces "latent alignment" in the disordered morphology. Subsequent thermal processing can then develop this directly into a uniaxially aligned morphology with low defect density. This deeper understanding of pathway-dependence may have broad implications in self-assembly.

Thermally-induced transition of lamellae orientation in block-copolymer films on 'neutral' nanoparticle-coated substrates

Block-copolymer orientation in thin films is controlled by the complex balance between interfacial free energies, including the inter-block segregation strength, the surface tensions of the blocks, and the relative substrate interactions. While block-copolymer lamellae orient horizontally when there is any preferential affinity of one block for the substrate, we recently described how nanoparticle-roughened substrates can be used to modify substrate interactions. We demonstrate how such 'neutral' substrates can be combined with control of annealing temperature to generate vertical lamellae orientations throughout a sample, at all thicknesses. We observe an orientational transition from vertical to horizontal lamellae upon heating, as confirmed using a combination of atomic force microscopy (AFM), neutron reflectometry (NR) and rotational small-angle neutron scattering (RSANS). Using molecular dynamics (MD) simulations, we identify substrate-localized distortions to the lamellar morphology as the physical basis of the novel behavior. In particular, under strong segregation conditions, bending of horizontal lamellae induce a large energetic cost. At higher temperatures, the energetic cost of conformal deformations of lamellae over the rough substrate is reduced, returning lamellae to the typical horizontal orientation. Thus, we find that both surface interactions and temperature play a crucial role in dictating block-copolymer lamellae orientation. Our combined experimental and simulation findings suggest that controlling substrate roughness should provide a useful and robust platform for controlling block-copolymer orientation in applications of these materials.

Millisecond Ordering of Block Copolymer Films via Photothermal Gradients

For the promise of self-assembly to be realized, processing techniques must be developed that simultaneously enable control of the nanoscale morphology, rapid assembly, and, ideally, the ability to pattern the nanostructure. Here, we demonstrate how photothermal gradients can be used to control the ordering of block copolymer thin films. Highly localized laser heating leads to intense thermal gradients, which induce a thermophoretic force on morphological defects. This increases the ordering kinetics by at least 3 orders of magnitude compared to conventional oven annealing. By simultaneously exploiting the thermal gradients to induce shear fields, we demonstrate uniaxial alignment of a block copolymer film in less than a second. Finally, we provide examples of how control of the incident light field can be used to generate prescribed configurations of block copolymer nanoscale patterns.

Prediction and validation of diffusion coefficients in a model drug delivery system using microsecond atomistic molecular dynamics simulation and vapour sorption analysis

Diffusion of small to medium sized molecules in polymeric medical device materials underlies a broad range of public health concerns related to unintended leaching from or uptake into implantable medical devices. However, obtaining accurate diffusion coefficients for such systems at physiological temperature represents a formidable challenge, both experimentally and computationally. While molecular dynamics simulation has been used to accurately predict the diffusion coefficients, D, of a handful of gases in various polymers, this success has not been extended to molecules larger than gases, e.g., condensable vapours, liquids, and drugs. We present atomistic molecular dynamics simulation predictions of diffusion in a model drug eluting system that represent a dramatic improvement in accuracy compared to previous simulation predictions for comparable systems. We find that, for simulations of insufficient duration, sub-diffusive dynamics can lead to dramatic over-prediction of D. We present useful metrics for monitoring the extent of sub-diffusive dynamics and explore how these metrics correlate to error in D. We also identify a relationship between diffusion and fast dynamics in our system, which may serve as a means to more rapidly predict diffusion in slowly diffusing systems. Our work provides important precedent and essential insights for utilizing atomistic molecular dynamics simulations to predict diffusion coefficients of small to medium sized molecules in condensed soft matter systems.

Selenophene-thiophene block copolymer solar cells with thermostable nanostructures

The nanostructure morphology and electron donor performance of a poly(3-hexylselenophene)-block-poly(3-hexylthiophene) (P3HS-b-P3HT) copolymer was studied in a photovoltaic device with a [6,6]-phenyl C61 butyric acid methyl ester (PCBM) acceptor. P3HS-b-P3HT forms fiberlike nanostructures spontaneously, which leads to an initial optimal device performance. Furthermore the nanostructure morphology is not greatly affected by annealing, which leads to a device stability that outperforms P3HT, P3HS, or a P3HS/P3HT mixture under identical conditions. External quantum efficiency, hole mobility, and current-voltage measurements show that the block copolymer also outperforms a ternary blend that consists of a physical mixture of P3HS, P3HT, and PCBM with the same overall composition. Overall, the observation of optimal device performance and morphology without annealing as well as enhanced thermal stability demonstrates the advantage of fully conjugated diblock copolymers in nanostructured devices.