Viscosity branched polymers

In terms of viscosity, branched polymers have lower zero shear viscosity than linear polymers of the same total molecular weight (Af > Me) when the branches are short (A/j, < Me). When Mb > Me, the branched chain viscosities overtake those of the equally massive linear chains. 

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... 

With the availability of the higher density polymers the value of the melt flow index as a measure of molecular weight diminishes. For example, it has been found that with two polymers of the same weight average molecular weight (4.2 X 10 ), the branched polymer (density = 0.92 g/cm ) had only 1/50 the viscosity of the more or less unbranched polymer (density = 0.96 g/cm ). This is due to long chain branches as explained above. 

Structurally viscous grades are based on branched polymers (branching being effected by the use of tri- or higher functional phenols). These polymers exhibit a sharp decrease in viscosity with increasing shear rate which makes them particularly suitable for extrusion and blow moulding and also, it is claimed, in reducing drip in case of fire. 

The first commercial grades were introduced by Phillips Petroleum in 1968 under the trade name Ryton. These were of two types, a thermoplastic branched polymer of very high viscosity which was processed by PTFE-type processes and an initially linear polymer which could be processed by compression moulding, including laminating with glass fibre, and which was subsequently oxidatively cross-linked. 

It has been shown" that branched polymers have lower melting points and viscosities than linear polymers of the same molecular weight. The viscosity of the silicone fluids is much less affected by temperature than with the corresponding paraffins (see Figure 29.2). 

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. 

Another investigation involved the SC VP of a macroinimer 8 via ATRP [46]. GPC/viscosity measurements indicated that the intrinsic viscosity of the branched polymer is less than 40% of that of the linear one at highest MW area (Fig. 6). A significantly lower value for the Mark-Houwink exponent (a=0.47 compared to a=0.80 for linear Pf-BuA) was also observed, indicating the compact nature of the branched macromolecules. 

The relationship between g and gu can be found through use of the Mark-Houwink relationship. "The intrinsic viscosity of a linear polymer of the same molecular weight (M. ) as the branched polymer is... 

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]. 

Unlike linear or ordinary branched polymers, dendrimers display intrinsically low viscosity, even at high mass. As standard polymeric molecules increase in mass and size, their viscosity normally increases continually. With dendrimers, viscosity increases only up to about the fourth generation, after which it actually begins to decline (Mourey, 1992 Frechet, 1994). In addition, with control over the type of pendent groups that adorn the surface, dendrimers can maintain high solubility regardless of size. 

The viscosity of polymer solutions has been considered theoretically by Flory,130 but although this theory has been applied to cellulose esters,131 no applications have yet been made in the case of the starch components. Theoretical predictions of the effect, on [17], of branching in a polymer molecule have been made,132 and this may be of importance with regard to the viscometric behavior of amylopectin. 

It is now recognized that a continuum of architecture and properties, which begins with the classical branched polymers, resides between these two classes. Typical branched structures such as starch or high pressures polyethylene are characterized by more than two terminal groups per molecule, possessing substantially smaller hydrodynamic volumes and different intrinsic viscosities compared to linear polymers, yet they often exhibit unexpected segmental expansion near the theta state . 

Rouse mechanism within the tube and the disengagement of the polymer from the tube. For a branched polymer the arm is tethered at one end so this restricts motion. In order for disengagement to occur the arm has to retract itself down the tube. This is the dominant timescale and determines the viscosity. We can think of this as akin to an activation energy process giving rise to an exponential dependence in the viscous process. As yet only qualitative agreement has been achieved. 

Solution viscosity measurements for Mn are calibrated from the flow characteristics of linear molecules of the equilibrium molecular weight distribution. Branched polymers have a lower radius of gyration for their molar mass than the corresponding linear molecule. One, therefore, expects different flow properties as branching increases, hence causing the viscosity numbers to become less and less accurate and so should only be used for trends - not exact calculations. 

Ferrocene-based Branched Polymers (Dendrimers). One of the topics in macromolecular chemistry is constituted by dendrimers, or hyperbranched macromolecules of tridimensional globular structure, the surface of which is characterized by a large number of functional groups, Scheme 4. Such functionalities impart to the molecules solubility, viscosity and thermal properties different from those of the common linear polymers.38c,d 44... 

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