Macromolecules, star-branched

As already outlined, star branched macromolecules resemble their linear chain analogues. The behavior becomes evident when for a given number of arms f the... 

Fig. 13. Chain length dependence of the second virial coefficient A2 for some star branched macromolecule, according to Casassa (full line). The data points correspond to measurements [89] (triangles 3-arm, circles 12-arm and rhombus 18-arm stars. Reprinted with permission from [89]. Copyright [1984] American Society...

The Schulz-Zimm distribution would be found for/end-to-end coupled linear chains which obey the most probable distribution, as well as for/of such chains which are coupled onto a star center. This behavior demonstrates once more the quasi-linear behavior of star branched macromolecules. In fact, to be sure of branching, other structural quantities have to be measured in addition to the molar mass distribution. 

In contrast to star-branched macromolecules, this relationship differs now from that of the non-fractionated samples... 

Fig. 22. KMHS relationships for the fractions of end-linked 3-arm star-branched polystyrene molecules and of linear polystyrene fractions. The data refer to three samples of different in the pregel state and one from the sol fraction of a gel. The curves for the branched macromolecules coincide within experimental error in the high molar mass region. The deviations at lowM result from a different amount of non-reacted end-functionalized stars. The exponents of the end-linked and linear PS chains are a =0.42 0.02 while that of linear chains is 0.70 0.01 [95,120,123,124]. Reprinted with permission from [95]. Copyright [1997] American Society...

Fig. 24. Contraction factors for star-branched macromolecules as a function of the number of arms. The full line represents strictly regular stars, the dashed line one that for stars with polydisperse arms (MyM =2), the dotted line according to Daoud and Cotton [29]. The symbols represent the data from the literature. The deviation at large / represents the stretching of the arms due to overcrowding...

Thus a simple power law behavior with an exponent of 1.5 would result if 0"= 1 [125]. Zimm and Kilb [128] made a first attempt to calculate g for star branched macromolecules on the basis of the Kirkwood-Riseman approximation for the hydrodynamic interaction. They came to the conclusion that... 

Fig. 25. The viscosity contraction factor g as a function of the geometric contraction factor g for star-branched macromolecules ( 3-128). No distinction was made between the chemical nature of the various arms and between the thermodynamic quality of the solvents used. See Table 3...

In some case, however, only a flattening of the osmotic modulus curve is observed. Such a case is found with star-branched macromolecules. This observation has rather comprehensively been investigated by Roovers et al. with stars of 64 and 128 arms [172]. The authors give the following explanation. At the point of coil overlap and at somewhat higher concentrations the stars feel the interaction as a quasi colloidal particle. Hence, a steeper increase of the osmotic mod-... 

Tian D, Dubois P, Jerome R, Teyssie P (1994) Macromolecular engineering of polylactones and polylactides. 18. Synthesis of star-branched aliphatic polyesters bearing various functional end-groups. Macromolecules 27 4134 144... 

Figure 2. Robust super high-spin oiganic macromolecules with linear and star-branched topologies.

In 1965, Milkovich (. ) reported that divinylbenzene could be utilized for the formation of star-branched macromolecules. Later, Rempp and coworkers (2, 3, 4) successfully applied this method for the synthesis of star-branched polystyrenes. Moreover, Fetters and coworkers (54 ) used this procedure for the synthesis of multi-arm star-branched polyisoprene homopolymers and poly-... 

Fig. 29. Zimm-plot and Kratky-plot from a star-branched macromolecule. Star centre nodule of densely cross-linked polydivinyl benzene rays monodisperse polystyrene chains. Measurement in toluene at 20 °C and with the three wavelengths 20 = 546, 436 and 365 nm"1...

A larger reduction in the mean square unperturbed dimensions can be achieved by rearrangement of the n + 1 atoms into an /-functional star-branched polymer. In this architecture, the macro molecule contains / branches (f> 2), each with n/f bonds, that emanate from a common atom. The same terminology is frequently used for branched macromolecules with very large/if the branches emanate from a collection of atoms that are constrained to remain close together, so that the origin of all of the branches is clustered in a volume much smaller than (s2)m. The influence of the star-branched architecture on the mean square dimensions is traditionally designated by a factor g that is defined as ... 

Equation (1.20) suggests that the mean square dimensions of the macrocycle are approximated by the star-branched polymer with five arms, for which g = 0.52. It also suggests that a macromolecule with a closer approach to the condensed state could be obtained by using f>5. 

The intrinsic viscosity [ry] of both linear and branched macromolecules and the branching parameter values of the star-branched copolymers were also calculated by the GPC software and are reported in Table IV. The ratio [vlhAvlim, between the intrinsic viscosity of the... 

Utracki, L.A. Roovers, J.E.L. Viscosity and normal stresses of linear and star branched polystyrene solution. I. Application of corresponding states principle to zero-shear viscosities. Macromolecules 1973, 6 (3), 366-372. 

Burchard W, Schmidt M, Stockmayer WH. Influence of hydrodynamic preaveraging on quasi-elastic scattering from flexible linear and star-branched macromolecules. Macromolecules 1980 13 580-587. 

The experimental evidence to-date suggests that the effects on stability arising from these higher order terms are negligible. This would not necessarily be the case, however, with star-branched macromolecules as stabilizers. Even in free solution, such polymers apparently display anom-... 

The nonlinear branched topology is expected to introduce novel specific features in the collapse transition of individual charged macromolecules, due to the interplay between intra- and interbranch Coulomb repulsion. Conformations of intrinsically hydrophobic star-branched PE have been studied experimentally in the past decade [50, 51]. Recently synthesized PDMAEMA stars responsive to both pH and temperature [47, 48] are expected to undergo an intramolecular collapse transition as a response to the increase in temperature. The latter provokes a decrease in the solubility of the monomers in the star arms. 

Dong, T., Dubois, P., Jdrdme, R., and Teyssie, P., 1994, Macromolecular Engineering of Polylactones and Polylactides. 18. Synthesis of Star-Branched Aliphatic Polyesters Bearing Various Functional End Groups. Macromolecules, 27 4134... 

F. Wang, M. S. Wilson, R. D. Rauh, P. Schottland, B. C. Thompson and J. R. Reynolds, Electrochromic linear and star branched poly(3,4-ethylenedioxythiophene-didodecyloxybenzene) polymers. Macromolecules, 33, 2083-2091 (2000). 

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