Segregated polymer brushes

The importance of polydispersity is an interesting clue that it may be possible to tailor the weak interactions between polymer brushes by controlled polydispersity, that is, designed mixtures of molecular weight. A mixture of two chain lengths in a flat tethered layer can be analyzed via the Alexander model since the extra chain length in the longer chains, like free chains, will not penetrate the denser, shorter brush. This is one aspect of the vertical segregation phenomenon discussed in the next section. 

From the theoretical viewpoint, much of the phase behaviour of blends containing block copolymers has been anticipated or accounted for. The primary approaches consist of theories based on polymer brushes (in this case block copolymer chains segregated to an interface), Flory-Huggins or random phase approximation mean field theories and the self-consistent mean field theory. The latter has an unsurpassed predictive capability but requires intensive numerical computations, and does not lead itself to intuitive relationships such as scaling laws. 

Polymer brush theory was applied to the compatibilization of homopolymers A and B by an AB diblock by Leibler (1988). The reduction in interfacial tension due to the segregation of copolymers to the interface was calculated. Considering a film of block copolymers at the homopolymer-homopolymer interface, the free energy was found to be... 

The interfacial phenomena of phase coexistence and segregation are described as observed in thin polymer films. This work also considers related issues in the focus of current research such as wetting phenomena, finite size effects expected in very thin films, surface (and bulk) properties of mixtures with stiffness disparity, and conformational properties of end-segregated macromolecules forming polymer brushes. 

Diblock copolymers A-N immersed in a homopolymer P matrix segregate to its interfaces. One of the copolymer blocks ( anchor moiety A) selectively attaches to the interface while the other ( buoy block N) dangles out to form a brush like layer, providing a simple means for the realization of polymer brushes (see Fig. 33). 

Diblock copolymers admixed to a homopolymer matrix segregate to its interface in a specific way. As well as other end-functioned molecules, diblock copolymers, attached by an anchoring block (or by a copolymer joint) to the interface, offer a convenient means for the realization of so-called polymer brushes. The structure of a polymer brush (characterized by its height and average composi-... 

The determination of the conformational and segregation properties of polymer brushes, created by diblock copolymers, has triggered their application to more complex problems. Diblock copolymers have been used to increase adhesion [277] or to eliminate the interfacial tension [256] between immiscible polymers. They may also modify the surface induced mode [116] and the bulk mode [278] of the spinodal decomposition observed in homopolymer blends. 

Finally, it has been found that the deuterium staining of individual molecules, commonly used in condensed matter studies, in case of polymers can lead to serious consequences in bulk and surface thermodynamics. This was shown in this work by the phase separation of isotopic blends (Sect. 2.2.2), isotope swapping effect in blend miscibility (Sect. 2.2.3) and surface segregation (Sect. 3.1.2.5) as well as by the specific scaling law (Eq. 61) which governs the polymer brush conformation (Sect. 4.2.1). 

A different approach was used by Milner [326] in order to predict the phase diagram for asymmetric copolymer architectures (for example A2B, A3B etc. types of miktoarm stars). The free energy of the system can be calculated by summing the free energies of the polymer brushes existing on the two sides of the interphase. Milner described the effects of both chain architecture (i.e., number of arms) and elastic (conformational) asymmetry of the dissimilar chains, in the strong segregation limit, by the parameter... 

Segregated Polymer Brushes via Grafting to and ATRP Grafting from Chain Anehoring... 

Scheme 2. Non-uniform surface response of segregated polymer brushes.

Segregated polymer brushes were fabricated utilizing phase-separation phenomena in ultrathin polymer blend films (PS-COOH/PMMA) and the combination of grafting-to and grafting-from methods. 

From a philosophical point of view, we may argue that even when large scale simulations can precisely reproduce experimental observations, we still may not understand the detailed principles at work. For this we need more deep and systematic insights in sub-problems that present themselves, e.g. with respect to the segregation of chains in the core or in the corona. For this reason, it is of considerable interest to focus here on the phase behaviour of a mixed spherical polymer brush, which mimics the behaviour of chains in a spherical corona. 

Fig. 7. Investigating phase segregation and formation of patterns in multicomponent polymer brushes as observed by AFM. In this case, glassy and rubbery binary components of grafted pol3rmethacrylate (PMA) and fluorinated polystyrene copol3rmer (PSF) were sensitively imaged and differentiated between topc aphy (left), phase imaging (right), and glassy (top) and rubbery (bottom) states of the binary brushes. Dimensions at 5 x 5 /rm. From Ref. 107.

Phase Segregation in Multicomponent Polymer Brushes. Phase segregation and ordering in multicomponent pol5uner brushes have also been extensively studied (Fig. 7) (106,107). In the presence of two tethered immiscible... 

In block-copolymer brushes (Fig. 18.6) two or more chemically different polymers (typically two or three different blocks) constitute a polymer brush with block-copolymer architecture. Responsiveness of these brushes is determined by phase segregation of unlike polymer blocks however, the structure of the brush layer depends on whether the AB block copolymer is tethered by the more (A) or the less (B) soluble block. In poor solvents... 

Minko S., Muller M., Usov D., Scholl A., Froeck C., and Stamm M., Lateral versus perpendicular segregation in mixed polymer brushes , Phys Rev Lett, 2002 88(3) 0355021-0355024. 

Here we outline a mean field Flory-type model introduced by de Gennes [230] and developed by Leibler [231] and Aubouy and Raphael [232]. This approach is less detailed than SCMF models but it captures the main features of the physics of segregated copolymers. Even though it makes a number of assumptions, which are a simplification in comparison with the SCMF models, its predictions of the main features (such as, e.g., variation of mean brush height L vs size and surface density o of the diblocks) agree [226] well with those of more detailed SCMF calculations [236-238]. Because of clearness and simplicity it has been used as a basic framework for many experimental papers on brush conformation [240-245] and segregation properties of end-adsorbing polymers [246-255]. 

Numerous experimental studies have dealt with the problem of the conformation of N-mer brush layers immersed in P-mer melts (P>N1/2), and created by diblock copolymers [240,241,261] or other end-functioned polymers [242-245, 249,262,264,265]. The volume fraction vs depth profiles ( >(z) of end-segregating polymers (as in Figs. 36), obtained in the course of these studies, yield the surface coverage o. o is related to the surface excess z as... 

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