Refractive index increments

Ball V and Ramsden J J 1998 Buffer dependence of refractive Index Increments of protein solutions Biopolymers 46 489-92... 

Table 2 Refractive index increments of some polysaccharides (data taken from [26] and references cited therein). DS degree of suhstitution. X wavelength...

Table 3 Refractive index increment and partial specific volume of hyaluronan (M 10 g/mol) determined at different salt concentrations (from [28])...

The polarisability, a, of the molecule is proportional to the refractive index increment dn/dc, and to the relative molar mass of the molecule in question. The full relationship is ... 

The variable quantities in the K term, i.e. rig, (AnMcf, and X, must be determined. Values of are available for most solvents from the literature X is obtained by dividing the value of X by the refractive index of the solution. The refractive index increment, (dn/dcj, must be determined to within 10 in dn using a differential refractometer. The choice of solvent is limited if dn/dc = 0, there is no scattering if dn/dc is greater than 0.3 cm g the Rayleigh ratio is no longer proportional to (dn/dc). ... 

Published refractive index data for the mobile phase, polystyrene, polyacrylonitrile, and the two monomers were used to calculate refractive index detector calibrations for the two homopolymers. The published data were used to determine relationship between refractive index increments of monomer and corresponding homopolymer. Chromatographic refractometer calibrations for the two homopelymers were then calculated from experimentally measured calibration data for the two monomers. 

The average value of the refractive index increment as determined using a Brice-Phoenix differential refractometer was (dn/dc) =... 

Huglin, M. B., Specific refractive index increments of polymers in dilute solutions, in Polymer Handbook, 2nd ed., Brandrup, J. and Immergut, E. H., Eds., John Wiley, New York, 1975, IV, 267-308. 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

Figure 14.3 Refractive index increment, dn/dc, in THF of PBzE monodendrons and tridendron dendrimers as a function of generation number, (according to ref. [15])...

Subsidiary Aspects Clarification, Refractive Index Increment and... 

Subsidiary Aspects Turbidity, Depolarisation, Absorption, Refractive Index Increment... 

An important characteristic of a solution with regard to its LS is the specific refractive index increment dn/dc (frequently denoted also by the symbol v). As will... 

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 ... 

As will be seen later (Section V.l), meaningful molecular weights in multicomponent systems can be determined, if the specific refractive index increment appertains to conditions of constant chemical potential of low molecular weight solvents (instead of at constant composition). Practically, this can be realised by dialysing the solution against the mixed solvent and then measuring the specific refractive index increment of the dialysed solution. The theory and practice have been reviewed4-14-1S> 72>. 

Provided the specific refractive index increment is large, solutions of ultra-high molecular weight polymers (M > ca. 3 x 106) do not necessitate that the highest... 

It is fortunate that theory has been extended to take into account selective interactions in multicomponent systems, and it is seen from Eq. (91) (which is the expression used for the plots in Fig. 42 b) that the intercept at infinite dilution of protein or other solute does give the reciprocal of its correct molecular weight M2. This procedure is a straightforward one whereby one specifies within the constant K [Eq. (24)] a specific refractive index increment (9n7dc2)TiM. The subscript (i (a shorter way of writing subscripts jUj and ju3) signifies that the increments are to be taken at constant chemical potential of all diffusible solutes, that is, the components other than the polymer. This constitutes the osmotic pressure condition whereby only the macromolecule (component-2) is non-diffusible through a semi-permeable membrane. The quantity... 

Fig. 47. Square root of apparent molecular weight by LS as a function of molar refractive index increment of salt for sodium polymethacrylic acid in aqueous solution of different sodium halides146 ...

A copolymer is a macromolecule comprising two chemically distinct types of monometer unit, A and B, whilst a terpolymer is composed of units A, B and C. The analytically determined composition of a copolymer is expressed as the weight fractions WA and WB of its constituents. For LS studies on a copolymer solution it is necessary to know the value of the specific refractive index increment v, which can be either measured or calculated from ... 

Fig. 54. Specific refractive index increments at constant composition (o) and constant chemical potential ( ) for solutions of nylon-6 in 2,2,3,3-tetrafluoropropanol/l-chlorophenol binary mixtures, is the volume fraction of l-chlorophenol and filled circles refer to the two pure single solvents161)...

Fig. 56. Dependence of specific refractive index increment on conversion of monomers to polymer for a styrene/acrylonitrile/methyl methacrylate terpolymer in methyl ethyl ketone at 20 °C and 436 nm. (a) - partial azeotrope, (b) terpolymer with composition distribution163 ...

The azeotropic terpolymer, being atypical in general, one is faced with the prospect of solving at least five simultaneous sets of Eq. (108) in order to obtain M. This manipulation is exact, but the inherent inaccuracies in five different measurements of M are coupled with those involved in measuring the refractive index increments. It is as true for a terpolymer as it is for a copolymer that the difference between specific increments (for example, vA - pB or — vc) must be measured for high... 

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