Process-Accessible States of Block Copolymers

Pathway-dependent Shape Transformation of Polymeric Vesicles under UV Light and the Assembly of UV-irradiated Polymer

Shape transformation of polymer particles is generally a nonequilibrium dynamics process. Controlling the shape transformation of polymers is increasingly attractive and challenging for scientists due to their extensive use in drug delivery and cancer therapy. Herein, we investigated the UV-triggered shape transformation pathway of polymeric vesicles assembled from Polystyrene-block-poly(4-vinylpyridine) and 4-hydroxyazobenzene (PS-b-P4VP(Azo-OH)) and the direct assembly pathway of UV-irradiated PS-b-P4VP(Azo-OH) homogeneous solution. In the shape transformation process, well-assembled vesicles can be transformed into toroid, cylindrical, rod-like, and spherical micelles. In the direct assembly pathway, rod-like and spherical micelles can be obtained. Interestingly, the toroid micelles can be obtained only from the UV-triggered shape transformation pathway. Contrasting the two pathways reveals the pathway dependence of PS-b-P4VP(Azo-OH) assembly, suggesting that the final assembly morphology is determined by the initial state and dynamic process. The speed of UV-triggered shape transformation and the final morphology of assemblies can be tuned easily by adjusting the UV illuminance, time, and content of Azo-OH addition. Moreover, the light-responsive polymeric vesicles can be used as drug carriers and have the potential to release drugs precisely.

The Process-Directed Self-Assembly of Block Copolymer Particles

The kinetic paths of structural evolution and formation of block copolymer (BCP) particles are explored using dynamic self-consistent field theory (DSCFT). It is shown that the process-directed self-assembly of BCP immersed in a poor solvent leads to the formation of striped ellipsoids, onion-like particles and double-spiral lamellar particles. The theory predicts a reversible path of shape transition between onion-like particles and striped ellipsoidal ones by regulating the temperature (related to the Flory-Huggins parameter between the two components of BCP, χAB ) and the selectivity of solvent toward one of the two BCP components. Furthermore, a kinetic path of shape transition from onion-like particles to double-spiral lamellar particles, and then back to onion-like particles is demonstrated. By investigating the inner-structural evolution of a BCP particle, it is identified that changing the intermediate bi-continuous structure into a layered one is crucial for the formation of striped ellipsoidal particles. Another interesting finding is that the formation of onion-like particles is characterized by a two-stage microphase separation. The first is induced by the solvent preference, and the second is controlled by the thermodynamics. The findings lead to an effective way of tailoring nanostructure of BCP particles for various industrial applications.

Enhanced dielectric permittivity of hierarchically double-gyroid nanocomposites via macromolecular engineering of block copolymers

It is a challenging task to realize the periodically bicontinuous gyroid nanostructures of flexible nanocomposites with high loading of functionalized nanoparticles, which could exhibit high dielectric permittivity for energy storage and electronic devices. Herein, with the aid of the concept of macromolecular engineering, we propose novel nanocomposites, composed of A'(A''B)_n miktoarm star copolymers and nanoparticles, to obtain a double-gyroid structure through self-consistent field theory coupled with density functional theory. By tailoring the architecture of this copolymer, a large window of the double-gyroid phase extending to a high loading concentration of nanoparticles is achieved, leading to a hierarchical structure of a percolation network of nanoparticles within the gyroid channels. Furthermore, the finite difference quasielectrostatic method is integrated to reveal an enhanced dielectric permittivity of the structured nanocomposites by increasing the loading concentration of nanoparticles. The simultaneous achievement of an ordered double-gyroid phase and high loading nanoparticles represents a crucial step toward the realization of fully three-dimensional network-like metamaterials via a rational molecular design of nanocomposites.

Kinetic Pathways of Block Copolymer Directed Self-Assembly: Insights from Efficient Continuum Modeling

We introduce a computationally efficient continuum technique to simulate the complex kinetic pathways of block copolymer self-assembly. Subdiffusive chain dynamics is taken into account via nonlocal Onsager coefficients. An application to directed self-assembly of thin films of diblock copolymers on patterned substrates reveals the conditions under which experimentally observed metastable structures intervene in the desired thin-film morphology. The approach generalizes easily to multiblock copolymers and more complex guiding patterns on the substrate, and its efficiency allows for the systematic optimization of guiding patterns and process conditions.

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 f_A < 1/2. Breaking this generic rule so that the spherical domains are formed by the majority A blocks (f_A > 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 f_A ∼ 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.

Numerical algorithms for solving self-consistent field theory reversely for block copolymer systems

Besides dictating the equilibrium phase diagram, the rugged free-energy landscape of AB block copolymers gives rise to a multitude of non-equilibrium phenomena. Self-consistent field theory (SCFT) can be employed to calculate the mean-field free energy, F [ ϕ A t a r g e t ] , of a non-equilibrium unstable state that is characterized by a given spatial density distribution, ϕ A t a r g e t , in the incompressible system. Such a free-energy functional is the basis of describing the structure formation by dynamic SCFT techniques or the identification of minimum free-energy paths via the string method. The crucial step consists in computing the external potential fields that generate the given density distribution in the corresponding system of non-interacting copolymers, i.e., the potential-to-density relation employed in equilibrium SCFT calculations has to be inverted (reverse SCFT calculation). We describe, generalize, and evaluate the computational efficiency of two different numerical algorithms for this reverse SCFT calculation-the Debye-function algorithm based on the structure factor and the field-theoretic umbrella-potential (FUP) algorithm. In contrast to the Debye-function algorithm, the FUP algorithm only yields the exact mean-field values of the given target densities in the limit of a strong umbrella potential, and we devise a two-step variant of the FUP algorithm that significantly mitigates this issue. For Gaussian copolymers, the Debye-function algorithm is more efficient for highly unstable states that are far away from the equilibrium, whereas the improved FUP algorithm outperforms the Debye-function algorithm closer to metastable states and is easily transferred to more complex molecular architectures.

Purely entropic self-assembly of the bicontinuous Ia3d gyroid phase in equilibrium hard-pear systems

We investigate a model of hard pear-shaped particles which forms the bicontinuous Ia[Formula: see text]d structure by entropic self-assembly, extending the previous observations of Barmes et al. (2003 Phys. Rev. E68, 021708. (doi:10.1103/PhysRevE.68.021708)) and Ellison et al. (2006 Phys. Rev. Lett.97, 237801. (doi:10.1103/PhysRevLett.97.237801)). We specifically provide the complete phase diagram of this system, with global density and particle shape as the two variable parameters, incorporating the gyroid phase as well as disordered isotropic, smectic and nematic phases. The phase diagram is obtained by two methods, one being a compression-decompression study and the other being a continuous change of the particle shape parameter at constant density. Additionally, we probe the mechanism by which interdigitating sheets of pears in these systems create surfaces with negative Gauss curvature, which is needed to form the gyroid minimal surface. This is achieved by the use of Voronoi tessellation, whereby both the shape and volume of Voronoi cells can be assessed in regard to the local Gauss curvature of the gyroid minimal surface. Through this, we show that the mechanisms prevalent in this entropy-driven system differ from those found in systems which form gyroid structures in nature (lipid bilayers) and from synthesized materials (di-block copolymers) and where the formation of the gyroid is enthalpically driven. We further argue that the gyroid phase formed in these systems is a realization of a modulated splay-bend phase in which the conventional nematic has been predicted to be destabilized at the mesoscale due to molecular-scale coupling of polar and orientational degrees of freedom.