Scattering polymer molecules

The overall result is that in the melt the polymer molecules adopt Gaussian configurations and behave as thermodynamically ideal entities. This combination of ideality and chain entanglement has been confirmed by neutron scattering experiments and is well established despite the apparent paradox. 

The synthesis of a given polymer molecule through condensation polymerization, on the other hand, is accomplished by a series of independent condensations, which ordinarily occur at intervals scattered... 

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. 

Apart from their utility in determining the correction factor 1/P( ), light-scattering dissymmetry measurements afford a measure of the dimensions of the randomly coiled polymer molecule in dilute solution. Thus the above analysis of measurements made at different angles yields the important ratio from which the root-mean-square... 

Before scattering intensity measurements can be converted to molecular weights, the two corrections previously discussed—the dissymmetry correction for intraparticle interference and the extrapolation to zero concentration—must be introduced, or established to be negligible. The relationships given in the preceding sections unfortunately account rigorously for either only in the absence of the other. The theory of the concentration dependence of the scattered intensity applies to the turbidity corrected for dissymmetry, and the treatment of dissymmetry is strictly valid only at zero concentration (where interference of radiation scattered by different polymer molecules vanishes). 

The temporal evolution of P(r,t 0,0) is determined by the diffusion coefficient D. Owing to the movement of the particles the phase of the scattered light shifts and this leads to intensity fluctuations by interference of the scattered light on the detector, as illustrated in Figure 9. Depending on the size of the polymers and the viscosity of the solvent the polymer molecules diffuse more or less rapidly. From the intensity fluctuations the intensity autocorrelation function... 

Equations 3.31, or 3.32 are found valid only when the size of the scattering solute particle is less than and this condition is seldom fulfilled by polymer molecules. In polymer solutions,... 

Assuming in the first instance that the polymer molecules are quite independent, then the situation is analogous to that in the preceding section, except that the scattering molecules (polymer) are now surrounded by solvent molecules of refractive index n0 instead of by free space of refractive index 1.0. The analogue of Eq. (15) becomes... 

Zimm plot analychem A graphical determination of the root-square-mean end-to-end distances of coillike polymer molecules during scattered-light photometric analyses. zim,plat ... 

The concentration of the polymer molecules eluting from SEC columns is continuously monitored by a detector. The most widely used detector in SEC is the differential reftactometer (DRI), which measures the difference in refractive index between solvent and solute. Other detectors commonly used for SEC are functional group detectors ultraviolet (UV) and infrared (IR), and absolute molecular weight detectors low angle laser light scattering (LALLS) and in-line continuous viscometers. Applications of these detectors to SEC analysis will be discussed later in the Multiple Detectors Section. Other detectors also being used are the densimeter (11-19) and the mass detector (20-23). 

The notion that molecules at a surface are in a two-dimensional state of matter is reminiscent of E. A. Abbott s science fiction classic, Flatland.Perusal of this book for quotations suitable for Chapters 6, 7, and 8 revealed other parallels also the color revolt and light scattering, "Attend to Your Configuration" and the shape of polymer molecules, and so on. Eventually, the objective of beginning each chapter with a quote from Flatland replaced the requirement that the passage cited have some actual connection with the contents of the chapter. As it ends up, the quotes are merely for fun Perhaps those who are not captivated by colloids and surfaces will at least enjoy this glimpse of Flatland. 

Polymer molecules in a solution undergo random thermal motions, which give rise to space and time fluctuations of the polymer concentration. If the concentration of the polymer solution is dilute enough, the interaction between individual polymer molecules is negligible. Then the random motions of the polymer can be described as a three dimensional random walk, which is characterized by the diffusion coefficient D. Light is scattered by the density fluctuations of the polymer solution. The propagation of phonons is overdamped in water and becomes a simple diffusion process. In the case of polymer networks, however, such a situation can never be attained because the interaction between chains (in... 

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