Morphology of multi-component polymer systems: single chain in mean field simulation studies

On the equivalence of the hybrid particle-field and Gaussian core models

Hybrid particle-field molecular dynamics is a molecular simulation strategy, wherein particles couple to a density field instead of through ordinary pair potentials. Traditionally considered a mean-field theory, a momentum and energy-conserving hybrid particle-field formalism has recently been introduced, which was demonstrated to approach the Gaussian Core model potential in the grid-converged limit. Here, we expand on and generalize the correspondence between the Hamiltonian hybrid particle-field method and particle-particle pair potentials. Using the spectral procedure suggested by Bore and Cascella, we establish compatibility to any local soft pair potential in the limit of infinitesimal grid spacing. Furthermore, we document how the mean-field regime often observed in hybrid particle-field simulations is due to the systems under consideration, and not an inherent property of the model. Considering the Gaussian filter form, in particular, we demonstrate the ability of the Hamiltonian hybrid particle-field model to recover all structural and dynamical properties of the Gaussian Core model, including solid phases, a first-order phase transition, and anomalous transport properties. We quantify the impact of the grid spacing on the correspondence, as well as the effect of the particle-field filtering length scale on the emergent particle-particle correlations.

HylleraasMD: A Domain Decomposition-Based Hybrid Particle-Field Software for Multiscale Simulations of Soft Matter

We present HylleraasMD (HyMD), a comprehensive implementation of the recently proposed Hamiltonian formulation of hybrid particle-field molecular dynamics. The methodology is based on a tunable, grid-independent length-scale of coarse graining, obtained by filtering particle densities in reciprocal space. This enables systematic convergence of energies and forces by grid refinement, also eliminating nonphysical force aliasing. Separating the time integration of fast modes associated with internal molecular motion from slow modes associated with their density fields, we enable the first time-reversible, energy-conserving hybrid particle-field simulations. HyMD comprises the optional use of explicit electrostatics, which, in this formalism, corresponds to the long-range potential in particle-mesh Ewald. We demonstrate the ability of HyMD to perform simulations in the microcanonical and canonical ensembles with a series of test cases, comprising lipid bilayers and vesicles, surfactant micelles, and polypeptide chains, comparing our results to established literature. An on-the-fly increase of the characteristic coarse-grain length significantly speeds up dynamics, accelerating self-diffusion and leading to expedited aggregation. Exploiting this acceleration, we find that the time scales involved in the self-assembly of polymeric structures can lie in the tens to hundreds of picoseconds instead of the multimicrosecond regime observed with comparable coarse-grained models.

Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations

We discuss the functional inverse problem in field-theoretic simulations for realistic pairwise potentials such as the Morse potential (widely used in particle simulations as an alternative to the 12-6 Lennard-Jones one), and we propose the following two solutions: (a) a numerical one based on direct inversion on a regular grid or deconvolution and (b) an analytical one by expressing attractive and repulsive contributions to the Morse potential as higher-order derivatives of the Dirac delta function; the resulting system of ordinary differential equations in the saddle-point approximation is solved numerically with appropriate model-consistent boundary conditions using a Newton-Raphson method. For the first time, exponential-like, physically realistic pair interactions are analytically treated and incorporated into a field-theoretic framework. The advantages and disadvantages of the two approaches are discussed in detail in connection with numerical findings from test simulations for the radial distribution function of a monatomic fluid at realistic densities providing direct evidence for the capability of the analytical method to resolve structural features down to the Angstrom scale.

Self-Aligned Assembly of a Poly(2-vinylpyridine)-b-Polystyrene-b-Poly(2-vinylpyridine) Triblock Copolymer on Graphene Nanoribbons

Directed self-assembly (DSA) of block copolymers is one of the most promising patterning techniques for patterning sub-10 nm features. However, at such small feature sizes, it is becoming increasingly difficult to fabricate the guiding pattern for the DSA process, and it is necessary to explore alternative guiding methods for DSA to achieve long-range ordered alignment. Here, we report the self-aligned assembly of a triblock copolymer, poly(2-vinylpyridine)-b-polystyrene-b-poly(2-vinylpyridine) (P2VP-b-PS-b-P2VP) on neutral graphene nanoribbons with the gap consisting of a P2VP-preferential silicon oxide (SiO₂) substrate via solvent vapor annealing. The assembled P2VP-b-PS-b-P2VP demonstrated long-range, one-dimensional alignment on the graphene substrate in a direction perpendicular to the boundary of the graphene and substrate with a half-pitch size of 8 nm, which greatly alleviates the lithography resolution required for traditional chemoepitaxy DSA. A wide processing window is demonstrated with the gap between graphene stripes varying from 10 to 100 nm, overcoming the restriction on widths of guiding patterns to have commensurate domain spacing. When the gap was reduced to 10 nm, P2VP-b-PS-b-P2VP formed a straight-line pattern on both the graphene and the substrate. Monte Carlo simulations showed that the self-aligned assembly of the triblock copolymer on the graphene nanoribbons is guided at the boundary of parallel and perpendicular lamellae on graphene and SiO₂, respectively. Simulations also indicate that the swelling of a system allows for rapid rearrangement of chains and quickly anneal any misaligned grains and defects. The effect of the interaction strength between SiO₂ and P2VP on the self-assembly is systematically investigated in simulations.

Multicore Assemblies from Three-Component Linear Homo-Copolymer Systems: A Coarse-Grained Modeling Study

Multicore polymer micelles and aggregates are assemblies that contain several cores. The dual-length-scale compartmentalized solvophobic–solvophilic molecular environment makes them useful for, e.g., advanced drug delivery, high-precision synthesis platforms, confined catalysis, and sensor device applications. However, designing and regulating polymer systems that self-assemble to such morphologies remains a challenge. Using dissipative particle dynamics (DPD) simulations, we demonstrate how simple, three-component linear polymer systems consisting of free solvophilic and solvophobic homopolymers, and di-block copolymers, can self-assemble in solution to form well-defined multicore assemblies. We examine the polymer property range over which multicore assemblies can be expected and how the assemblies can be tuned both in terms of their morphology and structure. For a fixed degree of polymerization, a certain level of hydrophobicity is required for the solvophobic component to lead to formation of multicore assemblies. Additionally, the transition from single-core to multicore requires a relatively high solvophobicity difference between the solvophilic and solvophobic polymer components. Furthermore, if the solvophilic polymer is replaced by a solvophobic species, well-defined multicore–multicompartment aggregates can be obtained. The findings provide guidelines for multicore assemblies’ formation from simple three-component systems and how to control polymer particle morphology and structure.

Efficient and realistic simulation of phase coexistence

We show how an existing concurrent multi-scale method named hybrid particle field-molecular dynamics (hPF-MD) can be adapted to enable the simulation of structure and/or structural dynamics in compressible systems. Implementing such new equations of state (EOS) into hPF-MD, while conserving the efficiency associated with treating intermolecular interactions in a continuum fashion, opens this method up to describe a new class of phenomena in which non-uniform densities play a role, for example, evaporation and crystallization. We carefully consider how compressible hPF-MD compares to its mean-field counterpart for two particular EOS, adopted from the Cell Model for polymers and the Carnahan-Starling expression for hard spheres. Here, we performed a very basic analysis for a single-component system, focusing on the significance of various particle-based parameters and the particle-to-field projection. Our results illustrate the key role of the particle density per field grid cell and show that projection based on a Gaussian kernel is preferred over the standard cloud-in-cell projection. They also suggest that the behavior of hPF-MD close to the critical point is non-classical, i.e., in agreement with a critical exponent for a pure particle description, despite the mean-field origin of the method.

Single chain in mean field simulation of flexible and semiflexible polymers: comparison with discrete chain self-consistent field theory

Single chain in mean field (SCMF) simulation is a theoretical framework performing Monte Carlo moves of explicit polymer chains under quasi-instantaneously updated external fields which were originally imported from the self-consistent field theory (SCFT). Even though functional-based hybrid simulations are often used to compare the results of SCFT and MC simulation, the adoption of a finite number of coarse-grained segments makes direct comparison rather difficult. In this study, we perform SCMF simulation of block copolymers using various chain models and quantitatively compare it with discrete chain SCFT (DCSCFT) which finds the mean field solution of polymers with a finite number of segments. By comparing free energy and natural period of the symmetric block copolymer lamellar phase, we systematically show that DCSCFT serves as an intermediate step between SCMF simulation and SCFT. In addition, by adopting angle dependent bond potential, we perform SCMF simulation of semiflexible polymers using bead-spring and freely jointed chain models. As the chain stiffness increases, the lamellar phase tends to align perpendicular to the surfaces when confined between two neutral walls. We also investigate the effects of fluctuation and chain stiffness on the distribution of chain ends. The tendency of chain end segregation towards the surfaces turns out to increase as the chain stiffness increases for both homopolymer and block copolymer systems.

A phase-field model for the evaporation of thin film mixtures

The performance of solution-processed solar cells strongly depends on the geometrical structure and roughness of the photovoltaic layers formed during film drying. During the drying process, the interplay of crystallization and liquid-liquid demixing leads to structure formation on the nano- and microscale and to the final rough film. In order to better understand how the film structure can be improved by process engineering, we aim at theoretically investigating these systems by means of phase-field simulations. We introduce an evaporation model based on the Cahn-Hilliard equation for the evolution of the fluid concentrations coupled to the Allen-Cahn equation for the liquid-vapour phase transformation. We demonstrate its ability to match the experimentally measured drying kinetics and study the impact of the parameters of our model. Furthermore, the evaporation of solvent blends and solvent-vapour annealing are investigated. The dry film roughness emerges naturally from our set of equations, as illustrated through preliminary simulations of spinodal decomposition and film drying on structured substrates.

100th Anniversary of Macromolecular Science Viewpoint: Opportunities in the Physics of Sequence-Defined Polymers

Polymer science has been driven by ever-increasing molecular complexity, as polymer synthesis expands an already-vast palette of chemical and architectural parameter space. Copolymers represent a key example, where simple homopolymers have given rise to random, alternating, gradient, and block copolymers. Polymer physics has provided the insight needed to explore this monomer sequence parameter space. The future of polymer science, however, must contend with further increases in monomer precision, as this class of macromolecules moves ever closer to the sequence-monodisperse polymers that are the workhorses of biology. The advent of sequence-defined polymers gives rise to opportunities for material design, with increasing levels of chemical information being incorporated into long-chain molecules; however, this also raises questions that polymer physics must address. What properties uniquely emerge from sequence-definition? Is this circumstance-dependent? How do we define and think about sequence dispersity? How do we think about a hierarchy of sequence effects? Are more sophisticated characterization methods, as well as theoretical and computational tools, needed to understand this class of macromolecules? The answers to these questions touch on many difficult scientific challenges, setting the stage for a rich future for sequence-defined polymers in polymer physics.

Numerical implementation of pseudo-spectral method in self-consistent mean field theory for discrete polymer chains

In the standard self-consistent field theory (SCFT), a polymer chain is modeled as an infinitely flexible Gaussian chain, and the partition function is calculated by solving a differential equation in the form of a modified diffusion equation. The Gaussian chain assumption makes the standard SCFT inappropriate for modeling of short polymers, and the discrete chain SCFT in which the partition function is obtained through recursive integrals has recently been suggested as an alternative method. However, the shape of the partition function integral makes this method much slower than the standard SCFT when calculated in the real space. In this paper, we implement the pseudospectral method for the discrete chain SCFT adopting the bead-spring or freely jointed chain (FJC) model, and a few issues such as the accurate discretization of the FJC bond function are settled in this process. With the adoption of the pseudospectral method, our calculation becomes as fast as that of the standard SCFT. The integral equation introduces a new boundary condition, the neutral boundary, which is not available in the standard SCFT solving the differential equation. This interesting physical situation is combined with the finite-range interaction model for the study of symmetric block copolymers within thin films. We find that the surface-perpendicular block copolymer lamellar phase becomes preferable to the surface-parallel one when both the top and bottom surfaces are neutral.

Phase diagram for two-dimensional layer of soft particles

The phase diagram of a monolayer of soft particles described by the Daoud-Cotton model for star polymers is presented. Ground state calculations and grand canonical Monte Carlo simulations are used to determine the phase behavior as a function of the number of arms on the star and the areal coverage of the soft particles. The phase diagram exhibits rich behavior including reentrant melting and freezing and solid-solid transitions with triangular, stripe, honeycomb and kagome phases. These structures in 2D are analogous to the structures observed in 3D. The evolution of the structure factor with density is qualitatively similar to that measured in experiments for polymer grafted nanocrystals [Chen et al., Macromolecules, 2017, 50, 9636].

Role of Penetrability into a Brush-Coated Surface in Directed Self-Assembly of Block Copolymers

High-density and high-resolution line and space patterns on surfaces are obtained by directed self-assembly of lamella-forming block copolymers (BCPs) using wide-stripe chemical guiding patterns. When the width of the chemical pattern is larger than the half-pitch of the BCP, the interaction energy between each BCP domain and the surface is crucial to obtain the desired segregated film morphology. We investigate how the intermixing between BCPs and polymer brush molecules on the surface influences the optimal surface and interface free energies to obtain a proper BCP alignment. We have found that computational models successfully predict the experimentally obtained guided patterns if the penetrability of the brush layer is taken into account instead of a hard, impenetrable surface. Experiments on directed self-assembly of lamella-forming poly(styrene- block-methyl methacrylate) using chemical guiding patterns corroborate the models used in the simulations, where the values of the surface free energy between the BCP and the guiding and background stripes are accurately determined using an experimental method based on the characterization of contact angles in droplets formed after dewetting of homopolymer blends.

Influence of topographically patterned angled guidelines on directed self-assembly of block copolymers

Single chain in mean-field Monte Carlo simulations were employed to study the self-assembly of block copolymers (BCP) in thin films that use trapezoidal guidelines to direct the orientation and alignment of lamellar patterns. The present study explored the influence of sidewall interactions and geometry of the trapezoidal guidelines on the self-assembly of perpendicularly oriented lamellar morphologies. When both the sidewall and the top surface exhibit preferential interactions to the same block of the BCP, trapezoidal guidelines with intermediate taper angles were found to result in less defective perpendicularly orientated morphologies. Similarly, when the sidewall and top surface are preferential to distinct blocks of the BCP, intermediate tapering angles were found to be optimal in promoting defect free structures. Such results are rationalized based on the energetics arising in the formation of perpendicularly oriented lamella on patterned substrates.

Ion transport mechanisms in lamellar phases of salt-doped PS-PEO block copolymer electrolytes

We use a multiscale simulation strategy to elucidate, at an atomistic level, the mechanisms underlying ion transport in the lamellar phase of polystyrene-polyethylene oxide (PS-PEO) block copolymer (BCP) electrolytes doped with LiPF₆ salts. Explicitly, we compare the results obtained for ion transport in the microphase separated block copolymer melts to those for salt-doped PEO homopolymer melts. In addition, we also present results for dynamics of the ions individually in the PEO and PS domains of the BCP melt, and locally as a function of the distance from the lamellar interfaces. When compared to the PEO homopolymer melt, ions were found to exhibit slower dynamics in both the block copolymer (overall) and in the PEO phase of the BCP melt. Such results are shown to arise from the effects of slower polymer segmental dynamics in the BCP melt and the coordination characteristics of the ions. Polymer backbone-ion residence times analyzed as a function of distance from the interface indicate that ions have a larger residence time near the interface compared to that near the bulk of lamella, and demonstrates the influence of the glassy PS blocks and microphase segregation on the ion transport properties. Ion transport mechanisms in BCP melts reveal that there exist five distinct mechanisms for ion transport along the backbone of the chain and exhibit qualitative differences from the behavior in homopolymer melts. We also present results as a function of salt concentration which show that the mean-squared displacements of the ions decrease with increasing salt concentration, and that the ion residence times near the polymer backbone increase with increasing salt concentration.

Combining cell-based hydrodynamics with hybrid particle-field simulations: efficient and realistic simulation of structuring dynamics

We have extended an existing hybrid MD-SCF simulation technique that employs a coarsening step to enhance the computational efficiency of evaluating non-bonded particle interactions. This technique is conceptually equivalent to the single chain in mean-field (SCMF) method in polymer physics, in the sense that non-bonded interactions are derived from the non-ideal chemical potential in self-consistent field (SCF) theory, after a particle-to-field projection. In contrast to SCMF, however, MD-SCF evolves particle coordinates by the usual Newton's equation of motion. Since collisions are seriously affected by the softening of non-bonded interactions that originates from their evaluation at the coarser continuum level, we have devised a way to reinsert the effect of collisions on the structural evolution. Merging MD-SCF with multi-particle collision dynamics (MPCD), we mimic particle collisions at the level of computational cells and at the same time properly account for the momentum transfer that is important for a realistic system evolution. The resulting hybrid MD-SCF/MPCD method was validated for a particular coarse-grained model of phospholipids in aqueous solution, against reference full-particle simulations and the original MD-SCF model. We additionally implemented and tested an alternative and more isotropic finite difference gradient. Our results show that efficiency is improved by merging MD-SCF with MPCD, as properly accounting for hydrodynamic interactions considerably speeds up the phase separation dynamics, with negligible additional computational costs compared to efficient MD-SCF. This new method enables realistic simulations of large-scale systems that are needed to investigate the applications of self-assembled structures of lipids in nanotechnologies.

Process-Accessible States of Block Copolymers

Process-directed self-assembly of block copolymers refers to thermodynamic processes that reproducibly direct the kinetics of structure formation from a starting, unstable state into a selected, metastable mesostructure. We investigate the kinetics of self-assembly of linear ACB triblock copolymers after a rapid transformation of the middle C block from B to A. This prototypical process (e.g., photochemical transformation) converts the initial, equilibrium mesophase of the ABB copolymer into a well-defined but unstable, starting state of the AAB copolymer. The spontaneous structure formation that ensues from this unstable state becomes trapped in a metastable mesostructure, and we systematically explore which metastable mesostructures can be fabricated by varying the block copolymer composition of the initial and final states. In addition to the equilibrium mesophases of linear AB diblock copolymers, this diagram of process-accessible states includes 7 metastable periodic mesostructures, inter alia, Schoen's F-RD periodic minimal surface. Generally, we observe that the final, metastable mesostructure of the AAB copolymer possesses the same symmetry as the initial, equilibrium mesophase of the ABB copolymer.

Ordering block copolymers with structured electrodes

We study the kinetics of alignment and registration of block copolymers in an inhomogeneous electric field by computer simulations of a soft, coarse-grained model. The two blocks of the symmetric diblock copolymers are characterized by different dielectric constants. First, we demonstrate that a combination of graphoepitaxy and a homogeneous electric field extends the maximal distance between the topographical guiding patterns that result in defect-free ordering compared to graphoepitaxy alone. In a second study, the electric field in the thin block copolymer film is fabricated by spatially structured electrodes on an isolating substrate arranged in a one-dimensional periodic array; no additional topographical guiding patterns are applied. The dielectrophoretic effect induces long-range orientational order of the lamellae and, additionally, registers the lamellar structure with the electrodes due to the field inhomogeneities at the edges of the structured electrodes. Thus, orientational and translational order is established by the inhomogeneous electric field. The simulations identify a process protocol of time-dependent electric potentials that suppresses defect formation by initially forming a sandwich-like structure and subsequently reorienting these lying into standing lamellae that are registered with the structure of the electrodes. This process-directed self-assembly results in large defect-free arrays of aligned and registered lamellae using electrodes with a saw-tooth period of 4 lamellar periodicities, L₀, and a spacing of 10L₀.

Single-chain-in-mean-field simulations of weak polyelectrolyte brushes

Structural properties of brushes which are composed of weak acidic and basic polyelectrolytes are studied in the framework of a particle-based approach that implicitly accounts for the solvent quality. Using a semi-grandcanonical partition function in the framework of the Single-Chain-in-Mean-Field (SCMF) algorithm, the weak polyelectrolyte is conceived as a supramolecular mixture of polymers in different dissociation states, which are explicitly treated in the partition function and sampled by the SCMF procedure. One obtains a local expression for the equilibrium acid-base reaction responsible for the regulation of the charged groups that is also incorporated to the SCMF sampling. Coupled to a simultaneous treatment of the electrostatics, the approach is shown to capture the main features of weak polyelectrolyte brushes as a function of the bulk pH in the solution, the salt concentration, and the grafting density. Results are compared to experimental and theoretical works from the literature using coarse-grained representations of poly(acrylic acid) (PAA) and poly(2-vinyl pyridine) (P2VP) polymer-based brushes. As the Born self-energy of ions can be straightforwardly included in the numerical approach, we also study its effect on the local charge regulation mechanism of the brush. We find that its effect becomes significant when the brush is dense and exposed to high salt concentrations. The numerical methodology is then applied (1) to the study of the kinetics of collapse/swelling of a P2VP brush and (2) to the ability of an applied voltage to induce collapse/swelling of a PAA brush in a pH range close to the pK_a value of the polymer.

Hybrid particle–field molecular dynamics simulation for polyelectrolyte systems

An effective hybrid computer simulation method combining molecular dynamics and self-consistent field theory is developed by including electrostatic interactions.

Directed self assembly of block copolymers using chemical patterns with sidewall guiding lines, backfilled with random copolymer brushes

Recently, alignment of block copolymer domains has been achieved using a topographically patterned substrate with a sidewall preferential to one of the blocks. This strategy has been suggested as an option to overcome the patterning resolution challenges facing chemoepitaxy strategies, which utilize chemical stripes with a width of about half the period of block copolymer to orient the equilibrium morphologies. In this work, single chain in mean field simulation methodology was used to study the self assembly of symmetric block copolymers on topographically patterned substrates with sidewall interactions. Random copolymer brushes grafted to the background region (space between patterns) were modeled explicitly. The effects of changes in pattern width, film thicknesses and strength of sidewall interaction on the resulting morphologies were examined and the conditions which led to perpendicular morphologies required for lithographic applications were identified. A number of density multiplication schemes were studied in order to gauge the efficiency with which the sidewall pattern can guide the self assembly of block copolymers. The results indicate that such a patterning technique can potentially utilize pattern widths of the order of one-two times the period of block copolymer and still be able to guide ordering of the block copolymer domains up to 8X density multiplication.

Alignment of Copolymer Morphology by Planar Step Elongation during Spinodal Self-Assembly

Using simulation and numerical self-consistent field theory of an unentangled diblock copolymer melt, we study the interplay between relaxation of molecular conformations from a highly stretched, nonequilibrium state and structure formation of the local, conserved density during self-assembly from a disordered state. We observe that the planar elongation of molecular conformations in the initial, disordered state results in an alignment of lamella normals perpendicular to the stretch direction during the subsequent self-assembly. Although thermodynamically the parallel orientation is favored, the alignment of the lamella normal perpendicular to the stretch direction is characterized by the larger growth rate of composition fluctuations during the spinodal ordering process.

Poly(N-isopropylacrylamide)-Based Mixed Brushes: A Computer Simulation Study

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPAM) polymer brushes of fixed molecular weight and grafting density are modeled in the framework of a coarse-grained model with soft, nonbonded interactions and an implicit solvent. This model has been developed to address experimentally relevant, large invariant degrees of polymerization, and nonbonded interactions are expressed via a third-order (virial) expansion of the equation of state. The choice of interaction parameters is intended to mimic the swelling behavior of PNIPAM in water as the temperature increases toward the lower critical solution temperature (T(LCST)). Results of molecular dynamics simulations for one component brushes are compared to experimental data. Mixed brushes incorporating small and large amounts of grafted poly(ethylene glycol) polymers are then considered. The effects of mixing polymer components on the response of the mixed brushes to temperature changes are monitored, and the results are compared to experimental data. In the end, two design principles for biomolecule triggering using temperature-sensitive mixed polymer brushes with functional and switchable end-groups are proposed and studied. This work is in favor of establishing qualitative rules for the design, optimization, and comprehension of binary polymer brushes for bioengineering purposes.

Characterizing the Three-Dimensional Structure of Block Copolymers via Sequential Infiltration Synthesis and Scanning Transmission Electron Tomography

Understanding and controlling the three-dimensional structure of block copolymer (BCP) thin films is critical for utilizing these materials for sub-20 nm nanopatterning in semiconductor devices, as well as in membranes and solar cell applications. Combining an atomic layer deposition (ALD)-based technique for enhancing the contrast of BCPs in transmission electron microscopy (TEM) together with scanning TEM (STEM) tomography reveals and characterizes the three-dimensional structures of poly(styrene-block-methyl methacrylate) (PS-b-PMMA) thin films with great clarity. Sequential infiltration synthesis (SIS), a block-selective technique for growing inorganic materials in BCPs films in an ALD tool and an emerging technique for enhancing the etch contrast of BCPs, was harnessed to significantly enhance the high-angle scattering from the polar domains of BCP films in the TEM. The power of combining SIS and STEM tomography for three-dimensional (3D) characterization of BCP films was demonstrated with the following cases: self-assembled cylindrical, lamellar, and spherical PS-b-PMMA thin films. In all cases, STEM tomography has revealed 3D structures that were hidden underneath the surface, including (1) the 3D structure of defects in cylindrical and lamellar phases, (2) the nonperpendicular 3D surface of grain boundaries in the cylindrical phase, and (3) the 3D arrangement of spheres in body-centered-cubic (BCC) and hexagonal-closed-pack (HCP) morphologies in the spherical phase. The 3D data of the spherical morphologies was compared to coarse-grained simulations and assisted in validating the simulations' parameters. STEM tomography of SIS-treated BCP films enables the characterization of the exact structure used for pattern transfer and can lead to a better understating of the physics that is utilized in BCP lithography.

Process-directed self-assembly of block copolymers: a computer simulation study

The free-energy landscape of self-assembling block copolymer systems is characterized by a multitude of metastable minima and concomitant protracted relaxation times of the morphology. Tailoring rapid changes (quench) of thermodynamic conditions, one can reproducibly trap the ensuing kinetics of self-assembly in a specific metastable state. To this end, it is necessary to (1) control the generation of well-defined, highly unstable states and (2) design the unstable state such that the ensuing spontaneous kinetics of structure formation reaches the desired metastable morphology. This process-directed self-assembly provides an alternative to fine-tuning molecular architecture by synthesis or blending, for instance, in order to fabricate complex network structures. Comparing our simulation results to recently developed free-energy techniques, we highlight the importance of non-equilibrium molecular conformations in the starting state and motivate the significance of the local conservation of density.

Generation of Well-Relaxed All-Atom Models of Large Molecular Weight Polymer Melts: A Hybrid Particle-Continuum Approach Based on Particle-Field Molecular Dynamics Simulations

A procedure based on Molecular Dynamics (MD) simulations employing soft potentials derived from self-consistent field (SCF) theory (named MD-SCF) able to generate well-relaxed all-atom structures of polymer melts is proposed. All-atom structures having structural correlations indistinguishable from ones obtained by long MD relaxations have been obtained for poly(methyl methacrylate) (PMMA) and poly(ethylene oxide) (PEO) melts. The proposed procedure leads to computational costs mainly related on system size rather than to the chain length. Several advantages of the proposed procedure over current coarse-graining/reverse mapping strategies are apparent. No parametrization is needed to generate relaxed structures of different polymers at different scales or resolutions. There is no need for special algorithms or back-mapping schemes to change the resolution of the models. This characteristic makes the procedure general and its extension to other polymer architectures straightforward. A similar procedure can be easily extended to the generation of all-atom structures of block copolymer melts and polymer nanocomposites.

Thin films of homopolymers and cylinder-forming diblock copolymers under shear

We study thin films of homopolymers (PS) and monolayers of cylinder-forming diblock copolymers (PS–PHMA) under shear. To this end, we employed both experiments and computer simulations that correctly take into account hydrodynamic interactions and chain entanglements. Excellent quantitative agreement for static as well as dynamic properties in both the homopolymer and diblock copolymer cases was achieved. In particular, we found that the homopolymer thin films exhibit a distinct shear thinning behavior, which is strongly correlated with the disentanglement and shear alignment of the constituent polymer chains. For the PS–PHMA films, we show that shear can be employed to induce long-range ordering to the spontaneously self-assembled microdomains, which is required for many applications such as the fabrication of nanowire arrays. We found that the impact of chemical incompatibility on the viscosity is only minor in shear-aligned films. Once the domains were aligned, the films exhibited an almost Newtonian response to shear because the cylindrical microdomains acted as guide rails, along which the constituent copolymer chains could simply slide. Furthermore, we developed a model for predicting the onset of shear alignment based on equilibrium dynamics data, and found good agreement with our shear simulations. The employed computational method holds promise for a faster and more cost-effective route for developing custom tailored materials.