Polymers tethered to a line

This angular correlation can only decay after two arms which are strongly entangled have disentangled. Overall rotation of the star does not affect Ce t). Simulation results for Ce t) clearly demonstrated a strong dependence of Te on f, but the decay was too slow to determine accurately. 

The three relaxation times discussed above are for the Rouse model, which applies to almost all the simulations on stars. However, experimentally hydrodynamic effects are important.At present it is only possible to include solvent molecules explicitly in a simulation for very small stars (Nf 50). Smit et have studied a 3-arm star with A = 6 in the presence of a solvent. While the introduction of hydrodynamic effects changes two of the relaxation times, there remain three distinct times for a star. In the Zimm ° model, one can show that Tei iV y(2-3 )/2 nd td Ar37-3(i-i )/2 As in the Rouse case, Tgi and td have the same A-depen-dence but very different / dependences. The prediction for remains unchanged. In a good solvent, Tgi A yo.i25 As stu- 

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. 

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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],... 

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. ... 

An extended brush-like layer is formed for the zwitterionically terminated polystyrene and comparison of force-distance curves before and after oscillatory motion showed that they were not displaced by the lubrication forces. These force-distance curves showed that the two brush-like layers interact at distances of about 2500 A. Above this separation, values of G scale with D in precisely the same manner both in the presence and in the absence of tethered polymer. The slopes of these lines, moreover, gave a viscosity (j/o) that agreed with the bulk viscosity of toluene. For the tethered pol)nner the line through these large separation data has an x axis intercept that corresponds closely to twice the polymer layer s thickness. Hence, in this region the shear plane in the system has shifted by a distance of 2Lh (Lr is hydrod5mamic layer thickness equilibrium layer thickness) and thus equation (3.4.13) becomes... 

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