Theoretical curves scattering

The same plot constructed with the Dr/Dr0 data from depolarized dynamic light scattering is shown in Fig. 27b. The data points of Kubota and Chu [131] for dimethylformamide solutions come closer to the theoretical curve than those... 

Fig 18 also shows exptl data. Agreement between the theoretical curves of Aziz et al and Lambourn and Hartley is quite good, but agreement between theory and expt is less satisfactory. The exptl data scatter rather widely, but their general trend is that predicted by theory except that the effect of m/c is less than predicted by theory... 

Fig. 31. Theoretical curves of the angular dependence of the anisotropic light scattering (vertical polarization detection of horizontal component) for a random collection of anisotropic rods of length L and diameter d, Eq. (IV-35) [Van Aartsen...

The theoretical light curve is shown in Pig. 1a together with the observed one (van Genderen A.M., The P.S., 1985, Space Sci. Rev., 39, 313). The theoretical curve properly reproduces the dimming timescale and the depth of the observed curve. Theoretical spectrum shown in Pig. 1b displays discrepancies with observations in short waves. The deficit of optical radiation can be explained only by non-uniformity of the dust envelope which increases the contribution of scattering. The slope of far infrared spectrum is due to the adopted extinction tables. Angular distribution of monochromatic brightness (normalized, in arbitrary units) is shown in Pig. 1d. 

A possible reason for the lack of agreement between the experimental and theoretical curves is the large scatter in depth of traps for e. This scatter may be due to both the different initial depth of the traps and its change (increase) with time, e.g. as a result of polarizing the medium with the electron charge. The data indicating the presence of scatter in depth of traps for etr in MTHF were already reported in Sect. 1. Beitz and Miller [96] also present data on the possibility of changes in the depth of traps with time. Under the conditions of scatter of traps for et" in depth the electrons stabilized in shallower traps will decay faster than those stabilized in deeper ones. As a result, the kinetic curves for etr decay in MTHF turn out to be more "flat than is predicted by eqn. (7) of Chap. 5. 

Treatment of Experimental Values. The experimental values are corrected for air scattering, polarization, but absorbtion - geometric (Lorentz) corrections are not made. After the variable 20 is transformed into s = 2 sin 6, the experimental curves are normalized, in electronic units, by adjustment to a theoretical curve. Theoretical curves (total scattering power, summing up coherent and incoherent scatterings) are calculated from the stoichiometric composition of polymers. 

In order to obtain good adjustement between experimental and theoretical curves, we correct for the absorbtion discrepancy between the coherent and incoherent scattering, which becomes larger at wide scattering angles. Because of this discrepancy, corrections are successively made to the ratio I (incoh) (3) for the... 

Theoretical curves of scattered intensity by PET and experimental normalized intensity by PET fibers... 

Finally, before carrying out the calculation, it is necessary to sketch the boundary between the crystalline peaks and the amorphous background. This line can be calculated if an amorphous sample has been used as a reference, such as for PET and cellulose fibers. If no amorphous standards are available, the background is drawn manually, following a line parallel to the theoretical curve (jt,5) (total scattering power summing up coherent and incoherent scattering). 

Fig. 2.8. Low energy positron-helium total scattering cross sections. Experimental data, main diagram x, Costello et al. (1972) , Canter et al. (1972, 1973) , Wilson (1978), after correction by Sinapius, Raith and Wilson (1980) , Stein et al. (1978) A, Coleman et al. (1979) A, Brenton et al. (1977) o, Griffith et al. (1979a). The experimental data in the inset are from Mizogawa et al. (1985) and they are compared there with the theoretical work of Campeanu and Humberston (CH, see text). Theoretical curves, main diagram — —, CH ...

It is instructive to make a quantitative comparison between the experimental and theoretical curves. The light scattering intensity, expressed as the Rayleigh ratio, is a function of the size and number of particles. If all three reactions shown in Figure 7 polymerize at the same rate, Rp, then at a given time, say 10 seconds, the total volume of polymer formed, VT, will be the same in all three. Under these conditions, the scattering intensity becomes a direct measure of the relative number of particles ... 

The applicability of relation (9.71) to a real polymer system was discussed in works by Pokrovskii et al. (1973) Pokrovskii and Kruchinin (1980) Pyshno-grai et al. (1994). Figure 19 represents the experimental values of the ratio A/77 depending on the invariant D for the polymer systems, listed in Table 3, in comparison with the universal theoretical curve calculated according to equation (9.71). The experimental results can be seen to have a definite scatter relative to the theoretical curve this can be ascribed to both natural experimental errors and the necessity of improving the theoretical calculation by appealing to the fuller set of constitutive relations (9.48)-(9.49). In the former case a variation of [3 in (9.49) leads to a set of A/77 vs D curves (Pyshnograi et al. 1994). 

Fig. 2.8. (a) Hall mobility as a function of the temperature for an undoped epitaxial ZnO layer and (b) Hall mobility of Ga-doped ZnO layers as a function of the carrier concentration. The ZnO films were grown epitaxially on lattice-matched ScAlMg04 (SCAM) by Makino et al. [64], In (a) the calculated mobilities for acoustical, polar-optical, piezoelectric, and ionized impurity scattering are shown, together with the total theoretical mobility. In (b) the solid curve is the fit curve (2.24) from Fig. 2.6, while the dashed line is the theoretical curve, calculated by Makino et al. [64]. The dotted line was calculated for transport across depletion regions at grain barriers (see Sect. 2.2.3), also present in epitaxial films [106]... 

From their light-scattering measurements Holtzer, Benoit, and Doty (126) concluded that the short-range interactions control the dimensions of cellulose nitrate chains, and they discussed their results in terms of the worm-like chain model of Kratky and Porod (142), obtaining a persistence length of about 34.7 A. In Fig. 21 these data are shown as a plot of (S yjMw against Mw. The open circles are the experimental points and the broken curve is that calculated from the equations for the worm-like chain model. The theoretical curve is claimed to reproduce the data to within the probable experimental error in all but two cases. 

To determine the average droplet size from the scattering data, theoretical curves of the ratio of I 0,d)/I 4°,d) were calculated as a function of 0 for a range of appropriate droplet diameters. 

Fig. 2. Correlation function Yo(r) calculated from the experimental scattering data of Gelsil 50 shown in the right panel (crosses). Right lixperimental scattering data compared to the theoretical curve I(q) which was recalculated from the correlation ftinction Yo(r) by use of Eq. (3).

The two theoretical curves are plotted in Fig. 12 as a function of conversion together with the experimental values of the elastic constant C22 of PTS in chain direction which have been obtained by Brillouin scattering At higher conversions the experi-... 

Fig. 8.6. The magnetic substate parameters A, R and I (8.17) for 54.4 eV electron scattering to the 2p state of hydrogen. Squares, Weigold, Frost and Nygaard (1979) and Hood, Weigold and Dixon (1979) circles, Williams (1981,1986). The theoretical curves are as for fig. 8.3.

Figure 4. Comparison of the experimental results with the theoretical curves for four contrast values (100, 60, 20 and 50 % of 0 22 surfactant/ % oil = 0.176, % water = 15]. ( ) experimental points. Theoretical curves of the intensity scattered...

Figure 3. Two-body depolarized scattering spectrum for CF4 gas at 294.5 K. The full circles ( ) indicate experimental data with error bars [8], Theoretical curves are provided for several...

FIG. 17 Scattering curve of a PEC between anionically and cationically modified PNIPAM (symbols) and its interpretation by theoretical curves of polydisperse systems of spheres of different polydispersity (see the inset table). 

It is evident that the theoretical curves do not give a good representation of the experimental results. However, the trend of the experimental results is only qualitatively apparent and their scatter is such that the validity of distinguishing any one set of results from another or from a theoretical curve might be questioned. In order to obtain a more quantitative interpretation of the results, we made use of statistical methods. 

Figure 6.9 Neutron scattering data from a binary mixture, annealed at 160°C, of a hydrogenous polystyrene (molecular weight 870,000) and a deuterated polystyrene (molecular weight 1,150,000). The solid curve is a fitted theoretical curve with x equal to 1.9 x 10-4, and the upper broken curve is for x =0 expected in the absence of the deuterium isotope effect. (From Bates and Wignall.19)...

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