Viscosity of branched polymers

We must be careful in assessing the experimental results on the viscosity of branched polymers. If we compare two polymers of identical molecular weight, one branched and the other unbranched, it is possible that the branched one would show lower viscosity. Two considerations enter the picture here. First, since the side chains contribute to the molecular weight, the backbone chain... 

In earlier studies of the intrinsic viscosities of branched polymers it was assumed that a relation of the form ... 

The problem of relating the intrinsic viscosity of branched polymers to their structure is an extremely difficult one theoretically, and it is not surprising that it cannot yet be considered as adequately solved. 

At present, it cannot be said that there is a satisfactory theory of even the low shear-rate viscosities of branched polymers, since no existing theory accounts for the observed enhancement of melt viscosity in the cases referred to. Treatments that do not even predict the sign of an effect reliably can hardly be expected to predict its magnitude. 

This theory seems not to have been extended to branched polymers in the non-Newtonian range so far as the extended theory does not agree very well with experiment in the Newtonian range, a satisfactory extension to predict the shear-rate dependence of the viscosities of branched polymers is likely to be difficult. The experimental evidence available is discussed in later sections. 

The polyethenes prepared with catalyst 2 (Fig. 3a) have greatly elevated elastic modulus G values due to LCB compared to the linear polymers shown in Fig. 3b. LCB also shifts the crossover point to lower frequencies and modulus values. The measured complex viscosities of branched polymers (see also Table 2) are more than an order of magnitude higher than calculated zero shear viscosities of polymers having the same molecular weight but a linear structure. The linear polymers have, in turn, t] (0.02 radvs)... 

Takahashi, Y. Suzuki, F. Miyachi, M. Noda, L Nagasawa, M. Zero-shear viscosity of branched polymer solutions. Polymer J. 1986, 1968 (18), 1-89. 

The intrinsic viscosity of branched polymers is conveniently described by the ratio... 

Viscosity of branched polymers in semidilute and concentrated regimes... 

Viscosity of Branched Polymers in Semidilute and Concentrated Regimes... 

A dependence of the intrinsic viscosity on the molar mass for branched polymers was already shown in Fig. 5.11. The intrinsic viscosity of branched polymers is lower than the intrinsic viscosity of linear polymers with the same molar mass. 

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. 

Similar results are obtained for linear, four and six-branched polyisoprenes at a concentration of 0.145 g/ml. In this case, however, at hi r concentrations more serious deviations occur from theory. The higher molecular weight samples can have zero shear viscosities higher than linear polymers of the same molecular wei t Such behavior was first noted in a study of melt viscosity of regular star-branched polybutadienesViscosities of the order of one hundred times that of a linear equivalent could be observed, but the effect decreased rapidly on dilution with solvents i.e. the viscosities of branched polymers were more sensitive to concentration than those of linear polymers. Star-branched polyisoprenes show viscosity enhance-... 

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. 

Lai et al. [100] proposed the use of the Dow Rheology Index (DRI) as an indicator for comparing branching level in industrial polymers. For a linear polymer molecule, like unbranched polyethylene, the viscosity of the polymer as a function of the applied shear rate is given by the Cross equation [84,100],... 

A viscosity online detector in a size exclusion chromatography (SEC) instrument allows for a universal calibration for polymers with known K- and a-values. For polymers that are only soluble at high temperature, e.g., polyolefines, high-temperature detectors are available, which can be operated up to 200°C. In addition to molar mass measurements, viscosity detectors have also been employed successfully to obtain structural information of branched polymers [28]. 

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.. 

Like SEC/LALLS, the viscosity detector is sensitive to high molecular weight fractions as shown in Fig, 7. A shoulder at 3,000,000 molecular weight detected by the DRI becomes a peak when detected by the viscometer detector. The usefulness of the SEC/Viscometer method is exemplified by the study of branched polymers. Fig. 8 shows a log [ ] vs. log M plot for a randomly branched polystyrene obtained from the SEC/ iscometer technique. 

Bueche s results apply to monodisperse polymers. Ajroldi and co-workers (62) have calculated the melt viscosity of polydisperse polymers such as would be produced by random trifunctional and tetrafunctional branching, as a function of Mw, assuming Eq. (5.1) to hold and making specific assumptions about the additivity of melt viscosity in polydisperse polymers. Because of these assumptions their results must be regarded as illustrative only but they show that large effects may be expected, the calculated melt viscosity of the branched polymer being lowered by more than two orders of magnitude in some cases. 

Branching factors were also determined by the ratio of concentrated solution viscosities of branched and linear polymers having the same weight-average molecular weight denoted by g" ... 

Two basic theoretical models exist to describe the degree of long-chain branching in dilute solution. According to the nondraining model depicted by Zimm and Kilb (25) and Kilb (26), the ratio of intrinsic viscosities of branched and linear polymers is given by ... 

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