Branched Flexible Random Coils

The bead-spring model with dominant hydrodynamic interaction was extended to star-shaped branched molecules by Zimm and Kilb. For/branches of equal length, each with Nb submolecules, equations 15,16,36, and 38 are replaced by 

Equation 26 still holds with the new definition of Si. The average distances between 

Logarithmic plots of [C ]r and [C 1r against w[ri risMIRT for linear f = 1) and nine-arm star (/ = 9) calculated from Zimm-Kilb theory for A = 0.25 and fV = lOO. - Reproduced, by permission, from Polymer Journal. 

Comparison of the frequency dependence of G and G for linear and star molecules depends on how the coordinates are scaled. If the reduced variables are plotted as in Figs. 9-11 and 9-12, [G ii at low frequencies is a line of identity for any molecule. A linear and nine-armed star are compared in this manner for h = 0.25 (0-solvent) and a somewhat unrealistically low value of A = 100 in Fig. 9-14. The branched molecule differs in displaying a bump near 1 on the abscissa scale (related to the large spacing between the first and third relaxation times which dominate the low-frequency behavior) and in having a much lower [G ]/j at low frequencies. The latter is reflected in low values of [Ac] and note that this effect of branching is opposite to that of molecular weight distribution. 

On the other hand, if one plots [G ] and [G ] logarithmically against frequency 

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Polymers are normally classified into four main architectural types linear (which includes rigid rod, flexible coil, cyclic, and polyrotaxane structures) branched (including random, regular comb-like, and star shaped) cross-linked (which includes the interpenetrating networks (IPNs)) and fairly recently the dendritic or hyperbranched polymers. I shall cover in some detail the first three types, but as we went to press very little DM work has been performed yet on the hyperbranched ones, which show some interesting properties. (Compared to linear polymers, solutions show a much lower viscosity and appear to be Newtonian rather than shear thinning [134].) Johansson [135] compares DM properties of some hyperbranched acrylates, alkyds. and unsaturated polyesters and notes that the properties of his cured resins so far are rather similar to conventional polyester systems. 

Even though there are objections to the theoretical model (hyphae treated as flexible chains forming spherical coils network interaction between branched hyphae randomizing effect of Brownian motion essential for validity of polymer rheology theory), this formal approach is quite useful (Metz et al., 1979). 

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