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 …

The molecular weight distribution (MWD) of a high polymer is calculated from a weakly perturbed Zimm-plot of the classical light scattering on dilute solutions of Gaussian polymer coils (theta state). A typical Zimm-plot is simulated corresponding to the measurements of high accuracy as would be obtained by using the laser photometer described by Hack and Meyerhoff. The accuracy as published by these authors for small dissymmetries is used. Two numerical methods for calculating the MWD are briefly described and tested, both using an empirical formula for the Laplace image of the calculated MWD.

The dynamical region of the measured calibration curves is investigated using the results of the theory published previously. The kinetic constants of the flow-equilibrium are calculated from the measurements according to two different models for a spontaneous polymer diffusion of the transported P-mer from sol into gel of the Phase Distribution Chromatography (PDC)-column. The corresponding lateral concentration profiles in the gel are found by analytical integration of Fick's second law under the corresponding boundaries. An energetic model of this flow-equilibrium is stated, giving the activation enthalpy and -entropy of the rediffusion of the polymer from gel into sol after some retarda…

Konstruktion eines vollautomatischen präzisionschromatographen auf der basis der phasendistributionschromatographie (PDC)

The design of a fully automatized chromatograph based on Phase Distribution Chromatography (PDC) is presented and some of the most important results of the measurements shown. PDC represents a dynamical phase separation as column method: the separation of the polymer components in a PDC-column is based on thermodynamic-kinetical interactions of the mobile phase (the polymer to be analyzed) below the theta temperature of the system by a gel of the same high polymer situated on the surface of small glass beads. The sigmoidal shape of the measured PDC calibration curves can be explained by introducing a dynamical flow-equilibrium in the system sol/gel which highly differs from the thermodynami…

In the present paper the connection between an arbitrary polydisperse property and the molecular weight distribution is investigated using exact mathematical methods. On the basis of the superposition principle a general equation is derived which can be applied e.g. to the polydispersity problems connected with the Gel Permeation Chromatography, to the light scattering from dilute solutions of high polymers, or the ultracentrifuge. From this point of view, each of these phenomena is described by help of a linear operator with a special kernel, the analytical or numerical inversion of the operator yielding the molecular weight distribution of the system by help of an uniform algorithm. In de…

Phase distribution chromatography (PDC) is demonstrated to be a powerful method for the correct determination of narrow molecular weight distributions. This is shown by comparing the molecular weight distributions (MWD) of polystyrenes obtained from PDC measurements with those obtained by Baker-Williams fractionation and by gel permeation chromatography. Four problems are formulated and analyzed which are closely connected with the calculation of the MWD from a measured PDC-elution curve at temperatures below the theta point of the system. Thus, the theory of PDC outlined previously is tested.

A phenomenological theory of the Phase Distribution Chromatography (PDC)-separation effect is outlined and a theoretical equation for the measured PDC-calibration curves is given. Assuming a reversible-thermodynamical equilibrium in the polystyrene-PDC-column, only a relatively small part of the measured PDC-calibration curves could be explained: namely those running below their tangents. In order to explain the whole sigmoidal shape of the experimental curves, a theory of steady state in the system sol/gel was developed assuming deformation of the polymer coil near the gel front due to the stress related to the velocity gradient. The resulting dynamical flow-equilibrium differs highly from…

Die Bestimmung der Molekulargewichtsverteilung von nichtkristallisierenden Polymeren mit dem Elektronenmikroskop, 6. Fehlerkorrektur der experimentellen Zahlenverteilungsfunktion

A mathematical treatment is described, by means of which the effect of the measuring errors on the number molecular weight distribution of polymers, as obtained with an electron microscope (EM), can be eliminated. It is shown, that the difference in the nonuniformities of the measured and the corrected distribution would be negligible only in the case of samples with high average degrees of polymerization and sufficiently broad distributions. Otherwise differences of 10% or more can be found, depending on the size of the actual measuring error. This is shown by means of four practical examples. For a practical application the measuring error may not exceed some critical value, which, though…

The molecular weight distribution (MWD) of a high polymer is calculated from a weakly perturbed Zimm-plot of the classical light scattering on dilute solutions of Gaussian polymer coils (theta state). A typical Zimm-plot is simulated corresponding to the measurements of high accuracy as would be obtained by using the laser photometer described by Hack and Meyerhoff. The accuracy as published by these authors for small dissymmetries is used. Two inversion procedures are described in detail and tested, both of them avoiding the use of an empirical formula for the Laplace image of the calculated MWD. A complete numerical analysis of the results is given. The results are compared with those of …