Network theory of the nonlinear behaviour of polymer melts. Simple shear flow

Summary The network model developed in a previous paper is applied to the simple shear flow of polymer melts. The constitutive equation obtained consists of two terms. One of them describes the stress due to the network strands which exist at the onset of the deformation, dissociate during the deformation and result in a single integral constitutive equation with a strain dependent damping function. The formulation of the damping function in invariant form seems to be almost impossible.The second normal stress differenceN ₂ of the model is not zero,but has negative values. According to our model this is a consequence of the deformation dependence of the disentanglement process. The theory is compared with experimental data for a LDPE melt. It is found that the model explains the main features of the shear flow behaviour of the LDPE melt investigated preciously.

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Zusammenfassung Das Netzwerk-Modell, das in einer vorangegangenen Arbeit entwickelt wurde, wird für die einfache Scherströmung von Polymerschelzen angewendet. Die abgeleitete rheologische Zustandsgleichung besteht aus zwei Gliedern. Das erste beschreibt die Spannung-Dehnung-Beziehung der Kettensegmente, die zu Beginn der Deformation existieren und während der Deformation aufgelöst werden. Es hat die Form der einfachen Integralbeziehung mit einer Gedächtnisfunktion. Es ist kaum möglich, die dabei erhaltene Gedächtnisfunktion als Funktion der Invarianten der der Tensoren darzustellen. Die zweite Normal-SpannungsdifferenzN ₂ des Modells ist nicht Null und hat einen negativen Wert. Dies ist nach unserem Modell eine Folge der Deformationsabhängigkeit des Entschlaufungsprozesses. Die Theorie wird mit dem experimentellen Daten für eine LDPE-Schmelze verglichen, wobei sich zeigt, daß das Modell die wesentlichen Merkmale des Scherverhaltens der LDPE-Schmelze gut erklärt.

     

On the configuration interaction method for singlet states

The direct CI method, which avoids explicit calculation of the Hamiltonian matrix, is presented in a new form. The method is linked with Davidson's algorithm for iterative evaluation of the ground state eigenvector. The viability of the method is indicated by the test calculations on water which are described.     

Enthalpies of mixing of binary and ternary mixtures containing diisopropylether,benzene and cyclohexane at 303.15 K

Enthalpies of mixing H have been measured for liquid binary mixtures of diisopropylether (DIPE)+benzene or cyclohexane and for liquid ternary mixtures diisopropylether+benzene+cyclohexane at 303.15 K and constant pressure using a C80 calorimeter. A Redlich-Kister type equation was used to correlate experimental results.     

Analysis of 19-norandrosterone in human urine by gas chromatography–isotope-dilution mass spectrometry: method adopted by LGC for participation in the Comité Consultatif pour la Quantité de Matière (CCQM) Pilot Study P68

The method used at LGC for analysis of “total” 19-norandrosterone (19-norandrosterone glucuronide plus “free” 19-norandrosterone) in urine for the Comité Consultatif pour la Quantité de Matière Pilot Study (CCQM-P68) is described. The analytical method used was a modified version of the method developed at the National Measurement Institute of Australia, which used a hydrolysis and derivatisation procedure first described by the German Sports University. This method is routinely used by World Anti-Doping Agency-accredited laboratories for sports drug testing. The main modifications made to the method were the use of 19-norandrosterone glucuronide as a calibration standard and 19-norandrosterone glucuronide-d4 as an isotopically labelled internal standard, and the use of a bench-top quadrupole gas chromatograph–mass spectrometer. The results produced by LGC (2.14 ± 0.15 ng g⁻¹ expanded uncertainty, coverage factor k = 2) were in excellent agreement with those from other participating national metrology institutes and thus further validates the exact-matching isotope-dilution mass spectrometric procedures used at LGC for a wide range of reference measurement applications, including measurement of ng g⁻¹ levels of steroids in a biological matrix.     

New Temperature Integral Approximate Formula for Non-isothermal Kinetic Analysis

A new approximate formula for temperature integral is proposed. The linear dependence of the new fomula on x has been established. Combining this linear dependence and integration-by-parts, new equation for the evaluation of kinetic parameters has been obtained from the above dependence. The validity of this equation has been tested with data from numerical calculating. And its deviation from the values calculated by Simpson's numerical integrating was discussed. Compared with several published approximate formulae, this new one is much superior to all other approximations and is the most suitable solution for the evaluation of kinetic parameters from TG experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Calculation of the proton affinities of polyfluorobenzenes and the activation energies for 1,2-hydrogen shifts in their carbocations

Isolated polyfluorobenzene (PFB) molecules and their protonated forms are investigated by the AM1 method with full geometry optimization. The proton affinities of PFB are estimated for different protonated positions. The proton affinity of PFB averaged over all isomers is shown to decrease monotonically as the number of fluorine atoms in the molecule increases. The relative populations of different isomers of arenonium ions (AI) formed by PFB protonation are determined. From the calculated data, the value of ⁺ for the F atom in theipso-position is estimated as 1.00. The activation energies of the 1,2-hydrogen shifts in AI are calculated. The dependences of the proton affinity and the activation energies of 1,2-hydrogen shifts on the number of halogen atoms are found to have distinct characters for PFB and polychlorobenzenes. The physical reasons for these difference are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1878–1882, November, 1993.     

Direct transformation of variational problems into Cauchy systems. I. Scalar-quadratic case

This series of papers addresses three interrelated problems: the solution of a variational minimization problem, the solution of integral equations, and the solution of an initial-valued system of integro-differential equations. It will be shown that a large class of minimization problems requires the solution of linear Fredholm integral equations. It has also been shown that the solution of a linear Fredholm integral equation is identical to the solution of a Cauchy system. In this paper, we bypass the Fredholm integral equations and show that the minimization problem directly implies a solution of a Cauchy system. This first paper in the series looks only at quadratic functionals and scalar functions.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-77-3383.     

Kinetic model ofCO oxidation on nonuniform surface analyzed regardingCOads spillover, 2. homotopic method. Effect ofm1 surface portion

The homotopic method has been used to analyze the kinetic model of three-stageCO oxidation on two nonuniform surface patches conjugated byCO ₂ spillover. Diagrams of steady states depending on the portion of surface patchm ₁ at various temperatures and pressure ratiosP(O ₂)/P(CO) have been constructed. The ratios of different type patches corresponding to the maximum overall reaction rate have been found.     

Conjugate-gradient method for computing the Moore-Penrose inverse and rank of a matrix

A conjugate-gradient method is developed for computing the Moore-Penrose generalized inverseA of a matrix and the associated projectors, by using the least-square characteristics of both the method and the inverseA . Two dual algorithms are introduced for computing the least-square and the minimum-norm generalized inverses, as well asA . It is shown that (i) these algorithms converge for any starting approximation; (ii) if they are started from the zero matrix, they converge toA ; and (iii) the trace of a sequence of approximations multiplied byA is a monotone increasing function converging to the rank ofA. A practical way of compensating the self-correcting feature in the computation ofA is devised by using the duality of the algorithms. Comparison with Ben-Israel's method is made through numerical examples. The conjugate-gradient method has an advantage over Ben-Israel's method.After having completed the present paper, the author received from Professor M. R. Hestenes his paper entitledPseudo Inverses and Conjugate Gradients. This paper treated the same subject and appeared in Communications of the ACM, Vol. 18, pp. 40–43, 1975.     

An intermediate spherical model of a ferromagnet

A one-parameter family of partition functions is considered which for zero value of the parameter reduces to the spherical model of a ferromagnet. The model for > 0 is closer to the usual discrete lattice spin model of a ferromagnet than is the spherical model. The first four terms in of the limiting value of the partition function are calculated above and below the critical temperature for arbitrary interactions using the saddle point method to calculate certain correlation functions for the spherical model. These calculations indicate that the critical temperature is independent of for small and certain interactions.Part of this research appeared in the author's doctoral thesis.⁽³⁾