Kinetic pathways of sheared block copolymer systems derived from Minkowski functionals

We employ Minkowski functionals to analyze the kinetics of pattern formation under an applied external shear flow. The considered pattern formation model describes the dynamics of phase separating block copolymer systems. For our purpose, we have chosen two block copolymer systems (a melt and a solution) that exhibit a hexagonal cylindrical morphology as an equilibrium structure. Our main objective is the determination of efficient choices for the treshold values that are required for the calculation of the Minkowski functionals. We find that a minimal set of two treshold values (one from which should be equal to an average density value and another to a higher density value) is sufficient to unraffle the phase separation kinetics. Given these choices, we focus on the influence of the degree of phase separation, and the instance at which the shear is applied, on the kinetic pathways. We also found a remarkable similarity of the time evolution of Euler characteristic and the segregation parameter for the average density choice.     

Improved configuration space sampling: Langevin dynamics with alternative mobility

We present a new and efficient method for determining optimal configurations of a large number (N) of interacting particles. We use a coarse-grained stochastic Langevin equation in the overdamped limit to describe the dynamics of this system and replace the standard mobility by an effective space dependent inverse Hessian correlation matrix. Due to the analogy of the drift term in the Langevin equation and the update scheme in Newton's method, we expect accelerated dynamics or improved convergence in the convex part of the potential energy surface Phi. The stochastic noise term, however, is not only essential for proper thermodynamic sampling but also allows the system to access transition states in the concave parts of Phi. We employ a Broyden-Fletcher-Goldfarb-Shannon method for updating the local mobility matrix. Quantitative analysis for one and two dimensional systems shows that the new method is indeed more efficient than standard methods with constant effective friction. Due to the construction, our effective mobility adapts high values/low friction in configurations which are less optimal and low values/high friction in configurations that are more optimal.     

Simulations of Electric Field Induced Lamellar Alignment in Block Copolymers in the Presence of Selective Electrodes

Computer simulations have been performed for electric field induced parallel‐perpendicular lamellar phase transition in the presence of electrodes. The simulations are based on the dynamic density functional theory. Here we provide the extension of earlier work in two dimensions (2D) to three dimensions (3D). The result is a vivid picture of the transitions through defect creation and collision.

Observed change in lamellar alignment with applied electric field.     

Liposome fusion with orthogonal coiled coil peptides as fusogens: the efficacy of roleplaying peptides

Biological membrane fusion is a highly specific and coordinated process as a multitude of vesicular fusion events proceed simultaneously in a complex environment with minimal off-target delivery. In this study, we develop a liposomal fusion model system with specific recognition using lipidated derivatives of a set of four de novo designed heterodimeric coiled coil (CC) peptide pairs. Content mixing was only obtained between liposomes functionalized with complementary peptides, demonstrating both fusogenic activity of CC peptides and the specificity of this model system. The diverse peptide fusogens revealed important relationships between the fusogenic efficacy and the peptide characteristics. The fusion efficiency increased from 20% to 70% as affinity between complementary peptides decreased, (from K_F ≈ 10⁸ to 10⁴ M⁻¹), and fusion efficiency also increased due to more pronounced asymmetric role-playing of membrane interacting ‘K’ peptides and homodimer-forming ‘E’ peptides. Furthermore, a new and highly fusogenic CC pair (E₃/P1_K) was discovered, providing an orthogonal peptide triad with the fusogenic CC pairs P2_E/P2_K and P3_E/P3_K. This E₃/P1_k pair was revealed, via molecular dynamics simulations, to have a shifted heptad repeat that can accommodate mismatched asparagine residues. These results will have broad implications not only for the fundamental understanding of CC design and how asparagine residues can be accommodated within the hydrophobic core, but also for drug delivery systems by revealing the necessary interplay of efficient peptide fusogens and enabling the targeted delivery of different carrier vesicles at various peptide-functionalized locations.

We developed a liposomal fusion model system with specific recognition using a set of heterodimeric coiled coil peptide pairs. This study unravels important structure–fusogenic efficacy relationships of peptide fusogens.     

Dynamics of terrace formation in a nanostructured thin block copolymer film

We have used dynamic self-consistent field (DSCF) theory to investigate the structural evolution of an ABA block copolymer thin film placed between a solid substrate and a free surface. In line with the few existing theoretical studies for pure homopolymers and mixtures, the free interface is introduced by a void component. In our calculations, the free surface experiences surface roughening and eventually the formation of terraces, as in the experiments. The kinetic pathway of the microstructures was compared to findings of an existing detailed experimental study (Knoll, A.; Lyakhova, K. S.; Horvat, A.; Krausch, G.; Sevink, G. J. A.; Zvelindovsky, A. V.; Magerle, R. Nat. Mater. 2004, 3, 886) and was found to be equivalent in detail. This corroborates our assumption in this earlier work that the pathway due to changing film thickness is similar to a pathway due to changing surface energetics. Moreover, our calculations show for the first time that microstructural transitions are a driving force of polymer/air interface curving and the formation of terraces.     

3D Nanometer‐Scale Study of Coexisting Bicontinuous Morphologies in a Block Copolymer/Homopolymer Blend

Summary: Coexisting bicontinuous morphologies, one ordered and one disordered, are investigated in a macrophase‐separated poly(styrene‐block‐isoprene) diblock copolymer/homopolystyrene (SI/hS) blend. Two‐phase behavior is attributed to the relatively high hS/S mass ratio (0.92). According to its crystallographic signature and channel coordination as discerned from three‐dimensional (3D) images generated by transmission electron microtomography (TEMT), the ordered morphology is classified as gyroid. The 3D local and global topological characteristics of both bicontinuous morphologies as measured directly from TEMT images are reported. The disordered morphology is further compared with molecular‐field simulations to ascertain the spatial distribution of the constituent species within the blend, thereby demonstrating the utility of high‐resolution 3D imaging coupled with molecular‐level simulations.

     

Mechanism of the transition between lamellar and gyroid phases formed by a diblock copolymer in aqueous solution

The mechanism of the transition from a lamellar phase to a gyroid phase in an aqueous solution of a diblock copolymer has been studied by time-resolved synchrotron small-angle X-ray scattering. The transition occurs via a metastable perforated lamellar structure. The perforations initially have liquidlike ordering before developing hexagonal packing. The transient phase of irregularly perforated layers is revealed by the development of diffuse scattering peaks, just below the Bragg peaks of the lamellar structure. The diffuse scattering is modeled by Monte Carlo simulations of perforated layers. Following the formation of perforations, Bragg peaks characteristic of a hexagonal structure signal an ordering into a hexagonal lattice (with the concomitant loss of diffuse scattering). Computer simulations based on a dynamic density functional model reproduce these features. The hexagonal perforated lamellar phase is rapidly replaced by the gyroid phase. The domain spacing of the gyroid phase is larger than that of the perforated lamellar structure. The perforated lamellar and gyroid phases coexist for a defined period. The reverse transition from gyroid to lamellae occurs directly, with no transient or metastable intermediates.     

Phase behavior in thin films of cylinder-forming ABA block copolymers: mesoscale modeling

The phase behavior of cylinder-forming ABA block copolymers in thin films is modeled in detail using dynamic density functional theory and compared with recent experiments on polystyrene-block-polybutadiene-block-polystyrene triblock copolymers. Deviations from the bulk structure, such as wetting layer, perforated lamella, and lamella, are identified as surface reconstructions. Their stability regions are determined by an interplay between surface fields and confinement effects. Our results give evidence for a general mechanism governing the phase behavior in thin films of modulated phases.