Scattering intensity, polymer solutions

Debye introduced this in the context of X-ray scattering where the RDGA is commonly valid he derived the general expression for the intensity of X-rays scattered by an ensemble of randomly oriented particles. Later on, Debye himself applied it to the scattering by polymer solutions [36, 37]. If the particle is rigid then distance between the elements that conforms to the object fly will be constant and Equation 18.39 reduces to... 

A light-scattering photometer. Polymer solution in cell is irradiated with an ineident beam, and scattered light intensity is measured at angle 0. 

As an example of the application of light scattering to polymer solutions, some results for an atactic polyacrylonitrile fraction in dimethylformamide are shown in Figure 5.12 [36]. Here the scattering intensity at scattering angles... 

In polymer solutions or blends, one of the most important thennodynamic parameters that can be calculated from the (neutron) scattering data is the enthalpic interaction parameter x between the components. Based on the Flory-Huggins theory [4T, 42], the scattering intensity from a polymer in a solution can be expressed as... 

Next let us consider the light scattered by liquids of low molecular weight compounds. We are actually not directly interested in this quantity per se, but in scattering by solutions-polymer solutions eventually, but for now solutions of small solute molecules. The solvent in such a solution does scatter, but, in practice, the intensity of light scattered by pure solvent is measured and subtracted as a blank correction from the scattering by the solution. 

Photomultipliers are used to measure the intensity of the scattered light. The output is compared to that of a second photocell located in the light trap which measures the intensity of the incident beam. In this way the ratio [J q is measured directly with built-in compensation for any variations in the source. When filters are used for measuring depolarization, their effect on the sensitivity of the photomultiplier and its output must also be considered. Instrument calibration can be accomplished using well-characterized polymer solutions, dispersions of colloidal silica, or opalescent glass as standards. 

Turbidimetry is ideally suited to detect the temperature at which a transparent polymer solution turns opaque. The temperature corresponding to the onset of the increase of the scattered light intensity is usually taken as the cloud-point temperature, TcP, although some authors define the cloud point as the temperature for which the transmittance is 80% (or 90%) of the initial value. This technique is commonly known as the cloud-point method [199]. Turbidimetry was employed, for instance, to show that the cloud-point temperature of aqueous PNIPAM solutions does not depend significantly on the molar mass of the polymer [150]. 

Fig. 28 Top Effect of dilution on Rh and Kc/lg o of the mesoglobules ( ) formed upon heating of 0.2 gL1 aqueous solution of PVCL-g-18. Bottom Scattering intensity at 90° from polymer solution of different concentration. (Reprinted with permission from Ref. [180] copyright 2005 Elsevier)... 

When a polymer absorbs very strongly in the visible region, near IR incident radiation is used. In a very coloured solution the scattered intensity is reduced by a factor exp(—e)2) where e is the absorption coefficient of the solvent. Hence i0 must be multiplied by exp(+e ) in order to obtain the true scattered intensity undiminished by absorption effects. For small values of efi, the quantity exp(efi) approximates well to (1 + e2) so that Eq. (42) becomes38. ... 

Process in which a precipitant is added incrementally to a highly dilute polymer solution and the intensity of light scattered by, or the turbidity due to, the finely dispersed particles of the polymer-rich phase is measured as a function of the amount of precipitant added. 

The intensity of scattered light or turbidity (t) is proportional to the square of the difference between the index of refraction (n) of the polymer solution and of the solvent ( o), to the molecular weight of the polymer (M ), and to the inverse fourth power of the wavelength of light used (A). Thus ... 

An absolute value of M for each of these branched PVAcs was obtained from light-scattering measurements. In each case five polymer solutions were made up in tetrahydrofuran (THF) solvent and a Chromatix KMX-6 LALLSP instrument was employed to measure the intensity of light scattered from these solutions at 7° to the incident laser beam. A Chromatix KMX-16 laser differential refractometer was used to determine the refractive index increments, dn/dc, of the polymer solutions under ambient conditions. 

For polymers whose Mw < 10,000, the intensity of light scattering from the solution differs so little from the neat solvent that the determination is not precise. For polymers whose Mw > 10,000, the need to measure the light scattering at very small values of 0 is beyond the capability of many older instruments. Special treatment is required for mixed solvent systems, copolymers, higher polymers, and polyelectrolytes. 

The scattered light intensity from a polymer solution arises from the fluctuations in both the solvent density and the polymer concentration. These fluctuations are considered as stable during the timescale of the measurement in the static mode of light scattering (for more details, see Evans (1972)). The light scattered from just the polymer (in excess of the light scattered from the pure solvent) is given by (Burchard, 1994)... 

The equilibrium structure is considered of flexible polymer chains within the RIS model. This model is solved by an irreducible tensor method which is somewhat different from, and simpler than, the approach of Flory and others. The results are used to compute the light scattering intensities from dilute solutions of flexible polymer chains, and the angle dependence is found... 

In the case of polymer solutions in the semi-dilute regime, the elastic scattered intensity is given by Omstein-Zernike (OZ) type equation [10, 73, 74]... 

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