Scattering dilute solutions

Quasi-elastic light scattering, dilute solution Rousselot gelatin. 

Quasi-elastic light scattering, dilute solution, Rousselot gelatin, photographic grade. My, = 1.9 x 10 , M /M = 2.3, concentration ranges from 5 to 15%... 

It is important to recognize the approximations made here the electric field is supposed to be sulficiently small so that the equilibrium distribution of velocities of the ions is essentially undisturbed. We are also assuming that the we can use the relaxation approximation, and that the relaxation time r is independent of the ionic concentration and velocity. We shall see below that these approximations break down at higher ionic concentrations a primary reason for this is that ion-ion interactions begin to affect both x and F, as we shall see in more detail below. However, in very dilute solutions, the ion scattering will be dominated by solvent molecules, and in this limiting region A2.4.31 will be an adequate description. 

One of the most important fiinctions in the application of light scattering is the ability to estimate the object dimensions. As we have discussed earlier for dilute solutions containing large molecules, equation (B 1.9.38) can be used to calculate tire radius of gyration , R, which is defined as the mean square distance from the centre of gravity [12]. The combined use of equation (B 1.9.3 8) equation (B 1.9.39) and equation (B 1.9.40) (tlie Zimm plot) will yield infonnation on R, A2 and molecular weight. 

Light scattering teclmiques play an important role in polymer characterization. In very dilute solution, where tire polymer chains are isolated from one anotlier, tire inverse of tire scattering function S (q) can be expressed in tire limit of vanishing scattering vector > 0 as 1121... 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

The last factor is equal to 1+cos 0. The combined intensity of scattered light at a distance r and in a direction specified by 6 (Fig. 43) due to all particles in unit volume (N/V) of the very dilute solution becomes... 

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... 

Kashiwagi, Y., Norisuye, T., and Fujita, H., Triple helix of schizophyllum commune polysaccharide in dilute solution. 4. Light scattering and viscosity, Macromolecules, 14, 1220, 1981. 

Sato, T., Norisuye, T., and Fujita, FI., Double-stranded helix of xanthan in dilute solution evidence from light-scattering, Polymer J., 16, 341, 1984. 

We report here the results of our recent studies of poly(alkyl/arylphosphazenes) with particular emphasis on the following areas (1) the overall scope of, and recent improvements in, the condensation polymerization method (2) the characterization of a representative series of these polymers by dilute solution techniques (viscosity, membrane osmometry, light scattering, and size exclusion chromatography), thermal analysis (TGA and DSC), NMR spectroscopy, and X-ray diffraction (3) the preparation and preliminary thermolysis reactions of new, functionalized phosphoranimine monomers and (4) the mechanism of the polymerization reaction. 

The paper is organized in the following way In Section 2, the principles of quasi-elastic neutron scattering are introduced, and the method of NSE is shortly outlined. Section 3 deals with the polymer dynamics in dense environments, addressing in particular the influence and origin of entanglements. In Section 4, polymer networks are treated. Section 5 reports on the dynamics of linear homo- and block copolymers, of cyclic and star-shaped polymers in dilute and semi-dilute solutions, respectively. Finally, Section 6 summarizes the conclusions and gives an outlook. 

For non-interacting, incompressible polymer systems the dynamic structure factors of Eq. (3) may be significantly simplified. The sums, which in Eq. (3) have to be carried out over all atoms or in the small Q limit over all monomers and solvent molecules in the sample, may be restricted to only one average chain yielding so-called form factors. With the exception of semi-dilute solutions in the following, we will always use this restriction. Thus, S(Q, t) and Sinc(Q, t) will be understood as dynamic structure factors of single chains. Under these circumstances the normalized, so-called macroscopic coherent cross section (scattering per unit volume) follows as... 

The best insight into the relaxation behavior of star polymers in dilute solution can be expected if, in addition to the whole star system, different parts of the star are considered separately. This can be achieved easily by neutron scattering techniques on systems where not only the entity of arms, but also single arms, the core or shell parts are labelled by proton deuterium exchange. With respect to the core-shell labelling it is convenient to build up the arms as diblock copolymers of A-B type with protonated or deuterated but otherwise chemically identical A and B blocks. 

Elastic and quasi-elastic (NSE) neutron scattering experiments were performed on dilute solutions of linear poly(isoprene) (PIP) polymers and of PIP stars (f = 4,12,18) [150]. In all cases the protonated polymers were dissolved in d-benzene and measured at T = 323 K, where benzene is a good solvent. Figure 50 shows the results of the static scattering profile in a scaled Kratky representation. In this plot the radii of gyration, obtained from a fit of the... 

When the various results obtained by combined elastic and quasielastic neutron scattering measurements on star shaped polymers in dilute solutions... 

Guinier s law exhibits two parameters, I (0) and R2, which describe structural aspects of the sample. The experimentalist should consider their determination, if the recorded SAXS data show a monotonous decay that is indicative for the scattering from uncorrelated1 particles. Particularly useful is the evaluation of Guinier s law, if almost identical particles like proteins or latices are studied in dilute solution (cf. Pilz in [101], Chap. 8). The absolute value of 1(0) is only accessible, if the scattering intensity is calibrated in absolute units (Sect. 7.10.2). 

Further measurements appear necessary before the molecular weights of the amylopectin component of starches can be adequately characterized, and it may well be that light-scattering is the only method which can be satisfactorily applied to these polysaccharides of very high molecular weight. Certainly, it is the only method which enables studies of very dilute solutions to be made with high accuracy, particularly in the case of aqueous solutions. 

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