Refractive index-osmotic pressure

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. 

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... 

In these equations ns is the solvent refractive index, dn/dc the refractive index increment, c the polymer concentration in g/ml, T the temperature in K, R the gas constant, NA Avogadro s number, and n the osmotic pressure. Equation (B.8) follows from Eq. (B.7) by using the familiar virial expansion of the osmotic pressure... 

Pure liquids and solutions have probably received a major portion of the experimental effort devoted to the nonspectroscopic methods of detection. The liquid phase is susceptible to simple techniques and is the naturally occurring state for many substances. The principal methods of study are vapor pressure measurements, cryoscopy, solubility, and partition studies. To a lesser degree parachor, refractive index, thermal and acoustic conductivity, osmotic pressure, and magnetic susceptibility measurements have been applied to H bonded materials. Unfortunately, the difficulty of giving an adequate description of the liquid state sometimes produces problems of interpretation. 

The CMC is also well defined experimentally by a number of other physical properties besides the variation of the surface tension. The variation of solution properties such as osmotic pressure, electrical conductance, molar conductivity, refractive index, intensity of scattered light, turbidity and the capacity to solubilize hydrocarbons with the increase of surfactant concentration will change sharply at the CMC as shown in Figure 5.8. The variation in these properties with the formation of micelles can be explained as follows. When surfactant molecules associate in solution to form micelles, the concentration of osmotic units loses its proportionality to the total solute concentration. The intensity of scattered light increases sharply at the CMC because the micelles scatter more light than the medium. The turbidity increases with micelle formation, because the solution is transparent at low surfactant concentrations, but it turns opaque after the CMC. Hydrophobic substances are poorly dissolved in aqueous solutions at concentrations below the CMC, but they start to be highly dissolved in the centers of the newly formed micelles, after the CMC. 

A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

This gives the equation correlating the mean square value of the fluctuation of polarizability with the corresponding fluctuation in the concentration. It is apparent that the proportionality factor relating these two quantities depends both on the square of the refractive index of the medium and on the square of the refractive increment of the solute. Details of the derivation may be found elsewhere (see for instance Zimm, Stein and Doty, 1945). The final equation, as given by Einstein, furnishes a direct correlation between the turbidity produced by the solute and the change of its osmotic pressure (P) with concentration. 

Fig. 2. Influence of the formation of micelles on the properties of Na dodecylsulphate at 20 and 25 C. (HF — conductivity for high frequency current, P == osmotic pressure, y Voo = conductivity coefficient, = surface tension, rjrei — relative viscosity, = change of specific volume, In = change of refractive index). From Hess, Philippoff, and Kiessig, 1939.

The critical micellar concentration of any detergent may be determined by a number of different methods, including the solubilization of insoluble dye, osmotic pressure, conductivity, surface tension, light scattering, nuclear magnetic resonance, refractive index, freezing point determination, vapor pressure, sound velocity, etc. (141). Each method may give a somewhat different value for CMC. 

In some cases, it is desirable to employ a mixed solvent, for example, to obtain a proper solution with copolymers, or to suppress electrostatic interactions with a polyelectrolyte. In this case, preferential distribution of the solvent components in the vicinity of the polymer can complicate the analysis, but use of the refractive index increment (dnldc ) determined at constant temperature, pressure and at osmotic equilibrium of the solution and the solute-free solvent mixture (e.g., by dialysis) gives the simple result [5, 15] ... 

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