The Berry-Plot

But for large globular particles, the angular dependence in the Berry plot... 

Fig. 24. a The three-functional regularly branched chain model with Gaussian behavior of the subchains, called the soft sphere model s). b The Berry-plot of the reciprocal particlescattering factor of the soft sphere model. Compare also Figs. 19, 25 and 27... 

Pig. 5.17 Angular dependence of [KC Ryy q) (the Berry plot) of hyper-(PtBA36-PS55-PrBA36)600 in THF, good for both PtBA and PS blocks and in cyclohexane, only selectively good from PlBA block... 

For long polymer chains, i.e., (Rg) > 1, the Berry plot is normally used. In static LLS, the scattering intensity was recorded at each angle three times and each time was averaged over 30 s. The scattering angle ranges from 12 to 120°. The refractive index increment of hyperbranched polystyrenes in toluene (dn/ dC = 0.111 mL/g at 25 °C and 633 nm) was determined by a precise differential refractometer. 

Figure 5.6 shows the same data plotted as a function of cM0 6S to test the low concentration reduction scheme based on c rf] with a typical value of the Mark-Houwink exponent for good solvents. The data have been shifted vertically to achieve superposition at high molecular weights. It is clear that the cM variable produces a better superposition of data at all molecular weights and concentrations. The apparent variation in the values of cM at the intersections in Fig. 5.4 (Table 5.1) is largely due to a lack of data to define the limiting behavior at low molecular weights at some concentrations. The intersection on the superposed plot in the composite Fig. 5.5 is cM = 30000, giving Mc = 30600 for undiluted polystyrene (q = 0.98 at T = 217° C, in good agreement with the value 31200 reported by Berry and Fox (16).

It was observed that the electrospinning of polymer solution below the Berry number of 10 yielded droplets or fibers with droplets and the nanofiber diameter increased with an increase in the Berry number from 65 nm to above submicron and micron size when the Berry number increased above 10. The data can be fitted using a set of straight lines with different slopes in two different regions (Fig. 1.8]. The correlation coefficient for the first trendline improved from 0.891 for the Berry number plot to 0.974 for the number of entanglements plot. ... 

With MALS detectors, the molar mass for every elution volume slice is obtained from a partial Zimm, Debye, or Berry plot, where the scattering intensity of aU angles is... 

Table 16.1 gives a FORTRAN program which generates the multivariable Nyquist plot for the Wood and Berry column. The subroutines given in Chap. 15 are used for manipulating the matrices with complex elements. The subroutines PROCTF and FEEDBC calculate the and complex numbers at each value of frequency. A general process transfer function is used for each of the elements in the matrix that has the form... 

Characteristic loci plots for the Wood and Berry column are shown in Fig. 16.3. They show that the empirical controllers settings give a stable closedloop system, but the ZN settings do not since the eigenvalue goes through the (- 1,0) point... 

The procedure is summarized in the program given in Table 16.4 which calculates the minimum singular value of the [ + g(7m)] matrix for the Wood and Berry column with the empirical controller settings. Figure 16.10 gives plots of the singular values as a function of frequency. The lowest dip occurs at 0.23 radians per minute and is about — 10.4 dB. 

To model the relationship between PLA and PLR, we used each of these in ordinary least squares (OLS) multiple regression to explore the relationship between the dependent variables Mean PLR or Mean PLA and the independent variables (Berry and Feldman, 1985).OLS regression was used because data satisfied OLS assumptions for the model as the best linear unbiased estimator (BLUE). Distribution of errors (residuals) is normal, they are uncorrelated with each other, and homoscedastic (constant variance among residuals), with the mean of 0. We also analyzed predicted values plotted against residuals, as they are a better indicator of non-normality in aggregated data, and found them also to be homoscedastic and independent of one other. 

The status of current theories of the low shear-rate viscosities (rj0) of polymer melts (and concentrated solutions) was reviewed by Berry and Fox in 1968 (52), since when there has been little development. The viscosity of linear polymers of low MW at constant temperature (or more precisely constant free volume is proportional to Mw, but at high MW it is proportional to a higher power M, where x is empirically about 3.4-3.5 the change of slope of a ogt]0/logMw plot is fairly abrupt The high exponent 3.4—3.5 is attributed to the effects of chain... 

The total number of berries with fruit rot symptoms and the number of berries with symptoms of anthracnose or stem end rot from the April 24 harvest time were significantly lower from plots treated with the fungicides Switch, Cabrio , CaptEvate , and Pristine than from those receiving no fungicide treatment (Table 2). The most prevalent diseases in the Louisiana field study were anthracnose caused... 

Figure 13.2 Analysis of raspberries by NIR imaging (third PC image) showing a grading in the maturity (Berries i = low maturity ii = medium maturity iii = ripe), (a) The figure shows the third PC image and (b) is a plot of the raw spectrum and the third PCA loading. From Walloon Agricultural Research Centre, Belgium.

Figure 17 Plot of the isomer shifts versus Fe oxidation state of a series of low-spin Fe(lll) Fe(IV), Fe(V), and Fe(VI) complexes with cyclam-related ligands. A plot of the Fe X-ray absorption spectroscopy (XAS) pre-edge peak energies of some complexes versus Fe oxidation state is also shown (open squares). The lines with dashes and dots represent least squares fits. (From J. F. Berry etal. (2006) Science 312 1937-1941. Reprinted with permission from AAAS)...

A plot of Sij[5ij(C) - <5jj(TBP)] versus 217.9° - [ (C) - (SP)] is linear. Consideration of a series of compounds with different ligands attached to the same central atom showed a spread of data about the theoretical Berry reaction coordinate. The method of Auf der Heyde and Nassimbini is more rigorous, as it uses all of the available information, whereas the previous approaches used only selected parameters. All three methods suffer from the fact that the relationship of structural data to only one reaction coordinate can be considered. 

Berry (ref.23) found that on a plot of rate (positive for oxidation) versus temperature, an isobar starts at a negligible rate at low temperature, rises as the kinetics become more favorable as the temperature increases, passes through a maximum and then falls to zero at the temperature given in Table 1 for the... 

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