Temperature specific refractive index increments

As indicated, the specific refractive index increment is best measured by differential refractometry or interferometry. Experimental procedures as well as tabulated values of dn/ dc for many systems have been presented elsewhere40,63K The relevant wavelength and temperature are those used for LS. The value of X0 is invariably 436 or 546 nm, but with the advent of laser LS, values of dn/dc at other wavelengths are required. These can be estimated with good reliability using a Cauchy type of dispersion (dn/dc a 1/Xq). For example the values of dn dc for aqueous solutions of the bacterium T-ferrioxidans at 18 °C are 0.159, 0.141 and 0.125 ml/gm at X0 = 488, 633 and 1060 nm respectively64 ... 

The quantity dn/dc is the specific refractive index increment and it represents the incremental change in solution refractive index with sample concentration at the wavelength, temperature, and pressure of the LALLS measurements. Since dn/dc reflects the optical characteristics of the polymer and solvent (their different optical polarizabilities), its value strongly depends on the chemical composition of both components ( 0). 

In obtaining Equation 11 it has been assumed that the partial specific volumes v of the associating species are equal we have also assumed that the specific refractive index increments of the associating solutes are equal. In Equation 12 R is the universal gas constant (8.314 X 107 ergs/deg-mole), p is the density of the solution (gram/ml), and T is the absolute temperature. Equation 11 is also valid for the Archibald experiment but only at rm or rb, the radial positions (in the solution column of the ultracentrifuge cell) of the air-solution meniscus and of the cell... 

One of the most important parameters in static LLS is the specific refractive index increment (dn/dC), defined as Zzmc o(dn/9C)T,p,A- Since this parameter is not an intrinsic property of the polymer, the conditions of fixing temperature T, pressure P and wavelength of light in vacuum X are needed in its definition. Note that, according to Eq. (2.1), an error of E% in dn/dC will lead to an error of 2E% in the derived Mw. 

The refractive indices of a vast number of solvents, as well as the specific refractive index increments of a vast number of polymer-solvent combinations, have been measured and listed in standard reference publications. The (dn/dc) values of 100 polymer-solvent combinations, involving a diverse set of 16 polymers, will now be calculated at room temperature, and compared with the experimental values. 

Figure 8.2. Comparison of the experimental values of the specific refractive index increment measured at or near room temperature using standard frequencies of light with calculated values, for 100 polymer-solvent combinations.

The specific refractive index increment (dn/dc) can be predicted at temperatures other than room temperature by utilizing Equation 8.5 or Equation 8.6 with RT T or RqD values calculated as will be discussed in Section 8.E to estimate nP(T), and the equations listed in Section 3.D to estimate pP(T), for use in Equation 8.16. Since nP and n both change in the same manner (i.e.,... 

Figure 8.3. Calculated specific refractive index increments, in water, at room temperature, of random copolymers of acrylamide with N-benzyl methacrylamide and N-methyl methacrylamide.

The accuracy of the light-scattering measurement depends on prior determinations of the solvent refractive index and of the specific refractive index increment dn/dc of the sample in the solvent [Equation (7)]. The solvent refractive index can be measured with a conventional refractometer or values found in the literature. The dn/dc value can be measured using either a differential refractometer or, less frequently, an interferometer. Measurements should be made at the same temperature as the light-scattering measurement and ideally at the same wavelength. Because of the dependence of the optical constant on the square of... 

This is the limiting value at c = 0 of the quantity (rt — iiq)/c, where n and no are the refractive indices of the solution and solvent, respectively, and c (g/ml) denotes the concentration of the polymer in solution. Conditions of constant pressure p, constant temperature T, and a fixed wavelength of light in vacuum, Ao, are imphed. Specific refractive index increments are required to determine the weight-average molecular weight, of a polymer and... 

Various optical properties will be discussed, a new correlation for the refractive index at room temperature will be presented, and the molar refraction of many polymers and the specific refractive increment of many polymer-solvent combinations will be calculated, in Chapter 8. 

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