Block copolymers fractionation systems

The majority of polymers are immiscible and, in bulk, they phase separate to form domains of varying sizes and shapes, depending on their relative volume fraction. This happens because of the very low entropy of mixing in the case of large polymeric molecules. Therefore, unless there is a large favorable enthalpic contribution, most polymers do not form molecularly miscible systems. The same is true for block copolymers, in which the length of each block exceeds a certain critical value. As mentioned earlier, block copolymers are systems wherein two (or more) different types of homopolymers are linked to each other at the chain end(s) diblock copolymers, represented as (A) -(B) , are systems in which two homopolymers are linked to each other at one end, while triblock copolymers, represented as (A)m-(B) -(C)p, are systems in which one central homopolymer block is linked at either end with two other homopolymers. The values m, n and p, represent the... 

Figure 7.14 Experimental and simulated morphologies of block copolymer/nanoparticle systems at two different particle volume fractions (10 and 35 vol.%). Simulations were performed using a hybrid SCFT method [113],...

As stated above, we postulated that fast, reversible chain transfer between two different catalysts would be an excellent way to make block copolymers catalytically. While CCTP is well established, the use of main-group metals to exchange polymer chains between two different catalysts has much less precedent. Chien and coworkers reported propylene polymerizations with a dual catalyst system comprising either of two isospecific metallocenes 5 and 6 with an aspecific metallocene 7 [20], They reported that the combinations gave polypropylene (PP) alloys composed of isotactic polypropylene (iPP), atactic polypropylene (aPP), and a small fraction (7-10%) claimed by 13C NMR to have a stereoblock structure. Chien later reported a product made from mixtures of isospecific and syndiospecific polypropylene precatalysts 5 and 8 [21] (detailed analysis using WAXS, NMR, SEC/FT-IR, and AFM were said to be done and details to be published in Makromolecular Chemistry... 

The authors conducted a similar investigation of precatalysts 7 and 11 using TiBA and trityl tetrakis(pentafluorophenyl)borate as the cocatalyst. They concluded that this material contained no fraction that could be characterized as blocky. It was therefore proposed that reversible chain transfer occurred only with MAO or TMA and not with TiBA. This stands in contrast to the work of Chien et al. [20] and Przybyla and Fink [22] (vida supra), who claim reversible chain transfer with TiBA in similar catalyst systems. Lieber and Brintzinger also investigated a mixture of isospecific 11 and syndiospecific 12 in attempts to prepare iPP/sPP block copolymers. Extraction of such similar polymers was acknowledged to be difficult and even preparative temperature rising elution fractionation (TREF) [26, 27] was only partially successful. 

Rytter et al. reported polymerizations with the dual precatalyst system 14/15 in presence of MAO [30]. Under ethylene-hexene copolymerization conditions, 14/MAO produced a polymer with 0.7 mol% hexene, while the 15/MAO gave a copolymer with ca. 5 mol% hexene. In the mixed catalyst system, the activity and comonomer incorporation were approximate averages of what would be expected for the two catalysts. Using crystallization analysis fractionation (CRYSTAF) and differential scanning calorimetry (DSC) analysis, it was concluded in a later paper by Rytter that the material was a blend containing no block copolymer [31],... 

The technique of self-nucleation can be very useful to study the nucleation and crystallization of block copolymers that are able to crystallize [29,97-103]. Previous works have shown that domain II or the exclusive self-nucleation domain disappears for systems where the crystallizable block [PE, PEO or poly(e-caprolactone), PCL] was strongly confined into small isolated MDs [29,97-101]. The need for a very large number of nuclei in order to nucleate crystals in every confined MD (e.g., of the order of 1016 nuclei cm 3 in the case of confined spheres) implies that the amount of material that needs to be left unmolten is so large that domain II disappears and annealing will always occur to a fraction of the polymer when self-nucleation is finally attained at lower Ts. This is a direct result of the extremely high number density of MDs that need to be self-nucleated when the crystallizable block is confined within small isolated MDs. Although this effect has been mainly studied in ABC triblock copolymers and will be discussed in Sect. 6.3, it has also been reported in PS-fc-PEO diblock copolymers [29,99]. 

Ceresa (78,79) studied in detail the system poly(methyl methacrylate)-acrylonitrile. Figure 25 shows the change in composition with mastication time. A study of gel formation by the block copolymers was made by subjecting the isolated fractions of block copolymers to further mastication. A wide range of block copolymers with varying composition and structure was obtained (Fig. 26). 

There have been a number of computer simulations of block copolymers by Binder and co-workers (Fried and Binder 1991a,ft), and this work was reviewed in Binder (1994). Although computer simulations are limited due to the restriction on short chain lengths that can be studied, finite size effects and equilibration problems at low temperatures, the advantages are that the models are perfectly well characterized and ideal (monodisperse, etc.) and microscopic details of the system can be computed (Binder 1994). In the simulations by Binder and co-workers, diblocks were modelled as self- and mutually-avoiding chains on a simple cubic lattice, with chain lengths N = 14 to 60 for/ = 1.A purely repulsive pairwise interaction between A and B segments on adjacent sites was assumed. A finite volume fraction of vacancies was included to speed the thermal equilibration process (Binder 1994). 

We note that earlier research focused on the similarities of defect interaction and their motion in block copolymers and thermotropic nematics or smectics [181, 182], Thermotropic liquid crystals, however, are one-component homogeneous systems and are characterized by a non-conserved orientational order parameter. In contrast, in block copolymers the local concentration difference between two components is essentially conserved. In this respect, the microphase-separated structures in block copolymers are anticipated to have close similarities to lyotropic systems, which are composed of a polar medium (water) and a non-polar medium (surfactant structure). The phases of the lyotropic systems (such as lamella, cylinder, or micellar phases) are determined by the surfactant concentration. Similarly to lyotropic phases, the morphology in block copolymers is ascertained by the volume fraction of the components and their interaction. Therefore, in lyotropic systems and in block copolymers, the dynamics and annihilation of structural defects require a change in the local concentration difference between components as well as a change in the orientational order. Consequently, if single defect transformations could be monitored in real time and space, block copolymers could be considered as suitable model systems for studying transport mechanisms and phase transitions in 2D fluid materials such as membranes [183], lyotropic liquid crystals [184], and microemulsions [185],... 

Fig. 29 Characteristic wave number q as a function of polymer volume fraction for the systems of protein-like copolymers with L = 63 and random-block copolymers with different block lengths. The domain spacing is defined as r = lir/q. Adapted from [153]...

Benoit et al. [11-12] and Akcasu et al. [13-15] have extended de Gennes formula to describe multicomponent polymer systems. Their results are reproduced in Appendix A in a matrix form (following Akcasu [13-15]). Consider a number of components (noted A, B, etc.) with degrees of polymerization NA, etc., volume fractions A, etc., monomer volumes vA, etc. Some of these components could be block copolymers. Having one of the components (called matrix component) as a homopolymer simplifies the calculations. The main result is ... 

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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