Dilute solution light scattering

Dilute Solution Light Scattering Homopolymers and Copoly-... 

Comparison with Experiment. These calculated Cj values are qualitatively in agreement with the preliminary experimental values of Cotts, et al., obtained from dilute solution light-scattering... 

Dilute solution light scattering and gel permeation chromatographic studies (performed in 1-chloronaphthalene at 220°C), and the inherent viscosity (performed in 1-chloronaphthalene at 206°C) is 0.16. The polymer is as polymerized, just before the curing step... 

Recently R. Kuhn etal.( 968a, b Kuhn, 1968) studied the phase relationships of polystyrene-poly(methyl methacrylate) by employing an ingenious dilute solution light-scattering technique. Equations derived from phase separation quantities could be extrapolated to the pure phases, yielding the conclusion that if both polymers had molecular weights less than about... 

We consider an experiment in which a monochromatic laser beam (with a frequency of the order of 10 s ) is incident into a small volume in a dilute polymer solution. Light scattered from that volume is received by a detector... 

Average Values Obtained by Light Scattering. In an ideal dilute solution, intensities scattered by the various scattering centers are additive. The constant K has the same value for the same type of polymer. The Rayleigh ratio for a disperse system is given by... 

For dilute solutions, the scattered light intensity can be written as the sum of those from solute and solvent,... 

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... 

W. Brown, R. Johnsen, P. Stilbs, B. Lindman. Size and shape of nonionic amphiphile (Ci2Eg) micelles in dilute aqueous solutions as derived from quasielastic and intensity of light scattering, sedimentation and pulsed-field-gradient nuclear magnetic resonance self-diffusion data. J Phys Chem 87 4548-4553, 1983. 

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. 

Under nitrogen, 2,2 -bipyridine (0.322 g, 2.07 mmol) was added to a mixture of Ni(COD)2 (0.570 g, 2.07 mmol) in anhydrous DMF (18 mL) and the mixture was stirred at room temperature for 1 h. Then 95 (0.510 g, 1.60 mmol) was added and the reaction mixture was stirred at 60-70°C for 28 h. After cooling to room temperature, HC1 (100 mL, 2 M) was added and the mixture was stirred overnight. After filtration, the solid was washed with a mixture of MeOH (60 mL) and concentrated HC1 (10 mL), a warm aqueous solution of ethylene-diaminetetraacetic acid (EDTA) (pH 9, then pH 3), dilute ammonia, water, and MeOH repeatedly and dried under vacuum for 20 h at 80°C. Polymer 96 was obtained in 100% yield (0.261 g). Light scattering gave Mw = 5400. 

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. 

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... 

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