Determination of molecular weight distribution by applying a modified regularization technique

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Abstract
Determination of a molecular weight distribution from equilibrium sedimentation has been significantly improved by incorporating linear programming into Tikhonov's regularization method. The conventional way of computation failed because the Fujita equations which relate the distribution function f(m) to the experimental data are improperly posed problems in the Hadamard sense. Their inverse solution necessary for determination of a molecular weight distribution is unstable. As a result such a solution leads to an erratic curve instead of the desired f(m). This erratic behavior is significantly improved by applying Tikhonov's regularization method. However, a certain amount of oscillation in the f(m) curve still remains uncorrected. Linear programming, which was originally introduced to eliminate undesired negative f(m) values, also served as an additional smoothing factor and improved the calculated f(m) curve. Good results were obtained in cases of a unimodal, a bimodal, and a trimodal distribution.

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