Domains in block copolymers

A number of researchers have used surface energy libraries to examine the self-assembly of block copolymer species in thin films. It is well known that substrate-block interactions can govern the orientation, wetting symmetry and even the pattern motif of self-assembled domains in block copolymer films [29]. A simple illustration of these effects in diblock copolymer films is shown schematically in Fig. 6. However, for most block copolymer systems the exact surface energy conditions needed to control these effects are unknown, and for many applications of self-assembly (e.g., nanolithography) such control is essential. 

Craze flow stress of PS with sorbed diluent at the solubility limit Cavitation strength of heterophase domain in block copolymer 6 Ratio of des( nding to the ascending slopes of the traction displacement law locally accompanying craze matter production, as defined in Ref. 

The efficiency of electric fields for the alignment of domains in block copolymer thin films has been mainly demonstrated in PS-b-PMMA systems where PS forms the matrix. 

The above equations gave reasonably reliable M value of SBS. Another approach to modeling the elastic behavior of SBS triblock copolymer has been developed [202]. The first one, the simple model, is obtained by a modification of classical rubber elasticity theory to account for the filler effect of the domain. The major objection was the simple application of mbber elasticity theory to block copolymers without considering the effect of the domain on the distribution function of the mbber matrix chain. In the derivation of classical equation of rabber elasticity, it is assumed that the chain has Gaussian distribution function. The use of this distribution function considers that aU spaces are accessible to a given chain. However, that is not the case of TPEs because the domain also takes up space in block copolymers. 

A. Haryono and W. H. Binder, Controlled arrangement of nanoparticle arrays in block-copolymer domains, Small, 2006, 2, 600. 

The more recently developed cryo-TEM technique has started to be used with increasing frequency for block copolymer micelle characterization in aqueous solution, as illustrated by the reports of Esselink and coworkers [49], Lam et al. [50], and Talmon et al. [51]. It has the advantage that it allows for direct observation of micelles in a glassy water phase and accordingly determines the characteristic dimensions of both the core and swollen corona provided that a sufficient electronic contrast is observed between these two domains. Very recent studies on core-shell structure in block copolymer micelles as visualized by the cryo-TEM technique have been reported by Talmon et al. [52] and Forster and coworkers [53]. In a very recent investigation, cryo-TEM was used to characterize aqueous micelles from metallosupramolecular copolymers (see Sect. 7.5 for further details) containing PS and PEO blocks. The results were compared to the covalent PS-PEO counterpart [54]. Figure 5 shows a typical cryo-TEM picture of both types of micelles. 

The self-assembly of block polymers, in the bulk, thin film and solution states, produces uniformly sized nanostructured patterns that are very useful for nanofabrication. Optimal utilization of these nanoscopic patterns requires complete spatial and orientational control of the microdomains. However, the microdomains in the bulk state normally have grain sizes in the submicron range and have random orientations. In block copolymer thin films, the natural domain orientations are generally not desirable for nanofabrication. In particular, for composition-asymmetric cylindrical thin films, experimental... 

Figure 10. Illustration of influence of domain formation in block copolymers according to the models of Helfand and coworkers. The free energy is shown as a function of the size and separation of the domains of varying composition. (The spontaneous separations may be analogous to the way superstructure is formed in natural polymers of plants and animals.)...

The properties of block copolymers are dependent on the length of the sequences of repeating units, or domains. The domains in typical commercial block copolymers of styrene and butadiene are sufficiently long such that the products are flexible plastics. They are called thermoplastic elastomers (TPE). It should be noted that although the Ts for random copolymers is between the T/s of the respective homopolymers, the repeating sequences in block copolymers exhibit their own characteristic Ff s. 

The properties of ordered structures in block copolymer melts have yet to be fully exploited, but the structural and rheological anisotropy is likely to lead to applications not all of which can be envisaged yet. The precision self-assembly of block copolymers into ordered structures for thin film and interfacial applications has enormous potential. Other applications such as nanoscale templates, membranes and filters could exploit the self-assembly of block copolymers into domains with periods 10-100 nm. The possibilities are limited only by the molecular engineer s imagination. 

The desirability of segregation in block copolymers can be demonstrated by considering the behaviour of SBS, which is one of the oldest types. It has about the same chain composition as SBR, but, rather than SBR, it shows two glass-rubber transitions, namely that of polybutadiene and that of polystyrene. Between these two temperatures it behaves as a rubber, in which the PS domains act as cross-links it is, therefore, a self-vulcanizing rubber (see also Figure 3.8 see Qu. 9.14). Moreover, the hard domains play the role of a reinforcing filler. 

The structure of polymer surfaces and thin polymeric films at the mesoscopic scale is of interest, both for application and basic research [1] As the size of many technological devices decreases, the natural length scales of many typical polymers such as the radius of gyration, the persistence length, or the domain size in block copolymers, match the feature size and thus the materials are expected to display a new behaviour [2-5], On the other hand, the tendency towards spontaneous structure forma-... 

The basic driving force for microdomain formation in block copolymers is the reduction in the positive surface free energy of the system resulting from the increase of the domain size. This domain size increase gives rise to a decrease in the volume fraction of interfacial region in which junction points of the copolymers must be distributed. In addition, configurations of the block chains must also change in order to even-up the density deficiency in the interior of the domains. 

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