Approach to generalization of concentration dependence of zero-shear viscosity in polymer solutions

The possibility of constructing zero-shear viscosity master curves valid for the entire range of concentration for a large number of polymer solutions in different solvents independent of molecular weight and the nature of the solvent is considered. The results obtained show that the parameters characterizing the individual macromolecular chain., viz., the dimensions of the polymer coil and the rheological effectiveness of segmental interactions, are significant in determining the viscosity of polymer solutions from very dilute to highly concentrated ones. The relation between the parameter of rheological interaction and characteristics of polymer solutions such as the flexibility of the polymer chain and the Flory-Huggins parameter is discussed. This permits one to separate the influence of the energy and entropy factors on the concentration dependence of zero-shear viscosity.     

The green function of the stationary schrödinger equation for a particle in a uniform magnetic field

The explicit expression for the Green function of the stationary two-dimensional Schrödinger equation for a particle in a uniform magnetic field is obtained in terms of the Whittaker function.     

Most important features of pre-stationary deformation regimes and stress relaxation of polymers in the viscous state

Summary In the prestationary deformation regime relaxation times decrease both before and after passage through the ultimate shear strength, i. e., independent of whether the stresses at which relaxation began were growing or decreasing.The relaxation properties of the system change the most intensively before the ultimate shear strength is passed. This occurs at the deformation where the viscosity and the elastic modulus reach their maximum values.The viscosity grows during relaxation. Increasing the temperature intensifies recovery of the broken down structure. Retarded recovery of the strength properties of the polymer correlate with retardation of reestablishment of the initial structure, characterized by attainment of the initial Newtonian viscosity and retardation of high-elastic recovery.By resolving deformations into their reversible and irreversible components it was found possible to estimate the amount of work done in destroying the initial structure network of the polymer when passing from a state of rest to steady flow. The work of structure breakdown increases markedly with increasing shear rate, and its rise is related linearly to development of the viscosity anomaly.

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Zusammenfassung In dem vorstationären Deformationsgebiet fallen die Relaxationszeiten sowohl vor als auch nach dem Durchwandern der Grenzschubspannung ab, d. h. sie sind unabhängig davon, ob die Spannungen, bei denen die Relaxation begann, sich vergrößerten oder abnahmen.Die Relaxationseigenschaften des Systems ändern sich am stärksten, bevor die Grenzschubspannung durchwandert wird. Dieser Zustand tritt bei der Deformation auf, bei welcher die Viskosität und der Elastizitätsmodul ihre Maximalwerte erreichen. Die Viskosität wächst während der Relaxation an. Ein Ansteigen der Temperatur verstärkt die Erholung der zerstörten Struktur. Die verzögerte Erholung der Pestigkeitseigenschaften des Polymeren ist korreliert mit der Verzögerung der Wiederherstellung der Ausgangsstruktur, die charakterisiert ist durch das Erreichen der ursprünglichen newtonschen Viskosität und der Verzögerung der elastischen Erholung.Durch die Zerlegung der Deformationen in ihre reversiblen und irreversiblen Anteile war es möglich, den Arbeitsanteil zur Zerstörung des ursprünglichen Struktur-Netzwerkes des Polymeren beim Übergang vom Ruhezustand zum stationären Fließen abzuschätzen. Die Arbeit zum Strukturzusammenbruch steigt mit wachsender Schergeschwindigkeit an, und der Anstieg ist linear mit der Ausbildung der Viskositätsanomalie verbunden.

     

Relaxation of normal stresses in flowing polymer systems

The authors discuss the relaxation of the first difference of the normal stresses σ(t) after cessation of steady shear flow in viscoelastic polymer systems in the linear region of their mechanical behavior. They show that this phenomenon is associated with a group of relaxation characteristics of the material. they discuss a method of calculating the relaxation spectrum from σ(t); the validity of this suggested method is verified experimentally.     

Integrals of the motion,green functions,and coherent states of dynamical systems

The connection between the integrals of the motion of a quantum system and its Green function is established. The Green function is shown to be the eigenfunction of the integrals of the motion which describe initial points of the system trajectory in the phase space of average coordinates and moments. The explicit expressions for the Green functions of theN-dimensional system with the Hamiltonian which is the most general quadratic form of coordinates and momenta with time-dependent coefficients is obtained in coordinate, momentum, and coherent states representations. The Green functions of the nonstationary singular oscillator and of the stationary Schrödinger equation are also obtained.     

Viscoelastic properties of butadiene-styrene block copolymers

Summary The viscous properties of SBS block copolymers (of Cariflex TR-1102 in this work) have been determined with the rate of shear being varied by 10⁸ times. It has been shown that in the region of low shear rates the polymer behaves as a structured highly concentrated disperse system which exhibits sharply pronounced thixotropy. In the region of high shear rates, the viscous properties of the polybutadiene matrix are of decisive importance. At low values of shear stress the compliance of the SBS block copolymer exceeds that of the polybutadiene matrix almost by a decimal order.At high shear stresses, just as in the case of viscous properties, the elastic behaviour of the SBS block copolymer approaches that of the polybutadiene matrix. Measurements of the dynamic characteristics at frequencies, which vary by a million times, most spectacularly point to the specificity of the viscoelastic properties over a wide temperature range. Under conditions of low temperatures the SBS block copolymer behaves as a rubber, while at temperatures above the glass transition temperature of polystyrene, at low loading intensities (low amplitudes and small deformations) the block copolymer shows low fluidity. This is most clearly seen from the frequency dependence of the loss modulus, especially in comparison with the relation typical of polybutadiene.

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Zusammenfassung Die viskosen Eigenschaften von SBS-Block-Copolymeren (hier Cariflex TR-1102) werden in einem Bereich von acht Zehnerpotenzen der Schergeschwindigkeit untersucht. Es wird gezeigt, daß im Bereich niedriger Schergeschwindigkeiten das Polymer sich wie ein strukturiertes hochkonzentriertes disperses System verhält, das eine ausgeprägte Thixotropie besitzt. Im Bereich hoher Schergeschwindigkeiten sind dagegen die viskosen Eigenschaften der Polybutadien-Matrix von entscheidender Bedeutung. Bei niedrigen Schubspannungswerten übersteigt die Komplianz des SBS-Block-Copolymeren diejenige der Polybutadien-Matrix höchstens um etwa 10%.Bei hohen Schubspannungen nähert sich das elastische Verhalten analog wie bei den viskosen Eigenschaften demjenigen der Polybutadien-Matrix an. Die Messung der dynamischen Charakteristiken über einem Frequenzbereich von sechs Zehnerpotenzen lassen die spezifischen viskoelastischen Eigenschaften in einem weiten Temperaturbereich sehr deutlich erkennen. Bei tiefen Temperaturen verhält sich das Polymer wie ein Gummi, während bei Temperaturen oberhalb der Glasübergangstemperatur des Polystyrols unter geringer Belastung (d.h. kleinen Amplituden bzw. Deformationen) das Polymer eine geringe Fluidität zeigt. Dies erkennt man am deutlichsten an der Frequenzabhängigkeit des Verlustmoduls, insbesondere durch Vergleich mit derjenigen bei Polybutadien.

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With 6 figures     

Suppression of superluminous precursors in high-power backward Raman amplifiers

The very promising scheme for producing ultrapowerful laser pulses through Raman backscattering of pump lasers in plasmas can be jeopardized by superluminous precursors. Growing from the leading part of the Raman pumped seed pulse, these precursors can disturb the plasma and the pump ahead of the pumped pulse. These ruinous effects, however, might be averted by a detuning, large enough to suppress the precursors, yet small enough to allow the desired backscatter effect.