Drude plots

The computations of the Moffitt parameters (see Equation 2), utilizing the statistical procedures with error analyses developed by Sogami, Leonard, and Foster (57) to determine the best Xo values, and of the Drude parameters see Equation 1 a modified Drude plot of [mf] vs. [ra ]X2 (67) was used with error analyses were performed with the IBM 7094 computer. Correction for the dispersion of refractive index of the solvent was made as outlined (46). 

Figure 3 shows typical Moffitt plots for the native and the 7M G-HC1 denatured protein in the 240- to 315-m/z region where A0 is 220 m/z. In this wavelength range the Drude plot for the native protein appears linear although the statistical analysis indicates much larger standard deviations for the slope and the intercept, especially the latter [nearly ten times as great as for the random form of the protein (46)]. Also, Xc and the Drude... 

Fig. 12. Drude plots of the system NH4BCS and the complex [Zn(phen)3]-(BCS)2. The solid lines (defined by circles) represent data taken from Pfeiffer s original work. The triangles (dotted lines) are for current studies. Unfilled data points (O and A) are for NH4BCS while filled points ( and A) are for [Zn(phen)3] (BCS)2. Single term Prude.

BCS (see Fig. 13), it is concluded that the source of the Pfeiffer rotation can neither be in the metal complex alone nor in the activating agent. Although there is some scattering in the Drude plots, the intersection points for both the Landis and Pfeiffer data are concordant. 

A similar Drude plot of Pfeiffer rotations in a variety of other active systems is shown in Fig. 16. The sign of rotation has been changed (those... 

Fig. 15. Drude plots of cinchonine (C), cinchonine with [Zn(phen)3] and the resulting Pfeiffer rotation (P). Rotatory dispersion data for C and CZ taken from Fig. 14.

An enhancement of the optical activity of the polymers is observed as compared to their model compound, its magnitude depending on the distance between the asymmetric site and the main chain. This enhancement was attributed to a conformational effect on the asymmetric center in the side chain. The rotatory dispersion curves fit the simple Drude plots and are essentially the same for both the polymer and the model compound. Specific rotation values are independent of intrinsic viscosity and crystallinity over the range measured. 

As an example of extinction by spherical particles in the surface plasmon region, Fig. 12.3 shows calculated results for aluminum spheres using optical constants from the Drude model taking into account the variation of the mean free path with radius by means of (12.23). Figure 9.11 and the attendant discussion have shown that the free-electron model accurately represents the bulk dielectric function of aluminum in the ultraviolet. In contrast with the Qext plot for SiC (Fig. 12.1), we now plot volume-normalized extinction. Because this measure of extinction is independent of radius in the small size... 

Fig. 2. Graphical treatment of dispersion data in Fig. 1 according to the simple Drude equation (11). The disordered forms of the synthetic polypeptides, poly-y-benzyl-L-glutamate (PBG, O — O) and poly-n-glutamio acid (PGA, A — A), give linear plots, which specify their dispersions as simple. The dispersions of bovine serum albumin (BSA) in both its native ( ---- ) and denatured ( — ) forms are...

The origin of nonzero bo values in these cases is not entirely clear, but it can be formally traced to the difference between Xo and values for the simple dispersion of random coils and hence to a failure of the assumption that Xo equals Xo. If K equals Xo, then the first term of the Moffitt equation will of course be the same as the simple Drude expression known to describe the data and, there being no necessity for a second term, bo will vanish. However, if Xo differs from Xo, the Moffitt plot may still be linear but with a nonvanishing slope. Thus dispersion data that are simple when referred to one dispersion constant may appear complex when plotted against another by a form that sees matters as complex, thereby generating what may be properly suspected as pseudocomplexity. The Moffitt equation was initially intended to describe the complex dispersion of polypeptides for which the simple Drude equation is inadequate, but, as will be seen, its form is also applied to protein dispersions which can be expressed equally well by either formula. It is therefore important to examine more fully the relation of the two equations for cases in which both fit the data. 

The general relation of X to the parameters of the Moffitt equation has been stated by Downie (1960). If a given set of dispersion data obey the simple Drude equation, Xo may be obtained from the slope of [m ]xX plotted against [m ], d([m ]xX )/d[m ]x (see Section II, B). If each value of [w ]x can also be accommodated by the Moffitt equation, a condition which is often satisfied for measurements in the spectral region 350-600 m, then Eq. (18) can be substituted into this slope and the appropriate differentiation carried out with the following result. 

The proposal to assimilate the rotatory dispersions of proteins to those of synthetic polypeptides is, in barest form, the recommendation to treat these same data by the Moffitt expression despite the fact that they can be described by the simple Drude equation. Thus one proceeds to plot [m ] -(X — Xo)/Xo against Xo/(X2 — Xo) with Xo set to 212 m/j, and thereby obtains an intercept, a , and a slope, which can be given conformational interpretations through Eqs. (35) and (36). These parameters, which are in general cited simply as Oo and foo when their experimental origin is... 

The last part of this paper concerns sum rule calculations, Drude fits and temperature dependence in the near infrared. In Fig. 3 is given a normalized sum rule plot for... 

A plot of [a] versus A would then be a complex curve with maxima and minima. The author completely agrees with the view expressed by Djerassi78 that the usefulness of the Drude equation for structural studies is limited. 

Successful quantitative measurements of the thickness of the squalane primary film were possible after 18 and 42 hours of drainage. The film profiles determined from these measurements are shown in Figure 4. The film thickness was measured at various distances from a reference line drawn on the metal plate. The points plotted at about 1200-A. thickness correspond to the first-order interference fringe. These measurements demonstrate a sharp change in the slope of the film and also a tendency for the primary film to thicken over the 24-hour period. Undoubtedly there is some error in the measurement of film thickness where the thickness is changing abruptly and also near 100 A., where the Drude calculations of film thickness are invalid. 

FIGURE 15.23 s(ai) plotted vs. 1/tu for selected PAN-CSA samples at room temperature. The linearity confirms that the low energy carriers are free (Drude) carriers. (From Kohlman, R.S. and Epstein, AJ., Handbook of conducting polymers, 2nd ed., eds. Skotheim, T.A, Elsenbaumer, R.L., and Reynolds, J.R., Marcel Dekker, New York, 1988, chap. 3. Reprinted from Routledge/Taylor Francis Group, LLC. With permission.)... 

Fig. 16. Pfeiffer rotations plotted according to the Drude equation for selected Pfeiffer active systems. Data for the complex [Zn(phen)3] with cinchonine (C), the complex with BCS (B), the complex with nicotine (N), and the complex with strychnine (S) are recorded. The rotatory signs have been changed for C and S to allow a comparison on the...

Figure 12.3 shows a typical rotatory dispersion curve, where there is no maximum or minimum. Figure 12.4 shows a plot of m versus X, in which a protein in denatured form is compared with the same protein in native form. The plot of the Moffit-Yang equation s shown in Rgure 12.5. If a synthetic polypeptide is in a random conformation, the rotatory dispersion, which is simple, may be adequately expressed by a one-term Drude equation. If a synthetic polypeptide is in an ot-helical conformation, the Moffitt-Yang plot may be employed to describe the rotatory dispersion. 

The ORD of poly-y-benzyl-L-glutamate in chloroform does not lit a simple Drude equation. Such dispersion results may be plotted in the general form proposed by Moffit. The data are as follows ... 

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