Schlieren optical system

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). 

The discussion to this point has centered on the limiting case D = 0. In many instances this limit may not be realistic for macromolecules. With D > 0, diffusion will cause a broadening of the shock interfaces, which will increase with time, as sketched in Fig. 5.5.4. Also shown there is the concentration gradient dp dr, which is what is commonly measured in an ultracentrifuge with a schlieren optical system. Actually, what is measured with a schlieren system is the gradient of refractive index, which can then be converted to dptdr when the solution is binary. 

Figure 1 shows a diagram of the combined Schlieren/Mach-Zehnder interferometer apparatus, used to obtain the experimental results that are to be presented in the next sections. This apparatus can be changed, by the insertion of mirrors (14) and (15), from the interferometer configuration to become a Schlieren optical system to enable it to be used for the visualisation of the interfaces across which mass transfer occurs. A detailed description of the integrated apparatus and techniques may be found in Agble and Mendes-Tatsis (2000). 

Example of Toepler-Schlieren optical system. LI, lens L2, Schlieren head L3, objective lens K1, first (aperture) K2, second knife edge. 

Fig.3. Sedimentation pattern of normal human serum in the ultracentrifuge, measured with a schlieren optical system. Left hand picture taken 51 min after start of centrifugation right hand picture after 125 min. Centrifugation at 59,800 rpm. A albumin, 4.5S G = globulin, 7S M = macroglobulin, 19S.

The Talaria system also uses the principle of deformation of an oil film to modulate light rays with video information. However, the oil film is transmissive rather than reflective. In addition, for full-color displays, only one gun is used to produce red, green, and blue colors. This is accomplished in a single light valve by the more complex Schlieren optical system shown in Fig. 5.125. 

The purpose of analytical ultracentrifugation is quantitative determination of the concentration and distribution of the lipoprotein species that are present. The lipoprotein concentrate obtained in any one of the preparative ultracentrifugal steps outlined above is immediately available for analytical ultracentrifugation without further manipulation. This step is performed in an analytical ultracentrifuge (Spinco model E) equipped with a diagonal wire cylindrical lens, Schlieren optical system, and camera. 

Fig. 3. (a) Schematic diagram of analytical ultracentrifuge cell containing a migrating lipoprotein species, (b) Representation of the concentration of this lipoprotein as a function of distance from the center of rotation, (c) Representation of refractive index gradient as a function of distance from the center of rotation. The Schlieren optical system of the Spinco model E ultracentrifuge actually provides this type of plot. 

Practically, a maaroscopic step-like concentration gradient can be established in a double-sector capillary-type ceD using an ultracentrifuge and the evolution of the concentration gradient is followed by means of the Schlieren optical system. Usually, this kind of experiment is called a classical gradient diffusion (CGD) experiment. The diffusion coefficient is obtained from photographs of the Schlieren pattern at different times The time span, in which the diffusion is measured, is typically 5 x itf s for a semi-dilute solution of PS in benzene (1%). 

---