Here, we report the mechanisms of chiral transfer at various length scales in the self-assembly of enantiomeric chiral block copolymers (BCPs*). We show the evolution of homochirality from molecular chirality into phase chirality in the self-assembly of the BCPs*. The chirality of the molecule in the BCP* is identified from circular dichroism (CD) spectra, while the handedness of the helical conformation in the BCP* is determined from a split-type Cotton effect in vibrational circular dichroism spectra. Microphase separation of the BCP* is exploited to form a helical (H*) phase, and the handedness of helical nanostructure in the BCP* is directly visualized from transmission electron microscopy tomography. As examined by CD and fluorescence experiments, significant induced CD signals and a bathochromic shift of fluorescence emission for the achiral perylene moiety as a chemical junction of the BCPs* can be found while the concentration of the BCPs* in toluene solution is higher than the critical micelle concentration, suggesting a twisting and shifting mechanism initiating from the microphase-separated interface of the BCPs* leading to formation of the H* phase from self-assembly.

The significance of chirality transfer is not only involved in biological systems, such as the origin of homochiral structures in life but also in man-made chemicals and materials. How the chiral bias transfers from molecular level (molecular chirality) to helical chain (conformational chirality) and then to helical superstructure or phase (hierarchical chirality) from self-assembly is vital for the chemical and biological processes in nature, such as communication, replication, and enzyme catalysis. In this Account, we summarize the methodologies for the examination of homochiral evolution at different length scales based on our recent studies with respect to the self-assembly of chiral polymers and chiral block copolymers (BCPs*). A helical (H*) phase to distinguish its P622 symmetry from that of normal hexagonally packed cylinder phase was discovered in the self-assembly of BCPs* due to the chirality effect on BCP self-assembly. Enantiomeric polylactide-containing BCPs*, polystyrene-b-poly(l-lactide) (PS-PLLA) and polystyrene-b-poly(d-lactide) (PS-PDLA), were synthesized for the examination of homochiral evolution. The optical activity (molecular chirality) of constituted chiral repeating unit in the chiral polylactide is detected by electronic circular dichroism (ECD) whereas the conformational chirality of helical polylactide chain can be explicitly determined by vibrational circular dichroism (VCD). The H* phases of the self-assembled polylactide-containing BCPs* can be directly visualized by 3D transmission electron microscopy (3D TEM) technique at which the handedness (hierarchical chirality) of the helical nanostructure is thus determined. The results from the ECD, VCD, and 3D TEM for the investigated chirality at different length scales suggest the homochiral evolution in the self-assembly of the BCPs*. For chiral polylactides, twisted lamellae in crystalline banded spherulite can be formed by dense packing scheme and effective interactions upon helical chains from self-assembly. The handedness of the twisted lamella can be determined by using rotation experiment of polarized light microscopy (PLM). Similar to the self-assembly of BCPs*, the examined results suggest the homochiral evolution in the crystallized chiral polylactides. The results presented in this Account demonstrate the notable progress in the spectral and morphological determination for the examination of molecular, conformational, and hierarchical chirality in self-assembled twisted superstructures of chiral polymers and helical phases of block copolymers and suggest the attainability of homochiral evolution in the self-assembly of chiral homopolymers and BCPs*. The suggested methodologies for the understanding of the mechanisms of the chirality transfer at different length scales provide the approaches to give Supporting Information for disclosing the mysteries of the homochiral evolution from molecular level.

Banded spherulites are formed by crystallization of a chiral polymer that is end-capped with chromophore. Induced circular dichroism (ICD) of the chromophore can be found in the crystallized chiral polymers, giving exclusive optical response of the ICD. The ICD signals are presumed to be driven by the lamellar twisting in the crystalline spherulites, and the exclusive optical activity is attributed to the chirality transfer from molecular level to macroscopic level. To verify the suggested mechanism, the sense of the lamellar twisting in the crystalline spherulite is determined using PLM for the comparison with the ICD signals of the chromophore in the electron circular dichroism spectrum. The conformational chirality of the chiral polymer is determined by the vibrational circular dichroism spectrum. On the basis of the chiroptical results, evolution of homochirality from helical polymer chains (conformational chirality) to lamellar twisting in the banded spherulite (hierachical chirality) is suggested.

In this paper, we study solutions of difference equations λ (y n , y n+1 ,. .. , y n+m) = 0, n ∈ Z, of order m with parameter λ, and consider the case when λ has a singular limit depending on a single variable as λ → λ 0 , i.e. λ 0 (y 0 ,. .. , y m) = ϕ(y N), where N is an integer with 0 N m and ϕ is a function. We prove that if ϕ has k simple zeros then for λ close enough to λ 0 , the difference equation has a k-horseshoe among its solutions, that is, the dynamics is conjugate to the full shift with k symbols. Moreover, we show that these horseshoes change continuously in the uniform topology as λ varies. As applications of these results, we establish the horseshoe structure in families of generalized Hénon-like maps and of Arneodo-Coullet-Tresser maps near their anti-integrable limits as well as in steady states for certain lattice models.

Stereoregular vinyl polymers, poly(2-vinyl pyridine)s (P2VPs), were synthesized to examine the tacticity effect on the induced circular dichroism (ICD) via association with chiral acids. The ICD was found to be strongly dependent on the isotacticity of the P2VPs and the acidity of chiral acid in addition to its bulkiness.

Banded spherulite resulting from lamellar twisting due to the imbalanced stresses at opposite fold surfaces can be formed by isothermal crystallization of chiral polylactide and its blends with poly­(ethylene glycol) (PEG). Using a polarized light microscope, the handedness of the twisted lamella in banded spherulite is determined. With the same growth axis along the radial direction as evidenced by wide-angle X-ray diffraction (WAXD) for isothermally crystallized samples at different temperatures, the twisted lamellae of chiral polylactides (poly­(l-lactide) (PLLA) and poly­(d-lactide) (PDLA)) display opposite handedness. The split-type Cotton effect on the CO stretching motion of vibrational circular dichroism (VCD) spectra helps determine the helix handedness (i.e., conformational chirality). The results indicate that the conformational chirality can be defined by the molecular chirality through intramolecular chiral interactions. Moreover, the preferred sense of the lamellar twist in the banded spherulite corresponds to the twisting direction identified by the C–O–C vibration motion of VCD spectra, reflecting the role of intermolecular chiral interactions in the packing of polylactide helices. Similar results are obtained in the blends of chiral polylactides and poly­(ethylene glycol) (PEG, a polymer compatible with polylactide), indicating that the impact of chirality is intrinsic irrespective of the specific crystallization conditions. In contrast to the chiral polylactides, the spectrum of the crystalline stereocomplex that associates PLLA and PDLA shows VCD silence. The spectroscopic results are in line with the morphological observations. No banded spherulites are observed in the stereocomplex crystallites due to the symmetric packing of mirror L- and D-chain conformations in the fold surfaces and the crystallites core.

Surface topography has a profound effect on the development of the nervous system, such as neuronal differentiation and morphogenesis. While the interaction of neurons and the surface topography of their local environment is well characterized, the neuron–topography interaction during the regeneration process remains largely unknown. To address this question, an anisotropic surface topography resembling linear grooves made from poly(ethylene‐vinyl acetate) (EVA), a soft and biocompatible polymer, using nanoimprinting, is established. It is found that neurons from both the central and peripheral nervous system can survive and grow on this grooved surface. Additionally, it is observed that axons but not dendrites specifically align with these grooves. Furthermore, it is demonstrated that neurons on the grooved surface are capable of regeneration after an on‐site injury. More importantly, these injured neurons have an accelerated and enhanced regeneration. Together, the data demonstrate that this anisotropic topography guides axon growth and improves axon regeneration. This opens up the possibility to study the effect of surface topography on regenerating axons and has the potential to be developed into a medical device for treating peripheral nerve injuries.

A series of poly(4-vinylpyridine)-b-poly(ε-caprolactone) (P4VP-PCL) diblock copolymers have been synthesized and used for the formation of nanostructures with tunable colors arising from the association of chromophores with P4VP block in P4VP-PCL. The association of chromophores leads to the bathochromical shifts of charge transfer absorption peaks, resulting in the color appearance into the visible region. To achieve the formation of well-defined nanostructured materials, the phase behavior of the mixtures of chromophore/P4VP-PCL was systematically examined. As evidenced by transmission electron microscopy and small-angle X-ray scattering (SAXS), the phase transformation of self-assembled nanostructures can be easily induced by introducing chromophores due to the association of 2-methylidenepropanedinitrile in the chromophores with the lone-pair electron of nitrogen in P4VP block (that is the increase on the effective volume fraction of P4VP, as identified by SAXS experiments through the analysis of one-dimensional correlation function). As a result, by taking advantage of charge transfer and corresponding morphologies from transformation, well-defined nanostructured films resulting from mixing of chromophore and P4VP-PCL offer the possibility to create stimuli-responsive nanomaterials with tunable color.