Star Branch point motion

The theories considered thus far have been limited to linear and star polymers, which have no more than a single branch point. The simplest polymer with more than one branch point is an H polymer, depicted in Fig. 9.4. An H polymer contains two branch points the segment of polymer connecting the two branch points is called the backbone . What is especially significant about such polymers is that the backbone cannot relax its configuration unless the branch points move. This contrasts with star polymers, which can relax completely without the branch point moving. Theories for polymers with more than one branch point require consideration of branch-point motion. 

How can a branch point move The repertoire of polymer movements that we have considered up to now reptation, primitive path fluctuations, and Rouse motion within the tube do not allow for branch-point motion, at least not directly. Yet, clearly, the branch points do move, for if they did not, branched polymers, including stars, would have zero center-of-mass diffusivity. 

The success of the slip link model for symmetric and asymmetric star polymers inspires its application to more complex architectures, such as H polymers. The mechanisms of relaxation and branch point motion were established in studies of symmetric and asymmetric star polymers, as were the parameters (Mf,, and Tg) that allow the simulations to be compared... 

For both linear and star polymers, the above-described theories assume the motion of a single molecule in a frozen system. In polymers melts, it has been shown, essentially from the study of binary blends, that a self-consistent treatment of the relaxation is required. This leads to the concepts of "constraint release" whereby a loss of segmental orientation is permitted by the motion of surrounding species. Retraction (for linear and star polymers) as well as reptation may induce constraint release [16,17,18]. In the homopol5mier case, the main effect is to decrease the relaxation times by roughly a factor of 1.5 (xb) or 2 (xq). In the case of star polymers, the factor v is also decreased [15]. These effects are extensively discussed in other chapters of this book especially for binary mixtures. In our work, we have assumed that their influence would be of second order compared to the relaxation processes themselves. However, they may contribute to an unexpected relaxation of parts of macromolecules which are assumed not to be reached by relaxation motions (central parts of linear chains or branch point in star polymers). 

Another case where tube contraction is important is the relaxation of branched polymers/as epitomized by star-polymers. Because the branch point is highly immobile, reptation by Brownian motion of an arm as a whole is strongly inhibited. Escape from the tube can only occur by contraction of the primitive path. Any significant contraction has a high free energy (discussed in the exercise above). The time for a fractional contraction i.e. A is... 

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