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

Directing the self-assembly of block copolymers into a metastable complex network phase via a deep and rapid quench

The free-energy landscape of self-assembling block copolymer systems is characterized by a multitude of metastable minima. Using particle-based simulations of a soft, coarse-grained model, we explore opportunities to reproducibly direct the spontaneous ordering of these self-assembling systems into a metastable complex network morphology--specifically, Schoen's I-WP periodic minimal surface--starting from a highly unstable state that is generated by a rapid expansion. This process-directed self-assembly provides an alternative to fine-tuning molecular architecture or blending for fabricating complex network structures. Comparing our particle-based simulation results to recently developed free-energy techniques, we critically assess their ability to predict spontaneous formation and highlight the importance of nonequilibrium molecular conformations in the starting state and the local conservation of density.

Stretching tethered polymer chains: density functional approach

We propose application of density functional theory to calculate the force acting on a selected segment of a tethered polymer chain that leads to stretching the chain. The density functional allows one to determine the effects due to the presence of other chains and solvent molecules. For high and moderate solvent densities the plot of the force versus the distance of the segment from the surface exhibits oscillatory behavior that has not been predicted by other approaches.

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.

Molecular transport and flow past hard and soft surfaces: computer simulation of model systems

The equilibrium and flow of polymer films and drops past a surface are characterized by the interface and surface tensions, viscosity, slip length and hydrodynamic boundary position. These parameters of the continuum description are extracted from molecular simulations of coarse-grained models. Hard, corrugated substrates are modelled by a Lennard-Jones solid while polymer brushes are studied as prototypes of soft, deformable surfaces. Four observations are discussed. (i) If the surface becomes strongly attractive or is coated with a brush, the Navier boundary condition fails to describe the effect of the surface independently of the strength and type of the flow. This failure stems from the formation of a boundary layer with an effective, higher viscosity. (ii) In the case of brush-coated surfaces, flow induces a cyclic, tumbling motion of the tethered chain molecules. Their collective motion gives rise to an inversion of the flow in the vicinity of the grafting surfaces and leads to strong, non-Gaussian fluctuations of the molecular orientations. The flow past a polymer brush cannot be described by Brinkman's equation. (iii) The hydrodynamic boundary condition is an important parameter for predicting the motion of polymer droplets on a surface under the influence of an external force. Their steady-state velocity is dictated by a balance between the power that is provided by the external force and the dissipation. If there is slippage at the liquid-solid interface, the friction at the solid-liquid interface and the viscous dissipation of the flow inside the drop will be the dominant dissipation mechanisms; dissipation at the three-phase contact line appears to be less important on a hard surface. (iv) On a soft, deformable substrate like a polymer brush, we observe a lifting-up of the three-phase contact line. Controlling the grafting density and the incompatibility between the brush and the polymer liquid we can independently tune the softness of the surface and the contact angle and thereby identify the parameters for maximizing the deformation at the three-phase contact.

Memory effects of diblock copolymer brushes and mixed brushes

Memory effects of microphase segregation in diblock copolymer brushes and binary mixed homopolymer brushes exposed to solvents of different quality and selectivity are studied using Single-Chain-in-Mean-Field (SCMF) simulations. We gauge these memory effects by a fluctuation memory measure, reflecting the correlation between the quenched fluctuations of grafting points and the microphase-separated morphology, and a domain memory measure, quantifying the correlation between surface morphologies during cyclic exposure to different solvents. The fluctuation and domain memory measures are closely correlated, and both of them have their root in the broken translational symmetry of the distribution of grafting points. They become stronger upon increasing the fluctuations of the grafting points. The effects of solvent quality and selectivity, grafting density, and composition of brushes on the memory measures are discussed.

Directed self-assembly of block copolymers for nanolithography: fabrication of isolated features and essential integrated circuit geometries

Self-assembling block copolymers are of interest for nanomanufacturing due to the ability to realize sub-100 nm dimensions, thermodynamic control over the size and uniformity and density of features, and inexpensive processing. The insertion point of these materials in the production of integrated circuits, however, is often conceptualized in the short term for niche applications using the dense periodic arrays of spots or lines that characterize bulk block copolymer morphologies, or in the long term for device layouts completely redesigned into periodic arrays. Here we show that the domain structure of block copolymers in thin films can be directed to assemble into nearly the complete set of essential dense and isolated patterns as currently defined by the semiconductor industry. These results suggest that block copolymer materials, with their intrinsically advantageous self-assembling properties, may be amenable for broad application in advanced lithography, including device layouts used in existing nanomanufacturing processes.

Memory of surface patterns in mixed polymer brushes: simulation and experiment

The correlation between the morphology of mixed polymer brushes and fluctuations of the grafting points is investigated by single-chain-in-mean-field simulations and experiments. The local topography of two types of mixed polystyrene-polymethylmethacrylate (PS-PMMA) brushes that differ in their modes of attachment has been studied during repeated microphase separation into laterally structured and homogeneous morphologies upon changing solvents. In the first type of brush (conventional), each of the surface-attached initiator groups starts the growth of either a PS or a PMMA chain in a random fashion. In the second case (Y-shaped mixed brushes), two chains of different types are attached to the same anchor group on the substrate. Whereas in the first case statistical fluctuations of the chemical composition occur on a local scale, such composition fluctuations are strongly suppressed in the latter case. The microphase-separated morphology is similar in both cases, but Y-shaped brushes exhibit a significantly weaker domain memory than do conventional PS-PMMA mixed brushes. The results of the experiment are compared with simulations, and a simple phenomenological argument and qualitative agreement are found. The observations demonstrate that small fluctuations in the grafting points are amplified by the microphase separation and nucleate the location of the domains in the mixed brush.

Single chain in mean field simulations: Quasi-instantaneous field approximation and quantitative comparison with Monte Carlo simulations

The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. In SCMF simulations one studies a large ensemble of noninteracting molecules subjected to real, external fields by Monte Carlo simulations. The external fields approximate nonbonded, instantaneous interactions between molecules. In the self-consistent mean field theory the external fields are static and fluctuation effects are ignored. In SCMF simulations, the external fields fluctuate since they are frequently recalculated from the instantaneous density distribution of the ensemble of molecules. In the limit of infinitely high density or instantaneous update of the external fields, the SCMF simulation method accurately describes long-wavelength fluctuations. At high but finite updating frequency the accuracy depends on the discretization of the model. The accuracy is illustrated by studying the single chain structure and intermolecular correlations in polymer melts, and fluctuation effects on the order-disorder transition of symmetric diblock copolymers.