Compositional and Orientational Ordering in Rod−Coil Diblock Copolymer Melts

General weak segregation theory with an application to monodisperse semi-flexible diblock copolymers

A general theory has been developed for a polydisperse semi-flexible multi-block copolymer melt. Using the Bawendi-Freed approach to model semi-flexible chains, an expression for the Landau free energy is derived in the weak segregation regime, which includes density and orientation order-parameters. The orientation order-parameter is described in the smectic phase and in more complicated structures, such as the hexagonal phase. The Landau free energy contains contributions of two kinds of interactions. The first kind is the Flory-Huggins interaction, which describes the incompatibility of chemically different blocks and may induce microphase separation. The second kind is the Maier-Saupe interaction, which may induce nematic ordering. In the framework of the weak segregation limit, the Landau theory allows us to predict phase structures in the melt as a function of the composition, persistence length, and the strength of the Flory-Huggins and Maier-Saupe interaction. The general theory is applied to a simple system of monodisperse semi-flexible diblock copolymers. In several phase diagrams, a number of possible phase structures are predicted, such as the bcc, hexagonal, smectic-A, smectic-C, and nematic phase. The influence of the Maier-Saupe interaction on the microphase structure is thoroughly discussed.

Liquid-Crystal Ordering and Microphase Separation in the Lamellar Phase of Rod-Coil-Rod Triblock Copolymers. Molecular Theory and Computer Simulations

A molecular model of the orientationally ordered lamellar phase exhibited by asymmetric rod-coil-rod triblock copolymers has been developed using the density-functional approach and generalizing the molecular-statistical theory of rod-coil diblock copolymers. An approximate expression for the free energy of the lamellar phase has been obtained in terms of the direct correlation functions of the system, the Flory-Huggins parameter and the Maier-Saupe orientational interaction potential between rods. A detailed derivation of several rod-rod and rod-coil density-density correlation functions required to evaluate the free energy is presented. The orientational and translational order parameters of rod and coil segments depending on the temperature and triblock asymmetry have been calculated numerically by direct minimization of the free energy. Different structure and ordering of the lamellar phase at high and low values of the triblock asymmetry is revealed and analyzed in detail. Asymmetric rod-coil-rod triblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter and for several values of the triblock asymmetry. It has been found that the lamellar phase appears to be the most stable one at strong segregation. The density distribution of the coil segments and the segments of the two different rods have been determined for different values of the segregation strength. The simulations confirm the existence of a weakly ordered lamellar phase predicted by the density-functional theory, in which the short rods separate from the long ones and are characterized by weak positional ordering.

Different Mechanisms of Translational Symmetry Breaking in Liquid-Crystal Coil–Rod–Coil Triblock Copolymers

A molecular-statistical theory of coil-rod–coil triblock copolymers with orientationally ordered rod-like fragments has been developed using the density functional approach. An explicit expression for the free energy has been obtained in terms of the direct correlation functions of the reference disordered phase, the Flory–Huggins parameter and the potential of anisotropic interaction between rigid rods. The theory has been used to derive several phase diagrams and to calculate numerically orientational and translational order parameter profiles for different polymer architecture as a function of the Flory–Huggins parameter, which specifies the short-range repulsion and as functions of temperature. In triblock copolymers, the nematic–lamellar transition is accompanied by the translational symmetry breaking, which can be caused by two different microscopic mechanisms. The first mechanism resembles a low dimensional crystallization and is typical for conventional smectic liquid crystals. The second mechanism is related to the repulsion between rod and coil segments and is typical for block copolymers. Both mechanisms are analyzed in detail as well as the effects of temperature, coil fraction and the triblock asymmetry on the transition into the lamellar phase.

Synthesis and Self-Assembly of Conjugated Block Copolymers

In the past two decades, conjugated polymers (CPs) have drawn great attention due to their excellent conductivity and charge mobility, rendering them broad applications in organic electronics. Controlling over the morphologies and nanostructures of CPs is very important to improve the performance of CP-based devices, which is still a tremendously difficult task. Conjugated block copolymers (cBCPs), composed of different CP blocks or CP coupled with coiled polymeric blocks, not only maintain the advantages of high conductivity and mobility but also demonstrate features of morphological versatility and tunability. Due to the strong π-π interaction and crystallinity of the conjugated backbones, the self-assembly behaviors of cBCPs are very complicated and largely remain to be explored. In this tutorial review, we first summarize the general synthetic methods for different types of cBCPs. Then, recent studies on the self-assembly behaviors of cBCPs are discussed, with an emphasis on the structural factors that affect the morphologies of cBCPs both in bulk and thin film states. Finally, we briefly provide our outlook on the future research of the self-assembly of cBCPs.

Liquid Crystal Ordering in the Hexagonal Phase of Rod-Coil Diblock Copolymers

Density functional theory of rod-coil diblock copolymers, developed recently by the authors, has been generalised and used to study the liquid crystal ordering and microphase separation effects in the hexagonal, lamellar and nematic phases. The translational order parameters of rod and coil monomers and the orientational order parameters of rod-like fragments of the copolymer chains have been determined numerically by direct minimization of the free energy. The phase diagram has been derived containing the isotropic, the lamellar and the hexagonal phases which is consistent with typical experimental data. The order parameter profiles as functions of temperature and the copolymer composition have also been determined in different anisotropic phases. Finally, the spatial distributions of the density of rigid rod fragments and of the corresponding orientational order parameter in the hexagonal phase have been calculated.

Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod-coil diblock copolymers

Symmetric rod-coil diblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter. It has been found that the tilted lamellar phase appears to be the most stable one at strong segregation. The rod-coil copolymer tilt angle and orientational order parameters have been determined as functions of the segregation strength. The density functional theory of rod-coil diblock copolymers has been generalized to the case of the tilted lamellar phase and used to study the stability of the orthogonal lamellar phase with respect to tilt. The orthogonal phase indeed appears to be unstable in the broad region of the parameter space in the case of relatively strong segregation. It has also been shown that the transition into the tilted lamellar phase is determined by a strong coupling between two independent tilt order parameters.

Molecular theory of liquid-crystal ordering in rod-coil diblock copolymers

Molecular-statistical theory of rod-coil diblock copolymers is proposed using the general density functional approach which enables one to consider the cases of both weak and strong segregation. The free energy of the system is expressed as a functional of the phase-space densities of rod and coil monomers, which depend on the orientational and translational order parameters. Temperature-concentration phase diagrams are obtained and the profiles of all order parameters are calculated numerically by minimizing the polymer free energy. The lamellar phase is shown to possess strong orientational order which is partially induced by the phase structural anisotropy. The enhanced stability of the lamellar phase is determined by a combination of the microphase separation effects and the emergence of long-range smectic order.

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.

Demixing by a Nematic Mean Field: Coarse-Grained Simulations of Liquid Crystalline Polymers

Liquid crystalline polymers exhibit a particular richness of behaviors that stems from their rigidity and their macromolecular nature. On the one hand, the orientational interaction between liquid-crystalline motifs promotes their alignment, thereby leading to the emergence of nematic phases. On the other hand, the large number of configurations associated with polymer chains favors formation of isotropic phases, with chain stiffness becoming the factor that tips the balance. In this work, a soft coarse-grained model is introduced to explore the interplay of chain stiffness, molecular weight and orientational coupling, and their role on the isotropic-nematic transition in homopolymer melts. We also study the structure of polymer mixtures composed of stiff and flexible polymeric molecules. We consider the effects of blend composition, persistence length, molecular weight and orientational coupling strength on the melt structure at the nano- and mesoscopic levels. Conditions are found where the systems separate into two phases, one isotropic and the other nematic. We confirm the existence of non-equilibrium states that exhibit sought-after percolating nematic domains, which are of interest for applications in organic photovoltaic and electronic devices.

Effect of Geometrical Asymmetry on the Phase Behavior of Rod-Coil Diblock Copolymers

The effect of geometrical asymmetry β (described by the length-diameter ratio of rods) on the rod-coil diblock copolymer phase behavior is studied by implementation of self-consistent field theory (SCFT) in three-dimensional (3D) position space while considering the rod orientation on the spherical surface. The phase diagrams at different geometrical asymmetry show that the aspect ratio of rods β influences not only the order-disorder transition (ODT) but also the order-order transition (OOT). By exploring the phase diagram with interactions between rods and coils plotted against β, the β effect on the phase diagram is similar to the copolymer composition f. This suggests that non-lamellae structures can be obtained by tuning β, besides f. When the rods are slim compared with the isotropic shape of the coil segment (β is relatively large), the phase behavior is quite different from that of coil-coil diblock copolymers. In this case, only hexagonal cylinders with the coil at the convex side of the interface and lamella phases are stable even in the absence of orientational interaction between rods. The phase diagram is no longer symmetrical about the symmetric copolymer composition and cylinder phases occupy the large area of the phase diagram. The ODT is much lower than that of the coil-coil diblock copolymer system and the triple point at which disordered, cylinder and lamella phases coexist in equilibrium is located at rod composition f_R = 0.66. In contrast, when the rods are short and stumpy (β is smaller), the stretching entropy cost of coils can be alleviated and the phase behavior is similar to coil-coil diblocks. Therefore, the hexagonal cylinder phase formed by coils is also found beside the former two structures. Moreover, the ODT may even become a little higher than that of the coil-coil diblock copolymers due to the large interfacial area per chain provided by the stumpy rods, thus compensating the stretching entropy loss of the coils.

Theoretical simulations of nanostructures self-assembled from copolymer systems

This article provides an overview of recent simulation investigations of the nanostructures and structure–property relationships in copolymer systems.

Nano-organization of amylose-b-polystyrene block copolymer films doped with bipyridine

This paper discusses the self-assembly of rod-coil amylose-b-polystyrene (Mal-b-PS) block copolymer thick and thin films. The nano-organization falls in an interdomain spacing d of about 10 nm, much smaller than flexible-flexible petrol block copolymer systems. Additionally, hydrogen-bonding interactions between carbohydrate rods (amylose) and 4',4-bipyridine (bipy) molecules induces phase transitions. Indeed, adding bipy in maltooctadecaose-block-polystyrene (Mal18-b-PS) copolymers results, at room temperature, in the formation of a lamellar phase having Mal18 bipy-rich nanodomains instead of hexagonal close-packed (HCP) of cylinders made of Mal18, whereas a coexistence of Mal7bipy-rich cylindrical and spherical nanodomains are formed from maltoheptaose-b-polystyrene (Mal7-b-PS) copolymers instead of a poorly organized array of Mal7-based cylinders. On heating, the Mal7bipy-b-PS system shows more rich phase behavior as compared to the Mal7-b-PS one due to weakening of hydrogen bonding with temperature. Such a system is of great interest in developing active layers in light-emitting diodes (LEDs) or in photovoltaic cells to realize devices with an optimal structure, that is, having large interface area and domain size with similar exciton diffusion length (10 nm).

In-situ template synthesis of a polymer/semiconductor nanohybrid using amphiphilic conducting block copolymers

In this study, we synthesized organic/inorganic hybrid materials containing cadmium sulfide (CdS) nanoparticles using a novel amphiphilic conducting block copolymer as a synergistic structure-directing template and an efficient exciton quencher of the hybrid. The amphiphilic rod-coil block copolymer of polyphenylene-b-poly(2-vinyl pyridine) (PPH-PVP) was first prepared from its coil-coil precursor block copolymer of poly(1,3-cyclohexadiene)-b-poly(2-vinyl pyridine) (PCHD-PVP) by using sequential anionic polymerization followed by the aromatization reaction of converting the PCHD block to form conducting PPH. The synthesized PCHD-PVP block copolymers self-assembled into different bulk nanostructures of lamellae, cylinders, and spheres at a volume fraction similar to that of many coil-coil block copolymer systems. However, an enhanced chain-stiffness-induced morphological transformation was observed after the aromatization reaction. This is evidenced by the TEM observation in which both spherical and cylindrical structured PCHD-PVPs transform into lamellar structured PPH-PVPs after aromatization. In addition to the bulk-phase transformation, the rigid-rod characteristic of the conducting PPH block also affects the self-assembling property of the block copolymers in their solution state. CdS nanoparticles were synthesized in situ in a selective solvent of THF using PCHD-PVP and PPH-PVP micelles as nanoreactors. The PPH-PVP/Cd ion in THF exhibits a new ringlike structure of uniform size (approximately 50 nm) with PPH in the inner rim and complexed PVP/Cd ions in the outer rim as a result of the effects of strong intermolecular forces between PPH segments and the solvophobic interaction. CdS nanoclusters were subsequently synthesized in situ from the PPH-PVP/Cd(2+) ring structure, forming a nanohybrid with intimate contact between the PPH domain and CdS nanoparticles. In particular, we found that there is an efficient energy/electron transfer between the conducting PPH domain and CdS nanoparticles in the hybrid, resulting in an enhanced PL quenching effect. The novel nanohybrid shows the potential to be used for optoelectronic applications.