Microphase Separation of Diblock Copolymers

Diblock copolymers can form only molecular-scale small domains of microphase separation rather than macroscopic phase separation, because of the constraint of the covalent bond between the two components. According to compositions, the major compruient forms the continuous matrix, while the minor component forms the microphase domains. The most conunMi equilibrium geometric shapes of microdomains can be lamellae, gyroids, cylinders and spheres, as illustrated in Fig. 9.11, which pack orderly into a nano-scale periodic pattern and be used as nano-scale templates for the fabrication of functional nano-materials (Bates and FredticksOTi 1990 1999). 

The l(Mig period of the regularly packed microdomains, as illustrated in Fig. 9.12, can be determined by the small-angle X-ray scattering. One may make a scaling analysis on the equilibrium domain sizes from the calculation of free energy changes as follows. In comparison to the macrophase-separated polymer blends, the microphase-separated diblock copolymer system contains mainly two 

At the interfaces, the critical mixing coil sizes (proportional to the reciprocal of the mixing interaction parameter) are comparable to the interface thickness. Accordingly, 

The seccHid contribution is from the confomiational entropy of deformed polymer chains due to the separation of two blocks at the two sides of the interfaces. Accordingly, 

Here assume R(xd and the ideal coil size Rq = The total free energy contribution 

As in the case of macrophase separation, the two competing terms of enthalpic and entropic nature govern the thermodynamics of block copolymers. Similar to binary polymer bends the phase behavior of diblock copolymer melts is primarily controlled by the segregation strength and the volume fractions /a and /b = 1 - /a of the two blocks. Being covalently bonded, repulsive blocks are prevented from separating on a macroscopic level. Hence, the segregation into A- and B-rich domains 

4 Voided Double-Gyroid Thin Film Templates 

Symmetric diblock copolymers (/a — /b) arrange into a lamellar morphology, with alternating layers of the constituent blocks. Asymmetric diblock copolymers (/a /b) self-assemble into morphologies where the minority component is 

At sufficiently high temperatures (small x) the entropic terms exceed the energetic interactions, and the chains are mixed homogeneously. In this case the free energy per chain can be approximated by the A-B contact energy [5] 

The first term in Eq. (4.6) is the entropic stretching penalty derived under the assumption that the chains are uniformly stretched to a length of one-half of the lamellar domain period A. The second term represents the repulsive energetic interactions confined to the (sharp) A-B interface. It is given by the product of the contact area per chain derived under volume filling constraint, A = Na /(X/2), and the interfacial 

---

The viscoelastic effects on the morphology and dynamics of microphase separation of diblock copolymers was simulated by Huo et al. [ 126] based on Tanaka s viscoelastic model [127] in the presence and absence of additional thermal noise. Their results indicate that for

bulk modulus of both blocks, the area fraction of the A-rich phase remains constant during the microphase separation process. For each block randomly oriented lamellae are preferred. 

Xu H, Liu H, Hu Y The effect of pressure on the microphase separation of diblock copolymer melts studied by dynamic density functional theory based on equation of state, Macromol Theory Simul 16(3) 262-268, 2007b. 

Li XJ, Guo JY, Liu Y, Liang HJ. Microphase separation of diblock copolymer poly(styrene-b-isoprene) A dissipative particle dynamics simulation study. J Chem Phys 2009 130 074908. 

Precisely this latter situation arises if the confining solid surface is endowed with a chemical pattern that is both nanoscopic in size and hnite in extent. Such chemical patterns may be created by lithographic methods [179]. Atomic beams have been employed to produce hexagonal nemostruc-tures [180]. Other methods capable of creating cliemically nanostnictured substrate surfaces involve microphase separation in diblock copolymer films [181] or the use of forc( microscopy to locally oxidize silicon surfaces [182]. 

A remarkable property of polymer melts is their ability to self-assemble, driven by thermodynamic incompatibilities of the different monomers. A brief introduction to the thermodynamic theory of macrophase separation in homopolymer blends and microphase separation in diblock copolymer melts is given. In particular, the effect of controllable parameters, including the monomer interactions, the block composition. 

Bendejacq, D., Ponsinet, V., Joanicot, M., Vacher, A., Airiau, M. Chemical tuning of the microphase separation in diblock copolymers from controlled radical polymerization. 

Figure 2.3 Microphase separation in diblock copolymers. The shaded regions represent domains rich in A or B monomers, (a) /a = /b = 1/2, lamellar phase separation with flat domain interfaces, (b) /a > 1/2, spontaneous curvature of domains toward the minority phase in gyroidal, cylindrical, or spherical morphologies. The characteristic domain spacing A is typically in the range 10-100 nm.

The thermodynamic properties of block copolymers in disordered state have been studied by Leibler (1980). Using the random phase approximation (de Gennes 1979), the author developed a relation between the segmental density correlation function and the scattering vector. An order parameter, related to the reduced segmental density, was introduced. In the disordered state, this order parameter is zero, whereas for the ordered phase, it is a periodic nonzero function. Leibler demonstrated that the critical condition for microphase separation in diblock copolymers is Xa c = 10.5. 

J. Peng, Y. Xnan, H.F. Wang, Y.M. Yang, B.Y. Li, Y.C. Han, Solvent-induced microphase separation in diblock copolymer thin films with reversibly switchable morphology, Journal of Chemical Physics 120 (2004) 11163-11170. 

The behavior of ternary polymer mixtures containing a diblock copolymer with homopolymer and toluene as a function of mixture composition and temperature were investigated to obtain experimental phase diagram for solvent/copolymer/ homopolymer mixture. In order to avoid the complications associated with the microphase separation of block copolymers, the molar mass of block copolymer was kept low in our experiment (Madbouly Wolf, 2002). 

In addition to monosized nanopartide, the morphology of binary nanopartides filled in microphase separating AB diblock copolymers has also been studied. For chemically identical spherical partides, large particles are concentrated in the preferred, compatible phase and small partides spread out in the interfacial regions and in the incompatible phase of the diblock copolymer [17]. Theoretical efforts have also been made toward the morphology of copolymer filled with anisotropic particles (e.g., rod-like partides, plate-like partides, or the mixtures of particles of different shapes). It is found that the distribution of partides within the copolymers depends not only on the relative interaction energies between nanopartides and different blocks but also on the aspect ratio of the rod-like nanopartides. 

The crystalline homopolymers spatially confined in nanocylinders can be prepared using the microphase separation of block copolymers, followed by the photocleavage of block junctions (Fig. 10.4), where o-nitrobenzyl (ONB) groups inserted between different blocks are conveniently used for the photocleavage reaetion [48]. Nojima et al. [44—47] synthesized poly(e-eaprolaetone)-WocA -polystyrene (PCL-ft-PS) diblock copolymers with ONB between PCL and... 

Recently, researchers paid more attention to the guided self-assembly of block copolymer thin films on a patterned surface. The patterned surface means the surface of a constrained situation is chemically or physically modified to form a pattern with specific property and size. A series of exquisite structures are found in the microphase separation of block copolymer under the patterned surface. In the theoretic work of Wu and Dzenis [43], they designed two kinds of patterned surface to direct the block copolymer self-assembly (Fig. 15.7). The self-assembled structures are found strongly influenced by the commensurability of polymer bulk period and pattern period. With mismatched patterns on two surfaces, both MC simulation [44] and SCFT researching [45] predicted the titled lamellae and perforated lamellae structures for symmetric diblock copolymers. Petrus et al. carried out a detailed investigation on the microphase separation of symmetric and asymmetric diblock copolymers confined between two planar surfaces using DPD simulation [46,47]. It is found that various nonbulk nanostructures can be fabricated by the nanopatterns on the surfaces. 

On the other hand, reports on microphase separation of star copolymers have apparently not been published to date. We have recently synthesized A B starlike (comb-shaped) copolymers by anionic polymerization of binary vinylbenzyl-terminated PS and PI macromonomers and investigated the mi-crophase-separated structures [75]. These A B star copolymers formed a clear microphase-separated structure. In this type of A B star copolymer, there are two entropic effects at work that oppose one another, according to de la Cruz and Sanchez s theory [3]. The first is the entropy of the melt. The entropy of the star copolymer is smaller than that of the corresponding diblock copolymer melt because of the additional constraints on the A-B junction point. However, for noncritical compositions, there will be a lowering of the transition entropy... 

Figure 7.24 (and on cover) from Groot R D and T J Madden 1998. Dynamic simulation of diblock copolymer microphase separation. The Journal of Chemical Physics 108 8713-8724. Americcm Institute of Physics. 

It is well known that block copolymers and graft copolymers composed of incompatible sequences form the self-assemblies (the microphase separations). These morphologies of the microphase separation are governed by Molau s law [1] in the solid state. Nowadays, not only the three basic morphologies but also novel morphologies, such as ordered bicontinuous double diamond structure, are reported [2-6]. The applications of the microphase separation are also investigated [7-12]. As one of the applications of the microphase separation of AB diblock copolymers, it is possible to synthesize coreshell type polymer microspheres upon crosslinking the spherical microdomains [13-16]. 

LeiblerL., Theory of microphase separation in block copolymers. Macromolecules, 13, 1602, 1980. Eoerster S., Khandpur A.K., Zhao J., Bates E.S., Hamley I.W., Ryan A.J., and Bras W. Complex phase behavior of polyisoprene-polystyrene diblock copolymers near the order-disorder transition. Macromolecules, 21, 6922, 1994. 

Similar to the branches in copolymer stars and miktoarms, the grafted chains in brushes can be of different chemical compositions. Brown et al. [223] studied the microphase separation of grafted mixtures of homopolymer chains composed of immiscible A and B units and also [224] of diblock AB copolymers. In the former case, the brushes expand laterally and then experience lateral microphase separation. In the latter case, however, monomers segregate vertically to the surface forming a three layer structure. 

Then we address the dynamics of diblock copolymer melts. There we discuss the single chain dynamics, the collective dynamics as well as the dynamics of the interfaces in microphase separated systems. The next degree of complication is reached when we discuss the dynamic of gels (Chap. 6.3) and that of polymer aggregates like micelles or polymers with complex architecture such as stars and dendrimers. Chapter 6.5 addresses the first measurements on a rubbery electrolyte. Some new results on polymer solutions are discussed in Chap. 6.6 with particular emphasis on theta solvents and hydrodynamic screening. Chapter 6.7 finally addresses experiments that have been performed on biological macromolecules. 

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. 

---