Specific refractive index increments

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. 

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... 

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 ...

We have noted that LS yields the weight average molecular weight M. If the solution comprises as solute a mixture of two polymers A and B each of identical molecular weight, LS distinguishes between these species only by virtue of their different specific refractive index increments vA and vB. Under these conditions a mixture of isorefractive polymers behaves as a single species solute of concentration equal to the sum of the two individual concentrations. 

The error in (a) is stated to compare favourably with calibration from benzene, since the absolute value of R90 is hardly known to this accuracy. In (b) the concentration of DNA was measured spectrophotometrically via the molar phosphorous extinction coefficient of 6415 (with a standard deviation of 2%). The low error in (c) arises from low levels of dust achieved as well as the integration over a period of 10 secs of the readings on a digital output. The specific refractive index increment used in (d) was an experimental one from the literature. In point of fact the assess-... 

A thermal treatment at 160°C for 1 hour has proved to be adequate for the removal of aggregates that persist at 145°C in TCB or ODCB solutions of polyethylene. Such a treatment enables one to obtain true solutions for use in SEC. Solution of polyethylene in aCN appears to be incomplete even after the 160 C treatment and aCN is therefore not recommended for use in SEC with polyethylene, despite the favorable specific refractive index Increment of its solutions. 

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). 

The MOLWT-II program calculates the molecular weight of species in retention volume v(M(v)), where v is one of 256 equivalent volumes defined by a convenient data acquisition time which spans elution of the sample. I oment of the molecular weight distribution (e.g., Mz. Mw. Mn ) are calculated from summation across the chromatogram. Along with injected mass and chromatographic data, such as the flow rate and LALLS instruments constants, one needs to supply a value for the optical constant K (Equation la), and second virial coefficient Ag (Equation 1). The value of K was calculated for each of the samples after determination of the specific refractive index increment (dn/dc) for the sample in the appropriate solvent. Values of Ag were derived from off-line (static) determinations of Mw. 

Differential Refractometry (dn/dc). Stock solutions of polymer were prepared with known concentrations (w/v) in the solvent of choice, and the specific refractive index increment (dn/dc) was measured at 26 deg C with a KMX-16 Laser Differential Refractometer (LDC/Milton Roy). Sample concentrations typically were ca. 5 x 10 3 gm/ml. 

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. 

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... 

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