EQUILIBRIUM SEDIMENTATION OF MONODISPERSE SOLUTES

Two procedures have been proposed to compute the z-average molecular weight, M$\sb{\rm z},$ of a solute from its equilibrium concentration curve in a solution sample in a controlled centrifugal field. The first proposed procedure operates on data from equilibrium sedimentation at a single rotor speed. Graphical differentiation is applied to the concentration curve to obtain a polynomial expression for the concentration gradient function of radial solution depth. The resulting polynomial expression is evaluated at the radial boundaries of the solution sample to obtain the concentration gradients required to compute M$\sb{\rm z}.$ The objective of this procedure is to obtain the concentration gradients at the boundaries as boundary intercepts rather than as boundary slopes. The proposed computation procedure was tested by its application to data from equilibrium sedimentation of the monodisperse solutes, sucrose and sucrose octaacetate. The proposed computation procedure, by graphical differentiation, was compared with the established computation procedure in which the required concentration gradients at the solution boundaries are obtained by numerical differentiation of a polynomial expression for the concentration curve. The M$\sb{\rm z}$ values from both procedures were equally higher than the known molecular weight of these two solutes. The ratios of M$\sb{\rm z}$ to the weight average molecular weight, M$\sb{\rm z}$/M$\sb{\rm w},$ were also computed by each procedure. The two sets of M$\sb{\rm z}/$M$\sb{\rm w}$ values were not significantly different. The proposed procedure to compute M$\sb{\rm z}$ by graphical differentiation of the concentration curve was also demonstrated by its application to data from equilibrium sedimentation of a polystyrene known to have a broad molecular weight distribution. The second proposed computation procedure operates on data from equilibrium sedimentation at a series of rotor speeds. The equation for this computation procedure,(UNFORMATTED TABLE OR EQUATION FOLLOWS)$${\rm M\sb{z} = {(dc/d\xi)\sb{b} - (dc/d\xi)\sb{m}\over\lambda(c\sb{b} - c\sb{m})},}$$(TABLE/EQUATION ENDS)is derived. This computation procedure is demonstrated by its application to polystyrene solution samples equilibrated in a wide range of centrifugal fields. In this procedure M$\sb{\rm z}$ is equal to the slope of a plot of the numerator versus the denominator in a multispeed experiment. The denominator provides the advantage of normalizing the data from multiple samples of the same solution in a series of centrifugal fields.