Frank-Kasper A15 Research Articles

Self-assembled complex micelle phase stability in ABA-type triblock copolymers and related core-shell bottlebrushes

We report the synthesis and temperature-dependent morphologies of a series of polylactide--poly (-decalactone)--polylactide (LDL) triblock copolymers with Mn=16.0–18.1kg/mol and volume fractions fL=0.27–0.31 and associated core-shell bottlebrush (csBB) polymers, which derive from enchaining LDL triblocks through a polymerizable midchain functionality. While the LDL triblocks form micellar Frank-Kasper A15 and phases due to the conformational asymmetry of this monomer pair, the csBB morphologies sensitively depend on the backbone degree of polymerization (Nbb). At low Nbb values, micellar Frank-Kasper phases with the brush backbone situated in the matrix domain are stable, albeit with a modest reduction in the mean interfacial curvature evidenced by a to A15 order-to-order transition. However, larger Nbb values drive csBBs to form hexagonally packed cylinders phases. This Nbb-dependent phase behavior is rationalized in terms of a star-to-bottlebrush transition. At low Nbb values, the csBBs are akin to star polymers with pointlike junctions that can support complex micelle packings. As Nbb increases, the csBBs adopt cylindrical molecular geometries with extended backbones situated in the matrix domain that prefer hexagonally packed cylinders morphologies. Published by the American Physical Society 2024

Experimental and Computational Evaluation of Self-Assembled Morphologies in Diblock Janus Bottlebrush Copolymers.

Diblock Janus-type "A-branch-B" bottlebrush copolymers (di-JBBCPs) consist of a backbone with alternating A and B side chains, in contrast to the side chain arrangement of conventional bottlebrush copolymers. As a result, A and B blocks of di-JBBCPs can microphase-separate perpendicular to the backbone, which is located at the interface between the two blocks. A reparametrized dissipative particle dynamics (DPD) model is used to theoretically investigate the self-assembly of di-JBBCPs and to compare with the experimental results of a range of polystyrene-branch-polydimethylsiloxane di-JBBCPs. The experimentally formed cylinder, gyroid, and lamellar morphologies showed good correspondence with the model phase diagram, and the effect of changing volume fraction and backbone length is revealed. The DPD model predicts a bulk-stable perforated lamella morphology together with two unconventional spherical phases, the Frank-Kasper A15 spheres and the hexagonally close-packed spheres, indicating the diversity of morphologies available from complex BCP molecular architectures.

Bayesian modeling of pattern formation from one snapshot of pattern.

Partial differential equations(PDEs) have been widely used to reproduce patterns in nature and to give insight into the mechanism underlying pattern formation. Although many PDE models have been proposed, they rely on the pre-request knowledge of physical laws and symmetries, and developing a model to reproduce a given desired pattern remains difficult. We propose a method, referred to as Bayesian modeling of PDEs (BM-PDEs), to estimate the best dynamical PDE for one snapshot of a objective pattern under the stationary state without ground truth. We apply BM-PDEs to nontrivial patterns, such as quasicrystals (QCs), a double gyroid, and Frank-Kasper structures. We also generate three-dimensional dodecagonal QCs from a PDE model. This is done by using the estimated parameters for the Frank-Kasper A15 structure, which closely approximates the local structures of QCs. Our method works for noisy patterns and the pattern synthesized without the ground-truth parameters, which are required for the application toward experimental data.

Discotic liquid crystals 45 years later. Dendronized discs and crowns increase liquid crystal complexity to columnar from spheres, cubic Frank-Kasper, liquid quasicrystals and memory-effect induced columnar-bundles

In 1977 Chandrasekhar laboratory reported the first examples of a new class of thermotropic liquid crystals self-organized from planar disc-like molecules substituted with alkyl groups. X-ray analysis demonstrated that these disc-like molecules stack on top of each other at irregular spacing in columns located in the paraffin melt of their alkyl groups. These supramolecular columns self-organize in a hexagonal array defined as the new thermotropic discotic or columnar hexagonal liquid crystal phase. This new thermotropic liquid crystal phase has translational periodicity in two dimensions and liquid-like disorder in the third one, along the column axis. In 2002 Bushby and Lozman dedicated a brief review article to the 25 anniversary of discotic liquid crystals. This review also included a brief discussion of supramolecular discs and columns self-organized from self-assembling dendrons and dendrimers. The current publication is not another review but a brief perspective on new liquid crystal phases self-organized from dendronized rigid planar and conformationally flexible discs as well as from crown-like molecules. Crown-like molecules are the most stable conformation of a transient unstable disc. All dendronized disc-like and crown molecules adopt a crown conformation that self-assemble helical columns and spherical helices. A large diversity of new liquid crystalline phases self-organize from these helical columns and spherical helices. They include helical columnar hexagonal phases from crowns and from supramolecular spheres, Frank-Kasper A15 (known as cubic phase of space group Pm3¯n), σ phase (also known as tetragonal of space group P42/mnm), 12-fold quasi liquid crystals (QLC) and supramolecular orientational memory (SOM) derived complex bundles of supramolecular columnar hexagonal arrays that are not yet completely elucidated. The impact of Chandrasekhar on the discovery of self-assembling dendrons and dendrimers via his biaxial nematic liquid crystal concept will also be discussed. This perspective is dedicated to the 45 anniversary of the discovery of discotic liquid crystals and to the memory of Professor Sivaramakrishna Chandrasekhar, a modest, respectful and great scientist.

Conformationally flexible dendronized cyclotetraveratrylenes (CTTV)s self-organize a large diversity of chiral columnar, Frank-Kasper and quasicrystal phases

Primary structure endows the tertiary structure while the tertiary structure determines the function of hierarchical self-organizations. This is a well-established fundamental principle both for biological and non-biological synthetic assemblies. The role of the conformational flexibility-rigidity in this process is less understood. Here we select the conformationally flexible monodisperse tetramer of veratrole, 2,3,7,8,12,13,17,18-octamethoxy-5,10,15,20-tetrahydrotetrabenzo[a,d,g,j]-cyclododecatetraene, known as cyclotetraveratrylene (CTTV) and use it as an apex model to compare with the less flexible corresponding trimer known as cyclotriveratrylenes (CTV) and with the rigid triphenylene (Tp) and 1,3,5-trihydroxybenzene (THB) when dendronized with libraries of self-assembling dendrons and with n-alkyl groups. Unexpectedly, a large diversity of chiral helical assemblies including supramolecular columns assembled from chiral spheres and crowns, 12-fold quasi liquid crystals (QLC), Frank-Kasper A15 (space group Pm3¯n) but not σ phases (space group P42/mnm), and supramolecular orientational memory effect (SOM) were observed in the case of the dendronized CTTV. The more rigid structures at the apex provide thermally more stable helical chiral periodic and quasiperiodic self-organizations with lowed dynamics which may facilitate the freezing of metastable rather than equilibrium structures. Conformational flexibility also changes the structure of the self-organization generated from supramolecular spheres. These experiments indicate that additional studies on the topic of conformational flexibility are desirable.

Precisely Encoding Geometric Features into Discrete Linear Polymer Chains for Robust Structural Engineering.

Molecular shape is an essential parameter that regulates the self-organization and recognition process, which has not yet been well appreciated and exploited in block polymers due to the lack of precise and efficient modulation methods. This work (i) develops a robust approach to break the intrinsic symmetry of linear polymers by introducing geometric features into otherwise homogeneous chains and (ii) quantitatively highlights the critical contribution of molecular geometry/architecture to the self-assembly behaviors. Iteratively connecting homologous monomers of different side chains according to pre-designed sequences generates discrete polymers with exact chemical structure, uniform chain length, and programmable side-chain gradient along the backbone, which transcribes into diverse shapes. The precise chemistry eliminates all the defects and heterogeneities, providing a delicate platform for fundamental inquiries into the role of molecular geometry. A rich collection of unconventional complex phases, including Frank-Kasper A15 and σ phases, as well as a dodecagonal quasicrystal phase, were captured in these rigorous single-component systems. The self-assembly behaviors are strikingly sensitive to subtle variations of geometry, such that simply migrating a few methylene units among the side chains would generate substantial differences in lattice size or phase stability, or even trigger a phase transition toward distinct structures. The phenomena can be rationalized with a geometric argument that nonuniform side chain distribution leads to conformational mismatch between two immiscible blocks, resulting in varied interfacial curvatures and distinct lattice symmetries. The profound contribution demonstrates that molecular geometry is an effective and robust parameter for structural engineering.

Self-organization of rectangular bipyramidal helical columns by supramolecular orientational memory epitaxially nucleated from a Frank-Kasper σ phase

Programming living and soft complex matter via primary structure and self-organization represents the key methodology employed to design functions in biological and synthetic nanoscience. Memory effects have been used to create commercial technologies including liquid crystal displays and biomedical applications based on shape memory polymers. Supramolecular orientational memory (SOM), induced by an epitaxial nucleation mediated by the close contact spheres of cubic phases, emerged as a pathway to engineer complex nanoscale soft matter of helical columnar hexagonal arrays. SOM preserves the crystallographic directions of close contact supramolecular spheres from the 3D phase upon cooling to the columnar hexagonal periodic array. Despite the diversity of 3D periodic and quasiperiodic nanoarrays of supramolecular dendrimers, including Frank-Kasper and quasicrystal, all examples of SOM to date were mediated by Im3¯m (body-centered cubic, BCC) and Pm3¯n (Frank-Kasper A15) cubic phases. Expanding the scope of SOM to non-cubic arrays is expected to generate additional morphologies that were not yet available by any other methods. Here we demonstrate the SOM of a dendronized triphenylene that self-organizes into helical columnar hexagonal and tetragonal P42/mnm (Frank-Kasper σ) phases. Structural analysis of oriented fibers by X-ray diffraction reveals that helical columnar hexagonal domains self-organize an unusual rectangular bipyramidal morphology upon cooling from the σ phase. The discovery of SOM in a non-cubic Frank-Kasper phase indicates that this methodology may be expanded to other periodic and quasiperiodic nanoarrays organized from self-assembling dendrimers and, most probably, to other soft and living complex matter.

Shear-Modulated Rates of Phase Transitions in Sphere-Forming Diblock Oligomer Lyotropic Liquid Crystals.

Hydration of the amphiphilic diblock oligomer C16H33(CH2CH2O)20OH (C16E20) leads to concentration-dependent formation of micellar body-centered cubic (BCC) and Frank-Kasper A15 lyotropic liquid crystals (LLCs). Quiescent thermal annealing of aqueous LLCs comprising 56-59 wt % C16E20 at 25 °C after quenching from high temperatures established their ability to form short-lived BCC phases, which transform into long-lived, transient Frank-Kasper σ phases en route to equilibrium A15 morphologies on a time scale of months. Here, the frequency and magnitude of applied oscillatory shear show the potential to either dynamically stabilize the metastable BCC phase at low frequencies or increase the rate of formation of the A15 to minutes at high frequencies. Time-resolved synchrotron small-angle X-ray scattering (TR-SAXS) provides in situ characterization of the structures during shear and thermal processing. This work shows that the LLC morphology and order-order phase transformation rates can be controlled by tuning the shear strain amplitude and frequency.

Self-organisation of rhombitruncated cuboctahedral hexagonal columns from an amphiphilic Janus dendrimer

Frank-Kasper phases are available in both hard and soft complex matter. They have been discovered in metal alloys and subsequently in self-organisations of supramolecular spheres from self-assembling dendrons, dendrimers and dendronized polymers. Recently, they were found in block copolymers, lipids, surfactants, giant surfactants, nanoparticles, DNA particles and even in condensed small molecules such as N2, O2, and CO. Here we report the discovery of an amphiphilic Janus dendrimer, that self-assembles in water into vesicles known as dendrimersomes, self-organised also in bulk state into helical columns and spheres forming columnar hexagonal and a Frank-Kasper A15 phase known as Pm n. These self-organisations display a supramolecular orientational memory (SOM) effect that is induced by an epitaxial nucleation at the transition from columns to spheres and during the reverse process. This SOM effect is mediated by the closed contact supramolecular spheres from the A15 phase. In this case a rhombitruncated cuboctahedral hexagonal columnar arrangement, that to the best of our knowledge is not known in biology or synthetic chemistry, was self-organised. We believe that the addition of amphiphilic Janus dendrimers to the classes of molecules displaying Frank-Kasper phases and the SOM effect will broaden our ability to discover additional complex soft condensed matter morphologies.

Small-Molecule Modulation of Soft-Matter Frank-Kasper Phases: A Method for Adding Function to Form.

Incorporation of small amounts of α-tocopherol (vitamin E) in blends with the cellobiose-triazole-linked atactic poly(4-methyl-1-pentene) (CB-aPMP) sugar-polyolefin conjugate can be used to exert external control over thermotropic phase behavior and provide access to non-canonical soft matter Frank-Kasper A15 and σ phases. These results establish a paradigm that can be used for the further design and development of scalable quantities of soft matter FK phases of increased structural complexity and functional capability.

A15, σ, and a Quasicrystal: Access to Complex Particle Packings via Bidisperse Diblock Copolymer Blends.

A renewed focus on the phase behavior of nominally single-component, compositionally asymmetric diblock copolymers has revealed a host of previously unanticipated Frank-Kasper (FK) and quasicrystalline phases. However, these periodic and aperiodic particle packings have thus far only been reported in low molecular weight, highly conformationally asymmetric diblock copolymers, leaving researchers with a relatively small library of polymers in which these phases can be studied. In this work, we report on a simple approach to access these morphologies: blending two diblock copolymers with the same corona block length and varied core block lengths. Compositionally symmetric and asymmetric polystyrene-b-1,4-polybutadiene (SB) diblock copolymers with constant corona block lengths were blended together and shown via small-angle X-ray scattering and transmission electron microscopy to order into the FK A15 and σ phases, as well as a dodecagonal quasicrystal, providing a route to various particle packings in high molecular weight diblock copolymer melts.

Supramolecular Spheres Self-Assembled from Conical Dendrons Are Chiral.

Frank-Kasper phases and liquid quasicrystals self-organize from supramolecular spheres of dendrimers, block copolymers, surfactants and other self-assembling molecules. These spheres are expected to be achiral due to their isotropic shape. Nevertheless, supramolecular spheres from short helical stacks of crown-like dendrimers self-organize a Pm3̅ n cubic (Frank-Kasper A15) phase which exhibits chirality on the macroscopic scale. However, the chirality of classic isotropic supramolecular micellar-like spheres, generated from conical dendrons, is unknown. Here we report a library of second and third generation biphenylpropyl dendrons with chiral groups at their apex that produces single-handed chiral supramolecular spheres. Up to 480 conical dendrons self-assemble to form micellar-like spheres, with a molar mass of up to 1.1 × 106 g/mol, that self-organize into a Pm3̅ n phase with chirality detectable on the macroscopic scale. This demonstration of chirality in micellar-like spheres of a Frank-Kasper phase raises the fundamental question whether micellar-like spheres forming 3D phases generated from other soft matter such as block copolymers, surfactants, and other molecules are chiral.

Facile synthesis and linker guided self-assembly of dendron-like amphiphiles

In this work, we studied the linker effect on the nanostructures of a serious of specifically designed, functionalized polyhedral oligomeric silsesquioxane (POSS) based Dendron-like macro-isomers. The varying linkers between hydrophilic and hydrophobic POSS cages lead to topological isomers with identical composition but different molecular shapes. Their unique phase behaviors highlight remarkable effects of molecular architectures on the formation of nanostructures. Due to topological constraints, these macro-isomers assume either a fan- or a cone-molecular shape, which assembles into either hexagonally packed cylindrical phase (HEX) or Frank-Kasper A15 phase. This work provides guiding rules on designing precise molecular nanostructures with desired properties via linker engineering.

Dendronized Poly(2-oxazoline) Displays within only Five Monomer Repeat Units Liquid Quasicrystal, A15 and σ Frank-Kasper Phases.

Liquid quasicrystals (LQC) have been discovered in self-assembling benzyl ether, biphenylmethyl ether, phenylpropyl ether, biphenylpropyl ether and some of their hybrid dendrons and subsequently in block copolymers, surfactants and other assemblies. These quasiperiodic arrays, which lack long-range translational periodicity, are approximated by two Frank-Kasper periodic arrays, Pm3̅ n cubic (Frank-Kasper A15) and P42/ mnm tetragonal (Frank-Kasper σ), which have been discovered in complex soft matter in the same order and compounds. Poly(2-oxazoline)s dendronized with (3,4) nG1 minidendrons (where n denotes an alkyl chain, C nH2 n+1) self-organize into the Pm3̅ n cubic phase ( n = 14 and 15) and, as reported recently, the P42/ mnm tetragonal phase ( n = 16). However, no LQC of a poly(2-oxazoline) is yet known. Here we report the synthesis, structural and retrostructural analysis of a dendronized poly(2-oxazoline) with n = 17 which self-organizes not only into the LQC but also in the above two Frank-Kasper approximants. All three phases are observed from the same polymer within a very narrow range of degree of polymerization that corresponds to only five monomer repeat units (5 ≤ DP ≤ 10). The formation of the Pm3̅ n cubic, P42/ mnm tetragonal and LQC phases from a single polymer chain within such a narrow range of DP raises the questions of how and why each of these phases is self-organized. This system may provide a model for theoretical investigations into the self-organization of soft matter into Frank-Kasper and related periodic and quasiperiodic arrays.

Hierarchical Self-Organization of Chiral Columns from Chiral Supramolecular Spheres.

The supramolecular column is an archetypal architecture in the field of periodic liquid crystalline and crystalline arrays. Columns are generated via self-assembly, coassembly, and polymerization of monomers containing molecules shaped as discs, tapered, twin- and Janus-tapered, crowns, hat-shaped crowns, and fragments thereof. These supramolecular columns can be helical and therefore exhibit chirality. In contrast, spheres represent a fundamentally distinct architecture, generated from conical and crown-like molecules, which self-organize into body-centered cubic, Pm3̅ n cubic (also known as Frank-Kasper A15), and tetragonal (also known as Frank-Kasper σ) phases. Supramolecular spherical aggregates are not known to further assemble into a columnar architecture, except as an intermediate state between a columnar periodic array and a cubic phase. In the present work, a chiral dendronized cyclotetraveratrylene (CTTV) derivative is demonstrated to self-organize into a supramolecular column unexpectedly constructed from supramolecular spheres, with no subsequent transition to a cubic phase. Structural and retrostructural analysis using a combination of differential scanning calorimetry, X-ray diffraction (XRD), molecular modeling, and simulation of XRD patterns reveals that this CTTV derivative, which is functionalized with eight chiral first-generation minidendrons, self-organizes via a column-from-spheres model. The transition from column to column-from-spheres was monitored by circular dichroism spectroscopy, which demonstrated that both the supramolecular column and supramolecular spheres are chiral. This column-from-spheres model, which unites two fundamentally distinct self-assembled architectures, provides a new mechanism to self-organize supramolecular columnar architectures.

Hierarchical Self-Organization of AB n Dendron-like Molecules into a Supramolecular Lattice Sequence.

To understand the hierarchical self-organization behaviors of soft materials as well as their dependence on molecular geometry, a series of ABn dendron-like molecules based on polyhedral oligomeric silsesquioxane (POSS) nanoparticles were designed and synthesized. The apex of these molecules is a hydrophilic POSS cage with 14 hydroxyl groups (denoted DPOSS). At its periphery, there are different numbers (n = 1–8) of hydrophobic POSS cages with seven isobutyl groups (denoted BPOSS), connected to the apical DPOSS via flexible dendron type linker(s). By varying the BPOSS number from one to seven, a supramolecular lattice formation sequence ranging from lamella (DPOSS-BPOSS), double gyroid (space group of Ia3̅d, DPOSS-BPOSS2), hexagonal cylinder (plane group of P6mm, DPOSS-BPOSS3), Frank–Kasper A15 (space group of Pm3̅n, DPOSS-BPOSS4, DPOSS-BPOSS5, and DPOSS-BPOSS6), to Frank–Kasper sigma (space group of P42/mnm, DPOSS-BPOSS7) phases can be observed. The nanostructure formations in this series of ABn dendron-like molecules are mainly directed by the molecular geometric shapes. Furthermore, within each spherical motif, the spherical core consists hydrophilic DPOSS cages with flexible linkages, while the hydrophobic BPOSS cages form the relative rigid shell, and contact with neighbors to provide decreased interfaces among the spherical motifs for constructing final polyhedral motifs in these Frank–Kasper lattices. This study provides the design principle of molecules with specific geometric shapes and functional groups to achieve anticipated structures and macroscopic properties.

Low-symmetry sphere packings of simple surfactant micelles induced by ionic sphericity

Supramolecular self-assembly enables access to designer soft materials that typically exhibit high-symmetry packing arrangements, which optimize the interactions between their mesoscopic constituents over multiple length scales. We report the discovery of an ionic small molecule surfactant that undergoes water-induced self-assembly into spherical micelles, which pack into a previously unknown, low-symmetry lyotropic liquid crystalline Frank-Kasper σ phase. Small-angle X-ray scattering studies reveal that this complex phase is characterized by a gigantic tetragonal unit cell, in which 30 sub-2-nm quasispherical micelles of five discrete sizes are arranged into a tetrahedral close packing, with exceptional translational order over length scales exceeding 100 nm. Varying the relative concentrations of water and surfactant in these lyotropic phases also triggers formation of the related Frank-Kasper A15 sphere packing as well as a common body-centered cubic structure. Molecular dynamics simulations reveal that the symmetry breaking that drives the formation of the σ and A15 phases arises from minimization of local deviations in surfactant headgroup and counterion solvation to maintain a nearly spherical counterion atmosphere around each micelle, while maximizing counterion-mediated electrostatic cohesion among the ensemble of charged particles.