Moving boundaries INDEX

Moving-boundary electrophoretic techniques, originally demonstrated by Tiselius in 1937, employ a U-tube with the sample occupying the lower part of the U and the two limbs being carefully filled with a buffered electrolyte so as to maintain sharp boundaries with the sample. Electrodes are immersed in the electrolyte and direct current passed between them. The rate of migration of the sample in the electric field is measured by observing the movement of the boundary as a function of time. For colourless samples, differences in refractive index may be used to detect the boundary. Such moving-boundary techniques are used mainly in either studies of the physical characteristics of molecules or bulk preparative processes. 

The cell in the rotor is sector shaped (Fig. 35.17). As the rotor spins, the macromolecule moves outward leaving the pure solvent behind. A moving boundary is established between the solution and the solvent. The position of the boundary can be detected by the difference in refractive index between the two parts of the cell. Using measurements of the positions and V2 at times and 2 we can calculate the value of 5 from Eq. (35.80). Alternatively, if In r is plotted against t, we can obtain the value of s from the slope. 

The moving boundary spreading in the electrophoresis of protein is usually measured in terms of the refractive index gradient dn/dr, where n is the refractive index. The results are often recorded as shown in Figure 13.12. The formation of the boundary, its spreading, and its separation (if any) are functions of diffusion. The equation of the moving boundary is given in the form... 

The generation of photoexcited species at a particular position in the film structure has been shown in (6.19) and (6.20) to be proportional to the product of the modulus squared of the electric field, the refractive index, and the absorption coefficient. The optical electric field is strongly influenced by the mirror electrode. In order to illustrate the difference between single (ITO/polymer/Al) and bilayer (ITO/polymer/Ceo/Al) devices, hypothetical distributions of the optical field inside the device are indicated by the gray dashed line in Fig. 6.1. Simulation of a bilayer diode (Fig. 6.1b) clearly demonstrates that geometries may now be chosen to optimize the device, by moving the dissociation region from the node at the metal contact to the heterojunction. Since the exciton dissociation in bilayer devices occurs near the interface of the photoactive materials with distinct electroaffinity values, the boundary condition imposed by the mirror electrode can be used to maximize the optical electric field E 2 at this interface [17]. 

The reflectance of a boundary plane between two non-absorbing media is a function of the refractive indices of the media examined. When light moves from a medium of refractive index rii into a second medium with refractive index n2, both reflection and transmission of the light may occur (Fig. 10.1). The relationship between 9 and 0, is given by Snellius law (angles are defined as the angle between the beam and the normal on the interface)... 

Figure 2 9 Sedimentation velocity measurement, (a) The distribution of protein in the cell a function of centrifugation time. The protein is sedimenting toward the right. (6) Schlien optics pattern. The optical system measures the change in refractive index of the soluiic Thus, the pattern gives the concentration gradient of protein along the sedimentation path, i Plot of log X versus time where x is the distance the boundary has moved (i.e., the distance frc the meniscus to the peak of the SchSeren pattern).

The actual implementation of the generalized GCA involves a variety of issues. The point reflection with respect to the pivot requires careful consideration of the periodic boundary conditions. Furthermore, as mentioned above, particles that have been translated via a point reflection must not be translated again within the same cluster move, and particles that interact with a given cluster particle both before and after the translation of that cluster particle must be considered only once, on the basis of the difference in pair potential. One way to account for all interacting pairs in an efficient manner is the use of the cell index method [25]. For mixtures with large size asymmetries (the situation where the generalized GCA excels), it is natural to set up different cell structures, with cell lengths based upon the cutoffs of the various particle... 

One of the more useful methods is the Becke test. Becke noticed that when the microscope is focused up and down a bright halo near the boundary of a particle moves in and out. The halo will always move toward the higher refractive index as the focus is raised and toward the lower refractive index as the focus is lowered. Thus if the particle has a refractive index higher than the liquid, the Becke line will move from outside the boundary to the inside as the focus is raised and vice versa. Figures 4 and 5 show the bright Becke line outside and inside the boundary, respectively. 

Particles are precipitated at the bottom of the container and in some time three areas with precise borders (Fig. 8.7, b) can be distinguished in the volume. The pure liquid layer is located on the top, followed by the suspension layer (note that the top border of the second layer shifts downwards with time), and finally, the last layer consists of solid sediment. After a certain time r all particles will precipitate from the liquid into the sediment, the suspension will be completely separated into the pure liquid, and the solid sediment layer and the process of sedimentation will be brought to completion by the establishment of sedimentation balance (Fig. 8.7, c). The boundaries between layers are characterized by jumps of density and known as contact discontinuities. Let us determine the velocities of motion of discontinuity surfaces. Consider the motion of the top border of the second layer in Fig. 8.7. Denote by u the velocity of the border s motion directed downwards. Following a common practice in hydrodynamics, choose the system of coordinates attached to the moving surface. In this system, the surface of discontinuity is motionless. Denote the values of parameters before the jump (above) by the index 1, and behind the jump (below) - by the index 2 (Fig. 8.8, a). 

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