Inclusion Complexes of Cyclodextrins with Tetrakis(4-carboxyphenyl)porphyrin and Tetrakis(4-sulfonatophenyl)porphyrin in Aqueous Solutions

In neutral and alkaline solutions, tetrakis(4-carboxyphenyl)porphyrin (TCPP) and tetrakis(4-sulfonatophenyl)porphyrin (TSPP) form 1:1 and 2:1 host–guest inclusion complexes with -cyclodextrin (-CD), -cyclodextrin (-CD), and 6-deoxy-6-diethylamino--CD (DEA--CD), except for DEA--CD in alkaline solution. On the other hand, TCPP and TSPP form only 1:1 inclusion complexes with 6-deoxy-6-dihexylamino--CD (DHA--CD). The limited solubilities of DEA--CD in alkaline solution and DHA--CD are likely responsible for no observation of the 2:1 inclusion complex containing DEA--CD in alkaline solution and that containing DHA--CD. The equilibrium constants (Ks) of TCPP and TSPP for the formation of the inclusion complexes have been estimated from the absorption and/or fluorescence intensity changes in neutral and alkaline solutions. The K₂ values, which are the equilibrium constants for the formation of the 2:1 host–guest inclusion complex from the 1:1 inclusion complex, are about one tenth the corresponding K₁ values, except for the -CD–TSPP system in alkaline solution. In neutral solution, where DEA--CD and DHA--CD are in protonated forms, the electrostatic force operates between DEA--CD (DHA--CD) and TCPP (TSPP), leading to the greater K values than those in alkaline solution, where DEA--CD and DHA--CD exist as neutral species.     

The solid-state structure of (+)-(i)-menthyl 2-formamido-4, 4,4-trifluorobutanoate and the hydrogenation of the 2-butenoate precursor

Hydrogenation ofZ-(–)-(1R, 3R, 4S)-menthyl 2-formamido-4,4,4-trifluoro-2-butenoate catalyzed by Pd/C was performed at atmospheric pressure to yield a mixture of (2R, 1R, 3R, 4S)- and (2S, 1R, 3R, 4S)-menthyl 2-formamido-4,4,4-trifluorobutanoate diastereomers in a 5545 ratio, respectively. Repeated fractional crystallization from ethyl acetate and vapor diffusion of petroleum ether afforded (+)–(2S, 1R, 3R, 4S)-menthyl 2-formamido-4,4,4-trifluorobutanoate as clear colorless, crystalline prisms which were subjected to single-crystal X-ray diffraction analysis. The crystals belong to the orthorhombic system P2₁2₁2₁, and at 213 K:a=5.054(1),b= 10.000(2),c=32.707(1) Å,V=1652.9(4) ų,Z=4,R(F)=0.040, andR _w (F)=0.037. The finding of the (2S)-configuration for the formamido-acid portion of the (+)-ester enabled the configurational assignment of the asymmetric hydrogenation products ofZ-methyl 2-formamido-4, 4,4-trifluoro-2-butenoate catalyzed by chiral diphosphine/rhodium(I) complexes.     

Relativistic perturbation theory of molecular structure

Summary The recently developed relativistic double perturbation theory is extended to handle relativistic changes of molecular structure more easily. This is achieved by simple coordinate scalings. Accurate higher order mixed perturbation energies for H ₂ ⁺ are calculated. The relativistic changes of bond energy,DE, of bond length,R _e , and especially of force constant,k, and of anharmonicity,a, are large, up to 100%·(Z/c)². The dominant contributions tok anda are due to the indirect change of the nonrelativistick anda connected with the relativistic change of bond length. Accordingly the relativistic changes obey Badger's and Gordy's rules (–RDEk).Dedicated to Prof. Klaus Ruedenberg in appreciation of his fundamental contributions to both formal theory and physical explanations in quantum chemistry     

Kinetics and mechanism of the hydrolysis of sodium carboxymethylcellulose (Na-CMC) by a cellulase complex

TheSomogyi-Nelson colorimetric method is applied in a new manner more suitable for evaluating the kinetics of the enzyme hydrolysis of sodium carboxymethylcellulose (Na-CMC) catalyzed by the cellulase complex. By means of selective inhibition of a chosen enzyme from the cellulase complex it became possible to trace the effect of the other enzymes included in its composition.

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Kinetik und Mechanismus der Hydrolyse von Natriumcarboxymethylcellulose (Na-CMC) durch einen Cellulase-Komplex

Zusammenfassung Die kolorimetrische Methode nachSomogyi undNelson wird nach einem neuen Verfahren zur Verfolgung der Kinetik der hydrolytischen Spaltung von Natriumcarboxymethylcellulose (Na-CMC), katalysiert durch den Cellulase-Komplex, angewandt. Durch selektive Inhibierung eines bestimmten Enzyms des Cellulase-Komplexes kann man die Wirkung der anderen zu seiner gesamten Zusammensetzung gehörenden Enzyme verfolgen.

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Symbols Used E enzyme (E—cellulase;E—exo-cellobiohydrolase;E—-glucosidase) - [E] _w weight concentration of enzymeE - S substrate (Na-CMC—sodium carboxymethylcellulose) - [S]₀ weight concentration of substrateS - I inhibitor (I—lactose;I—calcium chloride;I—condurrite-B-epoxide) - P product (P—oligosaccharides;P—cellobiose;P—D-glucose) - P end product (K , K , K ) - DP degree of polymerization - DS degree of substitution - ES enzyme-substrate complex (E S, E S, E S) - EP enzyme-product complex (E P, E P) - EI enzyme-inhibitor complex (E I, E I, E I) - M _s molecular mass of substrateS - K _s substrate constant (K _s , K _s , K _s ) - K _I inhibitor constant (K _I , K _I , K _I ) - K _m Michaelis-Menten constant - k ₊₁,k ₊₂ (k ₊₂ ,k ₊₂ ,k ₊₂ ) forward rate constants - k _–1 reverse rate constant - ₀ initial rate of reaction - V maximal reaction rate - A change in absorbance - molar absorption coefficient - wavelength Herrn Prof. Dr.Hans Tuppy zum 60. Geburtstag herzlichst gewidmet.     

The synthesis and structure of the [2.2]paracyclophane cluster Ru6C(CO)13(μ 3-η 2:η 2:η 2-C16H16)(PPh3) and a study of the 1H-n.m.r. spectra of [2.2]paracyclophane and benzene clusters

Summary The [2.2]paracyclophane cluster, Ru₆C(CO)₁₄( ₃- ^{2 2 2}-C₁₆H₁₆) (1), undergoes reaction with Me₃NO and triphenylphosphine to yield Ru₆C(CO)₁₃( ₃- ^{2 2 2}-C₁₆H₁₆)(PPh₃) (2), which may also be produced from (1) by thermolysis with PPh₃ in THF. Compound (2) has been fully characterized in solution by spectroscopy and in the solid state by a single crystal X-ray diffraction analysis at 277 K, and its structure is compared with that of the parent cluster, (1). Using the same synthetic procedures, the tricyclohexylphosphine analogue, Ru₆C(CO)₁₃( ₃- ^{2 2 2}-C₁₆H₁₆)(PCy₃) (3), has also been prepared and characterized spectroscopically. A comparison of the chemical shifts of the 577-01 protons in the ¹H-n.m.r. spectra of compounds (1)–(3) together with a variety of other [2.2]paracyclophane and benzene clusters has been made.     

The kinetic energy components of LCAO-molecular orbitals: A comment on the “Electron-in-a-Box”-“LCAO-MO-Model” analogy

In many textbooks attention is drawn to the close analogy that seems to exist between the Electron-in-a-Box-wave functions _n and their LCAO-MO counterparts _J (J = n) for the movement of an electron in a -system. It is often implied that the wave lengths of _n and of _J (J = n) which satisfy to a high degree the relation =, have the same physical meaning. It is shown that this is not the case. for a linear system (e.g. a one-dimensional Electron-in-a-Box-model) is directly connected with the momentum of the electron and therefore with its kinetic energy according to the deBroglie relation. However, there is no such simple relationship between A and the corresponding kinetic energy component in LCAO-MO's _J . (The necessary two-center kinetic energy integrals have been computed for 1s-type atomic orbitals.)

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Zusammenfassung In vielen elementaren Textbüchern wird die Aufmerksamkeit auf die scheinbar enge Verwandtschaft hingelenkt, die zwischen den Wellenfunktionen _n für ein Electron-in-a-Box-Modell und den entsprechenden LCAO-MOs _J (J=n) für die Bewegung eines Elektrons in einem -System besteht. Unter anderem wird oft implizit angenommen, daß die Wellenlängen der Funktion _n und von _J (J=n), die weitgehend der Bedingung = genügen, die gleiche physikalische Bedeutung haben. In dieser Arbeit wird gezeigt, daß dies nicht der Fall ist. Für ein lineares System (z. B. ein eindimensionales Electron-in-a-Box-Modell) ist über die deBroglie'sche Beziehung direkt mit dem Impuls und damit mit der kinetischen Energie des Elektrons verknüpft. Im Gegensatz dazu existiert keine einfache Beziehung zwischen und der entsprechenden Komponenten der kinetischen Energie in einem LCAO-MO _J . (Die notwendigen Zweizentrenintegrale der kinetischen Energie wurden für Atomorbitale vom 1s-Typus berechnet.)

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Résumé Dans les textes élémentaires de chimie théorique on attire souvent l'attention sur l'analogie qui semble exister entre les fonctions d'onde _n pour un modèle «Electron-in-a-Box» et les fonctions correspondantes LCAO-MO _J (J=n) décrivant le mouvement d'un électron dans un système . En particulier cette comparaison implique que les «longueurs d'onde» de _n et de _J (J=n), qui satisfont pratiquement la relation =, ont la même signification physique. Dans ce travail on montre, que ceci n'est pas le cas. Pour un système linéaire (c.à.d. un modèle linéaire du type «Electron-in-a-Box») est reliée directement à la quantité de mouvement et par là à l'énergie cinétique, par la relation de deBroglie. Par contre on ne trouve pas une dépendance analogue entre et la composante correspondante de l'énergie cinétique dans une orbitale moléculaire LCAO _J. (Les intégrales bicentriques pour les composantes d'énergie cinétique nécessaires à ce calcul ont été déterminées pour des orbitales atomiques du type 1s.)

     

σ-π separation: Excited H2 as a model system

The low-lying states of H₂ consist of one core () and one valence () electron and afford a direct evaluation of intershell - interaction. After resolution of the electronic energy into only, only, and - parts, it is shown that an electronic change in this model system is due solely to a change in the electrons. Simple Hückel theory is examined. If the molecular core is represented properly, regardless of the wave function the calculated and parameters are in reasonable agreement with the empirical parameters. This agreement appears to be due to a fortuitous cancellation of energy contributions.

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Zusammenfassung Die niedrig liegenden -Zustände des H₂ bestehen aus einem Rumpfelektron und einem Valenzelektron und ermöglichen eine direkte Auswertung der --Wechselwirkung zwischen zwei Schalen. Nach der Zerlegung der elektronischen Energie in -,- und --Anteile wird gezeigt, daß eine elektronische Veränderung in diesem Modellsystem nur auf eine Veränderung des -Elektronenanteils zurückgeht. Die einfache Hückeltheorie wird untersucht. Wenn der Molekülrumpf geeignet dargestellt wird, so sind, unabhängig von der -Wellenfunktion, die berechneten Parameter und in guter Übereinstimmung mit den empirischen Parametern. Diese Übereinstimmung scheint auf eine starke Auslöschung von Energieanteilen zurückzugehen.

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Résumé Les états inférieurs de H₂ consistent en un électron de coeur () et un électron de valence () et fournissent une évaluation directe de l'interaction entre couches -. Après expression de l'énergie électronique en parties , et -, on montre qu'une modification électronique de ce système modèle est due seulement à une modification des électrons . La théorie de Hückel simple est examinée. Si le coeur moléculaire est convenablement représenté, quelle que soit la fonction d'onde , les paramètres at calculés sont en accord raisonnable avec les paramètres empiriques. Cet accord apparaît comme le résultat d'une compensation fortuite de contributions énergétiques.

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Work performed in part under the auspices of the U.S. Atomic Energy Commission.

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Work aided by the U.S. Public Health Service via grant GM 08068.     

Indole derivatives

A series of -, -substituted -(3-indolyl) ketones was obtained by the reaction of indole with , -unsaturated ketones in the presence of perchloric acid.     

An empirical equation-of-state for solid-fluid interfacial free energies

The contact angle,, formed by a liquid on a solid surface in air depends on the solid-air ( _S ), liquid-air ( _L ) and solid-liquid ( _SL ) interfacial free energies, as described by Young's equation. Critical examination of reported contact angles for numerous liquids and solids leads to an empirical correlation between _sL and both _Y and _S . Combination of this correlation with Young's equation gives an empirical relation allowing calculation of _S from _L and Calculations made with these empirical relations agree well with estimations of _S obtained by the method of critical spreading, and are consistent with Young's equation.Founded and supported by F. Hoffmann-La Roche and Co., Limited Company, Basel, Switzerland.     

Vibrational isotope effect by the low rank perturbation method

Mathematical formalism of the low rank perturbation method (LRP) is applied to the vibrational isotope effect in the harmonic approximation. A pair of two n-atom isotopic molecules A and B which are identical except for isotopic substitutions at atomic sites is considered. Relations which express vibrational frequencies _k and normal modes _k of the perturbed isotopic molecule B in terms of the vibrational frequencies _i and normal modes _i of the unperturbed molecule A are derived. In these relations complete specification of the unperturbed normal modes _i is not required. Only amplitudes | _i of normal modes _i at sites affected by the isotopic substitution are needed.     

Prediction of the non-Newtonian viscosity and shear stability of polymer solutions

The structure-property relationships derived here permit the prediction of both the zero-shear viscosity ₀, as well as the shear rate dependent viscosity . Using this molecular modeling it is now possible to predict over the whole concentration range, independently of the molecular weight, polymer concentration and imposed shear rate. However, the widely accepted concept: dilute — concentrated, is insufficient. Moreover it is necessary to take five distinct states of solution into account if the viscous behavior of polymeric liquids is to be described satisfactorily. For non-homogeneous, semi-dilute (moderately concentrated) solutions the slope in the linear region of the flow curve (= must be standardized against the overlap parameterc · []. As with the ₀-M-c-relationship, a-M -c- relationship can now be formulated for the complete range of concentration and molecular weight. Furthermore, it is possible to predict the onset of shear induced degradation of polymeric liquids subjected to a laminar velocity field on the basis of molecular modeling. These theoretically obtained results lead to the previously made ad hoc conclusion (Kulicke, Porter [32]) that, experimentally, it is not possible to detect the second Newtonian region.Roman and Italian symbols a exponent of the Mark-Houwink relationship - b exponent of the third term of the ₀-M -c relationship - c concentration /g · cm^–3 - E number of entanglements per molecule - F(r) connector tension - f function - G _i ^A shear modulus; A indicates that it /Pa has been evaluated by a transient shear flow experiment; i is the shear rate to whichG ^A refers to - G storage modulus /Pa - G _p plateau modulus /Pa - H() relaxation spectrum /Pa - h shift factor (₀/_r) - K _H Huggins constant - K _b third constant of the ₀-M -c relationship - K constant of the Mark-Houwink relationship - M molecular weight /g · mol^–1 - M _e molecular weight between two /g · mol^–1 entanglement couplings - N number of segments per molecule - n slope in the power-law region of the flow curve - p p-th mode of the relaxation time spectrum - R gas constant /8.314 J·K^–1·mol^–1 - r direction vector - T temperature /K Greek symbols ß reduced shear rate - shear rate /s^–1 - shear viscosity /Pa·s - _s solvent viscosity /Pa·s - _sp specific viscosity - ₀ zero-shear viscosity /Pa·s - apparent viscosity at shear rate - reduced viscosity - viscosity of polymeric liquid in /Pa·s the second Newtonian region - [] intrinsic viscosity/cm³·g^–1 - screening length/m - /g·cm ^–3 density - relaxation time/s - ₀ experimentally derived relaxation time/s - angular frequency of oscillation Indices conc concentrated - corr slope corrected - cr critical - deg degradation - e entanglement - exp experimental - mod moderately concentrated/semi-dilute - n number average - p polymer - R Rouse - rep reptation - s solvent - sp specific - theo theoretical - weight average - relaxation time - o experimental or steady state - * critical - ** transition moderately conc. — conc. - + transition dilute — moderately cone. Paper presented at the 2nd bilateral U.S.-West German Polymer Symposium, Yountville, the 7th–11th September 1987.     

Relativistic virial theorem for diatomic molecules. Application to H 2 +

Summary The virial theorem for a molecule in the relativistic clamped-nuclei approximation is derived. The individual energy contributionsA (momentum energy),B (mass energy),T=A+B (kinetic energy) andV (potential energy) are expressed in terms ofE, E/R (derivate w.r.t. the nuclear coordinates) and the relativistic correction E/² (derivative w.r.t. Sommerfield's fine-structure constant ). IfE and E/R are known as functions of , then all individual energy terms are also known as functions of . As an example, numerical results for H ₂ ⁺ are presented. The relativistic and nonrelativistic potential energy curves and the paradoxical behavior of their different contributions are analyzed and interpreted in both the largeR and shortR ranges.Dedicated to Professor W. Kutzelnigg on the occasion of his 60th birthday     

The identification of small amounts of sugars by means of X-ray diffraction patterns

Summary The identification of small amounts of sugars by their X-ray powder diagrams is suggested as a most simple and practical method in routine analysis.It is especially valuable in working with minute amounts of material, and has proved very useful for the final identification of chromatographically-separated sugars.The characteristics of the powder diagrams of a number of monosaccharides of special interest to the physiological chemist are reported in detail. The substances thus investigated are- and-D-glucose and-glucose monohydrate,- and-D-galactose,- and-D-mannose,D-fructose,D-glucuronolactone,- and-D-glucosamine hydrochloride,- and-D-galactosamine (chondrosamine) hydrochloride,-L-fucose, andD-ribose. For various reasons arabinose, lyxose, and xylose have also been included.It is clear from the powder diagrams of the galactoses that the crystalstructure earlier ascribed to-galactose is that of-galactose.A single-crystal study of-glucosamine hydrochloride was carried out by theWeissenberg technique. The crystal-dimensions obtained agree with those earlier found byCox et al^{5, 7}.The optical rotation of chondrosamine hydrochloride was found to be [] _D ^20° = - 135° - 93° - 39°, the first value being considerably higher than that given for the-form byLevene. A method for the preparation of-mannose is described.

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Zusammenfassung Die Identifizierung kleiner Mengen verschiedener Zuckerarten mit Hilfe ihrer Röntgen-Pulverdiagramme wird als einfache und praktische Routinemethode vorgeschlagen.Diese Methode ist besonders wertvoll, wenn nur kleine Substanzmengen zur Verfügung stehen, und hat sich für die endgültige Identifizierung von chromatographisch getrennten Zuckern als sehr geeignet erwiesen.Die Einzelheiten der Pulverdiagramme folgender physiologisch-chemisch bedeutungsvoller Monosaccharide werden mitgeteilt:- und-D-Glukose und Glukosehydrat,- und-D-Galaktose,- und-D-Mannose,D-Fruktose,D-Glukuronolakton,- und-D-Glukosaminhydrochlorid,- und-D-Galaktosamin-(Chondrosamin)-hydrochlorid,-L-Fukose, dieD-Pentosen Arabinose, Lyxose, Ribose und Xylose.Aus den Pulverdiagrammen der Galaktosen geht deutlich hervor, daß die Krystallstruktur, die früher der-Galaktose zugeschrieben wurde, tatsächlich diejenige der-Form ist.Die Untersuchung eines Einzelkristalles von-Glukosaminhydrochlorid wurde nach derWeissenberg-Technik ausgeführt. Die erhaltenen Werte stimmen mit den früher vonCox und Mitarbeitern gefundenen überein.Die optische Drehung des Chondrosaminhydrochlorids wurde zu [] _D ^20° = + 135° + 93° + 39° gefunden. Der erstgenannte Wert ist größer als der entsprechende, vonLevene angegebene Drehungswert.Eine Methode zur Darstellung von-Mannose wird beschrieben.

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Résumé On propose une méthode de routine simple et pratique pour l'identification de petites quantités de divers sucres au moyen de leur diagramme de poudres aux rayons X. Cette méthode est particulièrement précieuse quand on n'a que de petites quantités de matière à sa disposition et elle s'est montrée très convenable pour l'identification finale de sucres séparés par chromatographie. Des particularités des diagrammes de poudres des monosaccharides suivants intéressent le chimiste physiologiste: et-D-glucose et hydrate de glucose, et-D-galactose, et-D-mannose, D-fructose,D-glucuronolactone, chlorhydrate d' et-D-glucosamine, chlorhydrate d' et-D-galactosamine (chondrosamine), l'-L-fucose, lesD-pentoses, l'arabinose, le lyxose, le ribose, le xylose. Des diagrammes de poudres des galactoses découle clairement le fait que la structure cristalline qui fut attribuée précédemment à l'-galactose est celle de la forme. L'expérience sur un cristal unique de chlorhydrate d'-glucosamine a été effectuée d'après la technique deWeissenberg. Les valeurs obtenues concordent avec celles trouvées précédemment parCox et ses collaborateurs. Le pouvoir rotatoire du chlorhydrate de chondrosamine a été trouvé égal à _D ²⁰ = + 135° + 93° + 39°. La première valeur est plus grande que celle donnée parLevene. On décrit une préparation de l'-mannose.

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With 3 figures.     

ESR and ENDOR Investigations on Various <Emphasis Type="Italic">Wurster</Emphasis>’s Radical Cations in Solution. Experimental Results,Theoretical <Emphasis Type="Italic">Ab Initio</Emphasis>, and DFT Calculations

Summary. ESR and ENDOR spectra are reported of several symmetrical substituted N,N,N,N-tetraalkyl-p-phenylenediamine radical cations in solution. Different N,N-alkyl substituted para-phenylenediamines, like the ethyl, n-propyl, and iso-propyl derivative are compared with the parent N,N,N,N-tetramethyl-p-phenylenediamine (Wursters Blue Cation). N,N,N,N-Tetrabenzyl-p-phenylenediamine, 1,4-dipyrrolidinylbenzene, and N,N-bis[4-(dimethylamino)phenyl]piperazine are additionally investigated. Experimental and calculated hyperfine coupling constants are compared. Characteristic UV-VIS data and redox potentials in acetonitrile are reported, together with the syntheses of the compounds.     

Rearrangement ofα -trifluoromethyl-β-dialkylamino-β-fluoroacrylic acid N.N-dialkylamides

Conclusions When heated in the presence of a catalytic amount of BF₃ etherate,-trifluoromethyl--diethylamino--fluoroacrylic acid N, N-dimethylamide is reversibly isomerized to-trifluoromethyl--dimethylamino--fluoroacrylic acid N, N-diethylamide. The methyl esters of-trifluoromethyl--diethylammo--fluoroacrylic acid and-trifluoromethyl--phenoxy--fluoroacrylic acid N,N-dimethylamide are not isomerized under the same conditions.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No.1, pp.137–141, January, 1976.     

Analysis of the Temperature and Composition Dependence of Viscosimetric Properties of 2-Butanone <Emphasis Type="Bold">+</Emphasis> 2-Butanol Solvent Mixtures

Kinematic viscosities were measured for 2-butanone + 2-butanol binary liquid mixtures with a capillary Ubbelohde routine viscometer in the temperature range from 273.15 to 353.15 K at atmospheric pressure, and covering the whole miscibility field (0x_i1). Experimental data have been correlated by means of different empirical or semiempirical relationships, such as =(T), =(x_i), and =(T, x_i). Viscosity deviations, , from ideal behavior are negative at all experimental conditions, confirming that structure breaking effects prevail in the liquids. Furthermore, the thermodynamics of viscous flow and excess Gibbs energy of activation of viscous flow, G*^E, have been calculated. As an alternative and complementary approach to such investigations, the fluidity () of this binary system has been analyzed by the modified—Batschinski theory. The results are discussed in terms of the specific molecular interactions between the mixture components.     

Effect of fusion conditions ofβ-polypropylene on the new crystallization

The new crystallization of -modification of polypropylene (-PP) was studied after melring as a function of the final temperature of fusion (T _F ). The new crystallization, thermal characteristics, polymorphic composition, and structure of recrystallized samples were highly influenced by theT _F level. As a function ofT _F , three characteristic regions were outlined: Region I below the melting point of -modification, region II between the melting points of - and -modifications, and region III above the melting point of -modification. In the vicinity of the melting points of both modifications, two narrow transition regions are observed where the crystallization and structural characteristics changed abruptly withT _F . AtT _F values in region I, recrystallization of -modification proceeded without any change in the modification. IfT _F fell in region II, the sample crystallized newly into -modification. The optically negative -ring-spherulites were replaced by positive microclusters of -modification and a marked structural memory effect was observed. In region III, the above characteristic became invariant withT _F (region of blank melt). These observations may be interpreted by the role of self nuclei.     

Researches on imidazoles

A study is made of the reaction of the sodium and ammonium salts of 1 -alkyl- and 1, 2-dialkyl-4-nitro-5 mercaptoimidazoles with -halogenoketones, -halogenoalcohols, and — and -halogeno acids, to give a number of 1 -alkyl- and 1, 2-dialkyl-4-nitro-5- [-ketoalkyl (aralkyl)-, -hydroxyethyl-, and -and -carboxyalkyl] mercaptoimidazoles.For Part XXIV see [6].     

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.