Diblock copolymer weak segregation

Figure B3.6.5. Phase diagram of a ternary polymer blend consisting of two homopolymers, A and B, and a synnnetric AB diblock copolymer as calculated by self-consistent field theory. All species have the same chain length A and the figure displays a cut tlirough the phase prism at%N= 11 (which corresponds to weak segregation). The phase diagram contains two homopolymer-rich phases A and B, a synnnetric lamellar phase L and asynnnetric lamellar phases, which are rich in the A component or rich in the B component ig, respectively. From Janert and Schick [68].

The phase diagram for weakly segregated diblocks was first computed within the Landau mean field approximation by Leibler (1980). Because it has proved to be one of the most influential theories for microphase separation in block copolymers, an outline of its essential features is given here.The reader is referred to the original paper by Leibler (1980) for a complete account of the theory. 

The expressions 2.7-2.12 which define the Leibler structure factor have been widely used to interpret scattering data from block copolymers (Bates and Fredrickson 1990 Mori et al. 1996 Rosedale et al. 1995 Schwahn et al. 1996 Stiihn et al. 1992 Wolff et al. 1993). The structure factor calculated for a diblock with / = 0.25 is shown in Fig. 2.39 for different degrees of segregation JV. Due to the Gaussian conformation assumed for the chains (Leibler 1980), the domain spacing in the weak segregation limit is expected to scale as d Nm. 

Fig. 2.40 Phase diagram for diblock copolymers in the weak segregation limit (Leibler 1980).

Computer simulations of a range of properties of block copolymer micelles have been performed by Mattice and co-workers.These simulations have been based on bead models for copolymer chains on a cubic lattice. Types of allowed moves for bead chains are illustrated in Fig. 3.27. The formation of micelles by diblock copolymers under weak segregation conditions was simulated with pairwise interactions between A and B beads and between the A bead and vacant sites occupied by solvent, S (Wang et al. 19936). This leads to the formation of micelles with a B core. The cmc was found to depend strongly on fVB and % = x.w = %AS. In the range 3 < (xlz)N < 6, where z is the lattice constant, the cmc was found to be exponentially dependent onIt was found than in the micelles the insoluble block is slightly collapsed, and that the soluble block becomes stretched as Na increases, with [Pg.178]

Figure 13.11 Phase diagram for a diblock copolymer in the weak-segregation limit predicted by (a) the Leibler mean-field theory and (b) the Fredrickson-Helfand fluctuation theory. (From Bates et al., reprinted with permission from J. Chem, Phys. 92 6255, Copyright 1990, American Institute of Physics.)...

A weak-segregation theory has also been developed by Fredrickson (1994) to explain the alignment behavior of diblock copolymers. In this theory, perpendicular alignment is predicted near Toot at frequencies that are high compared to rates of fluctuations (but low compared to molecular time scales) as a result of coupling of composition fluctuations to the shearing field. Well below Todt, these fluctuations are small, and mechanical contrast between the blocks, however small, dominates and favors parallel alignment. 

Fig. 3. Computer simulation results using a time-dependent Ginzburg-Landau approach, showing the microstructural evolution after a temperature jump from the lamellar phase to the hexagonal cylinder phase for a moderately asymmetric diblock copolymer. The time units are arbitrary. (Reprinted with permission from Polymer 39, S. Y. Qi and Z.-G. Zheng, Weakly segregated block copolymers Anisotropic fluctuations and kinetics of order-order and order-disorder transitions, 4639-4648, copyright 1998, with permission of Excerpta Medica Inc.)...

Fig. 42. Theoretical phase diagram for diblock copolymers in the weak segregation limit The left side shows the mean field result of LeiUer [43], the right side the theory of Fredrickson and Jfelfand [58] which includes fluctuation corrections, for an effective degree of polymerization N = 104. LAM, Hex, BCC denote the various mesophases lamellar, hexagonal (Le., cylindrical morphology) and body-centered cubic (i.e., spherical micellar morphology). From Bates and Fredrickson (39)...

Predictions (61) and (62) have been qualitatively confirmed in experiments for a symmetrical diblock copolymer melt [147] (see Fig. 12). We show in Sec.V.B that these systems are indeed closely related to ternary amphiphilic systems, and, in the weak segregation regime, can be described by the same Ginzburg-Landau models. 

Tsori Y, Andelman D (2001) Diblock copolymer thin 1ms Parallel and perpendicular lamellar phases in the weak segregation limit. Eiu Phys JE 5 605-614... 

Hajduk DA, Harper PE, Gruner SM, Honeker CC, Kim G, Thomas EL, Fetters LJ (1994) The Gyroid A New Equilibrium Morphology in Weakly Segregated Diblock Copolymers. Macromolecules 27 4063-4075. 

For blends containing diblock copolymers, interface enrichment by the copolymers as well as the potential reduction of the interfacial tension was investigated by Muller and Binder recently (Muller and Binder 2000). For weak segregation, the addition of copolymers led to compatibilization. At high incompatibilities, the homopolymer-rich phase could accommodate only a small fraction of the copolymer before the formation of a copolymer lamellar phase. The analysis of interfacial fluctuations yielded an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation. 

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