Viscosity 286 molar mass distribution

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The experimental zero-shear viscosities obtained for polystyrene (PS) of different molar masses (with a very narrow molar mass distribution Mw/Mn=1.06-1.30) and different concentrations in toluene and fra s-decalin are plotted as log r sp vs. log (c- [r ]) in Fig. 6. 

Table 1. Characterisation data and viscosities, ri0, of polystyrene (molar mass distribution Mw/Mn<1.3) in toluene at 25 °C. Theoretical viscosities, ri0(theor), were calculated from Eq. (14). In the last column A represents the relative deviation of ri0(theor) from T 0(exp) ...

Polymers in solution or as melts exhibit a shear rate dependent viscosity above a critical shear rate, ycrit. The region in which the viscosity is a decreasing function of shear rate is called the non-Newtonian or power-law region. As the concentration increases, for constant molar mass, the value of ycrit is shifted to lower shear rates. Below ycrit the solution viscosity is independent of shear rate and is called the zero-shear viscosity, q0. Flow curves (plots of log q vs. log y) for a very high molar mass polystyrene in toluene at various concentrations are presented in Fig. 9. The transition from the shear-rate independent to the shear-rate dependent viscosity occurs over a relatively small region due to the narrow molar mass distribution of the PS sample. 

Many polymer properties can be expressed as power laws of the molar mass. Some examples for such scaling laws that have already been discussed are the scaling law of the diffusion coefficient (Equation (57)) and the Mark-Houwink-Sakurada equation for the intrinsic viscosity (Equation (36)). Under certain circumstances scaling laws can be employed advantageously for the determination of molar mass distributions, as shown by the following two examples. 

The melt flow index is a useful indication of the molar mass, since it is a reciprocal measure of the melt viscosity p. p depends very strongly on 77 ( ) (doubling of results in a 10.6 times higher 77 ). This relation is valid for the zero-shear viscosity the melt index is measured at a shear stress where the non-Newtonian behaviour, and thus the width of the molar mass distribution, is already playing a part (see MT 5.3.2). The melt index is a functional measure for the molar mass, because for a producer of end products the processability is often of primary importance. 

From the results of the light scattering experiments it follows that A and B have the sameM. The viscosity average,My, is for A higher than for B, and is thus closer toMw. A has, therefore, a narrower molar mass distribution and a higher M. The osmotic pressure IT is therefore lower. 

The whole curve is thus shifted upward by a factor 10 (one unit on the log scale). Broadening of the molar mass distribution shifts the curve to the left the zero-shear viscosity does not change. 

First a broad molar mass distribution helps to lower the apparent viscosity at high shear stresses and shear rates, so that thiimer films can be produced at the same pressure. 

FIGURE 16.1 Schematic differential (—) and integral (—) representations of amount of polymer with certain molar mass present in the sample. The narrow, broad, and bimodal molar mass distributions are shown. The typical positions of weight, viscosity, number, and z-molar mass averages are depicted. 

Although average molar masses are convenient for evaluation of G(S) and G(X), we have shown that the molar mass distribution should be considered (5). In particular, the formation of a high molar mass tail can result in serious underestimation of the correct average molar masses, especially after high doses of radiation. Cross-linking causes changes in the hydrodynamic volume of the polymer molecules relative to linear molecules and this affects viscosity and GPC estimates of molar mass, which should be taken into consideration. 

The influence of molar mass distribution on the viscosity function is shown in Fig. 3.16 on the basis of dynamic viscosities of different polystyrenes (PS), which were normalized with respect to their zero shear viscosity. A wider molar mass distribution results in a higher shear thinning in the normalized viscosity function, i. e., the drop in viscosity starts at lower normalized angle frequencies and/or shear rates. 

This can be clearly seen in the comparison of viscosity functions of polystyrene 1 and polystyrene 2. If we add a very high-molecular weight component to polystyrene 2, we obtain polystyrene 3. It is therefore evident that the bimodal molar mass distribution causes the shear thinning to increase further, although not as far as the polydispersity change of the molar mass distribution between polystyrene 1 and polystyrene 2. In the case of higher shear rates, all flow curves proceed to similar viscosity functions. 

Figure 3.16 Influence of molar mass distribution on the normalized viscosity function (data from [9]). Inside figure Molar mass distribution w(M) of the three polystyrenes investigated...

The viscosity of a dilute polymer solution depends on the nature of polymer and solvent, the concentration of the polymer, its average molar mass and molar mass distribution, the temperature and the rate of deformation. In the following exposition it is assumed that the rate of deformation is so low, that its influence can be neglected. 

SEC-VIS Intrinsic viscosity distribution Molar mass distribution... 

Gel permeation chromatography (GPC) is the established method for the determination of molar mass averages and the molar mass distributions of polymers. GPC retention is based on the separation of macromolecules in solution by molecular sizes and, therefore, requires a molar mass calibration to transform elution time or elution volume into molar mass information. This kind of calibration is typically performed with narrow molecular mass distribution polymer standards, universal, or broad calibration methods or molar-mass-sensitive detectors like light-scattering or viscosity detectors. 

Determine the moment of the molar mass distribution measured by intrinsic viscosity of a polydisperse sample. 

Size-exclusion chromatography (SEC) has become the technique of choice in measuring the molar-mass distributions of polymers that are soluble in easily handled solvents (Dawkins, 1989). The technique as widely practised is not an absolute method and a typical SEC system must be calibrated using chemically identical polymers of known molar mass with a narrow distribution unless a combined detector system (viscosity, light scattering and refractive index) is employed. 

The condensation process of PF resins can be followed by monitoring the increase in viscosity and by gel permeation chromatography (GPC) to measure the molar mass distribution. Chromatograms have been obtained by Duval et al. [122], Ellis and Steiner [127], Gobec et al. [128], Kim et al. [129], and Nieh and Sellers [130]. 

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