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This paper presents an analytical calculation of the relaxation and retardation spectra for narrow distribution polymers, binary blends and whole polymers. The retardation spectrum exhibits two peaks, one independent of molecular weight (transition region), and one shifting toward long times as the molecular weight increases (terminal region). The relaxation spectrum derived from this analytical retardation spectrum is shown to have a sharp cut-off at large times, this cutoff being smoothened when using conventional approximation methods to deriveH(τ) from the experimental data. — The analytical retardation spectra of integrated relaxation spectra (from the retardation spectra) should be useful in the tests of constitutive equations.

This article describes work with model polymers to explore the effects of long branches on polyethylene melt rheology. Dynamic moduli were measured at two or more temperatures on melts, blends, and solutions of linear (L) and star (B) hydrogenated polybutadiene (HPB). Enhancement factor Γ and temperature coefficient (flow activation energy Ea) were determined from viscosity data and correlated with arm molecular weight Mb and volume fraction of the star component Φ. As in other species, Γ for a given branch point functionality is roughly an exponential function of Φ11/6Mb in entangled melts and solutions. In contrast with other species, however, (Ea)B and (Ea)L are different; (Ea)B – (Ea)L is directly proportional to ΦMb, and the degree of thermorheological complexity varies primarily with (Ea)B – (Ea)L. In blends with linear HPB of comparable viscosity, Γ for the star component remains essentially constant, and (Ea)B – (Ea)L is directly proportional to the volume fraction of the star component.

The method of BAMFORD and TOMPA has been used to investigate two statistical problems in free radical polymerization, namely the broadening of molecular weight distribution by long chain branching, and the formation of gel in diene polymerizations. Pn and Pw as functions of conversion were calculated rigorously for the case of branching by polymer transfer and terminal double bond polymerization. The results of some careful experiments on vinyl acetate polymerization, recently published by STEIN, were analyzed, and excellent agreement between theory and experiment was found. The value obtained for the polymer transfer constant, Cp = 1.2·10−4, was somewhat lower than that reported by STEIN. A slight extension of the BAMFORD-TOMPA theory was used to relate the gel-point conversion in diene polymerizations to the degree of cross-linking. Appreciable differences from the predictions of random cross-linking theory are found only when gelation occurs at high conversion. Die Methode von BAMFORD und TOMPA wurde angewandt, um zwei statistische Probleme der Radikalpolymerisation zu untersuchen, namlich die Verbreiterung der Molekulargewichtsverteilung durch Kettenverzweigung und die Gelbildung bei Dienpolymerisationen. Fur den Fall von Verzweigungen durch Polymerubertragungen und Polymerisation der endstandigen Doppelbindungen wurden Pn und Pw als Funktionen des Umsatzes genau berechnet. Die Ergebnisse von einigen sorgfaltig ausgefuhrten Experimenten bei der Vinylacetat-Polymerisation, kurzlich von STEIN veroffentlicht, wurden analysiert, und eine gute Ubereinstimmung der Experimente mit der Theorie wurde festgestellt. Der fur die Polymer-Ubertragungskonstante gefundene Wert, Cp = 1,2·10−4, war etwas niedriger als der von STEIN angegebene. Eine geringe Erweiterung der BAMFORD-TOMPA-Theorie wurde herangezogen, um den Gelpunkt-Umsatz bei der Dienpolymerisation mit dem Grad der Verknupfung zu verbinden. Beachtliche Unterschiede gegenuber den Voraussagen der Zufallverknupfungs-Theorie wurden nur gefunden, wenn die Gelbildung bei hohem Umsatz stattfindet.

The study of the viscoelastic properties of polymer solutions has a double interest: from a theoretical point of view, the variations of the elastic (limiting compliance, plateau modulus) and viscous (zero-shear viscosity) parameters as a function of polymer concentration, are a definite test for the various theories on the relaxation and diffusion of long and flexible chains. From a practical point of view, such studies will allow to better understand the effects of the addition of plastifiers on the melt rheology of commercial polymers (viscosity, die swell, glass transition temperatures, etc...).