Light scattering refractive index increment

Huglin, M. B., Specific refractive index increments, in Light Scattering from Polymer Solutions, Huglin, M. B., Ed., Academic Press, New York, 1972, chap. 6. 

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. 

DLS- 700S light scattering photometer at 633nm, calibrated with benzene. The optical clarification was performed with teflon filters. The specific refractive index increment (dn/dc) was obtained with Chromatix KMX-16 reffactometer at the same wavelength, calibrated with NaCl solution. 

As has been pointed out (63), this is a rather artificial model and, moreover, its application is quite unnecessary. In fact, (a> can be calculated from the refractive index increment (dnjdc), as has extensively been done in the field of light scattering. This procedure is applicable also to the form birefringence effect of coil molecules, as the mean excess polarizability of a coil molecule as a whole is not influenced by the form effect. It is still built up additively of the mean excess polarizabilities of the random links. This reasoning is justified by the low density of links within a coil. In fact, if the coil is replaced by an equivalent ellipsoid consisting of an isotropic material of a refractive index not very much different from that of the solvent, its mean excess polarizability is equal to that of a sphere of equal volume [cf. also Bullough (145)]. 

The analysis of mixed associations by light scattering and sedimentation equilibrium experiments has been restricted so far to ideal, dilute solutions. Also it has been necessary to assume that the refractive index increments as well as the partial specific volumes of the associating species are equal. These two restrictions are removed in this study. Using some simple assumptions, methods are reported for the analysis of ideal or nonideal mixed associations by either experimental technique. The advantages and disadvantages of these two techniques for studying mixed associations are discussed. The application of these methods to various types of mixed associations is presented. 

Table 13. Refractive index and refractive index increments for light scattering solvents...

The first section will deal with the preparation of the HEC solutions, the determination of the refractive index increment, and the exact Mw determination by light scattering before and after endocellulase attack, using a simultaneous zero-angle and zero-concentration extrapolation of the reduced scattering values. 

Determination of the Refractive Index Increment. In order to be able to calculate results obtained from light-scattering measurements, the refractive index increment (dn/dc) of HEC must be known. For this reason, an absolute differential refractometer (Brice-Phoenix Instrument Company, Philadelphia 40, PA type 1120) was calibrated geometrically (18), using the next formula ... 

Other anomalies were observed, since Beer s law was fulfilled at 220 nm and between 0 and 2 g/L and not at other wavelengths. Considering the possibility of unattended anomalies of the HEC after fractionation, we had to abandon this detection method. For this reason, for the continuous concentration determination, we used a flow-differential refractometer (type R403, Waters Associates, Milford, MA, USA) connected to an integrating recorder. Since there is no monochromator on the apparatus, it was not possible to use the refractive index increment value used for the light-scattering measurements. 

In this study, we employed PCS to measure the decay rate of the order-parameter fluctuations in dilute supercritical solutions of heptane, benzene, and decane in CC - The refractive index increment with concentration is much larger than the refractive index increment with temperature in these systems. Therefore the order-parameter fluctuations detected by light scattering are mainly concentration fluctuations and their decay rate T is proportional to the binary diffusion coefficient, D = V/q. The... 

The constant depends on the radiation used, as does (dp Jdc ), which is the refractive index increment for light, the electron density increment for X-rays, and the neutron scattering density increment for neutrons. 

Here iujj is the intensity of the scattered light at an angle 9 to the incident beam 7o is that of the polarized primary beam r. the distance between the scattering molecule and the detector Ao, the wavelength of the laser beam in vacuum n 0, the solvent refractive index dn/ dc. the specific refractive index increment of the solution, M, the molar mass of the scattering particle and c. its concentration. For a dilute solution, at a given concentration, the scattered intensity can be rewritten as ... 

The refractive index increment dn/dc was measured on solutions of BBB used for light scattering studies. A differential refractometer described previously (5) except for the incorporation of a laser source was utilized. A very large value dn/dc = 0.785 cc./gram was found for BBB. Comparably large values were found for the cis and trans model compounds, each of which had a value of dn/dc different from the polymer. 

The index of refraction and the specific refractive index increment (an important quantity in light scattering) can be estimated via additive molar properties. Light absorption, on the other hand, does not show additivity, but is a typically constitutive property. Other optical properties, such as light reflection, are dependent on both refraction and absorption. 

Accurate values of the specific refractive index increment are required in light scattering equation because dn/dc appears in a quadratic form in Eq. (4). 

Since the square of the specific refractive index increment (dn/dc) appears in the light scattering equations, this value must be accurately known in order to measure Mv,- (An error of x% in dn/dc will result in a corresponding error of about 2x% in M. ) The value of dn/dc is needed at infinite dilution, but there is very little concentration dependence for polymer concentrations in the normal range used for light scattering. The required value can therefore be obtained from... 

---