Equations for testing Onsager's reciprocal relations for isothermal diffusion depend on the frame of reference chosen for the flows. This subject is considered for certain frames of reference, as is the problem of measuring diffusion coefficients when there is a change of volume on mixing. Frames of reference discussed are those moving with the local center of mass, the local center of volume, the local velocity of the solvent (or of any single component), and that fixed on the diffusion cell. Multicomponent systems, both of strong electrolytes and nonelectrolytes, are considered. An expression is derived which relates the flow of a component in the cell-fixed frame of reference to the flows in any other frame of reference when there is a change of volume on mixing. This relation is used to show that a flow relative to the cell becomes identical to that in the volume-fixed frame as the initial differences in concentration within the diffusion cell are made sufficiently small. Throughout this article a special effort has been made to present derivations and final equations in a form well adapted for use in experimental work.
should be increased but, owing to the decrease in the magnitude of the density gradients that stabilize the boundary, more careful control of the temperature would be required. Since it appears essential to have homogeneous layers of solution of appreciable thickness above and below the boundary, the period of observation can only be extended by increasing the height of the cell. Although the fringes are compressed as diffusion proceeds the resolving power of the available photographic emul-sions17 is such that this is not a limiting factor.It is a pleasure to acknowledge my indebtedness to D. A. Maclnnes of these laboratories for his care in the review of this manuscript and to Gerson Kegeles of the University of Wisconsin for clarifying correspondence throughout the course of the investigation.(17) "Photographic Plates for Use in Spectroscopy an4 Astronomy," Eastman Kodak Co., 5th edition, 1946, Rochester, N. Y.
Within the last several years Archibald has indicated how molecular weights and sedimentation coefficients may be calculated from the ultracentrifuge data during the period of ap roach toward sedimentation equilibrium in a sector shaped cell. Applications of this method have been made to smat molecules by Porath and by Brown, Kritchevsky and Davies. Gutfreund and Ogston, and Baldwin have devised an independent method fqr the determination of sedimentation coefficients based on the flow of solute past a fixed surface in the cell, and have applied this to the study of polypeptides. In the present study we have correlated the two methods so that they may be applied simultaneously to the data obtained in a single experiment. The method employs phase-contrast schlieren optics of Wolter, Armbruster, Kossel and Strohmeier and Trautman and Burns. A two-coordinate comparator is used to measure diagrams from standard ultracentrifuge cells as well as from a boundary-forming cell described by Kegeles, and used here as a refractometer. We have found that both molecular weights and Sedimentation coefficients may be determined reliably within one hour of centrifugntion for raffinose and for bovine plasma albumin, by the proper choice of speed.
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