Molar mass determination, light scattering

Figure 6.3 Diagram of apparatus for determining molar mass by light scattering...

Fig. 4. Critical concentrations of polystyrene/toluene and polyacrylamide/water at 25 °C in relation to molar mass determined by viscometry and light scattering... 

It took a long time before the percolation theory could be proved to be the better one in most cases. The reason for this delay resulted in part from the fact that until ten years ago the size exclusion chromatography (SEC) with on-hne light scattering was not sufficiently well developed. A direct molar mass determination is, however, imperative, since the separation in SEC is due to the hydrodynamic volume of the particles. A branched macromolecule has, however, a significantly higher molar mass than a linear one of the same hydrodynamic volume. Since 1989 a number of results have been reported which all strongly supported the percolation theory [109,111-116]. 

According to the derivation. Equation (9-45) is valid for infinitely dilute solutions. It is the basis of molar mass determinations by the light-scattering method. The molar mass Mi obtained here is the mass-average molar mass Mw), as shown in the following derivation ... 

In 1956, Walther Burchard, a Diploma Physicist, entered the institute and built up the new light scattering (LS) technique. After 7 months, reliable LS measurements could be performed. The required molar mass determination of the enzymatically synthesized amylose was possible after full derivatization of the OH-groups with phenyl isocyanate that led to good solubility in organic solvents. Since amylose and cellulose differ chemically solely by the type of the glycosidic bond, the derivatized cellulose was also included in this study. The structural influence of the different glycosidic links could clearly be demonstrated [1]. 

Molar mass determination requires the knowledge of the specific RI increment dn/dc, which in the case of complex polymers depends on chemical composition. Copolymer RI increments (dn/dc)copo can be accurately calculated for chemically monodisperse fractions if comonomer weight fraaions /, and homopolymer values are known, which is rarely the case. Light-scattering investigations of copolymers are even further complicated by the fact that SEC does not separate into chemically monodisperse fractions. Accordingly, due to compositional heterogeneity, the RI increment of a particular... 

Figure 17 Molar mass distributions of polystyrene in ethyl acetate obtained by dynamic light scattering (photon correlation spectroscopy, PCS) and TDFRS with short and long exposure time tp. The dashed curves represent the distribution as determined by SEC. Reproduced with permission from Rossmanith and Kohler [107]. Copyright 1996 American Chemical Society.

Light scattering and electron microscopy studies of aqueous PVME solutions and PVME microgels were carried out by Arndt et al. [329,330]. They noted that the Mw of PVME in water was always higher (up to 20 times) than its value (Mw = 46 000gmoH) determined in organic solvent (butanone), even for dilute aqueous PVME solutions well below the phase-separation temperature [330]. Moreover the molar masses of the polymer in water depended on solution preparation conditions. The authors concluded that PVME does not exist as isolated chains in water, but forms loose aggregates (Rh = 200-220 nm) which decrease in size as the solution temperature passes... 

The flow-through light scattering detectors combined with the concentration detectors provide the values needed for the direct calculation of molar mass values for the given polymer in a given eluent. If the dn/dc and A2 values are not available, they can be determined by the independent... 

The light scattering method is considerably more involved (theoretically and practically too) than the other methods. It can be used at extremely low concentrations of solution with sufficient accuracy. A wide range of molar mass (from a few hundreds to a few lakhs) can be determined and it is one of the most reliable methods for determining the shapes of large molecules. 

Due to the dark color of alkali lignins, their molar masses cannot be determined by means of the light-scattering method. However, as shown by Figure 10, elution with sodium hydroxide also brings about a consistent elution pattern of lignin sulfonates and polypeptides. It is assumed that this also applies to the kraft lignins. 

The mass-average molar mass of the block copolymer solute, M , and the second virial coefficient, A2, can be obtained from SLS. These quantities can be determined from the concentration dependence of the scattered light intensity using the relationship (cf. Section 1.4.10)... 

For the analysis of light scattering experiments the refractive indices of the DADMAC/AAM solutions at dialysis equilibrium were determined, showing the validity of the additivity principle [67]. The additivity could also be proven for the partial specific volumes which are necessary to calculate molar masses from ultracentrifugation experiments [131]. These dependencies are summarized in Fig. 24. 

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