Polymer viscosity average

Use of pseudoplastic solution flow curve data and the Graessley model may enable prediction of polymer viscosity average molecular weight. Confirmation of this method for accurate molecular weight determination is presently underway. 

JPolymer molecular weight as the polymer viscosity average molecular weight (Mv). nr = not reported. 

Mao and co-workers [189] have developed a new method for the determination of polymer viscosity-average molecular weights using flow piezoelectric quartz crystal (PQC) viscosity sensing. Experimental apparatus with a 9 MHz AT-cut quartz crystal and a flow detection cell was constructed and shown to give highly reproducible data at a temperature of 25 0.1 °C and fluid flow rate of 1.3-1.6 ml/min. A response model for the PQC in contact with the dilute polymer solutions (concentration less than 0.01 g/ml) was proposed in which the frequency change from the pure solvents, Af, follows Af = + kj, where... 

The viscosity average molecular weight is not an absolute value, but a relative molecular weight based on prior calibration with known molecular weights for the same polymer-solvent-temperature conditions. The parameter a depends on all three of these it is called the Mark-Houwink exponent, and tables of experimental values are available for different systems. 

Hven fractionated polymer samples are generally polydisperse, which means that the molecular weight determined from intrinsic viscosity experiments is an average value. The average obtained is the viscosity average as defined by Eqs. (1.20) and (2.40) as seen by the following argument ... 

The viscosity average molecular weight depends on the nature of the intrinsic viscosity-molecular weight relationship in each particular case, as represented by the exponent a of the empirical relationship (52), or (55). However, it is not very sensitive to the value of a over the range of concern. For polymers having the most probable distribution to be discussed in the next chapter, it may be shown, for example, that... 

To perform this analysis, we first prepare a dilute solution of polymer with an accurately known concentration. We then inject an aliquot of this solution into a viscometer that is maintained at a precisely controlled temperature, typically well above room temperature. We calculate the solution s viscosity from the time that it takes a given volume of the solution to flow through a capillary. Replicate measurements are made for several different concentrations, from which the viscosity at infinite dilution is obtained by extrapolation. We calculate the viscosity average molecular weight from the Mark-Houwink-Sakurada equation (Eq. 5.5). 

Fiber orientation uniformity is also affected by small-scale or timewise variations in polymer viscosity, related to breakage of polymer chains during the extrusion process. The degradation occurs as a result of residual moisture that immediately reacts to break chains, and by thermal degradation that occurs more gradually over time. Different residence times and temperature histories within the laminar flow streamlines lead to different viscosities, and hence different average orientation levels in the different fibers. 

Rheological behaviour, viscosity and plasticity under given conditions are affected by the nature of the polymer, the average molecular weight, its distribution, and the molecular structure, branching, stereo-arrangement... 

Finally, a solvent viscosity method is often used to measure the molecular weight of many polymers such as PET, and this viscosity average molecular weight Is often close to the weight average molecular weight. 

Figure 4-5 shows the viscosity-average molecular weights in the emulsion polymerizations of styrene of Fig. 4-3. The results are in line with Eq. 4-7 in that the polymer size increases with the emulsifier concentration.

Equation (32) has been compared with phase boundary concentration data in the following way. For each solution, N of the polymer sample is estimated from Mw or the viscosity-average molecular weight Mv along with the molecular parameters ML and q listed in Table 1, and d is calculated with d from II or 0II/0c data. For systems which lack these data, the values of d from the (partial) specific volume vsp may be substituted. Table 2 lists the resulting values of d from II, 0II/0c, or vsp for various systems. The phase boundary volume fractions vc v ( = vc v v = I and A) are calculated from experimental phase boundary weight fractions (or mass concentrations) with d, Mw (or Mv), and Ml. Finally, with these numerical results, [vc v/dav(d)] — AV(N, d) is computed... 

Gamma radiation can be used with macroscopic amounts of polymer. This is particularly welcome when polymers are not compatible with the GPC technique. Larger samples can be characterized by viscosity changes, usually measured in dilute solutions. All that is needed is a suitable solvent. If the Mark-Houwink parameters are known, it is possible to calculate viscosity-average molecular weight, Mv, from dilute solution viscosities. However, even the raw viscosity-concentration data in terms of the reduced viscosity may be enough to indicate the sensitivity of a given polymer in qualitative terms. The reduced viscosity at concentrations c is isp/c where t]sp — (solution viscosity — solvent viscosity)/solvent viscosity. 

Tn the previous papers of this series (1, 2, 3, 4) calibration and repro- ducibility of gel permeation chromatography (GPC) have been extensively examined. This paper describes the application of GPC to two selected samples of linear polyethylenes, one having a narrow molecular weight distribution (NMWD) and another a broad molecular weight distribution (BMWD). These samples were distributed by the Macro-molecular Division of IUPAC (5) for the molecular characterization of commercial polymers. The average molecular weights by GPC are compared with the data obtained from infrared spectroscopy, osmotic pressure, melt viscosity, and intrinsic viscosity. Problems associated with data interpretation are discussed. 

The intrinsic viscosities of the polymers prepared in tetrahydrofuran increased throughout the experiment. This system thus exhibits some of the aspects of living polymerization—that is, catalyst activity over an extended period, and increasing viscosity average molecular weights with added amounts of monomer. The rather broad molecular-weight distributions of these polymers, however, differentiates this system from that of the classical case in which polymerization proceeds in the complete absence of a termination process. 

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