Dilute solution light scattering theory

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

Therefore we expect Df, identified as the fast diffusion coefficient measured in dynamic light-scattering experiments, in infinitely dilute polyelectrolyte solutions to be very high at low salt concentrations and to decrease to self-diffusion coefficient D KRg 1) as the salt concentration is increased. The above result for KRg 1 limit is analogous to the Nernst-Hartley equation reported in Ref. 33. The theory described here accounts for stmctural correlations inside poly electrolyte chains. 

The Rayleigh approximation shows that the intensity of scattered light depends on the wavelength of the light, the refractive index of the system (subject to the limitation already cited), the angle of observation, and the concentration of the solution (which is also restricted to dilute solutions). In the Rayleigh theory, the size and shape of the scatterers (M and B) enter the picture through thermodynamic rather than optical considerations. 

An alternative (but equivalent) approach is the so-called fluctuation theory, in which light scattering is treated as a consequence of random non-uniformities of concentration and, hence, refractive index, arising from random molecular movement (see page 26). Using this approach, the above relationship can be written in the quantitative form derived by Debye140 for dilute macromolecular solutions ... 

Experimentally the overall size of the polymer chain can be studied by light scattering and neutron scattering. A great deal of theoretical work is present in the literature which tries to predict the properties of mixtures in terms of their components. The analytical model by Rouse-Zimm [85,86] is one of the earliest works to derive fundamental properties of polymer solutions. Advances were made subsequently in dilute and concentrated solutions using perturbation theory [87], self-consistent field theory [88], and scaling theory [89],... 

The exponent v characterizes the swelling of a long polymer chain in very dilute solutions. In theory, it could be measured in several ways. However, can we trust results obtained by the simplest technique which consists in measuring the intrinsic viscosity These measurements produce values for the exponent v which are always lower than those obtained by light scattering measurements of the radius of gyration. It was necessary to explain this discrepancy in order to make a proper comparison between experimental and theoretical values of the exponent v. 

The light-scattering spectrum which is related to 7 (q, /) by Eq. (3.3.3) consequently probes how a density fluctuation <5/ (q) spontaneously arises and decays due to the thermal motion of the molecules. Density disturbances in macroscopic systems can propagate in the form of sound waves. It follows that light scattering in pure fluids and mixtures will eventually require the use of thermodynamic and hydrodynamic models. In this chapter we do not deal with these complicated theories (see Chapters 9-13) but rather with the simplest possible systems that do not require these theories. Examples of such systems are dilute macromolecular solutions, ideal gases, and bacterial dispersions. ... 

A detailed experimental study of the isotropic component of light scattered from dilute solutions of tobacco mosaic virus (a rod-like molecule with L = 3000 A and cross section diameter = 180 A) has been perfomed by Cummins et al. (1969) using spectrum analysis techniques. These authors found that the measured spectrum fit the theory described above rather well. Wada et al. (1971) repeated these experiments using an autocorrelator with similar results. 

In the first section, we introduce the general theory of light scattering. The second section is devoted to SLS, and we give some examples of its application. In the third section, we discuss the principles of DLS and we apply these to the study of the dynamics of different systems, whether dilute or concentrated solutions. 

In recent years, the quasi-elastic light scattering (QELS) method has become increasingly routine in experimental studies of polymer dynamics in both dilute and concentrated solutions. It allows us to obtain information about the possible modes of Brownian motion of a polymer molecule either isolated or entangled with others. Leaving its technical details and various practical applications to reference books [38], we here give a brief account of its important aspects which are closely related to the current theory of dilute polymer solutions. 

Flory theory of light scattering in dilute solution... 

The theoretical analysis of the scattered spectrum was first presented by Komarov and Fisher (3) and Pecora (4) independently in 1963. In 1964 the spectrum of laser light scattered by dilute solutions of polystyrene latex spheres was observed (5) and was foimd to exhibit a lineshape in good agreement with theory. In a typical scattering experiment (6) a monochromatic beam of radiation is incident on the material the wave vector is denoted as ko and the frequency by coo- The scattered radiation is recorded as a function of the scattering angle and frequency shift co, where... 

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