Viscosity-average molecular weight polymers

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. 

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). 

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. 

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. 

These two types of molecular weight averages are representative of the type called absolute methods, in that well-established thermodynamic equations can be used to convert the experimental data directly into a value of the molecular weight. However, some other methods require calibration. The most important of these indirect methods involves a measurement of the intrinsic viscosity. This quantity is a measure of the extent to which a polymer molecule increases the viscosity of the solvent in which it is dissolved. The viscosity method can be calibrated to yield a viscosity-average molecular weight, defined by... 

The dichloride complex was used as the reference for the ethylene, see reference [ 18]. a Toluene. b Dichloromethane. c Activity, g polymer-mol Zr -lr1. d Melting point. e Polymer fraction. f Molecular weight distribution. g Viscosity average molecular weight. h Elastomer. 

Intrinsic viscosities were obtained using a Cannon-Penske viscometer and the usual method of extrapolation to zero concentration by measuring the reduced viscosities at 0.1%, 0.05% and 0.025% by weight of polymer in benzene. The mean viscosity average molecular weights were determined using the Mark-Houwlnk equation and an "a" value of 0.72 and a "K" value of 12.3 x 10 - ( ) ... 

Polymers. High molecular weight poly(n-butyl methacrylate) (PBMA) was obtained from Scientific Polymer Products Inc. and used as such. The viscosity-average molecular weight, Rv, was determined by the Kark-Houwink-Sakurada equation... 

To this point we have considered the solution properties of a monodisperse polymer. The MHS relation will also apply to a polydisperse sample, but M in this equation is now an average value where we denote the viscosity average molecular weight. Thus, in general. 

With a particular poly(vinyl alcohol) sample no periodic acid is consumed, within the limits of analytical aecuracy. This indicates no apparent (1,2-diol) cleavage. However, the viscosity average molecular weight of the sample decreased from 250,000 to 100,0(X), Explain these results in terms of the structures of po y(vinyl acetate) and polyfvinyl alcohol). [The analytical technique is described by P. J. Flory and F. S, Leutner, J. Polym. Set. 3,880 (1948) 5, 267(1950).]... 

Isobutylene polymerizations were carried out by charging isobutylene, methyl chloride, and the alkylaluminum compound in methyl chloride solution and adding the t-butyl halide initiator in methyl chloride rapidly. Polymerizations ensued immediately and were over in 5-10 min. The reactions were terminated after 15 min by the addition of prechilled methanol. The polymers were dried in vacuum at 40° to constant weight and were characterized by number average and viscosity average molecular weights. All reactions were carried out in duplicate. 

The exponent a is a measure of the interaction of the solvent and polymer. It is a function of the shape of the polymer coil in a solution, and usually has a value between 0.5 (for a randomly coiled polymer in a 0 solvent) and 0.8 (when the polymer coils expand in good solvents). The a value is 0 for spheres, about 1 for semicoils, and is between 1.8 and 2.0 for a rigid polymer chain extended to its full contour length. The proportionality constant K is characteristic of the polymer and solvent. The constants K and a are the intercept and slope, respectively, of a plot of log [ 7] versus log Af of a series of fractionated polymer samples. Viscosity average molecular weights he between those of the corresponding... 

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