Diffusion coefficients from stopped-flow gas chromatography

Summary Mutual diffusion coefficients of two gases A and B can be determined in an empty gas chromatographic column by letting component B enter at an intermediate position of the column and continuously flow through a part only of it, as a carrier gas. The other component A is injected in a small amount instantaneously at the closed end of the column with the detector placed at the other end. By repeatedly stopping and then restoring after a short time the flow of B, narrow extra peaks are produced on the chromatographic elution curve, owing to diffusion of A into B. An equation is derived giving the area under the curve of each stop-peak as a function of time of the corresponding stop. Plotting the experimental data according to this equation permits the determination of the diffusion coefficient of A into B. Some results obtained by this method show negligible variations with changes in the experimental parameters.     

Mono- and diboronates derived from tridentate ONO ligands and arylboronic acids

The syntheses of eight [4.3.0] heterobicyclic boronates containing a N → B coordinative bond are described. The monomeric compounds were prepared by reaction of arylboronic acids with a tridentate ligand having the ONO donor set of atoms. It was shown that substituents at the para-position of the B-phenyl moiety transmit electronic effects to the CN bond which in turn is polarized by formation of the N → B coordination bond. At the same time, related tridentate ligands were also reacted with 1,4-benzenediboronic acid in order to prepare benzene diboron complexes. The structure of this type of compounds was confirmed by X-ray analysis for one of the derivatives.     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

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.     

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.