Dynamic light scattering
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
660
2025-12-17
52
Dynamic light scattering
A special laser scattering technique, dynamic light scattering, can be used to investigate the diffusion of polymers in solution. Consider two polymer molecules being irradiated by a laser beam. Suppose that at a time t the scattered waves from these particles interfere constructively at the detector, leading to a large signal. However, as the molecules move through the solution, the scattered waves may interfere destructively at another time t′ and result in no signal. When this behaviour is extended to a very large number of molecules in solution, it results in fluctuations in light intensity that depend on the diffusion coefficient, D, which is a measure of the rate of molecular motion and is given by the Stokes–Einstein relation (which is discussed further in Section 21.9e):
D= 
where f is the frictional coefficient, a measure of the forces that retard a molecule’s motion. Table 19.2 lists some typical values of D. For a spherical particle of radius a in a solvent of viscosity η (see Section 19.6), the frictional coefficient is given by Stokes’s relation:
f = 6πaη
If the molecule is not spherical, we use appropriate values of f given in Table 19.3. Hence, dynamic light scattering measurements give the diffusion coefficient and molecular size, in cases where the molecular shape is known. For dilute monodisperse systems of random coils, it has been found empirically that D is related to the molar mass M of the polymer by:
D=βDM−0.6
The coefficientβDis obtained by determining D at fixed viscosity and temperature for a variety of standard samples with known molar masses. As we should expect, bulky polymers of high molar mass migrate more slowly (have a lower diffusion coefficient) through a solvent than polymers of low molar mass.
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