The osmotic virial formulation of the free energy of polymer mixing.

We derive an alternative formulation of the free energy of polymer mixing in terms of an osmotic virial expansion. Starting from a generalized free energy of mixing, and the assumption that the internal energy of mixing is analytic in the polymer composition variable, we demonstrate that the free energy of mixing can be represented as an infinite series in the osmotic virial coefficients. This osmotic virial formulation is consistent with, but more general than, a relationship derived for polymer blends with structured monomers by Dudowicz, Freed, and Douglas [J. Chem. Phys. 116, 9983 (2002)] and Douglas, Dudowicz, and Freed [J. Chem. Phys. 127, 224901 (2007)].

Assessing the Huang-Brown Description of Tie Chains for Charge Transport in Conjugated Polymers.

Intercrystallite molecular connections are widely recognized to tremendously impact the macroscopic properties of semicrystalline polymers. Because it is challenging to directly probe such connections, theoretical frameworks have been developed to quantify their concentrations and predict the mechanical properties that result from these connections. Tie-chain connectivity similarly impacts the electrical properties in semicrystalline conjugated polymers. Yet, its quantitative impact has eluded the community. Here, we assess the Huang-Brown model, a framework commonly used to describe the structural origins of mechanical properties in polyolefins, to quantitatively elucidate the effect of tie chains on the electrical properties of a model conjugated polymer. We found that a critical tie-chain fraction of 10-3 is needed to support macroscopic charge transport, below which intercrystallite connectivity limits charge transport, and above which intracrystallite disorder is the bottleneck. Extending the Huang-Brown framework to conjugated polymers enables the prediction of macroscopic electrical properties based on experimentally accessible morphological parameters. Our study implicates the importance of long and rigid polymer chains for efficient charge transport over device length scales.

Self-consistent field theory simulations of block copolymer assembly on a sphere.

Recently there has been a strong interest in the area of defect formation in ordered structures on curved surfaces. Here we explore the closely related topic of self-assembly in thin block copolymer melt films confined to the surface of a sphere. Our study is based on a self-consistent field theory (SCFT) model of block copolymers that is numerically simulated by spectral collocation with a spherical harmonic basis and an extension of the Rasmussen-Kalosakas operator splitting algorithm [J. Polym. Sci. Part B: Polym. Phys. 40, 1777 (2002)]. In this model, we assume that the composition of the thin block copolymer film varies only in longitude and colatitude and is constant in the radial direction. Using this approach we are able to study the formation of defects in the lamellar and cylindrical phases, and their dependence on sphere radius. Specifically, we compute ground-state (i.e., lowest-energy) configurations on the sphere for both the cylindrical and lamellar phases. Grain boundary scars are also observed in our simulations of the cylindrical phase when the sphere radius surpasses a threshold value R_{c} approximately 5d , where d is the natural lattice spacing of the cylindrical phase, which is consistent with theoretical predictions [Bowick, Phys. Rev. B 62, 8738 (2000); Bausch, Science 299, 1716 (2003)]. A strong segregation limit approximate free energy is also presented, along with simple microdomain packing arguments, to shed light on the observed SCFT simulation results.

Thermal composition fluctuations in an ordered lamellar mesophase.

We derive an approximate analytic expression for the structure factor of equilibrium, thermal composition fluctuations in an ordered lamellar mesophase. In order to test the validity of the equation, we perform a series of stochastic simulations using an established model of block copolymer ordering and demonstrate that the equation fits the simulation data with zero adjustable fit parameters over a reasonably wide range of system and simulation parameters.

Directed Self-Assembly of Lamellar Copolymers: Effects of Interfacial Interactions on Domain Shape.

The depth-dependent structure of a poly(styrene-b-methylmethacrylate) (PS-PMMA) line grating (46 nm pitch) was calculated from quantitative analysis of small-angle X-ray scattering profiles. These data demonstrate that domain shapes are significantly deformed near the substrate interface, where the local PS domain shape resembles an hourglass. The bulk equilibrium dimension is recovered near the center of a 64 nm thick film. Simulations based on self-consistent field theory suggest that deformations near the substrate are caused by extensive penetration of the copolymer domains into the underlying substrate coating (a PS-brush). These findings suggest that new coatings for block copolymer directed self-assembly should consider copolymer penetration lengths in addition to tailoring surface energetics. Furthermore, given the resolution and ensemble-averaging features of synchrotron X-ray scattering, we argue that it has the potential to emerge as a "gold-standard" or "benchmark" dimensional metrology and library validation tool for high density, sub-10 nm features.

Block-copolymer ordering with a spatiotemporally heterogeneous mobility.

Motivated by recent zone annealing measurements on stripe-forming block-copolymer films [B. C. Berry, Nano Lett. 7, 2789 (2007)], we study block-copolymer ordering with a spatiotemporally heterogeneous mobility. Specifically, we implement a time- and space-dependent mobility field in the relaxation of a diblock copolymer self-consistent field theory. The model includes a gradient in the local mobility and intrinsic nanoscale mobility variations characteristic of glass phenomenology. The simulations demonstrate that a spatiotemporally heterogeneous mobility can have a significant influence on microdomain ordering in block-copolymer systems, and that nanoscale dynamic heterogeneities associated with glass formation can impact the structure of the ordered block-copolymer microphase.

Orientational order in block copolymer films zone annealed below the order--disorder transition temperature.

We report measurements of rapid ordering and preferential alignment in block copolymer films zone annealed below the order-disorder transition temperature. The orientational correlation lengths measured after approximately 5 h above the glass-transition temperature ( approximately 2 microm) were an order of magnitude greater than that obtained under equivalent static annealing. The ability to rapidly process polymers with inaccessible order-disorder transition temperatures suggests zone annealing as a route toward more robust nanomanufacturing methods based on block copolymer self-assembly.