Weight average molar mass measurement

Figure 5.1 An experimental Zimin plot (equation (5.26)) for an aqueous solution of high-methoxy pectin (DE 58%) (pH = 8.0, 0.3 mol/dm3 NaCl, 0.01 mol/dm3 mercaptoethanol, 25 °C). The measurements were made at various pectin concentrations ch c2, etc., and at various scattering angles 0. The intersection point on the ordinate for c - 0 and - 0 is the reciprocal weight-average molar mass, 1 /Mw. Replotted from Semenova et al. (1990).

If a mixture is made of individual polymer chains and polymer clusters, the measurement of static LLS will lead to an apparent weight-average molar mass Mw>app which is expressed by... 

In static LLS [43], the angular dependence of the excess absolute time-averaged scattering intensity, known as the Rayleigh ratio Rw(< )> is measured. For a dilute solution measured at a relatively small angle (6), Rw(q) can be related to the weight average molar mass (Mw), the root mean square... 

Recently, Siu et al. [139] studied the effect of comonomer composition on the formation of the mesoglobular phase of amphiphilic copolymer chains in dilute solutions. The copolymer used was made of monomers, N,N-diethylacrylamide (DEA) and N,N-dimethylacrylamide (DMA). like PNI-PAM, PDEA is also a thermally sensitive polymer with a similar LCST, but PDMA remains water-soluble in the temperature range (< 60 °C) studied. At room temperature, copolymers made of DMA and DEA are hydrophilic, but become amphiphilic at temperatures higher than 32 °C. Before the association study, each P(DEA-co-DMA) copolymer was characterized by laser light scattering to determine its weight average molar mass (Mw) and its chain size ( Rg) and (R )). The copolymer solutions (6.0 x 10 A g/mL) were clarified with a 0.45 xm Millipore Millex-LCR filter to remove dust before the LLS measurement. 

Three copolymers, PNIPAM-co-l.O-MACA, PNIPAM-co-2.9-MACA and PNIPAM-co-4.9-MACA were used. Their weight-average molar masses (Mw) are 9.4 x 105, 8.3 x 105 and 6.5 x 105 g/mol, respectively. In order to avoid possible interchain association, we kept each dilute solution in a refrigerator for at least one day to ensure a complete dissolution. The solution was clarified by a 0.45 Millipore (Hydrophlic Millex-LCR, PTFE) filter and then kept in a refrigerator again for a few days before LLS measurements. 

The amount of light scattered (in excess of that scattered by the mobile phase) at 0 0 is directly proportional to the product of the weight-average molar mass and the concentration (ergo, measure the concentration and derive the mass ). 

In Section 1.7.2, we will see that the weight-average molar mass can be measured by light scattering from a dilute polymer solution. The viscosity of polymer liquids correlates well with the weight-average molar mass. 

Weight-average molar mass can be measured by scattering and by ultra-centrifugation. Recent developments in photodetector technology have... 

The final relation was obtained using Eq. (1.31). Hence, dilute scattering measurements give the weight-average molar mass of a polydisperse polymer sample. 

For branched polymers and for linear polymers that do not have an established Mark-Houwink equation, SEC is typically used in conjunction with light scattering and viscosity detectors. These detectors measure the weight-average molar mass and viscosity of each elution volume. In principle, this experiment directly determines both M and [rj] for any polymer that is soluble in the SEC solvent, but in practice the determination also requires that the polymer have an appreciable difference in refractive index from the solvent so that in Eq. (1.88), dn/dc >0.05 mL g . Often a new polymerization is not understood sufficiently to know for certain whether the polymer produced will have branched chains present or... 

Equations (6.148) and (6.149) provide a way of obtaining weight- and z-average molar masses from size exclusion chromatography. Are they approximate or exact methods If the concentration c, and weight-average molar mass of each elution volume are accurately measured, would the correct and Af, of the whole sample he known ... 

Viscosity studies of dilute solutions provide a convenient relative measure of the molar mass and the resultant average, M will lie closer to than to M . The behaviour of polymer melts will be discussed in detail later, but it is noted that the melt viscosity is a strong function of the weight-average molar mass since the parameter m in the relation... 

From light-scattering measurements, a method depending on the size rather than the number of molecules, a weight-average molar mass M is obtained. This is defined as... 

Dynamic LLS is famous for its application in particle sizing. G(F) obtained from a dilute dispersion is converted to the hydrod5mamic size distribution /(iSh) by means of D = Vlq and the Stokes-Einstein relation D = k TI6nr)R with k, T, and ri being the Boltzmann constant, the absolute temperature, and solvent viscosity, respectively. All the parameters in the conversion are either well-known constants or precisely measurable by other methods. Therefore, using dynamic LLS to size the particle size distribution is an absolute method without any calibration. Many commercial instruments have been successfully developed on this principle details have been compiled in a book (32). However, a combination of static and dynamic LLS can provide much more than the characterization of the weight-average molar mass and the particle size distribntion. 

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