Concentration dependence refractive index

There is a host of other intriguing phenomena associated with the structure and dynamics of stars, which we only list here. The inhomogeneous monomer density distribution in Fig. 2 is responsible for temperature and/or solvency variation in analogy to polymer brushes attached on a flat solid surface [198]. In fact, multiarm star solutions display a reversible thermoresponsive vitrification (see also Sect. 5) which, in contrast to polymer solutions, occurs upon heating rather than on cooling [199]. Another effect is the organization of multiarm stars in filaments induced by weak laser light due to action of electrostrictive forces [200]. This effect was recently attributed [201] to local concentration fluctuations which provide localized-intensity dependent refractive index variations. Hence, the structure factor speciflc to the particular material plays a crucial role in the pattern formation. 

Fundamental Limitations to Beers Law Beer s law is a limiting law that is valid only for low concentrations of analyte. There are two contributions to this fundamental limitation to Beer s law. At higher concentrations the individual particles of analyte no longer behave independently of one another. The resulting interaction between particles of analyte may change the value of 8. A second contribution is that the absorptivity, a, and molar absorptivity, 8, depend on the sample s refractive index. Since the refractive index varies with the analyte s concentration, the values of a and 8 will change. For sufficiently low concentrations of analyte, the refractive index remains essentially constant, and the calibration curve is linear. 

The transparency and refractive power of the lenses of our eyes depend on a smooth gradient of refractive index for visible light. This is achieved partly by a regular packing arrangement of the cells in the lens and partly by a smoothly changing concentration gradient of lens-specific proteins, the crystallins. 

In Raman spectroscopy the intensity of scattered radiation depends not only on the polarizability and concentration of the analyte molecules, but also on the optical properties of the sample and the adjustment of the instrument. Absolute Raman intensities are not, therefore, inherently a very accurate measure of concentration. These intensities are, of course, useful for quantification under well-defined experimental conditions and for well characterized samples otherwise relative intensities should be used instead. Raman bands of the major component, the solvent, or another component of known concentration can be used as internal standards. For isotropic phases, intensity ratios of Raman bands of the analyte and the reference compound depend linearly on the concentration ratio over a wide concentration range and are, therefore, very well-suited for quantification. Changes of temperature and the refractive index of the sample can, however, influence Raman intensities, and the band positions can be shifted by different solvation at higher concentrations or... 

Quantification at surfaces is more difficult, because the Raman intensities depend not only on the surface concentration but also on the orientation of the Raman scat-terers and the, usually unknown, refractive index of the surface layer. If noticeable changes of orientation and refractive index can be excluded, the Raman intensities are roughly proportional to the surface concentration, and intensity ratios with a reference substance at the surface give quite accurate concentration data. 

The deflection refractometer (Fig. 8.4), which measures the deflection of a beam of monochromatic light by a double prism in which the reference and sample cells are separated by a diagonal glass divide. When both cells contain solvent of the same composition, no deflection of the light beam occurs if, however, the composition of the column mobile phase is changed because of the presence of a solute, then the altered refractive index causes the beam to be deflected. The magnitude of this deflection is dependent on the concentration of the solute in the mobile phase. 

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

Ethers are unaffected by sodium and by acetyl (or benzoyl) chloride. Both the purely aliphatic ethers e.g., di-n-butyl ether (C4H, )30 and the mixed aliphatic - aromatic ethers (e.g., anisole C3HSOCH3) are encountered in Solubility Group V the purely aromatic ethers e.g., diphenyl ether (C,Hj)20 are generally insoluble in concentrated sulphuric acid and are found in Solubility Group VI. The purely aliphatic ethers are very inert and their final identification may, of necessity, depend upon their physical properties (b.p., density and/or refractive index). Ethers do, however, suffer fission when heated with excess of 67 per cent, hydriodic acid, but the reaction is generally only of value for the characterisation of symmetrical ethers (R = R ) ... 

It was mentioned previously that the narrow range of concentrations in which sudden changes are produced in the physicochemical properties in solutions of surfactants is known as critical micelle concentration. To determine the value of this parameter the change in one of these properties can be used so normally electrical conductivity, surface tension, or refraction index can be measured. Numerous cmc values have been published, most of them for surfactants that contain hydrocarbon chains of between 10 and 16 carbon atoms [1, 3, 7], The value of the cmc depends on several factors such as the length of the surfactant chain, the presence of electrolytes, temperature, and pressure [7, 14], Some of these values of cmc are shown in Table 2. 

Upon selective absorption of analyte molecules from the ambient environment, the zeolite thin film increases its refractive index. Correspondingly, release of adsorbed molecules from the zeolite pore results in the decrease of its refractive index. The absorption/desorption of molecules depends on the molecule concentration in the environment to be monitored. Therefore, monitoring of the refractive index change induced phase shift in the interference spectrum can detect the presence and amount of the target analyte existing in the environment. 

Seisakusho differential refractometer). For a solution of known concentration, the difference in refractive index, (n - nj>), between the liquid in the prism and that in the solvent bath causes refraction of the light beam, which is observed as a displacement 8 of the image at a distance d from the prism centre. The overall sensitivity depends on the precision of measuring 8 and the refractive index difference is given by... 

In all cases the dielectric constant used is that of the pure solvent. Neglect of the solute is usually justified by its low concentration and the assumption that any necessary correction would be additive. In at least a few cases where the first two expressions have been employed the linearity of the results is to some extent dependent on how closely the refractive index of the solute meets the conditions n2 = 2.0 or 2.5 a situation not always recognized by the investigators. In one instance attempts have been made to clarify the role of solvent reaction field by examining solutes with different dipole moment orientations relative to the bonds involving coupled atoms. 

The measurement of the width of the metastable zone is discussed in Section 15.2.4, and typical data are shown in Table 15.2. Provided the actual solution concentration and the corresponding equilibrium saturation concentration at a given temperature are known, the supersaturation may be calculated from equations 15.1-15.3. Data on the solubility for two- and three-component systems have been presented by Seidell and Linkiv22 , Stephen et alS23, > and Broul et a/. 24. Supersaturation concentrations may be determined by measuring a concentration-dependent property of the system such as density or refractive index, preferably in situ on the plant. On industrial plant, both temperature and feedstock concentration can fluctuate, making the assessment of supersaturation difficult. Under these conditions, the use of a mass balance based on feedstock and exit-liquor concentrations and crystal production rates, averaged over a period of time, is usually an adequate approach. 

Matrix effects in the analysis of nutrients in seawater are caused by differences in background electrolyte composition and concentration (salinity) between the standard solutions and samples. This effect causes several methodological difficulties. First, the effect of ionic strength on the kinetics of colorimetric reactions results in color intensity changes with matrix composition and electrolyte concentration. In practice, analytical sensitivity depends upon the actual sample matrix. This effect is most serious in silicate analysis using the molybdenum blue method. Second, matrix differences can also cause refractive index interference in automated continuous flow analysis, the most popular technique for routine nutrient measurement. To deal with these matrix effects, seawater of... 

P has a very suggestive form in relation to Figure 8.26. For a large concentration of acceptors, the second term in the denominator can be made considerably smaller than 1 (i.e., Xt is proportional to acceptor concentration [A]), and P will be independent of concentration. On the other hand, for a small concentration of acceptors, the second term in the denominator can be made considerably larger than 1, and P will fall off linearly as the concentration is reduced. The scale factor in all of this is Q. With Q large, the transition from concentration independence to linear concentration dependence will be at low acceptor concentrations. P falls to 5 when the second term in the denominator of Eq. (8.27) is equal to 1, and so a critical concentration of acceptors [A], /2 can be defined to characterize the falloff. Expressing Xt in terms of molecular parameters (x, = em[A] ln(10)/, where n is the particle refractive index, em is the molar decadic extinction coefficient, [A] is the concentration of acceptors, and k is 2n/X) yields... 

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). 

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