Nanocrystal Assemblies: Current Advances and Open Problems.

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

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.

Rotational Dynamics of Discoid Colloidal Particles in Attractive Quasi-Two-Dimensional Plastic Crystals.

Plastic crystals formed from anisotropic molecules or particles are an important state of matter characterized by the presence of long-range positional order and the lack of long-range orientational order. The rotational motion of molecules or particles in plastic crystals is the most attractive characteristic of the system. Here the rotational dynamics of the discoid particles in quasi-two-dimensional colloidal plastic crystals stabilized via depletion interactions are quantitatively studied using time-resolved confocal microscopy. The measured probability distribution of particle orientation reveals the existence of a strong coupling between the lattice symmetry and particle rotation, resulting in anisotropic rotational dynamics modes resembling the underlying hexagonal crystalline symmetry. Furthermore, the orientational distribution function provides information about the potential surface of rotational dynamics. The observed slow rotational diffusion can be attributed to the presence of orientational minima and potential barriers on the potential surface. Our findings with a real experimental system provide important insights into the role of attraction in the phase behaviors of plastic crystals.

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.

Polymer Translocation Time.

The force- and flow-induced translocation processes of linear and ring polymers are studied using a combination of multiparticle collision dynamics and molecular dynamics, focusing on the behavior of the polymer translocation time. We compare the force- and flow-induced translocations of linear and ring polymers. It is found that when the translocation time (τ*) is characterized by scaling exponents, δ, δ', and α, via the relations τ* ∼ fδNα and τ* ∼ Jδ'Nα, the scaling exponents are not constants. For long chains tested, α = 1.0 for both force- and flow-induced translocations. The difference between the force- and flow-induced translocations stems from different monomer crowding effects due to distinct flow patterns outside the channel. Furthermore, general relations for polymer translocation time are derived for these two translocation processes, which are in good agreement with the simulation results. Our results provide clear molecular pictures for the force- and flow-induced translocations, which shed light on the understanding of translocation dynamics and provide guidance for practical applications such as molecular sequencing and ultrafiltration.

Frustration in block copolymer assemblies.

Frustration is ubiquitous in condensed matter systems and it provides a central concept to understand the self-assembly of soft matter. Frustration is found at multiple scales in polymeric systems containing block copolymers. At the molecular scale, frustration arises because the chemically distinct blocks repel each other whereas the chain connectivity prevents a macroscopic separation. At the mesoscopic scale, frustration occurs due to the competition between the tendency for the block copolymer assemblies to maintain their native shape and the requirement to fill the space. At an even larger scale, frustrations could be induced by external fields or spatial confinement. Recent theoretical and experimental studies provide a good understanding of the origin of various frustrations in the self-assembly of block copolymers. Furthermore, it has been demonstrated that designed block copolymer systems, either in the form of multiblock copolymers with different architectures or block copolymer blends, could be utilized to regulate frustrations resulting in the formation of complex ordered and hierarchically structured phases.

Multiphase Coacervates Driven by Electrostatic Correlations.

The liquid-liquid phase separation of a polyelectrolyte solution containing one type of negatively and two types of positively charged polymers with different charge densities is studied theoretically by random phase approximation (RPA). It is predicted that multicoacervate phases could coexist, driven purely by electrostatic correlations. The asymmetry of the linear charge density could induce an effective immiscibility between two positively charged polyelectrolytes, leading to the multiphase separation. Adding salt will induce the disappearance of the dilute phase, forming two coexisting complex phases, instead of fusion between coacervates. Raising temperature could either induce a two coexisting complex phase, or a dilute phase coexisting with a coacervate phase, depending on the bulk concentration. Our predictions are in good agreement with experiments and provide insights in the further designing of the multiphase coacervation system.

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 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.

Formation and Regulation of Multicompartment Vesicles from Cyclic Diblock Copolymer Solutions: A Simulation Study.

The self-assembly of a cyclic AB copolymer system with relatively long A blocks and short B blocks in B-selective solvents is investigated using a simulated annealing method. By investigating the effect of the lengths and solubilities of A and B blocks (N A and N B, εAS and εBS), the incompatibility between A and B blocks (εAB), as well as the polymer concentration (C p) and the conditions for the formation of multicompartment vesicles in cyclic diblock copolymer solutions, is predicted. The phase diagrams in terms of N B, εAS, and C p are constructed. The mechanism of the morphological transition is elucidated. It is shown that for cyclic copolymers the change in the above factors relating to the polymer and solvent properties all can lead to the transition from simple vesicles to multicompartment vesicles, but two different transition mechanisms are revealed. In addition, our simulations demonstrate that the self-assembly of cyclic copolymers could provide a powerful strategy for regulating the compartment number and the wall thickness of the multicompartment vesicles by adjusting the block solubilities and block lengths, respectively. These findings will facilitate the application of multicompartment architectures in cell mimicry, drug delivery, and nanoreactors.

Stabilizing Phases of Block Copolymers with Gigantic Spheres via Designed Chain Architectures.

It is generally believed that the spherical domains self-assembled from AB-type block copolymers are composed of the minority A blocks with a volume fraction of fA < 1/2. Breaking this generic rule so that the spherical domains are formed by the majority A blocks (fA > 1/2) requires mechanisms to drastically expand the stable region of spherical packing phases. Self-consistent field theory predicts that dendron-like AB-type block copolymers, composed of G - 1 generations of A blocks connected with the outermost generation of B blocks, exhibit a stable region of spherical packing phases extending to fA ∼ 0.7. The extremely expanded spherical regions shed light on the mechanisms governing the self-assembly of amphiphilic macromolecules, as well as provide opportunities to engineer complex spherical packing phases.

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 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.

Superstretchable Dynamic Polymer Networks.

Superstretchable materials have many applications in advanced technological fields but are difficult to stretch to more than 1000× their original length. A superstretchable dynamic polymer network that can be stretched to 13 000× its original length is designed. It is revealed that superstretchability of the polymer network is derived from the synergistic effect of two different types of dynamic bonds, including a small number of strong dynamic imine bonds to maintain the network integrity during stretching and a large number of weak ionic hydrogen bonds to dissipate energy. This approach provides new insights into the design of superstretchable polymers.

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.

Elastic property of membranes self-assembled from diblock and triblock copolymers.

The elastic property of membranes self-assembled from AB diblock and ABA triblock copolymers, as coarse-grained model of lipids and the bolalipids, are studied using the self-consistent field theory (SCFT). Specifically, solutions of the SCFT equations, corresponding to membranes in different geometries (planar, cylindrical, spherical, and pore) have been obtained for a model system composed of amphiphilic AB diblock copolymers and ABA triblock copolymers dissolved in A homopolymers. The free energy of the membranes with different geometries is then used to extract the bending modulus, Gaussian modulus, and line tension of the membranes. The results reveal that the bending modulus of the triblock membrane is greater than that of the diblock membrane. Furthermore, the Gaussian modulus and line tension of the triblock membrane indicate that the triblock membranes have higher pore formation energy than that of the diblock membranes. The equilibrium bridging and looping fractions of the triblock copolymers are also obtained. Implications of the theoretical results on the elastic properties of biologically equivalent lipid bilayers and the bolalipid membranes are discussed.

Membrane-Modulating Drugs can Affect the Size of Amyloid-ß25-35 Aggregates in Anionic Membranes.

The formation of amyloid-ß plaques is one of the hallmarks of Alzheimer's disease. The presence of an amphiphatic cell membrane can accelerate the formation of amyloid-ß aggregates, making it a potential druggable target to delay the progression of Alzheimer's disease. We have prepared unsaturated anionic membranes made of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) and 1,2-dimyristoyl-sn-glycero-3-phospho-L-serine (DMPS) and added the trans-membrane segment Aß25-35. Peptide plaques spontaneously form in these membranes at high peptide concentrations of 20 mol%, which show the characteristic cross-ß motif (concentrations are relative to the number of membrane lipids and indicate the peptide-to-lipid ratio). We used atomic force microscopy, fluorescence microscopy, x-ray microscopy, x-ray diffraction, UV-vis spectroscopy and Molecular Dynamics (MD) simulations to study three membrane-active molecules which have been speculated to have an effect in Alzheimer's disease: melatonin, acetylsalicyclic acid (ASA) and curcumin at concentrations of 5 mol% (drug-to-peptide ratio). Melatonin did not change the structural parameters of the membranes and did not impact the size or extent of peptide clusters. While ASA led to a membrane thickening and stiffening, curcumin made membranes softer and thinner. As a result, ASA was found to lead to the formation of larger peptide aggregates, whereas curcumin reduced the volume fraction of cross-ß sheets by ~70%. We speculate that the interface between membrane and peptide cluster becomes less favorable in thick and stiff membranes, which favors the formation of larger aggregates, while the corresponding energy mismatch is reduced in soft and thin membranes. Our results present evidence that cross-ß sheets of Aß25-35 in anionic unsaturated lipid membranes can be re-dissolved by changing membrane properties to reduce domain mismatch.

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.

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.