Intrinsic viscosity branching factor

The value of a can be used to determine macromolecular chain conformation and the presence of branching. The intrinsic viscosity branching factor can also be used to study branching as a function of M ... 

This branching factor g is related to the intrinsic viscosity branching factor by... 

Relationships between dilute solution viscosity and MW have been determined for many hyperbranched systems and the Mark-Houwink constant typically varies between 0.5 and 0.2, depending on the DB. In contrast, the exponent is typically in the region of 0.6-0.8 for linear homopolymers in a good solvent with a random coil conformation. The contraction factors [84], g=< g >branched/ <-Rg >iinear. =[ l]branched/[ l]iinear. are another Way of cxprcssing the compact structure of branched polymers. Experimentally, g is computed from the intrinsic viscosity ratio at constant MW. The contraction factor can be expressed as the averaged value over the MWD or as a continuous fraction of MW. 

Fig. 7. a Mark-Houwink plot of highly branched PMMA obtained by SCVCP of MMA with the inimer 12. (-)RI signal ( ) intrinsic viscosity of feed, ( ) intrinsic viscosity of linear PMMA (O) contraction factor, g. b Separation of feed polymer into fractions by preparative SEC. (-) RI signal of fractions (-) accumulated RI signals (.) RI signal of feed polymer. (Repro-... 

Since our indirect method produces both the linear (b=0) and branched intrinsic viscosities across the chromatogram, it is possible to estimate several LCB parameters as a function of elution volume or number average molecular weight. The branching factor G(V) can be written as... 

Much easier, and with higher precision, on-line intrinsic viscosity measurements are possible. Unfortunately, new problems arise from the insufficiently well known interdependence between g and g. The relationship between the intrinsic viscosity and the radius of gyration is fairly well settled for linear chains [3,71] and is satisfactorily described by the Fox-Flory equation (Eq. 21), but for the branched chains the 0-factor for branched chains may be different. In general one has [49]... 

The effect of branching is to increase the segment density within the molecular coil. Thus a branched molecule occupies a smaller volume and has a lower intrinsic viscosity than a similar linear molecule of the same molecular weight. The degree of branching is often characterized in terms of the branching factor [1] in Eq. (14), where the subscripts B and L, respectively, refer to branched and linear polymers of the same molecular weight ... 

In principle, intrinsic viscosities used for estimating branching should be measured under conditions where the expansion factor a is unity, but as indicated in Section 6, it is not easy to identify such conditions. Some authors, e.g. Moore and Millns (40) have measured [tf at the theta-temperature of the corresponding linear polymer, but it is doubtful whether a is unity at that temperature for either linear or branched polymer, if the theories of Casassa or of Candau et al. are valid. If a were the same for both linear and branched polymers under the same conditions g would be unaffected and g could be measured at any convenient temperature some authors have presented data suggesting that g is nearly the same in good and poor solvents, e.g. Hama (42) and Graessley (477), but other authors, e.g. Berry (43) have found g to vary. The best that can be done at present would appear to be to measure g at the theta-temperature on the assumption that this ratio will be less temperature-sensitive than either intrinsic viscosity, and that even if this temperature is not the correct one it will be near it. Errors in estimates of branching due to this effect are likely to be much less serious than those due to the use of an incorrect relation between g and g0. 

Since intrinsic viscosity but not concentrated solution viscosity is known to be sensitive to polydispersity (10, 19), a correction has been applied to g according to the calculations of Berger and Shultz (20). A value of zero was taken for b, exponent a was set equal to 0.75, and Qbi/Qlin was related to Mw/Mn using Equation 21 of Shultz (19). The branching factor corrected for polydispersity, g corr, is given by... 

Because of the ease in measuring intrinsic viscosity relative to the radius of gyration, considerably more experimental works have reported intrinsic viscosity data for branched molecules. As a result, attempts have been made to relate the two contraction factors. However, the efforts to And an encompassing relationship have not been completely successful. Thurmond and Zimm proposed the following equation ... 

Thus, the fractal analysis methods were used above for treatment of comb-like poly(sodiumoxi) methylsylseskvioxanes behavior in solution. It has been shown that the intrinsic viscosity reduction at transition from a linear analog to a branched one is due to the sole factor, namely, to a macromolecule connectivity degree enhancement, characterized by spectral dimension. This conclusion is confirmed by a good correspondence of the experimental and calculated according to Mark-Kuhn-Houwink equation fiactal variant intrinsic viscosity values. It has been shown that qualitative transition of the stmcture of branched polymer macromolecular coil from a good solvent to 0-solvent can be reached by a solvent change. 

Intrinsic viscosity reflects the hydrodynamic volume of a molecule, but a more fundamental parameter describing molecular size is the radius of gyration. And the effect of branching on molecular size is more commonly described in terms of the branching factor, g, which was defined in Eq. 2.16 as the ratio of the mean square radii of gyration of branched and linear molecules having the same molecular weight. 

---