Molar mass viscosity average

For polydisperse samples, the weight average intrinsic viscosity [p])w is measured (Equation (8)) and the so-called viscosity averaged molar mass is obtained ... 

Our calculation of (ro2) is therefore, for polymer solutions, only valid for theta conditions. We shall consider this case in somewhat more detail. We have seen that for the determination of the viscosity average molar mass, the Mark-Houwink... 

This is the Mark-Houwink equation, where the formal dimension of K is equal to cm3/g x (g/mol)a. In general, however, K is tacitly expressed and tabulated in the same dimension as [r ] and the resulting polymer molecular weight M is then expressed in g/mol. For polydis-perse polymers, M is replaced by Mv the so-called viscosity-average molar mass, so that... 

Knowing the values of a and K, for a polymer-solvent system, the viscosity-average molar mass Mvis can be easily determined from intrinsic viscosity measurements. 

Find the intrinsic viscosity and viscosity average molar mass on the basis that the viscosity of the system obeys [r ] = K Mvisa with K = 3.80 10"5 dm3 g-1 and a = 0.63. 

Example The following data were obtained for the intrinsic viscosity of poly isobutylene in CC14 solution at 30 C as a function of viscosity average molar mass... 

We shall now comment on the viscosity-average molar mass, Mvigc If the exponent a in the Mark-Houwink equation, we, [ri]... 

Therefore, the viscosity-average molar mass can be written as... 

Equation (7) also holds for a polydisperse sample of PVOH, but the molar mass in this case is, the viscosity-average molar mass defined below. 

Number-Average and Viscosity-Average Molar Mass. For a polydisperse polymer, any determination of molar mass must yield an average of some sort. When a col-ligative property such as osmotic pressure is used, the average is a number average ... 

Viscosity average molar mass, as measured in CC14 at 25° C, is related to intrinsic viscosity by the following relationship [64] ... 

Figure 3.41 Concentration of hydroxyethyl cellulose at which depletion flocculation occurred, Cf, as a function of the viscosity-average molar mass of the polymer. Reproduced by permission of The Royal Society of Chemistry from ref. [133]...

Figure 6-19. Dependence of the volume fraction 03 of the precipitant on the logarithm of the volume fraction 02 of the solute at the point of incipient turbidity for polystyrenes of different viscosity-average molar masses in a benzene-isopropanol system at 25 C (after A. Stasko and H.-G. Elias).

The best known of these one-moment exponent averages is what is known as the viscosity-average molar mass ... 

The viscosity measurement yields the viscosity-average molar mass, Mv, which is given by... 

The number-average molar mass thus possesses very low values at the gel point, whereas the mass-average shows infinitely high values. The viscosity-average molar mass also assumes high values at the gel point. 

The ratio A//A/ is called polydispersity (the previously used term was poly-molecularity) of a polymer and it gives important information on the width of its molar mass dispersity. Less frequently, the viscosity average molar mass, A/, and the artificial z and z+1 averages of molar mass. A/ and Af are considered. M is defined... 

The ratio of [tj]/[tj]0 is called the viscosity expansion factor a. The viscosity-averaged molar mass (A/ ) obtained from the MHSS equation may also be used to get information about the degree of molar mass dispersion from the comparison of the M values of a polymer sample in two different solvents [5,6],... 

Fig. 2.2. Schematic molar mass distribution with number average molar mass Mn. mass average molar mass centrifuge average molar mass and viscosity-average molar mass...

With viscosimetry, a viscosity average molar mass is determined. As can be seen in Fig. 2.2, it lies between and M. Its definition and determination is described in... 

The molar mass determined with an [/jJ-M-relationship is the so-called viscosity average molar masses M, rather than mass (M ) or number average (MJ molar mass (see Chap. 2). This seems to be peculiar on first glance, since the molar masses used for the determination of the [ /]-M-relationships were either number or mass average molar masses (depending on the determination method). However, the samples used for the determination of the [/j]-M-relationship should have had a very narrow molar mass distribution. The unknown sample on the other hand has an unknown distribution function of the molar mass. Only in the case that the distribution function of the unknown sample and the sample used for the determination are the same, or M are determined directly from the viscosimetric measurement. 

The viscosity average molar mass is only obtained from [qj-M-relationships that have been determined with polymer samples of a polydispersity of Q=l. For those cases, where the [qj-M-relationship was determined from polymer samples with polydispersities Q>1 and the average molar mass or was used, the [ q] -M-relationship can be corrected with a factor if the distribution function of the molar mass is known ... 

Number average molar mass Molar mass of a monomer unit Mass average molar mass Centrifuge average molar mass Viscosity average molar mass... 

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