Abstract
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 fR = 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.
Highlights
In recent years, rod-coil diblock copolymers have increasingly attracted significant attention both in theory and in experiments as they can simultaneously show liquid crystalline behavior alongside microphase separation as coil-coil diblock copolymers [1,2]
In most previous papers the orientational interaction was chosen as μN = 4χN to ensure the liquid crystalline phase behavior of the diblock copolymer system with rods aligning in a strong packing formation with each other during phase separation to form a flat interface, which is a lamellar structure [9,14]
[31], formed byby rods only occur at relatively highhigh coil and hexagonal hexagonal cylinders cylinderswith withelliptical ellipticalcross-sections cross-sections formed rods only occur at relatively fractions and strong orientational interactions between rods
Summary
Rod-coil diblock copolymers have increasingly attracted significant attention both in theory and in experiments as they can simultaneously show liquid crystalline behavior alongside microphase separation as coil-coil diblock copolymers [1,2]. After ignoring the orientational interaction to manifest the rod stiffness effect, Müller and Schick further pointed out that only structures with coils at the convex side of the rod-coil interface were stable by the self-consistent field equations through a partially numerical evaluation of the single chain partition function [20] These results are not quantified in terms of changing the geometry asymmetry and did not take the rod diameter Matsen and Barett calculated the phase behavior of rod-coil diblock copolymers in one-dimensional (1D) space by SCFT, in which the geometrical asymmetry parameter ν was firstly introduced, incorporating the effect of the rod diameter, which makes it possible to discuss the interface effect of rods and coils [8] This parameter was defined as ν = aN1/2 /Nb, where a, b and N are the coil Kuhn length, the rod Kuhn length and the total molecular weight, respectively. The full understanding of the geometrical asymmetry effect on the phase behavior will provide guidance to designing the self-assembled microstructures in experiments
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