S U M M A R Y :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. Z U S A M M E N F A S S U N G :Fur das direkte und das inverse Problem der Lichtstreuung von verdunnten Polymerlosungen GAussscher Knauel am Thetapunkt wird eine Losung gefunden. Dazu werden theoretische Streufunktionen und ihre Ableitungen fur die allgemeine Gammaverteilung des Molekulargewichts analytisch berechnet in Abhangigkeit von der Uneinheitlichkeit und vom Gewichtsmittel der Molekulargewichtsverteilung sowie fur verschiedene Verhaltnisse der statistischen Segmentlange des Knauels zur Wellenlange des Streulichtes. Aufgrund der Analyse des Operators in der ZIMMSChen Gleichung werden die Asymptote und die Tangente zu P: analytisch bestimmt und im Winkelbereich von 150" bis 180" miteinander verglichen. Streufunktionen von Mikrogelsystemen werden analytisch berechnet und diskutiert. Um die Molekulargewichtsverteilung (MGV) aus einem gegebenen ZIMM-Diagramm fur GAusssche Knauel am Thetapunkt zu berechnen, wird das zugehorige inverse Problem analytisch gelost, wobei die benotigtenullte Naherung fur die Segmentlange des Knauels aus viskosimetrischen Messungen genommen wird. Mit Hilfe dieser Methode konnen die MGV und die korrekte Segmentlange theoretisch mit beliebig (vernunftig) hoher Genauigkeit berechnet werden. Die Rechnung zeigt jedoch, daR fur die praktische Anwendung eine extrem hohe MeRgenauigkeit der Lichtstreuungsmessungen notig ist.

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 thermodynamic equilibrium at low temperatures of the column.

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. ZUSAMMENFASSUNG:I n der vorliegenden Arbeit wird mit Hilfe von exakten mathematischen Mitteln der Zusammenhang zwischen einer beliebigen polydispersen Eigenschaft und der Molekulargewichtsverteilung untersucht. Auf Grund des Superpositionsprinzips wurde eine allge-

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 retardation time in the gel. The influence of the gel mass of the column on its resolution is briefly investigated. Since the measurements show that the resolution of the PDC-column vanishes in the vicinity of the theta point, spreading phenomena in the column can be investigated by means of analysis of the corresponding PDC elution curves. The results give a basis for the numerical computation of the molecular weight distribution of narrowly distributed polystyrenes from PDC elution curves at sufficiently low column temperatures. The PDC-separation effect is opposite to that of gel permeation chromatography (GPC).

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