Phase diagram for diblock copolymers calculated with the SCFT showing regions of stability for disordered (DIS), lamellar (L), bicontinuous gyroid with symmetry (), cylindrical (H), BCC packed spheres (), and closed packed spheres (CPS) phases (Ref. 4).
Schematic representation of a diblock copolymer chain modeled as two soft spheres with fluctuating radii of gyration and distance between their centers of mass (Ref. 36).
Isotropically averaged structure factor of the minority component A calculated in the disordered phase for various χN in the system with M = 4000 chains. Continuous curves are data fits obtained with a modified Leibler structure factor, Eq. (3.15).
Inverse of the peak intensity of the structure factor for various χN in the system with M = 4000 chains. The ODT as evaluated by a linear extrapolation of the data toward is
Mean-square radii of gyration of the A and B blocks, , , and mean-square radius of gyration of the whole chain at various χN both in the disordered and ordered phases (M = 4000). Values are normalized with respect to χN = 0.
Snapshot of the cylindrical morphology shown as isosurfaces obtained in the simulation, χN = 30.0, (), and M = 4000 chains.
Structure factor of the minority component calculated for the system with M = 4000 chains at χN = 30.0 . The structure factor has two higher order peaks characteristic of the cylindrical morphology.
Structure factor of the minority component calculated for the system with M = 4000 chains at χN = 70.0 . The structure factor has five higher order peaks characteristic of the gyroid morphology. In addition, there are two peaks between and which are not typical for the gyroid.
Region of stability of the gyroid phase as calculated with the SCFT (Ref. 3).
Snapshot of one unit cell of the gyroid morphology obtained in the simulation. Here χN = 40.0, (), and M = 2430 chains.
Structure factor calculated for the simulated gyroid morphology showing ten higher order peaks characteristic of the gyroid. The structure factor was averaged over the last 20 000 MCS. The system parameters are the same as in Fig. 10.
Simulated phase diagram for the pure diblock copolymer system (G gyroid, H cylindrical, L lamellar, Co disordered continuous network, and Dis disordered). The gyroid phase is limited by the cylindrical phase on the left and a metastable perforated morphology on the right that converged into the lamellar phase as the simulation proceeded. Below χN = 26.0 a narrow region of the cylindrical morphology is encountered, whereas above χN = 44.0, a disordered continuous network is found resembling a defect gyroid phase. Dashed straight lines depict approximately the region of stability of the gyroid phase. Five independent runs were performed to obtain the structures at each set of parameters and χN on the phase diagram.
Structure factor calculated for the simulated gyroid morphology in the vicinity of the order–order transition point between cylindrical and gyroid phases, χN = 26.0 ( M = 1701 chains). The structure factor has only two higher order peaks of the gyroid located at relative positions and , the second order peak is absent. The structure factor was averaged over the last 20 000 MCS.
Mean-square radii of gyration of the minority A-blocks and the majority B-blocks near the center of the node. The system parameters are the same as in Fig. 10.
Mean-square distance between blocks A and B of the chain near the center of the node. The system parameters are the same as in Fig. 10.
Values of fitting parameters α, , δ and the radius of gyration of the whole chain .
Free energy per chain in units calculated for various simulated morphologies: gyroid (G), cylindrical (H), lamellar (L), and disordered continuous network (CN).
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