Light scattering thermodynamic limit

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. 

In Chapter 3, we will learn about the dynamics of an isolated polymer chain in the dilute solution limit and the first-order change in the dynamics with polymer concentration. We will also learn typical experimental methods to investigate the dynamics—dynamic light scattering and viscosity. The dynamics of polymer solutions above the overlap concentration will be discussed in Chapter 4, along with their thermodynamics. 

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. 

Important characteristics that describe static mass, conformations, and dimensions of polymer molecules have been surveyed. This has been followed by hydrodynamic properties such as diffusion and viscosity. A separate section has been used to describe the salient aspects of charged polymers and colloids in solution. From there, the collective properties of polymers were briefly introduced in terms of their solution thermodynamics, the relationship of these to the scattering of light, and to phase behavior and transitions. Concentrated polymer solutions and melts become extraordinarily complex, with time response behavior depending on polymer architecture and interactions, and this has been briefly discussed in the area of rheology. In the solid-state limit of rheology, polymers take on myriad applications in materials engineering applications, in electronics, optics, and other areas. 

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