Branching Intrinsic viscosity, effect

The reason for the low intrinsic viscosities in solution is that dendrimers exist as tightly packed balls. This is by contrast with linear polymers, which tend to form flexible coils. The effect of this difference is that, whereas polymer solutions tend to be of high viscosity, dendrimer solutions are of very low viscosity. In fact, as dendrimers are prepared, their intrinsic viscosity increases as far as the addition of the fourth monomer unit to growing branches (the so-called fourth generation), but this is the maximum value that the viscosity reaches, and as the side chains grow beyond that, the viscosity decreases. 

Branching Parameter g from. SEC/LALLS. The effect of polymer branching upon the dilute solution configuration of polymers is conveniently expressed as the ratio of intrinsic viscosities of branched and linear polymers of the same chemical composition and molecular weight (35), i.e.. 

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. 

The application of refractive index and differential viscometer detection in SEC has been discussed by a number of authors [66-68]. Lew et al. presented the quantitative analysis of polyolefins by high-temperature SEC and dual refractive index-viscosity detection [69]. They applied a systematic approach for multidetector operation, assessed the effect of branching on the SEC calibration curve, and used a signal averaging procedure to better define intrinsic viscosity as a function of retention volume. The combination of SEC with refractive index, UV, and viscosity detectors was used to determine molar mass and functionality of polytetrahydrofuran simultaneously [70]. Long chain branching in EPDM copolymers by SEC-viscometry was analyzed by Chiantore et al. [71]. 

Branching. So far our discussion has been limited to linear polymer chains. The effect of branching on viscosity is still not well understood. The statistics of certain simple types of branched chains has been studied by Zimm and Stockmayer (1949) and Stockmayer and Fixman (1953). Since branching produces a less extended hydrodynamic volume than would be expected for a linear chain of the same molecular weight, conceivably the intrinsic viscosity for a branched polymer would be smaller and the sedimentation coefficient larger than those for a linear polymer. At present quantitative treatments are still scarce. 

Again the utility of this equation has been confirmed via Monte Carlo simulations on a lattice [Shida et al., 1998]. Comparing Eqs. (1.71) through (1.74), it turns out that 1 < gnlgi] < 1.39, indicating that the effect of branching is greater in the intrinsic viscosity than in the frictional coefficient. 

Branching reduces the hydrodynamic volume relative to the mass of the coil. The intrinsic viscosity of branched macromolecules is thus lower than that of their unbranched (linear) counterparts. The effect is particularly marked in the case of long-chain branching. If the number of branch points in a polymer homologous series increases with the molar mass, then the [rj] values also decrease relative to those of linear molecules. Thus, the slope of the log f (log 2) curve continuously decreases with increasing molar mass,... 

Solution properties of the polymers are primarily determined by the high polyethylene content, and at the concentrations present short-chain branching is assumed to have little or no effect on chain dimensions and hence intrinsic viscosity. Accordingly, SEC analyses of LLDPE have invariably been carried out assuming that the molecules elute as linear polyethylene. 

This effect increases with an increasing molar mass. Hence, [/2]- -relationships for branched polymers are only valid for very narrow molar mass ranges. As can be seen in Fig. 5.11, the intrinsic viscosity of branched polymers becomes nearly independent of the molar mass at high molar masses. The slope a of [/jl-M-rela-tionships for high molar masses of branched polymers is therefore low and can acquire values of a<0.5. 

The effect of branching on the zero-shear-rate intrinsic viscosity is often expressed in terms of branching index, g, defined as the ratio of the zero-shear-rate intrinsic viscosities of a branched to a linear polymer of the same composition and molecular weight. 

The family of curves found shows a minimum value of intrinsic viscosity around the value of 10 at. The descending branch of curves p = 5-10 at) evidences a decrease of [rj] with pressure, the effect being induced, obviously, by the intensification of the shearing stress at the capillary wall. 

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