Refractive increments systems

The summation is tdken over all but one of the components. Generally it is most convenient to omit the solvent from the summation to compensate for this omission the complete equation should include a term for the turbidity of the pure solvent, arising from density fluctuations in it. This term is generally small, in systems containing large molecules, and for brevity it is omitted from (27). However, in practice, we have generally determined the turbidity of the pure solvent and subtracted it from that of the solution. IP, denotes the molar refractive increment of component i that is An per mol of solute per liter of solution (or per kg. solvent). The terms in the determinant ,j denote the coefficients... 

The most reliable results of studies of the light scattering and specific refractive increment behaviour of amylose in dimethyl sulphoxide-water are obtained with dialysed solution-solvent systems. Discrepancies in published literature are probably caused by differences in the preparation of the sample and the botanical source of the amylose. 

It follows from equations (119) and (120) that an analysis of light-scattering data on the three-component system that ignores the presence of two solvents and uses the conventional refractive increment for the polymer, measured at fixed 3, leads to an apparent molecular weight = Q M, which depends on the preferential interaction and the refractive increments of solute and one (either) of the solvents. It turns out, however, that the light-scattering relation can be formulated, within inconsequential error, in terms of a refractive increment of the polymer defined by osmotic equilibrium... 

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>. 

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... 

Adjective describing components of a multicomponent system having zero refractive index increments with respect to each other. 

The sedimentation equilibrium experiment requires much smaller volumes of solution, about 0.15 ml. With six-hole rotors and multichannel centerpieces (41) it is potentially possible to do fifteen experiments at the same time. For situations where the photoelectric scanner can be used one might (depending on the extinct coefficients) be able to go to much lower concentrations. Dust is no problem since the centrifugal field causes it to go to the cell bottom. For conventional sedimentation equilibrium experiments, the analysis of mixed associations under nonideal conditions may be virtually impossible. Also, sedimentation equilibrium experiments take time, although methods are available to reduce this somewhat (42, 43). For certain situations the combination of optical systems available to the ultracentrifuge may allow for the most precise analysis of a mixed association. The Archibald experiment may suffer some loss in precision since one must extrapolate the data to the cell extremes (rm and r6) to obtain MW(M, which must then be extrapolated to zero time. Nevertheless, all three methods indicate that it is quite possible to study mixed associations. We have indicated some approaches that could be used to overcome problems of nonideality, unequal refractive index increments, and unequal partial specific volumes. 

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... 

This more complex form of the refractive index function resulted from theoretical studies. In the hands of Eisenlohr and others this additive function became the basis of a system of increments. Many years later Vogel (1948) found that the simplest combination, viz. n-M is also additive, though not temperature independent. Finally Looyenga (1965) showed that... 

Detectors. Most detectors for liquid chromatography can also be used in FFF systems. Refractive index detectors [132] are the most popular for soluble macromolecules. Designed as differential detectors, they measure differences in refractive indices of eluate relative to pure eluent, Anr This difference is proportional to the solute concentration in the eluate through the refractive index increment dnr/dc. The major problem associated with the use of a refractometer is the dependence of the refractive index on temperature and pressure, which can cause baseline drifts and fluctuations. 

Optical Materials. The polyphosphazene skeleton is electron-rich, which means that it provides a refractive index increment compared to conventional saturated organic backbones. In addition, the macromolecular substitution synthesis aUows highly unsaturated organic side groups to be linked to the skeleton in ways that allow the refractive index, the color, the liquid crystalline, and nonlinear optical characteristics of the polymer to be finely tuned. Thus, the use of these polymers in opto-electronic (photonic) switches and lens systems is a subject of growing interest. 

The higher the equilibrium chain rigidity and the increment of refractive index dn/dc in the polymer-solvent system, the more pronounced is this effect. For a rigid-chain polymer the Aa value in Eq. (49) is calculated according to )... 

Refractive index and specific refractive index increments - (k = dn/dc) of polymers in solution have been studied extensively in connection with light scattering measurements and size exclusion chromatography applications to polymer characterization for which refractometers are used as standard concentration detectors. Contrary to the observations made in the infrared region (12), refractive index increments have been shown to be a function of the molecular weight of the polymers (2) and, in some cases, of the copolymer composition (17). Therefore, the assumptions of linearity and additivity (Eq. 1 to 4) have to be verified for each particular polymer system. In the case of styrene/acrylonitrile copolymers, there is an additional uncertainty due to the... 

In a multicomponent system the mean square value of the fluctuation in refractive index (zl )2, which determines the total turbidity, is a function of the concentrations, and refractive index increments, of each of the components of the system. It also involves cross terms, involving the correlation between the fluctuations of the concentrations of different components. For a given pair of components, i and /, the cross term is zero if the chemical potential of i is unaffected by a variation of the mass of j in the system but if the chemical potentials are not independent in this manner the cross terms do not vanish. 

In evaluating Debye s factor H (equation 16), the refractive index increment of the solute must be accurately known. This determination is conveniently carried out with the differential refractometer of P. P. Debye (1946), in which the solution is contained in a hollow glass prism of triangular cross section, immersed in a cell containing the pure solvent. The deflection of a light beam passing through the system is a nearly linear function of the refractive index difference n — n0, which may thus be measured to about 0.000,003. 

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