Long-chain branching relaxation time, polymers

From the foregoing it will be clear that whenever entanglements and long chain branching are both present the dynamics in a polymer melt are highly co-operative. The orientational relaxation time of chain segments is exponentially dependent on both the contour distance to the nearest effective free end and on the effective entanglement density of its enviroiunent at all previous timescales. 

Fig. 3.12 (a) A pom-pom with three arms at each branch point (q = 3). At short times the polymer chains are confined to the Doi-Edwards tuhe. Sc is the dimensionless length of branch point retraction into the tube X is the stretch ratio where L is the curvilinear length of the crossbar and Lq is the curvilinear equilibrium length, (b) Relaxation process of a long-chain-branched molecule such as LDPE. At a given flow rate e the molecule contains an unrelaxed core of relaxation times t > g 1 connected to an outer fuzz of relaxed material of relaxation t < g 1, behaving as solvent. [Reprinted by permission from N. J. Inkson et al., J. Rheol., 43(4), 873 (1999).]... 

Mendelson et al. 1970). The Bueche theory predicts that the viscosity of branched flexible homopolymers is lower than that of linear homopolymers of the same The reduction of melt viscosity in the presence of long-chain branching may be attributed to (1) a reduction in relaxation times and (2) a reduction in chain entanglements or other interactions between polymer molecules in the bulk. It appears that the reduction in relaxation times may be related to g given in Eq. (6.40), and the reduction in chain entanglements or other interactions between polymer molecules may be related to E(g) given in Eq. (6.41). 

From the considerations presented in the previous section, it is evident that it is desirable to choose MC moves X X such that the relaxation time resulting from a Markov chain of such moves for the configurations of the polymer chains is as small as possible. This is particularly important for dense melts of long (and hence mutually entangled ) polymer chains, where the reptation concepts imply an asymptotic scaling rocN , that is, the relaxation is distinctly slower than for isolated chains (cf. eqns [13]-[16]).The situation would be even worse for dense melts of star polymers (or other branched polymers) where even an exponential scaling (lnr°=N) may result. ... 

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