Debye plot

Debye plots, vs. q, also provide a convenient measurement of a (slope/intercept)Thus, the correlation volume for random two-phase systems is given by... 

Figure 5. Typical Guinier and Debye plots observed for PBLG-138,000/toluene prepared by quenching to various temperatures a) T = 28.2. Continued on next page.

Figure 5.—Continued. Typical Guinier and Debye plots observed for PBLG-138,000/toulene prepared by quenching to various temperatures d) T = 28.3, NOT RENEWED. Comparing a) and d) shows the effect of not renewing the sample by a long, high temperature melt between runs the intensity of the unrenewed sample is much less, resulting in some imprecision at the lowest angles. Fully darkened points were not used in obtaining slopes.

Related to the Zimm plot is the Debye plot. In the Zimm approach, different concentrations of the polymer solution are used. In the Debye approach, one low concentration sample is used with 1 /M plotted against sin B/2), essentially one-half of the Zimm plot. 

Equation (7.36) is known as the Debye plot. Figure 7.11a and Figure 7.11b show the excess Rayleigh scattering intensities of polyacrylamide from MALLSP (multi angle laser light scattering photometer) and LALLSP, respectively. 

Figure 49 shows the Debye plot of the SAXS data on Fiberite 934 resin. Heterogeneity of the dimension 37.0 Angstroms was observed in as-cast resin. After the postcuring schedule, the size of the heterogeneity shrinked apparently to 33.3 Ang-... 

Fig. 49. Debye plot of SAXS data of Fiberite 934 epoxy resin...

Thus, My, is directly obtained from the /-intercept of the Debye plot. The mean square radius is obtained from the slope of the Debye plot by... 

Figure 2 shows the Debye plot for the slice at the elution volume of 3.7 mL. The values of dn/dc and A2 were taken as 0.19 and zero. 

With its multiangle capability, MALLS can be used to measure the size as well as the absolute MW of polymers. The multiangle capability seems to be particularly important for the determination of MW and RMS radius of ultrahigh MW polymers as the Debye plot deviates from the linearity. It is also important for the analysis of ultrahigh MW polymers to use accurate A2 value as well as dn/dc as the resulting MW and RMS radius tend to vary with those values. 

Fig. 12.4. Left The dipole moment in Debye plotted against the time step. Right Distribution of dipole moments (left-hand-side region smaller dipole moments right-hand-side region larger dipole moments). Both data sets were calculated from a Car-Parrinello molecular dynamics simulation of an isolated tetralactam macrocycle [227].

Sketch Debye plots for gaseous HF, HCl, HBr and HI. Indicate the relative sizes of the intercepts and the slopes. 

Figure 4, The Debye plots for the scattering power, extrapolated to zero scattering angle, of solutions of copolymers of acrylamide and varying amounts of incorporated octylacrylamide as a function of polymer concentration.

In a light-scattering study of dihydroxy bile salts, Kratohvil and Del-licolli (120) estimated the fractional micellar charge, pjn, of NaTDC in 0.15 M NaCl from Debye plots. Here p represents the number of fundamental charges per micelle and n the number of monomer ions per micelle. Since m is the number of counterions bound to a micelle, then pin is equal to 1 — in/n. The fractional micellar charge pin was 0.29 in 0.15 M NaCl. From the present data pin for zero excess counterion (i.e., in water) concentration is 0.77. 

Figure 3. Debye plot of SAXS intensity (after fluorescent background subtraction) for PAN-I-Co sample 1.85T, showing data (O) and best-fit line.

Experimentally, V y° and V y° are separated as follows By rearranging Equation 2.25, a plot of V y versus (the Debye plot) yields a straight line, and the correlation length D can be determined by D = (A/2 r)/(slope/intercept) /. Therefore, by gradually changing the Vy value from 0 to the observed Vy, the V y° at which the Debye plot becomes closest to a straight line is obtained by a least-squares technique. 

DLS-700 Otsuka Elec. He-Ne laser 632.8 Photomult. 12,21 5-150 Zimm, Berry, Debye plots... 

The parameter for the amorphous region can be obtained from Eq. (8) by the Debye plot vs q ) of the scattering curve ... 

Fig. 8.1. Master scattering curves of polydisperse systems of spheres (Debye plot). Each curve is shifted by 1 unit upwards from the previous one with increasing values of a.

For a given structure type we obtain one set of master curves in dependence on the polydispersity. Model calculations were carried out for polydisperse systems of spheres and Gaussian coils, which cover the scattering behavior, observed on PEC particle systems. Figure 1 gives the master representation of the Debye plot for polydisperse spheres, showing significant deviations for different polydispersities. 

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