Mathematical properties of polydisperse systems, 2. Application to light scattering

The direct and the inverse problem of the light scattering from dilute polymer solutions is solved for GAUssian coils at the theta point. Theoretical scattering functions and their derivatives are analytically calculated for the general gamma distribution of molecular weights as a function of the non‐uniformity and the weight average molecular weight, and also for various ratios of the statistical segment length of the coil to the wave length of the scattered light. The asymptote and the tangent of P are obtained by analysing the operator in the ZIMM equation and their mutual position is compared in the angle range 150° to 180°. The scattering envelopes of microgel systems are analytically calculated and discussed. In order to obtain the molecular weight distribution (MWD) from a given ZIMM diagram of GAUssian coils at the theta point, the corresponding inverse problem is solved analytically, the necessary zero approximation of the segment length being taken from viscometric measurements. With the help of the presented method the MWD and the correct statistical segment length of the coil can theoretically be computed with any reasonable accuracy. However, the calculation shows that for practical use extremely high accuracy of the light scattering measurements is necessary.