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.

     

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.     

NMR investigation on the conformational properties of N-[2-pyridyl-N-oxide]-amino derivatives

The proton NMR spectra of N-[2-pyridyl-N-oxide]-derivatives of primary and secondary ethylamines, containing a substituent R on the C atom bearing the amino function, have been completely analysed in terms of the fundamental NMR parameters. The preferred conformations of the compounds investigated were established by the indications from NOE experiments as well as: (1) the long range coupling across the five bond between the aminic hydrogen and the proton in 4-position of the pyridine-N-oxide ring (⁵J_m^H,NH ～ 0·5 c/s), (2) the value of the vicinal coupling constant in the fragment CHNH (³J_NHCH ～ 7–9 c/s), (3) the large deshielding (Δτ ～ 1–1·5 ppm) observed for the resonance position of the proton on the asymmetric C atom in secondary amine derivatives with respect to the corresponding primary ones, and (4) the diamagnetic shielding produced on protons in position 3 and 4 of the pyridine-N-oxide ring by different aromatic groups introduced in the R substituent.The NMR data confirmed the preferred rotamers previously suggested on the basis of ORD and CD measurements.     

Viscosity of aqueous solutions of polysaccharides and hydrophobically modified polysaccharides: Application of Fedors equation

Amphiphilic polysaccharides have been obtained by hydrophobic modification of a neutral bacterial polysaccharide, dextran. Various amounts and types of aliphatic hydrocarbon groups have been attached to dextran.The solution behaviour of unmodified dextran samples and amphiphilic dextran derivatives is characterized by viscometric measurements. The overall viscosity behaviour of unmodified polysaccharides is described up to C × [η] = 3, using the equation of Fedors [Fedors RF. Polymer 1979;20:225] which involves only a concentration parameter. The latter is shown to depend on the hydrodynamic volume of the macromolecules in solution.The equation of Fedors is shown to conveniently estimate the viscosity behaviour of amphiphilic dextran derivatives up to C × [η] = 1. The interdependence between Fedors parameter and other viscometric characteristics (intrinsic viscosity, Huggins coefficient) is evidenced. These results are extended to the data of other authors.     

Monolayer adsorption isotherms and a disordered medium model

A model of disordered medium is proposed to describe the monolayer adsorption isotherm on heterogeneous surfaces. The model is based on the premise that adsorption medium consists of separate regions in each of which there is a permanent local equilibrium constant, the character of the changes of which is determined by the disorder parameter of the medium. __________ Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 42, No. 3, pp. 189–193, May–June, 2006.     

Application of coset representations to the construction of symmetry adapted functions

Summary A coset representation (G(/G _i )), which is defined algebraically by a coset decomposition of a finite groupG by its subgroupG _i , is shown to be a method for the decomposition of a regular body into its point group orbits. This proof also shows that each member of theG(/G _i ) orbit belongs to theG _i site-symmetry. In addition, a general equation concerning the multiplicities of such coset representations is derived and shown to involve Brester's equations and thek-value equations of framework groups as special cases. The relationship of the coset representation and the site-symmetry affords a general procedure for obtaining symmetry adapted functions.     

Necessary and sufficient conditions for the existence of positive solutions to algebraic Riccati equations with indefinite quadratic term

Necessary and sufficient conditions are established in this paper for the existence of positive- and/or negative-definite solutions to the algebraic Riccati equation with indefinite coefficient. An iterative procedure is also given for computing such a solution.Project supported by the National Science Foundation of China and by the special program of the State Education Commission of China under grant 9033507.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Significance of Non-isothermal Kinetic Data. A statistical study

Arrhenius parameters values, in non-isothermal kinetic vaporisation processes for a series of compounds with related structures, have been calculated. This was made using a method of calculation that allows to find the most probable vaporisation mechanisms. According to this method DTG curves were compared with some theoretical ones reported in literature, whose shape results to be only a function of the mechanisms. In this way the choice of the mathematical functions which can be inserted in the kinetic equations, was influenced by the shape of the DTG plots and other thermal analysis signals thus allowing to choose the most probable mechanisms. The kinetic parameters derived from these mechanisms were compared, using statistical analysis, with those obtained from another method of calculation based on ‘a priori’ vaporisation mechanism chosen for the investigated liquid–gas transition. The standard deviations of the slope and of the intercept, together with the standard deviation and the square correlation coefficient (r ²) of the linear regression equations related to the mechanisms of the two methods were calculated. Student t-test, Fisher F-test, confidence intervals (c.i.) and residuals valueswere also given. Statistical analysis shows that the mechanisms obtained with the former method (diffusive and geometrical models) and the related Arrhenius parameters result to be more significant (in terms of probability) than the corresponding quantities of the latter for which a first-order model was chosen. This revised version was published online in August 2006 with corrections to the Cover Date.     

激光通道传输热特性对远场光束质量的影响

 通过仿真计算分析了激光在光束控制系统通道内传输所产生的热效应及其对远场光束质量的影响。激光传播由近轴波方程描述，用快速傅里叶变换技术求解；激光热效应引起的流场密度变化采用完全Navier-Stokes方程计算。计算给出了不同波长、不同吸收系数条件下的远场光斑情况。计算结果表明，在典型的工作条件和状态下，较高能量激光在光束控制系统通道内产生的热效应影响不容忽视，它会明显降低远场目标处的能量集中度，增大光斑的发散。