Transition pathways connecting crystals and quasicrystals.

Due to structural incommensurability, the emergence of a quasicrystal from a crystalline phase represents a challenge to computational physics. Here, the nucleation of quasicrystals is investigated by using an efficient computational method applied to a Landau free-energy functional. Specifically, transition pathways connecting different local minima of the Lifshitz-Petrich model are obtained by using the high-index saddle dynamics. Saddle points on these paths are identified as the critical nuclei of the 6-fold crystals and 12-fold quasicrystals. The results reveal that phase transitions between the crystalline and quasicrystalline phases could follow two possible pathways, corresponding to a one-stage phase transition and a two-stage phase transition involving a metastable lamellar quasicrystalline state, respectively.

Phase Behavior of Binary Blends of Diblock Copolymers: Progress and Opportunities.

The phase behavior of binary blends of diblock copolymers has been examined extensively in the past decades. Experimental and theoretical studies have demonstrated that mixing two different block copolymers provides an efficient and versatile route to regulate their self-assembled morphologies. A good understanding of the principles governing the self-assembly of block copolymer blends has been obtained from the study of A1B1/A2B2 diblock copolymer blends. The second (A2B2) diblocks could act synergistically as fillers and cosurfactants to regulate the domain size and interfacial properties, resulting in the formation of ordered phases not found in the parent (A1B1 or A2B2) diblock copolymer melts. The study of A1B1/A2B2 block copolymer blends further provides a solid foundation for future research on more complex block copolymer blends.

Origins of low-symmetry phases in asymmetric diblock copolymer melts.

Cooling disordered compositionally asymmetric diblock copolymers leads to the formation of nearly spherical particles, each containing hundreds of molecules, which crystallize upon cooling below the order-disorder transition temperature (TODT). Self-consistent field theory (SCFT) reveals that dispersity in the block degrees of polymerization stabilizes various Frank-Kasper phases, including the C14 and C15 Laves phases, which have been accessed experimentally in low-molar-mass poly(isoprene)-b-poly(lactide) (PI-PLA) diblock copolymers using thermal processing strategies. Heating and cooling a specimen containing 15% PLA above and below the TODT from the body-centered cubic (BCC) or C14 states regenerates the same crystalline order established at lower temperatures. This memory effect is also demonstrated with a specimen containing 20% PLA, which recrystallizes to either C15 or hexagonally ordered cylinders (HEXC) upon heating and cooling. The process-path-dependent formation of crystalline order shapes the number of particles per unit volume, n/V, which is retained in the highly structured disordered liquid as revealed by small-angle X-ray scattering (SAXS) experiments. We hypothesize that symmetry breaking during crystallization is governed by the particle number density imprinted in the liquid during ordering at lower temperature, and this metastable liquid is kinetically constrained from equilibrating due to prohibitively large free energy barriers for micelle fusion and fission. Ordering at fixed n/V is enabled by facile chain exchange, which redistributes mass as required to meet the multiple particle sizes and packing associated with specific low-symmetry Frank-Kasper phases. This discovery exposes universal concepts related to order and disorder in self-assembled soft materials.

Pathways connecting two opposed bilayers with a fusion pore: a molecularly-informed phase field approach.

A phase field model with two phase fields, representing the concentration and the head-tail separation of amphiphilic molecules, respectively, has been constructed using an extension of the Ohta-Kawasaki model (Macromolecules, 1986, 19, 2621-2632). It is shown that this molecularly-informed phase field model is capable of producing various self-assembled amphiphilic aggregates, such as bilayers, vesicles and micelles. Furthermore, pathways connecting two opposed bilayers with a fusion pore are obtained by using a combination of the phase field model and the string method. Multiple fusion pathways, including a classical pathway and a leaky pathway, have been obtained depending on the initial separation of the two bilayers. The study shed light on the understanding of the membrane fusion pathways and, more importantly, laid a foundation for further investigation of more complex membrane morphologies and transitions.

Elastic properties of self-assembled bilayer membranes: Analytic expressions via asymptotic expansion.

Bilayer membranes self-assembled from amphiphilic molecules are ubiquitous in biological and soft matter systems. The elastic properties of bilayer membranes are essential in determining the shape and structure of bilayers. A novel method to calculate the elastic moduli of the self-assembled bilayers within the framework of the self-consistent field theory is developed based on an asymptotic expansion of the order parameters in terms of the bilayer curvature. In particular, the asymptotic expansion method is used to derive analytic expressions of the elastic moduli, which allows us to design more efficient numerical schemes. The efficiency of the proposed method is illustrated by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents.

Spherical Supramolecular Structures Constructed via Chemically Symmetric Perylene Bisimides: Beyond Columnar Assembly.

Like other discotic molecules, self-assembled supramolecular structures of perylene bisimides (PBIs) are commonly limited to columnar or lamellar structures due to their distinct π-conjugated scaffolds and unique rectangular shape of perylene cores. The discovery of PBIs with supramolecular structures beyond layers and columns may expand the scope of PBI-based materials. A series of unconventional spherical packing phases in PBIs, including A15 phase, σ phase, dodecagonal quasicrystalline (DQC) phase, and body-centered cubic (BCC) phase, is reported. A strategy involving functionalization of perylene core with several polyhedral oligomeric silsesquioxane (POSS) cages achieved spherical assemblies of PBIs, instead of columnar assemblies, due to the significantly increased steric hindrance at the periphery. This strategy may also be employed for the discovery of unconventional spherical assemblies in other related discotic molecules by the introduction of similar bulky functional groups at their periphery. An unusual inverse phase transition sequence from a BCC phase to a σ phase was observed by increasing annealing temperature.

Elastic properties of liquid-crystalline bilayers self-assembled from semiflexible-flexible diblock copolymers.

The mechanical response and shape of self-assembled bilayer membranes depend crucially on their elastic properties. Most of the studies focused on the elastic properties of fluid membranes, despite the ubiquitous presence of membranes with liquid-crystalline order. Here the elastic properties of liquid-crystalline bilayers self-assembled from diblock copolymers composed of a semiflexible block are studied theoretically. Specifically, the self-consistent field theory (SCFT) is applied to a model system composed of semiflexible-flexible diblock copolymers dissolved in flexible homopolymers that act as solvents. The free energy of self-assembled tensionless bilayer membranes in three different geometries, i.e. planar, cylindrical and spherical, is obtained by solving the SCFT equations using a hybrid method, in which the orientation-dependent functions are treated using the spherical harmonics, whereas the position-dependent operators are treated using the compact difference schemes. The bending modulus κM and Gaussian modulus κG of the bilayer are extracted from the free energies. The effects of the molecular parameters of the system, such as the chain rigidity and the orientational interaction, are systematically examined.

Dual Cross-linked Vinyl Vitrimer with Efficient Self-Catalysis Achieving Triple-Shape-Memory Properties.

As an emerging class of dynamic cross-linked network, vitrimers have attracted much attention due to the combination of mechanical advantages of thermosets and recyclability of thermoplastics at an elevated temperature. In particular, most vitrimers with multi-shape memory properties usually involve more than one thermal transition or molecular switch, which might pose a challenge for facile sample fabrication and potentially limits their applications. In pursuit of a more universal and simple route, utilizing commercially available and inexpensive reagents to prepare shape-memory vitrimers with dual cross-linked network from vinyl monomer-derived prepolymers is reported here. Copolymerization of desired vinyl monomers gives prepolymers containing carboxyl and zinc carboxylate groups, which are later converted into vitrimers in a single step by post-curing with diglycidylether of bisphenol A. The Zn2+ ions can not only act as physical crosslinking points through ionic coordination interactions, thus providing the triple-shape-memory properties, but also play the role of catalyst to activate transesterification in the dynamic covalent network. This new self-catalyzed vitrimer has excellent transesterification efficiency, triple-shape-memory properties, and can be sufficiently healed and reprocessed at an elevated temperature. The proposed molecular design of self-catalyzed materials opens a new avenue toward commercially relevant fabrication of high-performance vitrimers with multiple shape-memory properties.

Breaking Parallel Orientation of Rods via a Dendritic Architecture toward Diverse Supramolecular Structures.

Self-assembled nanostructures of rod-like molecules are commonly limited to nematic or layered smectic structures dominated by the parallel arrangement of the rod-like components. Distinct self-assembly behavior of four categories of dendritic rods constructed by placing a tri(hydroxy) group at the apex of dendritic oligo-fluorenes is observed. Designed hydrogen bonding and dendritic architecture break the parallel arrangement of the rods, resulting in molecules with specific (fan-like or cone-like) shapes. While the fan-shaped molecules tend to form hexagonal packing cylindrical phases, the cone-shaped molecules could form spherical motifs to pack into various ordered structures, including the Frank-Kasper A15 phase and dodecagonal quasicrystal. This study provides a model system to engineer diverse supramolecular structures by rod-like molecules and sheds new light into the mechanisms of the formation of unconventional spherical packing structures in soft matter.

Effect of Chain Architecture on Self-Assembled Aggregates from Cyclic AB Diblock and Linear ABA Triblock Copolymers in Solution.

The self-assembly behaviors of two block copolymers with the same chain length but different chain architectures (cyclic AB, linear ABA) in B-selective solvents are investigated using Monte Carlo simulations. A morphological transition sequence, from spherical micelles to cylindrical micelles, to vesicles and then to multicompartment vesicles, is observed for both copolymer systems when the interaction between the solvophobic A-block and the solvent is increased. In particular, toroidal micelles could be formed in triblock systems due to the presence of the bridging chains at the parameter region between cylindrical micelles and vesicles whereas disklike micelles are formed in cyclic systems. The simulation results demonstrated that the architecture of block copolymers could be used to regulate the structural characteristics and thermal stability of these self-assembled aggregates.

Liquid crystalline bilayers self-assembled from rod-coil diblock copolymers.

The structure and phase behaviour of bilayer membranes self-assembled from rod-coil diblock copolymers are studied using the self-consistent field theory, focusing on the occurrence and relative stability of liquid crystalline phases induced by the geometric shape and orientational interaction of the rod-blocks. A variety of liquid crystalline bilayers, corresponding to the smectic phases in bulk systems, are predicted to occur as equilibrium phases of the system. The ordered morphologies and phase behaviour of the system are analyzed. Phase diagrams of the self-assembled bilayers are constructed. The theoretical results provide an understanding of the formation mechanisms of these intricate phases.

Tetragonal phase of cylinders self-assembled from binary blends of AB diblock and (A'B)n star copolymers.

The phase behavior of binary blends composed of AB diblock and (A'B)n star copolymers is studied using the polymeric self-consistent field theory, focusing on the formation and stability of the stable tetragonal phase of cylinders. In general, cylindrical domains self-assembled from AB-type block copolymers are packed into a hexagonal array, although a tetragonal array of cylinders could be more favourable for lithography applications in microelectronics. The polymer blends are designed such that there is an attractive interaction between the A and A' blocks, which increases the compatibility between the two copolymers and thus suppresses the macroscopic phase separation of the blends. With an appropriate choice of system parameters, a considerable stability window for the targeted tetragonal phase is identified in the blends. Importantly, the transition mechanism between the hexagonal and tetragonal phases is elucidated by examining the distribution of the two types of copolymers in the unit cell of the structure. The results reveal that the short (A'B)n star copolymers are preferentially located in the bonding area connecting two neighboring domains in order to reduce extra stretching, whereas the long AB diblock copolymers are extended to further space of the unit cell.

Partitioning of caffeine in lipid bilayers reduces membrane fluidity and increases membrane thickness.

Caffeine is a small amphiphilic molecule, which is widely consumed as a stimulant to prevent fatigue, but is also used as a common drug adjuvant in modern medicine. Here, we show that caffeine interacts with unsaturated lipid membranes made of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC). By combining X-ray diffraction and molecular dynamics simulations, we present evidence that caffeine partitions in lipid membranes and locates at the head group-tail group interface of the bilayers. By attracting water molecules from neighboring lipid molecules, it leads to the formation of "water pockets", i.e., a local increase of water density at this interface. Through this mechanism, caffeine leads to an overall decrease of the gauche defect density in the membranes and an increase of membrane thickness, indicating a loss of membrane fluidity. These non-specific membrane interactions may increase the efficacy of analgesic drugs through changes in the bioavailability and rate of metabolism of these drugs.

Formation of Nonclassical Ordered Phases of AB-Type Multiarm Block Copolymers.

The formation of ordered phases from block copolymers is driven by a delicate balance between the monomer-monomer interaction and chain configurational entropy. The configurational entropy can be regulated by designed chain architecture, resulting in a new entropy-driven mechanism to control the self-assembly of ordered phases from block copolymers. An effective routine to regulate the configurational entropy is to utilize multiarm architecture, in which the entropic contribution to the free energy could be qualitatively controlled by the fraction of bridging configurations. As an illustration of this mechanism, the phase behavior of two AB-type multiarm block copolymers, B0-(Bi-Ai)m and (B1-Ai-B2)m where the minority A blocks form cylindrical or spherical domains, are examined using the self-consistent field theory (SCFT). The SCFT results demonstrate that the packing symmetry of the cylinders or spheres can be controlled by the length of the bridging B blocks. Several nonclassical ordered phases, including a novel square array cylinder with p4mm symmetry, are predicted to form from the AB-type multiarm block copolymers.

Influence of Grafting Point Distribution on the Surface Structures of Y-Shaped Polymer Brushes in Solution.

We report a simulated annealing study of surface structures of the Y-shaped copolymers grafted onto a planar substrate in nonselective solvents. The influences of the lateral size of the grafting surface and the distribution manner of the grafting point on the order degree of the ripple structures are investigated. Under uniformly distribution conditions, it is found that the well-defined ripple structures can be formed when the lateral size less than a threshold which depends on the solvent quality and grafting density. However, introducing a density fluctuation into the uniformly distribution grafting points in different ways, the defects with different degrees are observed in the ripple structures. The influence of the density fluctuations on the ripple phase are studied quantitatively. Furthermore, the possibility of the formation of surface structures with long-range order induced by directed self-assembly is investigated. The findings provide guidelines for fabricating patterned surfaces with highly ordered structures.

Stability of the Frank-Kasper σ-phase in BABC linear tetrablock terpolymers.

The phase behavior of B1AB2C tetrablock terpolymer melts is systematically studied using the self-consistent field theory, focusing on the emergence and stability of the complex Frank-Kasper σ-phase. Our study starts with an investigation of the stability region of the σ phase for a generic model of B1AB2C terpolymers, in which the C-blocks form spherical domains immersed in the A/B matrix. Then, we examine the stability of the σ phase for a model system with a specific set of parameters mimicking poly(styrene-b-isoprene-b-styrene-b-ethylene oxide) (SISO) block copolymers which were examined in recent experiments. Our results reveal that the formation of the σ phase is mainly governed by two factors. The first factor is the conformational asymmetry between the A/B-blocks and the C-block, similar to that in conformationally asymmetric AB-type block copolymers. The second factor is the specific chain architecture of B1AB2C. The tetrablock architecture with a specific set of interaction parameters and compositions leads to the formation of large core-shell spherical domains, which amplifies the effect of interfacial energy and thereby stabilizes the σ phase.

Emergence of ordered network mesophases in kinetic pathways of order-order transition for linear ABC triblock terpolymers.

Applying the string method to the self-consistent field theory (SCFT) of ABC linear triblock copolymers, we developed a new strategy to design kinetic pathways for the formation of stable or metastable network mesophases in order-order transition (OOT) processes. The design principle regarding the kinetic pathways between distinct mesophases is based on the matching relationships of both domain spacing and dominant Fourier components of the density distributions. The results suggest that complex ordered network mesophases, such as alternating diamond (DA) and alternating plumber's nightmare (PA) could be obtained in kinetic pathways between simple phases covering lamellae, cylinders and spheres. By virtue of the minimal free energy pathway (MEP) obtained, we could acquire the epitaxial relationship and phase transition mechanism. Furthermore, we managed to regulate the MEP by changing the block composition to adjust packing frustration. Two new metastable networks, core-shell five-pronged and six-pronged morphologies, were found in the kinetic pathways, further demonstrating the regulating mechanism. The results will contribute to a better understanding of the kinetic relationship between simple phases and complex networks, thus providing a platform for soft materials design via the OOT route and guiding experimental procedures to fabricate ordered network mesophases.

Amyloid-ß(25-35) peptides aggregate into cross-ß sheets in unsaturated anionic lipid membranes at high peptide concentrations.

One of the hallmarks of Alzheimer's disease is the formation of protein plaques in the brain, which mainly consist of amyloid-ß peptides of different lengths. While the role of these plaques in the pathology of the disease is not clear, the mechanism behind peptide aggregation is a topic of intense research and discussion. Because of their simplicity, synthetic membranes are promising model systems to identify the elementary processes involved. We prepared unsaturated zwitterionic/anionic lipid membranes made of 1-palmitoyl-2-oleoyl-sn-glycero-phosphocholine (POPC) and 1,2-dimyristoyl-sn-glycero-3-phospho-l-serine (DMPS) at concentrations of POPC/3 mol% DMPS containing 0 mol%, 3 mol%, 10 mol%, and 20 mol% amyloid-ß25-35 peptides. Membrane-embedded peptide clusters were observed at peptide concentrations of 10 and 20 mol% with a typical cluster size of ∼11 µm. Cluster density increased with peptide concentration from 59 (±3) clusters per mm(2) to 920 (±64) clusters per mm(2), respectively. While monomeric peptides take an α-helical state when embedded in lipid bilayers at low peptide concentrations, the peptides in peptide clusters were found to form cross-ß sheets and showed the characteristic pattern in X-ray experiments. The presence of the peptides was accompanied by an elastic distortion of the bilayers, which can induce a long range interaction between the peptides. The experimentally observed cluster patterns agree well with Monte Carlo simulations of long-range interacting peptides. This interaction may be the fundamental process behind cross-ß sheet formation in membranes and these sheets may serve as seeds for further growth into amyloid fibrils.

Hybrid particle-field molecular dynamics simulation for polyelectrolyte systems.

To achieve simulations on large spatial and temporal scales with high molecular chemical specificity, a hybrid particle-field method was proposed recently. This method is developed by combining molecular dynamics and self-consistent field theory (MD-SCF). The MD-SCF method has been validated by successfully predicting the experimentally observable properties of several systems. Here we propose an efficient scheme for the inclusion of electrostatic interactions in the MD-SCF framework. In this scheme, charged molecules are interacting with the external fields that are self-consistently determined from the charge densities. This method is validated by comparing the structural properties of polyelectrolytes in solution obtained from the MD-SCF and particle-based simulations. Moreover, taking PMMA-b-PEO and LiCF3SO3 as examples, the enhancement of immiscibility between the ion-dissolving block and the inert block by doping lithium salts into the copolymer is examined by using the MD-SCF method. By employing GPU-acceleration, the high performance of the MD-SCF method with explicit treatment of electrostatics facilitates the simulation study of many problems involving polyelectrolytes.

Giant surfactants provide a versatile platform for sub-10-nm nanostructure engineering.

The engineering of structures across different length scales is central to the design of novel materials with controlled macroscopic properties. Herein, we introduce a unique class of self-assembling materials, which are built upon shape- and volume-persistent molecular nanoparticles and other structural motifs, such as polymers, and can be viewed as a size-amplified version of the corresponding small-molecule counterparts. Among them, "giant surfactants" with precise molecular structures have been synthesized by "clicking" compact and polar molecular nanoparticles to flexible polymer tails of various composition and architecture at specific sites. Capturing the structural features of small-molecule surfactants but possessing much larger sizes, giant surfactants bridge the gap between small-molecule surfactants and block copolymers and demonstrate a duality of both materials in terms of their self-assembly behaviors. The controlled structural variations of these giant surfactants through precision synthesis further reveal that their self-assemblies are remarkably sensitive to primary chemical structures, leading to highly diverse, thermodynamically stable nanostructures with feature sizes around 10 nm or smaller in the bulk, thin-film, and solution states, as dictated by the collective physical interactions and geometric constraints. The results suggest that this class of materials provides a versatile platform for engineering nanostructures with sub-10-nm feature sizes. These findings are not only scientifically intriguing in understanding the chemical and physical principles of the self-assembly, but also technologically relevant, such as in nanopatterning technology and microelectronics.