Dilute solutions INDEX

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. 

Power law depentanizer f(c/c ) = const(c/c )m is postulated for the semi-diluted solution (c/c 1), in which the unknown index m accordingly to the second position of the Scaling method is from independence n on the length of a chain. This leads to the value m = 1/(3 v— l), that is m = 4/5 for d= 3-dimensional space. That is why the expression (6) is as follow... 

CUMULATIVE INDEX, VOLUMES 1-13 Infrared Spectroscopy, Conformational Analysis of Intramolecular Hydrogen-Bonded Compounds in Dilute Solution by (Aaron). VOL. 11 487 PAGE 1... 

The actual measurement of the refractive index of the solution poses no difficulty, but the evaluation of the refractive index gradient is more troublesome. The assumptions of the derivation of Equation (23) restrict its applicability to dilute solutions. The refractive index of a dilute solution changes very gradually with concentration hence a plot of n versus c, the slope of which equals dn/dc, will be nearly horizontal. Since the intensity ratio depends on the square of dn/dc, it is clear that successful interpretation of Equation (23) depends on the accuracy with which this small quantity is evaluated. Measuring the absolute refractive indices of various solutions and determining dn/dc by difference or graphically would introduce an unacceptable error. A more precise method must be used to measure this quantity. 

The Rayleigh approximation shows that the intensity of scattered light depends on the wavelength of the light, the refractive index of the system (subject to the limitation already cited), the angle of observation, and the concentration of the solution (which is also restricted to dilute solutions). In the Rayleigh theory, the size and shape of the scatterers (M and B) enter the picture through thermodynamic rather than optical considerations. 

The methods of measuring the liquid phase properties were described previously [1], It was observed that heat was evolved during the preparation of all these mixtures. It should be mentioned that the electrical conductivities of the sulphuric acid-nitromethane mixtures were not constant, but were found to increase with time. Reliable data could therefore not be obtained. This is due to the fact that nitromethane reacts with sulphuric acid in dilute solutions, as has been recently discussed by Gillespie and Solomons [6]. All other properties of these mixtures were constant at 25° and measurements were restricted to this temperature. For the other four systems the viscosity, electrical conductivity and density were investigated at two temperatures 25° and 40°), because of the importance of the temperature coefficients of viscosity and electrical conductivity. The refractive indexes were measured only at 25°. The investigation of the liquid phase properties of the system with p-nitro toluene at these temperatures was possible only up to 50 mole % of p-nitrotoluene, i.e. until the solutions became saturated with respect to p-nitrotoluene. The refractive indexes of these solutions were not measured. 

On the other hand, for dilute solutions one must take care of the refractive indices of polymer and solvent. The refractive index increment dnjdc of the polymer for the chosen solvent must be as small as possible, since otherwise the influence of the shape of the coil (form birefringence) would be noticeable. A more detailed discussion of this problem, however, is postponed to Section 5.1.1. Solvents with a sufficiently small refractive index increment have been called matching solvents. 

The most evident reason is that dilute solution measurements can preferably be compared directly with the unmodified dilute solution theory as reviewed in Chapter 3. As has already been pointed out in Section 2.6.1, the form birefringence in dilute solution can effectively be suppressed by the choice of a solvent of practically the same refractive index as the polymer. In such a "matching solvent the contrast between the coil of the macromolecule and its surrounding practically disappears. This means that, at the same time, the influence of the shape (form) of the coil disappears. Also the comparison with measurements on con-... 

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. 

All potentially molar-mass-dependent quantities have been labelled with a summation index k in Eq. (30), which, in this form, also holds for dilute solutions of mixtures of chemically different species or copolymers with heterogeneity of both chemical composition and degree of polymerization. 

In another publication [75] the adsorption behavior of the same materials from dilute solutions on silicon wafers was studied by ellipsometry. A mixture of cyclohexane and toluene (50 50 by volume) was used in order to provide enough refractive index contrast for the measurements and also to inhibit association of the end groups, which would influence the adsorption process. 

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 ... 

Also for these dilute solutions, the refractive index increment is a constant for a given polymer, solvent and temperature, and is normally measured with an interferometer or with a differential refractometer. 

Orthophosphorio Acid —Preparation—Physical Properties of Solid Hydrates of P2Os—Solubilities, Melting-points and Eutectics of the System HjP04-Ha0—Densities of Aqueous Solutions—Vapour Pressures—Conductivities of Concentrated and Dilute Solutions—Viscosities—Refractive Index—Basicity and Neutralisation of the Phosphoric Acids—Constitution... 

The Batelle workers report an index difference of 0.15 for these isomers, based on the extrapolation of index measurements made on dilute solutions. Their data yield nQ = 3.9 x 10- cm3 for system. This is a large difference, comparable to photodimer changes. 

Succinonitrile. Measurements should be made on pure benzene and on dilute solutions of succinonitrile and propionitrile (or acetonitrile). Make up 50 or 100 mL of each solution in the same manner as described above. Densities can be calculated and/or refractive indexes can be measured. 

Here, n is the refractive index of the solvent. Both equations have been widely used and tested for a large number of compounds [136-144] and have proved to be vahd only in a very limited range in dilute solutions of nonpolar solvents, where specific... 

Standard chemical potential of solute i standard chemical potential of solute i at infinite dilution refractive index (at sodium D line)... 

Finally, solid films of some polysilylenes exhibit thermochromism and undergo true thermodynamic order-disorder phase transitions at much higher temperatures 18, 19, 47, 48) than in solution (typically, Tq 40-80 °C). In the context of the theory, a larger refractive index of the neat solid compared with that of the dilute solution results in a higher predicted Tq 21). However, we do not believe that the observed high TqS in films can be explained solely by this effect. Previous explanations have been made exclusively in terms of side-chain crystallization 18, 19, 48). Packing effects should be more important in the solid state, but both intramolecular and intermolecular packing effects must be carefully considered. Indeed, the fact... 

---