Optics, Schlieren

This shows that Schlieren optics provide a means for directly monitoring concentration gradients. The value of the diffusion coefficient which is consistent with the variation of dn/dx with x and t can be determined from the normal distribution function. Methods that avoid the difficulty associated with locating the inflection point have been developed, and it can be shown that the area under a Schlieren peak divided by its maximum height equals (47rDt). Since there are no unknown proportionality factors in this expression, D can be determined from Schlieren spectra measured at known times. 

In a solution of molecules of uniform molecular weight, all particles settle with the same value of v. If diffusion is ignored, a sharp boundary forms between the top portion of the cell, which has been swept free of solute, and the bottom, which still contains solute. Figure 9.13a shows schematically how the concentration profile varies with time under these conditions. It is apparent that the Schlieren optical system described in the last section is ideally suited for measuring the displacement of this boundary with time. Since the velocity of the boundary and that of the particles are the same, the sedimentation coefficient is readily measured. 

Techniques which seem less suitable for routine size analysis are (1) analytical ultracentrifugation combined with a Schlieren optical system (Mason and Huang, 1978 Weder and Zumbuehl, 1984) (2) the sedimentation field flow fractionation (SFFF) technique to separate heterogeneous dispersions (e.g., Kirkland et al., 1982). 

Transport Analysis Using the Ultracentrifuge Schlieren Optics... 

The formation of a boundary between the dextran solution and the dextran solution containing PVP 360 (concentration 5 kg m 3) yields an apparently normal Gaussian distribution of the material detected by Schlieren optics. The various apparent diffusion coefficients obtained by an analysis of the Schlieren curves, which include diffusion coefficients obtained by the reduced height-area ratio method, the reduced second-moment and the width-at-half-height method, show the same qualitative behavior although quantitative differences do exist. This is seen in Fig. 7 where the... 

The time-dependent development of the initial absorption scans of the PVP transport in dextran, monitored at 237 nm, is shown in Fig. 8. The anomalous feature of these scans is that material which absorbs at 237 nm rapidly accumulates on the left-hand side of the boundary. This material appears to be evenly distributed in this region and would therefore not be detected by Schlieren optics. We have shown that accumulation of absorbing material on the LHS of the boundary is exactly balanced by the depletion of absorbing material on the RHS of the boundary. 

The schlieren system of optics is an analytical method that is particularly well suited to following the location of a chemical boundary with time. It is routinely employed in ultracentrifuges and also in electrophoresis experiments, as we see in Chapter 12. Schlieren optics produces an effect that depends on the way the refractive index varies with position, that is, the refractive index gradient rather than on the refractive index itself. Therefore, the schlieren effect is the same at all locations along the axis of sedimentation, except at any place where the refractive index is changing. In such a region, it will produce an optical effect that is proportional to the refractive index gradient. The boundary between two layers is thus per-... 

FIG. 2.7 Location of the boundary for particles settling in an ultracentrifuge (a) concentration profile and (b) derivative profile as revealed by schlieren optics. (Redrawn with permission of P. C. Hiemenz, Polymer Chemistry The Basic Concepts, Marcel Dekker, New York, 1984.)... 

The curves in Figure 2.10 are drawn for an arbitrary value of the diffusion coefficient. The experimental profiles produced by the schlieren optics are characterized by the diffusion coefficient of the experimental system. The remaining question is how to extract the appropriate D value from the experimental observations. 

The method of equilibrium ultracentrifugation described by Yphantis (28) was used in these studies. A double-sector centerpiece with two 2 1/2° sectors 12 mm. in length was used with standard Schlieren optics. Apparent molecular weights, M, were determined from the equation ... 

Equation 54 is analogous to Equation 28, and one can take three values of nr at different radial positions to solve for cAfm> cBrm, an( KcArmcBrm, and from this evaluate K. With the schlieren optics one obtains... 

A similar equation results for cBrm. Now a priori we do not know (d In Ja/dcB), cAr, cBr, or K we do not know BAa and Bbb (see Equations 67 and 68) from measurements on pure A and pure B. We have no way of knowing ir a priori, so we cannot use equations similar to 28 or 31. Similar considerations apply if vA vB and = b- Thus, it appears at present that we are forced to use the Archibald experiment or sedimentation equilibrium experiments at different speeds to analyze mixed associations when one is restricted to Rayleigh and/or schlieren optics. 

From Rayleigh and schlieren optics, one could calculate cMwa, and hence one could calculate A (cMwa) at every r in the solution column of the ultracentrifuge cell and use the analysis used with the other methods (see Equation 76 and the discussion following it). This could also be done even if only one of the reactants had an absorption spectrum, since c = cA° + cB°. The other possibility is that the complex AnBm has a different absorption spectrum from the reactants, or that in the formation of AnBw some chromophoric groups are buried so that the absorbance of A and B represents a quantity proportional to cA and cB. In either case one could then calculate... 

Fio. 3. Sedimentation coefficient and molecular weight as functions of pH. (A) Sedimentation coefficients as a function of pH. (O) s°0 w values were determined for samples adjusted from neutral pH to each pH value. The concentrations were 72 mg/ml, except at pH 5 and pH 4, where they were 4j0 mg/ml in 0.01 Af tris-0.01 Af sodium acetate. (0) s°0 w values were determined for samples adjusted from neutral pH to the given pH. Concentrations were 0.62 mg/ml in 0.1 Af NaCl-0.01 Af tris-0.01 M sodium acetate. ( ) s° w values were determined for samples prepared at pH 2, then dialyzed at the appropriate pH. Concentrations were 0.62 mg/ml in 0.1 M NaCl-0.01 Af tris-0.01 M sodium acetate. (O) Determinations with Schlieren optics all other determinations were made with the use of ultraviolet optics with the photoelectric scanner. (B) Weight average molecular weight as a function of pH. (0) M values were determined for samples adjusted from neutral pH to each pH indicated, by dialysis, 0.62 mg/ml, in 0.1 M NaCl-0.01 M tris-0.01 M sodium acetate. (O) Mw values were determined for samples prepared at pH 2, then dialyzed at the appropriate pH, 0.62 mg/ml in 0.1 M NaCl-0.01 Af tris-0.01 Af sodium acetate. 

In these density profiles the latex particles, added before starting the experiment, migrate to that position in the cell where their density coincides with the density of the surrounding medium. The position of the particles can be recorded by schlieren optics or, if there is a particle density distribution, more precisely by scanning extinction measurements normally used for the characterization of proteins. Thus the density and extinction profile in the ultracentrifugation cell yield a criterion for the density distribution and hence, because of the correlation between chemical composition and particle density, a criterion for the composition distribution or heterogeneity of the latex particles. 

The local position of the particles in the cell can be recorded in all cases by scanning extinction measurements. Only in the special case of chemically uniform particles can the schlieren optical method also be used. 

A practical difficulty, encountered in this study was performing the AUC runs at temperatures higher than 40 °C at such high temperatures, the oil vapors from the diffusion pump interfere with the UV absorption optics. They circumvented this problem by using a different type of optical scanning known as the Schlieren optics, which generates the data as profiles of radial derivative of concentration distributions as a function of radius (as opposed to the concentration versus radius scans obtained from UV optics). 

FIG. 16 Schlieren optical texture observed for a thin pel of ca. 2 wt /f CAQ in l-octanol between crossed polarizers at ambient temperature. (Front Ref. 94.)... 

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