Ratio dissymmetry

In Example 10.5 we extracted both the molecular weight and the radius of gyration from Ught-scattering data. There may be circumstances, however, when nothing more than the dimensions of the molecule are sought. In this case a simple alternative to the analysis discussed above can be followed. This technique is called the dissymmetry method and involves measuring the ratio of intensities scattered at 45° and 135°. The ratio of these intensities is called the dissymmetry ratio z ... 

Figure 10.13 Variation of the dissymmetry ratio z with a characteristic dimension D (relative to X) for spheres, random coils, and rods. (Data from Ref. 4.)...

Draw a plot in polar coordinates of the scattering envelope in the xy plane. How would the envelope of a Rayleigh scatterer compare with this plot By interpolation, evaluate 145, iiss, and z. Use Fig. 10.13 to estimate the value of rrms to which this dissymmetry ratio corresponds if X (in toluene) is 364 nm. What are some practical and theoretical objections to this procedure for estimating rrms ... 

Fig. 46.—Dissymmetry ratio for light scattered at 45° and 135° as a function of -x/r /X for random coil polymer chains. ...

Mixed solvents are generally unsatisfactory for use in the determination of polymer molecular weights owing to the likelihood of selective absorption of one of the solvent components by the polymer coil. The excess of polarizabilit f of the polymer particle (polymer plus occluded solvent) is not then equal to the difference between the polarizabilities of the polymer and the solvent mixture. For this reason the refractive increment dn/dc which would be required for calculation of K, or of i7, cannot be assumed to equal the observed change in refractive index of the medium as a whole when polymer is added to it, unless the refractive indexes of the solvent components happen to be the same. The size Vmay, however, be measured in a mixed solvent, since only the dissymmetry ratio is required for this purpose. 

Figure 4.5 Characteristics of UV and CD intensities at around 323 nm in isooctane at 20°C of 14 samples isolated from 9 poly( -a kyl(5)-2-methylbutylsilane) derivatives as a function of the degree of polymerization (DPW) in isooctane at 20°C (a) and Ae and (b) the dissymmetry ratio.

Figure 4.8 Values of (a) dissymmetry ratio (gabg) and (b) Xmax in a series of copolymers 10 and 11 as function of mole fraction of n-hexyl-(lS )-2-methylbutylsilane and n-hexyl-(R)-2-methyl-butylsilane in isooctane at —5°C.

Figure 4.13 (a) Temperature dependence of dissymmetry ratios of poly ( S )-3,7-dimethy locty 1-3-methylbutylsilane (16) (three different Mw samples) and poly (5) -3,7-dimethyloctyl-2-methyl-propylsilane (17) (a purely P helix) in isooctane, (b) Temperature dependence of P and M populations of 16 in isooctane by reference to the regression curve of gabs values in 17. 

To investigate cooperativity in these copolymers, the gabs ratios were evaluated. The dissymmetry ratio, gabs, is displayed as a function of chiral content for 47, 50, 51, and 53-58 at 20°C in Figure 4.40. It is evident that the absolute magnitudes of gabs (i.e., independent of sign) for the pa ra - phe n y I - su b stituted... 

Figure 4.40 Dissymmetry ratio gabs as a function of chiral content for 50, 51, and 53-58 at 20°C.

Figure 42 Kuhn dissymmetry ratio for the series of co-polymers 112 as function of (P)- or (S)-enantiomer mole fraction.323 Reprinted with permission of the author from Fujiki, M. Polym. Prepr. (Am. Chem. Soc. Div. Polym. Chem.) 1996, 37, 454-455.

In the determination of M , the intensity of scattered light is measured at different concentrations and at different angles 6). The incident light sends out a scattering envelope that has four equal quadrants (Figure 3.11a) for small particles. The ratio of scattering at 45° compared with that at 135° is called the dissymmetry factor or dissymmetry ratio Z. The reduced dissymmetry factor Z is the intercept of the plot of Z as a function of concentration extrapolated to zero concentration. 

If the intensity of light scattered by a colloidal dispersion is measured as a function of c and 0, the Zimm method enables us to convert this information into several parameters that characterize the colloid M, B, and Rg. In some situations this is more information than is actually needed. If spatial extension is the only information sought, a simpler method for evaluating it employs the so-called dissymmetry ratio. 

With this result —or its equivalent made with less restrictive approximations —values of z can be evaluated as a function of Rg/. From tables or plots of such calculated results, experimental dissymmetry ratios — extrapolated to c = 0 to eliminate the effects of solution nonideality—can be directly interpreted in terms of Rg. 

Tn the critical region of mixtures of two or more components some physical properties such as light scattering, ultrasonic absorption, heat capacity, and viscosity show anomalous behavior. At the critical concentration of a binary system the sound absorption (13, 26), dissymmetry ratio of scattered light (2, 4-7, II, 12, 23), temperature coefficient of the viscosity (8,14,15,18), and the heat capacity (15) show a maximum at the critical temperature, whereas the diffusion coefficient (27, 28) tends to a minimum. Starting from the fluctuation theory and the basic considerations of Omstein and Zemike (25), Debye (3) made the assumption that near the critical point, the work which is necessary to establish a composition fluctuation depends not only on the average square of the amplitude but also on the average square of the local... 

Figure 5. Dissymmetry ratio IiS/I1S5 vs. concentration of polystyrene in cyclohexane at different temperatures above the phase-separation temperature...

In circularly polarized luminescence spectroscopy, one normally reports the ratio of Al to the total intensity 7. The results are most often reported in terms of the luminescence dissymmetry ratio, glum, which is defined as the ratio of the differential emission intensity to the average total emission intensity.75... 

Although CPL from crystals containing Eu(DPA)33 are not possible to obtain, it is possible to obtain the absolute value of the dissymmetry ratio for a pure enantiomer as... 

Fig. 8 Values of a dissymmetry ratio (gabs) and b Amax in a series of copolymer 10 and 11 as a function of mole fraction of n-hexyl-(S)-2-methylbutylsilane and w-hexyl-CR)-2-methylbutylsilane in isooctane at - 5 °C...

Figure 13 plots the temperature dependence of the dissymmetry ratios and the PM-populations in three different samples of 16 with different Mw... 

Fig. 29 Relative Kuhn dissymmetry ratios of chemically grafted 10 - spin-coated 32 (filled square) and spin-coated 10 - spin-coated 32 (filled circle) on quartz surface before annealing (gBA) and after annealing (gAA) as a function of total film thickness...

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