Theories for blends of two block copolymers

Theory for blends of two homopolymers with block copolymers was developed by Noolandi and Hong (1982) using the SCF method. They considered a quaternary system with a diblock in a good solvent for two incompatible homopolymers. Calculation of density profiles revealed that the block copolymer tends to be selectively located at the interface, and that the homopolymer tends to be excluded from the interphase. This is illustrated by the representative density profiles in Fig. 6.37. The exclusion of homopolymer from the interphase was found to be enhanced by increasing the molecular weight of the block... 

Theories for blends of block copolymers with two homopolymers... 

Noolandi et al. developed a theory for the interfacial region in three-component polymeric systems comprising di-block copolymer. There are two aspects to consider the phase separation in block copolymer upon addition of one or two homopolymers, and the modification of the A/B blend properties upon addition of a block copolymer (either A-B or X-Y type). The second aspect is more pertinent for the polymer blend technology. In particular, the ternary blends comprising two homopolymers and a copolymer, either A/B/A-B, or A/B/X-Y are of industrial interest. 

A summary of the phase behavior of a block copolymer swollen with a nonselective solvent follows the dilution approximation says that interaction parameter in a polymer scales with the volume fraction of the polymer in the solvent-polymer blend. This is attributed to the alteration of the interaction of the two blocks due to selective segregation of the solvent to the interface between the blocks. Comparison of this theory with experimental results for the shift in ODT has found that an exponent a must be added to adjust for nonideal behavior (Eqn. 3) in ideal behavior, a would have value of 1, but experimental values have ranged from 1.2 - 1.6. The value of the exponent cannot be predicted, but depends on the solvent and block copolymer system. This nonideal behavior is only observed for ODTs OOTs follow the dilution approximation with a equal to 1. 

The isothermal crystallization of PEO in a PEO-PMMA diblock was monitored by observation of the increase in radius of spherulites or the enthalpy of fusion as a function of time by Richardson etal. (1995). Comparative experiments were also made on blends of the two homopolymers. The block copolymer was observed to have a lower melting point and lower spherulitic growth rate compared to the blend with the same composition. The growth rates extracted from optical microscopy were interpreted in terms of the kinetic nucleation theory of Hoffman and co-workers (Hoffman and Miller 1989 Lauritzen and Hoffman 1960) (Section 5.3.3). The fold surface free energy obtained using this model (ere 2.5-3 kJ mol"1) was close to that obtained for PEO/PPO copolymers by Booth and co-workers (Ashman and Booth 1975 Ashman et al. 1975) using the Flory-Vrij theory. 

Cho et al. (2000) studied the segregation dynamics of block copolymers to the interface of an immiscible polymer blend and compared experimental results to the predictions of various theories for a poly(styrene-b-dimethylsiloxane) [P(S-b-DMS) M = 13,000] symmetric diblock copolymer system added to a molten blend of the corresponding immiscible homopolymers. They used the pendant drop technique at intermediate times and compared their results to the predictions of diffusion-limited segregation models proposed by Budkowski, Losch, and Klein (BLK) and by Semenov that have been modified to treat interfacial tension data. The apparent block copolymer diffusion coefficients obtained from the two analyses fall in the range of 10 -10 cm /s, in agreement with the estimated self-diffusion coefficient of the PDMS homopolymer matrix. 

Fig. 58 Mean-field density profiles obtained fiom self-consistent field theory simulations. A- versus B-rich domains are displayed for a blend of A- and B-homopolymers (a) and for AB-diblock-copolymer melts (b, c). In each case, all A-, and B-blocks contain equal numbers of monomers. Here, spherical confinement is implemented by blending either A- and B-homopolymws (a), or AB-diblock-copolymers (b, c) with C-homopolymers. The C-homopolymers act as a very bad solvent, thus enforcing the formation of A-, and B-rich spherical domains. In this case, the geometry of the confined polymer phases is studied in two dimensions. Whether Janus (a), core-shell (b), or onion (c) particles form depends on the number of monomers per block, and the interactirais between different monomer species. From (a) to (c), the length of A-, and B-sequences steadily decreases the sequences in (a) are roughly four times as long as in (b), and are about 15 times as long as in (c). To form Janus particles, the A-C versus B-C inlmactions need to be equal. To form layered structures, there has to be a significant difference...

Simple theory says that a blend of A + B should be compatibilized by a block copolymer of A-B. Where this is not readily available, theorists generally concede that the blocks of the compatibilizer need not be identical with A and B, so long as they are miscible or at least compatible with A and B [6, 7, 9, 10, 31]. For example, typical estimates conclude that the solubility parameters of the blocks in the compatibilizer must be within 0.2 1.0 units of those in A and B [6, 7]. In practice, most researchers compromise between the two extremes, using a block copolymer A to com-patibilize a blend of A + B, by choosing block C for compatibility with B. 

Lee et al. [21] conducted molecular dynamics simulations of the flow of a com-positionally symmetric diblock copolymer into the galleries between two siUcate sheets whose surfaces were modified by grafted surfactant chains. In these simulations they assumed that block copolymers and surfactants were represented by chains of soft spheres connected by an finitely extensible nonlinear elastic potential, non-Hookean dumbbells [22], which had been employed earlier in the simulations of the dynamics of polymer blends and block copolymers by Grest et al. [23] and Murat et al. [24]. To describe the interactions among the four components, namely the surfaces, the surfactant, and two blocks, Lee et al. [21] employed a Lennard-Jones potential having the energy parameters which are associated with the type of interactions often employed for lattice systems such as in the Flory-Huggins theory. 

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