Equilibrium equation, basic sedimentation

Basic Sedimentation Equilibrium Equation. Sedimentation equilibrium experiments are performed at constant temperature. The condition for sedimentation equilibrium is that the total molar potential, m, for all components i be constant everywhere in the solution column of the ultracentrifuge cell. Mathematically this can be expressed as... 

This then is experiments. our basic, working equation in sedimentation equilibrium To obtain the weight-average molecular weight, Mw, it is ... 

Estimation of the Ideal Values for d In c/d(r2) and dc/d . For the nonideal case we can use Equations 1-4 and 6 to obtain the basic sedimentation equilibrium equation for component i. In the Fujita notation (17) this equation is... 

There are three points to emphasize. First, the expressions for the concentration or concentration gradient distribution for non-sector-shaped centerpieces can be applied to other methods for obtaining MWD s, such as the Fourier convolution theorem method (JO, 15, 16), or to more recent methods developed by Gehatia and Wiff (38-40). The second point is that the method for the nonideal correction is general. Since these corrections are applied to the basic sedimentation equilibrium equation, the treatment is universal. The corrected sedimentation equilibrium equation (see Equation 78 or 83) forms the basis for any treatment of MWD s. Third, the Laplace transform method described here and elsewhere (11, 12) is not restricted to the three examples presented here. For those cases where the plots of F(n, u) vs. u will not fit the three cases described in Table I, it should still be possible to obtain an analytical expression for F(n, u) which is different from those in Table I. This expression for F (n, u) could then be used to obtain an equation in s using procedures described in the text (see Equations 39 and 44). Equation 39 would then be used to obtain the desired Laplace transform. 

Analysis of Mixed Associations from Conventional Sedimentation Equilibrium Experiments. In these experiments one measures a quantity Mieq (14, 28) instead of Mweq. The basic sedimentation equilibrium equation for each reactant is... 

Analysis by the Archibald Method or by Sedimentation Equilibrium Experiments at Different Speeds. Instead of using Mweq here, one uses Mwa, the apparent weight-average molecular weight. For the Archibald experiment one obtains Mwa,t at rm or r6 by the application of Equations 13-16. The extrapolation of Mwa>t to zero time gives Mwo. For sedimentation equilibrium experiments at different speeds, one can evaluate Mwa by two different methods here one uses either Equations 17 or 18. For a mixed association such as A + B AB, the basic sedimentation equilibrium equation can be written as... 

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