Block Copolymers in the Strong Segregation Limit

In this section, we consider confined symmetric diblock copolymers in the limit %N— °o then the lamellar phase consists of a sequence of essentially pure A domains and pure B domains, separated by sharp interfaces (of width 

YAB=VxV6b 2per unit area) and the free energy at the walls, which involves interfacial tensions yAW, yBW. Such an approach was first attempted by Turner 

The first term is the entropic contribution in the bulk ( gaussian springs ), the second term accounts for the A-B interfaces. Minimization of Eq. (85) with respect to X yields the corresponding equilibrium period A,b and free energy Fb, 

Now the free energy of thin films is modified due to the appearance of surface terms yAW, yBW, and also the period may be expanded (or compressed) relative to A,b. For parallel (or horizontal , respectively) arrangements, we can write the free energy in terms of the normalized period X = X / as [36] 

In the perpendicular (or vertical ) morphology, Fig. 3b, the imposed thickness constraint acts perpendicular to the lamellar ordering, and hence the bulk period A,b is still realized. Now the amount of interface between A-rich phase and the walls and of B-rich phase and the walls is exactly the same for the anti-sym-metric arrangement (Fig. 4a) and the vertical arrangement (Fig. 3b), if one neglects the (relatively very small) regions of width w where AB-interfaces meet the walls (in case of Fig. 3b). Since the sample volume is fixed by the amount of 

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Usually the discussion of the ODT of highly asymmetric block copolymers in the strong segregation limit starts from a body-centred cubic (bcc) array of the minority phase. Phase transitions were calculated using SOFT accounting for both the translational entropy of the micelles in a disordered micelle regime and the intermicelle free energy [129]. Results indicate that the ODT occurs between ordered bcc spheres and disordered micelles. 

Figure 6.25. A lamellar microphase-separated block copolymer in the strong segregation limit - the domain size d is very much bigger than the interfacial width w.

Fig. 6. Phase diagram in the strong segregation limit for star-block copolymers with nA, A arms and nB, B arms as a function of volume fraction of the B monomer...

Floudas et al. (1997) studied theoretically and experimentally microphase segregation in block copolymer/homopolymer blends for an asymmetric diblock copolymer and homopolymer concentrations of less than 25 %. It was observed that the minority phase could solubilize only a small amount of added homopolymer. The addition of higher amounts resulted in the formation of nonequilibrium structures. Theoretical predictions in the strong segregation limit showed that (xN)c,... 

Ueda et al. [46] have measured the crystalUzation rate of the polyethylene block within polyethylene-6-(atactic polypropylene), PE-6-aPP, with a PE volume fraction of 0.48. The crystaUization of the PE block occurs with a molten aPP block covalently bonded to it. The copolymer is reported to be in the strong segregation limit. They also found a substantially lowered crystalUzation rate as compared to an analog neat PE, which was attributed to a mo-biUty reduction of the chains close to the interphase, and to the presence of non-crystallizable aPP chains close to the growth face which couid hinder the growth process. 

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