Molar mass light-scattering

Hence, the value of I/Iq is dependent on relative molar mass of the molecules involved in the light scattering. The Rayleigh ratio, Rg, may be defined as ... 

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

Overall, as is apparent from this description, light scattering is a difficult, time-consuming technique, despite its great importance. Despite this, the technique has been used to measure relative molar masses as low as that of sucrose and as high as those of proteins, and has been found to have a useful range for polymers of relative molar masses between ten thousand and ten million. 

In order to understand polymer solution behaviour, the samples have to be characterised with respect to their molecular configuration, their molar mass and polydispersity, the polymer concentration and the shear rate. Classical techniques of polymer characterisation (light scattering, viscometry, ultracentrifugation, etc.) yield information on the solution structure and conformation of single macromolecules, as well as on the thermodynamic interactions with the solvent. In technical concentrations the behaviour of the dissolved polymer is more complicated because additional intramolecular and intermolecular interactions between polymer segments appear. 

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

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.

Simple homopolymers, where monodisperse standards and suitable solvents are available, are easily characterized by SEC. Homopolymers for which no monodisperse standards are available additionally require some more elaborate detection system for transformation of the retention time into molecular weight. This can be done by, e.g., universal calibration. Alternatively, an absolute molar mass detector, like an on-line light scattering detector or mass spectrometer, can be used. 

Turbidimetry is ideally suited to detect the temperature at which a transparent polymer solution turns opaque. The temperature corresponding to the onset of the increase of the scattered light intensity is usually taken as the cloud-point temperature, TcP, although some authors define the cloud point as the temperature for which the transmittance is 80% (or 90%) of the initial value. This technique is commonly known as the cloud-point method [199]. Turbidimetry was employed, for instance, to show that the cloud-point temperature of aqueous PNIPAM solutions does not depend significantly on the molar mass of the polymer [150]. 

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... 

Now, when measuring the intrinsic viscosity by common capillary viscome-try and the molar mass by static light scattering, two quantities are compared which correspond to different types of averages over the size distribution. From light scattering one has but the average of the intrinsic viscosity is... 

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]. 

Note 1 An infinite number of molar-mass averages can in principle be defined, but only a few types of averages are directly accessible experimentally. The most important averages are defined by simple moments of the distribution functions and are obtained by methods applied to systems in thermodynamic equilibrium, such as osmometry, light scattering and sedimentation equilibrium. Hydrodynamic methods, as a rule, yield more complex molar-mass averages. 

A universal calibration is therefore possible for SEC by plotting log ([q] M) vs. Vg when a viscosity detector is used. Absolute molar masses can be obtained using a light-scattering detector. 

From the results of the light scattering experiments it follows that A and B have the sameM. The viscosity average,My, is for A higher than for B, and is thus closer toMw. A has, therefore, a narrower molar mass distribution and a higher M. The osmotic pressure IT is therefore lower. 

Its related value was originally denoted as X- Numerous % values in terms of volume fractions are collected in Ref. [37]. Unfortunately the scatter in % values found in the literature is large as they reflect also both the polymer source (e.g., narrow molar mass fractions or anionically prepared samples) and the method of measurement, for example, light scattering, osmometry, or inverse gas chromatography. The interaction parameters g (%) for the polymer-good solvent systems assume values between 0 and 0.5 [37]. 

Some specific properties of macromolecules are employed for the detection in polymer HPLC. It is primarily the large size of detected species, which is comparable with the wavelength of the visible light. As a result, the light beam interacting with the macromolecules is intensively scattered [272]. The extent of light scattering under otherwise constant experimental conditions depends on the molar mass of macromolecules. 

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... 

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