Light scattering from dilute polymer solutions

8 Light scattering from dilute polymer solutions 

The scattering process is also characterized by a scattering vector q whose length is equal to q and whose direction is given by the vector difference between a unit vector in the scattering direction and a unit vector in the incident direction. 

The theoretical description of the scattering function is facilitated by dividing the chain into m identical subxmits characterized by an excess polarizability density. All the subunits are identical in composition, so it is not necessary to weight the result by the local polarizability density. The scattering function can then be expressed as  

To appreciate the overall shape of S(q), it is necessary to make measurements at large values of . If the only quantity that is desired is the mean-squared radius of gyration, it is possible to consider data only in the range where m 1. A mathematical expansion of the scattering function in the low-M regime yields  

Measurements of tiie excess scattered intensity of a dilute polymer solution can then be used to calculate the mean-squared radius of gyration for the macromolecule. The result shown in Equation 3.9 is quite general for macromolecules that can be divided into identical subunits. If the macromolecule is a Gaussian chain, = (1/6).  

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McIntyre, D., Gornick F. (eds.) Light scattering from dilute polymer solutions. New York Gordon and Breach 1964... 

P. Debye, in Light Scattering from Dilute Polymer Solutions (D. McIntyre and F. Gornick, eds.), p. 13, Gordon and Breach, New York, 1964. 

M.B. Huglin (Ed.), Light Scattering from Dilute Polymer Solutions, Academic Press, London, 1972. 

Doty, P. Depolarization of Light Scattered from Dilute Macromolecular Solutions. I. Theoretical Discussion. J. Polymer Sci. 3, 750—762 (1948). 

The second virial coefficient A2 is determined from the concentration dependence of osmotic pressure [Eq. (1-76)] or scattered light intensity [Eq. (1.91)] from dilute polymer solutions. A2 is a direct measure of excluded volume interactions between pairs of chains. 

Dynamic light scattering from dilute solutions provides the value of the diffusion coefficient, which can be converted to hydrodynamic radius J h,star of the star polymer. The ratio Rh/(Rg) characterizes the compactness of the macromolecule for the uniform hard sphere impenettable for the flow, it is Rb/Rg= (5/3) 1.29, whereas for the Gaussian coil, Rh/(Rg) = 3a- / /8 0.66. For ideal stars (without excluded-volume interactions), the ratio Rh/(Rg) can be derived within the Kirkwood-Riseman approximation, which gives the value of Rh/(Rg) 0.93. Reported experimental values of the Rh/(Rg) ratio for star polymers and starlike block copolymer micelles are usually found close... 

SLS from Dilute Polymer Solutions The intensity iu.0(one) of light scattered by one isolated small isotropic particle being much smaller than the wavelength 2 of incident wnpolarized light of intensity Iq is given by Equation 3.12 ... 

So, Equation 12-37 is the general equation for light scattering from polymers. If you ve jumped from page 367, you should know that the factor P 9) depends upon the shape of the molecule. Our interest is in the most common case of random coils in dilute solution, where P(B) can be simply expressed as a series in 9. It is usual to truncate this series after the second term, giving our final result, shown in Equation 12-38 in all its complex glory. 

A dilute polymer solution has a turbidity of 0.0100 cm . Assuming that the solute molecules are small compared to the wavelength of the incident light, calculate the ratio of the scattered to incident light intensities at 90° angle to the incident beam and 20 cm from 2 ml of solution. Assume that all the solution is irradiated. 

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. 

Hara M, Nakajima A. Characteristic behavior of light scattering from polyelectrolyte in dilute solution region. Polymer Journal 1980 12 701-709. 

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