Polymers tethered to a point

As in any semidilute solution, each blob contains n r) monomers. 

Here i/ is the correlation length exponent, which is 0.588 for a good solvent in three dimensions. From this picture, one can easily verify that p r), the number density of monomers falls off as 

This last result is also valid in the intermediate region, though the crossover from the outer to the intermediate region has not been observed. 

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Highly branched polymers, polymer adsorption and the mesophases of block copolymers may seem weakly connected subjects. However, in this review we bring out some important common features related to the tethering experienced by the polymer chains in all of these structures. Tethered polymer chains, in our parlance, are chains attached to a point, a line, a surface or an interface by their ends. In this view, one may think of the arms of a star polymer as chains tethered to a point [1], or of polymerized macromonomers as chains tethered to a line [2-4]. Adsorption or grafting of end-functionalized polymers to a surface exemplifies a tethered surface layer [5] (a polymer brush ), whereas block copolymers straddling phase boundaries give rise to chains tethered to an interface [6],... 

Constrained Polymers. The conformation of polymers constrained in various ways, for example, grafted to a flat surface ( brush ), adsorbed on a spherical colloidal particle, or tethered to a central branch point as in star polymers. All such problems involve potentially large nonideal conformational effects and also introduce additional complications associated with site inequivalence within the PRISM formalism. Progress for star polymers is briefly described in the next section. 

Polymers attached to a linear backbone form another class of tethered chains, which are intermediate between the stars and brushes. Long-chain comb polymers are branched polymers in which branches of length A are attached to a flexible polymer chain. The branches can either be equally spaced or random. When the branches are long and closely spaced, excluded volume interactions among the tethered side chains can significantly stiffen the central contour. Though such bottlebrush polymers have been synthesized, so far the backbone has been substantially shorter than the side branches. In this case, the structure will not be very different than for a star polymer in which the branches (arms) are attached to a central point. Diblock copolymers in a selective solvent can also form cyhndrical micelles that have similar structures. 

There is a large range of resins available for SPOS. These resins are derivatised polymer supports with a range of linkers. The roles of linkers are (i) to provide point(s) of attachment for the tethered molecule, akin to a solid supported protecting group(s), (ii) to provide distance from the polymeric backbone in order to minimise interactions with the backbone, (iii) to enable cleavage of product molecules under conditions compatible with the stability of the molecules and the reaction conditions employed for chemical transformations. Hence in order to... 

The study of tethered polymer chains is an area which has received increasing attention in recent years. These are systems in which one or both ends of the chain are constrained in their motion because they are attached to a d dimensional surface. This surface could be a point or small central core (d = 0) as in the case of a many-arm star polymer, a line (d = 1) as in the case of a comb polymer, or a flat surface (d = 2) as in the case of a polymer brush. Polymers attached to themselves to form a polymer network or a tethered membrane are also examples of tethered chain systems. An interesting example of a tethered membrane is the spectrin/actin membrane skeleton of the red blood cell skeleton. A schematic illustration of these four examples of tethered chain is shown in Fig. 9.1. Additional interest in tethered chains is due to their technological applications in colloidal stabilization and lubrication. ... 

Another class of branched polymers is polymer bmshes. They have a type of surface modification where reartive end groups of polymer chains are physically or chemically end-tethered (grafted or anchored) at one end to a surface or interface, and where the distance between anchor points is smaller than the tmperturbed width of the polymer.Incorporating the long-chain polymers on the surface of a substrate in a polymer bmsh offers a versatile way to introduce new functionalities, and to help improve polymer properties such as hydrophilicity, biocompatibility, and conductivity. ... 

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