Marginal electron density and density-difference functions

Summary For visual analysis of the density reorganization and distortion, the one-dimensional cut (x, y ₀,z ₀) and the two-dimensional cut (x, y, z ₀) of the three-dimensional electron density difference function (x, y, z) are frequently employed. However, these cut functions do not satisfy any sum rules in contrast to the original difference function (x, y, z). To avoid this difficulty, the use of the marginal electron density functions _x (x) and _xy (x, y) and their difference functions _x (x) and _xy (x, y) is proposed. The marginal densities are condensation of the three-dimensional density onto a particular plane or line of our interest, and they satisfy the sum rule (i.e., the conservation of the number of electrons) exactly. Some basic properties of the marginal electron density are clarified for typical diatomic molecular orbitals. An illustrative application is given for the bonding and antibonding processes in the H₂ system.     

Molekülordnung und Kristallinität in Polyhexamethylenadipamid

Zusammenfassung Kalorimetrische, röntgenographische und IR-spektroskopische Untersuchungen und Dichtemessungen ergaben für PA 66 eine bei anderen Polymeren unbekannte Anomalie. Die Abhängigkeit der Röntgenkristallinitätw _c und der kristallinitätsproportionalen Größen (experimentelle Schmelzwärme H ^*, IR-Bandenintensität) vom spezifischen Volumen ändert sich mit den Kiistallisationsbedingungen. Dies ist die Folge eines konformationsbedingten Übergangs zwichen zwei triklinen Modifikationen unterschiedlicher Dichte. Für aus der Schmelze, dem Glaszustand und verdünnter Lösung kristallisierte Proben treten bei allen drei Meßmethoden hinsichtlich der Abhängigkeit vom spezifischen Volumen drei Bereiche auf. Bereich I: Die Proben enthalten 1-Kristalle mit _c ^I =1,22 =1,22 gcm-³,H _M ^I =235 Jg^–1 und=1,095 gcm _u–3. Bereich II: Die Proben enthalten _II -Kristalle mit _cII=1,165 gcm^–3.H _M ^II =185 Jg _u ^–1 1 und pa =1,095 gcm^–3. Bereich III: Übergangsbereich, in dem sich das spezifische Volumen stärker ändert als we und H ^*, weil die Kristalldichte zwischen _c ^I und ell variiert.Die _c -Wertr wurden außer durch Extrapolation über dem spezifischen Volumen auch aus der Invarianten der Röntgenkleinwinkelstreuung bestimmt. In allen Fällen ist eine .röntgenographische Kristallinitätsbestimmung bei PA 66 willkürfrei und reproduzierbar möglich. Aus Dichte oder Schmelzwärme kannw _c unter Verwendung der ermittelten _c- und H_M-Werte nur bestimmt werden, falls die Proben den Bereichen I oder II angehören. Mit den üblichen Verarbeitungsmethoden erhält man jedoch meist Proben im Bereich III.

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Summary From the results of calorimetric, X-ray and infrared spectroscopic investigations and density measurements an anomaly is found for polyamide 66 which is not known for other polymers. The dependence of X-ray crystallinityw _c and other properties proportional to crystallinity (experimental heat of fusion H ^*, intensity of IR-absorptions) on the specific volume varies with the conditions of crystallization. This is due to a conformational transition between two triclinic modifications with different densities.Samples of polyamide 66 were isothermally crystallized from the melt, from dilute solution and from the glassy state at different crystallization temperatures. The results of each of the three experimental methods, when plotted versus specific volume, exhibit three sections Section I: The samples contain _I -crystals with _c =1.22 gcm^–3, H _M ^I = 235 Jg^–1 and _a =1.095 gcm^–3 Section II: The samples contain air-crystals with _c ^I =1.165 gcm-3, H _M ^II =185 Jg^–1 and ppa =1.095 gcm^–s; Section III: Transition range, where the change in the specific volume is greater than that inw _c and H ^*, because the crystal density varies continuously between _c ^I and _c ^II The crystal densities have been determined not only by specific volume extrapolations, but also from the mean square electron density fluctuation of the small angle X-ray scattering. In all cases it is possible to determine the crystallinity of polyamide 66 from X-ray measurements in an unequivocal and reproducible way. The calculation of crystallinity from density or heat of fusion is only possible, if the samples belong to section I or II. The usual processing methods, however, produce samples which belong to section III.

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Mit 15 Abbildungen und 2 Tabellen

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Herrn Professor Dr. Horst Pommer zum 60. Ge burtstag gewidmet.     

Non-equilibrium rate coefficients and isotope effect with bimolecular ion-(polar) molecule reactions in xenon

Using the Fokker-Planck version of an approximate Boltzmann equation for the ion (translational) energy distribution function f _I the departure, k, of the non-equilibrium ion-(polar) molecule reaction rate coefficient k _non from its equilibrium value k ^(eq) is calculated. k enhances considerably with an increase of the dipole moment of the reacting molecular species (locked dipole reaction model). But the k-values, e.g. for reactions of H^–(D^–) and nitromethane in xenon enhance also with increasing ratio of the concentrations of CH₃NO₂ and Xe and decrease with enhancing gas temperature T. The reaction-induced (translational) non-equilibrium effect leads to a (non-equilibrium) kinetic isotope effect depending on and T. At T=300 K the example yields k _H /k _d =1.345(=5 · 10^–4),=1.409 (=10^–5) and=1.414–k _H ^/(eq) /k _D ^(eq) (10^–6).     

Critical behavior and interfacial tension of mixtures of propylene glycol and ethylene glycol oligomers

This investigation presents an analysis of the critical behavior of mixtures of oligomers of propylene glycol, PG₁₇, and ethylene glycol, EG_n, withn=3, 4, 5, 6.4, 8.7, 12.1 and 22.1. The critical coordinates, _c andT _c were determined from the phase diagrams. The critical compositions compare very well with the Huggins-Flory predictions. The interaction parameter _n is around one for EG₃, EG₄ and EG₅ and it increases up to two for the higher oligomers. The break in the interaction parameter also corresponds to a minimum in the critical temperature. The phase diagrams and the interfacial tension were used to get the critical exponents and , respectively. The data were analysed with two approaches. First, from the temperature dependence of the length of the tie-lines and of the interfacial tension up to the upper critical solution temperature, UCST. Second, with the data at 30°C using the critical temperature of the systems as the variable. The first method led to =0.39±0.05 in good agreement with the result of the second method, =0.37±0.04. The exponents for the interfacial tension, , determined with the first method for PG₁₇ with EG_6.4, EG_8.7 and EG_12.1 are =1.66±0.11, 1.46±0.25 and 1.73±0.18, respectively. The second method led to =1.17±0.14. The critical exponents are compared to mean field and ising-3D predictions.     

Die Bedeutung der mittleren Probendichte für die quantitative Interpretation der Röntgenkleinwinkelstreuung teilkristalliner Polymerer

Zusammenfassung Die Bestimmung von überstrukturdaten polymerer Lamellenclustersysteme kann über Modellrechnungen der Röntgenkleinwinkelstreukurven erfolgen. Es wird gezeigt, daß in vielen Fällen die Modulation der Streukurve nicht allein durch die innere Struktur der Cluster bestimmt ist, vielmehr muß die mittlere Elektronendichte der Umgebung der Cluster mitberücksichtigt werden. An den Systemen HDPE, PP und iPS/PPO wird gezeigt, daß die Verwendung eines einfacheren Modells, in dem die kristalline Dichte _c = 1 und die amorphe Dichte _a = 0 gesetzt wird (schwarzweiß-Modell), für kleine Lamellenzahlen pro Cluster zu einer Scheinanpassung führt. Die BerÜcksichtigung der mittleren Probendichte fÜhrt zu abweichenden Anpassungsparametern bei der Berechnung der experimentellen Streukurve und damit zu anderen Über-rstrukturdaten. Der Einfluß der Umgebungsdichte wird vernachlässigbar klein, wenn die Zahl der lagekorrelierten Lamellen pro Cluster größer als 10 wird.

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Summary Superstructural parameters of polymeric material composed of clusters of lamella-shaped crystals can be obtained by model-calculations of their small-angle x-ray scattering curves. In this paper it has been demonstrated, that in many cases the modulation of the scattering curve is determined not only by the inner structure of the cluster but also dependent on the average (electron) density of the cluster environment, the mean sample density. Discussing the SAXS of the systems HDPE, PP and iPS/PPO it has been shown, that the use of a simpler ,black-white model, in which the crystalline density has been set _c = 1 and the amorphous density _a = 0, leads to a phony fit. The incorporation of the mean sample density into the model yields a different set of parameters. The mean sample density can be neglected as soon as the number of lamellae per cluster exceeds the value of 10.

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Mit 4 Abbildungen und 1 Tabelle     

The relation of directly bonded C-H coupling constants to s-characters revisited

Summary Following earlier theoretical studies of orbital delocalization effects on one-bond ¹³C-H coupling constants (¹ J _CH) an approximate proportionality of (¹ J _CH) to ^3/2, where is the s-character of the carbon hybrid orbital appropriate to the construction of the best localized molecular orbitals, is predicted and verified by using published data. It is proposed that this proportionality should replace the previous linear correlations of (¹ J _CH) with , which involve large additive constants.     

Elastizitätsmodul und Dichte von kaltverstrecktem und druckbehandeltem Polyäthylen

Zusammenfassung Proben aus Polyäthylen hoher Dichte wurden bei Raumtemperatur mit verschiedenen Geschwindigkeitenv _ver auf einer Zugprüfmaschine verstreckt. Beiv _ver 10 mm/min beobachtet man eine fast isotherm verlaufende inhomogene Deformation, die zu Verstreckungsgraden=8–13 und mittleren Dichten = 0.80 g/cm³ in den verstreckten Probenbereichen führt. Die bei höherenv _ver bis zu 50 mm/min eintretende adiabatische Erwähnung ergibt höhere Verstreckungsgrade=13–18 und geringere Dichten = 0.64 g/cm³. Es existiert kein natürlicher Verstreckungsgrad. Der Dichteabfall mit zunehmendem kann durch eine Gerade repräsentiert werden; der ElastizitätsmodulE ergibt eine mit zunehmende Kurve.Nach einer Druckbehandlung der Proben mit 5600 bar bei Raumtemperatur erreichte ihre Dichte fast wieder den Anfangswert vor der Verstreckung, wobei keine Abhängigkeit von oder anderen Parametern zeigte. Der ModulE hatte zugenommen, aber nicht proportional zur Dichte. Der Vergleich von undE verstreckter Proben vor und nach der Druckbehandlung weist auf den Netzwerkcharakter von kaltverstrecktem Polyäthylen hin.Herrn Prof. Dr. K. Ueberreiter zum 70. Geburtstag gewidmet.     

Untersuchungen der Absolutintensität der Röntgenkleinwinkelstreuung an Polyäthylenterephthalat in Abhängigkeit von den Kristallisationsbedingungen

Zusammenfassung Es wurden Messungen der Dichte sowie der absoluten Intensität der Röntgenkleinwinkelstreuung an teilkristallinem Polyäthylenterephthalat durchgeführt. Aus den erhaltenen Resultaten wurden der Volumenanteil der Kristallite, die Dichte der Kristallitek und die Dichte der nichtkristallinen Bereiche _a berechnet. Bei Proben, die bei tiefer Temperatur kristallisiert worden waren, lagk unterhalb von 1,455 g/cm³, dem Wert, der aus den Abmessungen der Elementarzelle einer möglichst gut kristallisierten Probe bestimmt wurde. _a war bei allen Proben kleiner als die Dichte des völlig amorphen Stoffes. lag jeweils über dem Wert, der allein aus der Dichte in konventioneller Weise bestimmt wurde.

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Summary Measurements of the density and the absolute intensity of small angle X-ray scattering of semicrystalline polyethylenterephthalate were performed. From the results obtained the crystalline volume fraction, the density of the crystalsk and the density of the noncrystalline regions _a were calculated. With samples crystallized at lower temperatures,k lies below 1,455 g/cm³, the value obtained from the crystal unit cell dimension on a material crystallized as well as possible. _a is generally smaller than the density of a completely amorphous sample. For higher temperatures of crystallization, is larger than the values obtained simply from the density by conventional methods.

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Vorgetragen auf der Arbeitssitzung des Fachausschusses Physik der Hochpolymeren in der Frühjahrstagung Berlin 1971 vom 9. bis 13. März des Regionalverbandes Physikalische Gesellschaft zu Berlin.

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Wir danken Herrn Prof. Dr.E. W. Fischer für zahlreiche wertvolle Diskussionen. Unser Dank gilt ferner der Deutschen Forschungsgemeinschaft für die finanzielle Unterstützung dieser Arbeit, sowie der Fa. Kalle A. G., Wiesbaden, für die Überlassung der Folien.     

Spin density calculations in semiempirical restricted and unrestricted SCF MO methods

In the present paper spin densities are calculated by ten methods on chosen radical systems. - interaction parameters for the individual methods are determined by McConnel's relation a _i =Q _i and by that of Colpa-Bolton a _i =(Q+K _i ) _i and the correlation between the results of the individual methods is studied.

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Zusammenfassung In der vorliegenden Arbeit werden Spindichten anhand von zehn Methoden an ausgewählten Radikalsystemen ermittelt. Die --Kopplungsparameter für die einzelnen Methoden werden nach den McConnell a _i =Q _i - und Colpa-Bolton a _i =(Q+K _i ) _i -Beziehungen bestimmt. Die zwischen den Ergebnissen der einzelnen Methoden bestehende Korrelation wird untersucht.

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Résumé Dans ce travail les densitées de spin sont calculées par dix méthodes sur un système des radicaux choisis. On détermine des parametres - d'interaction pour les méthodes individuelles dans la relation de McConnell a _i =Q _i et celle de Colpa-Bolton a _i =(Q+K _i ) _i et étudie la correlation entre les résultats des méthodes individuelles.

     

Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach

The electrostatic interaction pressure of charged surface layers is considered qualitatively and quantitatively. In the case of mutual penetration of the surface layers in addition to Maxwell stress and osmotic resp. hydrostatic pressure an isotropic stress on the fixed charges carrying molecules of the surface layers has to be taken into account. The derivation of the pressure-distance equations is given starting from both thermodynamic/electrostatic and hydrostatic/electrostatic principles. A possible biological significance of the additional stress is discussed emphasizing its role in modifying the structure of surface layer molecules.List of symbols e ₀ elementary charge - k Boltzmann constant - n _i concentration of theith ionic species in the bulk solution - P hydrostatic pressure - P hydrostatic pressure in the bulk volume (× ) - P ^h integration constant, independent on ×:P ^h =P(h) - T absolute temperature - Z _i electrovalence of theith ionic species - thickness of the surface layer - , ₀ relative and absolute permittivities - II(×) osmotic pressure at position × - II osmotic pressure in the bulk solution (× ) - osmotic pressure in the symmetry plane of interacting identical surface layers (electric field strength equals zero) - integration constant, independent on ×: - _e ^h electrostatic component of the disjoining pressure _e ^h = _e (h) - (×) mobile charge density profile (cations and anions of the electrolyte) - (×) fixed charge density profile - ^t(x) total charge density profile ( ^t = +) - ¹(x) fixed charge density profile of one of the two surface layers ( ¹(×) 0 for 0×) - (×) electric potential profile     

A representation of the polarization term in the interaction energy between a molecule and a point-like charge

The interaction energy of a molecule M with a point-like charge q can be partitioned into simpler contributions, two of which can be expressed in terms of the charge distribution _M of the sole M. The first term, qV(r), represents the interaction of q with the undistorted charge _M ⁰ of M while the second q ² P(r) gives the additional contributions due to the polarization of _M ⁰ under the influence of the charge q placed at the point r. In this paper we investigate the possibility of getting an inexpensive and sufficiently accurate analytical representation of P(r) over the whole space outside the van der Waals volume of M.     

Thermal conductivity of the urea-hexadecane inclusion compound

The thermal conductivity and the heat capacity per unit volumec _p have been measured for the urea-hexadecane inclusion compound using the transient hot-wire method. Measurements were made under isobaric conditions at a pressure of 0.1 GPa and in the temperature range of 100–300 K. There was evidence for a phase transition at a temperature of about 160 K, in reasonable agreement with previous work. For the high-temperature phase was independent of temperature within ±1%. The low-temperature phase showed a weak temperature dependence, with (d In/d InT) _p = –0.13. It was inferred that interaction between acoustic phonons and low-frequency vibrational excitations of the guest molecules made a major contribution to the thermal resistivity. For the quantityc _p a weak maximum was observed in the region of the phase transition temperature.Dedicated to Dr D. W. Davidson in honor of his great contributions to the sciences of inclusion phenomena.     

Bestimmung der molaren Masse und der Ladungszahl von Polymerelektrolyten mit der Ultrazentrifuge

Zusammenfassung In der vorliegenden Arbeit wird das Sedimentationsgleichgewicht der Systeme Na₆[H₂W₁₂O₄₀]—NaCI—H₂O und Na₆[H₂W₁₂O₄₀]—NaClO₄— H2O untersucht. Die scheinbare molare Masse Mapp des Natriummetawolframats wird in beiden Systemen als Funktion der Natriummetawolfrarnat-Anfangspartialdichte ₀ ^PX _z gemessen. Durch lineare Extrapolation der Funktion Mapp = Mapp (PP,, ) auf die Polymerelektrolyt-Anfangspartialdichte Null können die Grenzwerte der scheinbaren molaren Masse (Mapp)o ermittelt werden. Aus den (Mapp)o-Werten wird die Abhängigkeit der Größe (ln _PXz /m _BX ) _mPXz von der NaCI- bzw. NaClO₄-Molalität berechnet.Die Bestimmung der molaren Masse und der (stöchiometrischen) Ladungszahl eines Polymerelektrolyten aus den experimentell ermittelten (Mapp)o-Werten unter Anwendung der Lamm-Williams-Gleichung wird diskutiert. Zur Ermittlung der beiden Größen müssen mehrere Versuchsreihen mit zwei verschiedenen Fremdelektrolyten durchgeführt werden. Externe Messungen sind nicht erforderlich.Man erhält auf diese Weise verläßliche Werte so-wohl der molaren Masse als auch der (stächiometrischen) Ladungszahl.

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Summary The sedimentation equilibria of the systems sodium metatungstate-sodium chloride-water and sodium metatungstate-sodium perchlorate-water are investiated. In both systems the apparent molecular mass Mapp of sodium metatungstate (PX _z) is measured in dependence on partial density ₀ ^PX _z before centrifugation. By linear extrapolation of the function Mapp = Mapp ( ₀ ^PX _z the limiting value (Mapp)o for ₀ ^PX _z = 0 is obtained. The variation with sodium chloride and sodium perchlorate molality of the quantity (ln _{PX z} ^m _BX )mPX_z is calculated from (Mapp)o data.The determination of the molecular mass and the algebraic valency of a polymeric ion by means of the (Mapp)o values calculated by Lamm-Williams equation is discussed. In order to obtain these two quantities at least two series of experiments are required, each of which using a different supporting electrolyte. External measurements are not necessary. In this way reliable values for the molecular mass as well as for the stoichiometric valency are obtained.

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Mit 5 Abbildungen und 3 Tabellen     

Light scattering studies on solutions of chlorinated rubber

Summary Measurements have been made of the depolarisation factors _u , _v , _h, and the intensity of scattering in the horizontal transverse direction, in the case of solutions of four different samples of chlorinated rubber in carbon tetrachloride. The size, shape and molecular weight of the micelles have been deduced by the application of the light scattering theories of Gans, Vrklajan and Katalinic and Debye. The extent to which the degradation of the rubber molecule occurs on chlorination has also been assessed.

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Zusammenfassung Für Lösungen von vier verschiedenen Proben von chloriertem Kautschuk in Tetrachlorkohlenstoff wurden Messungen der Depolarisation und der Lichtstreuung durchgeführt. Größe, Gestalt und Molekulargewicht wurden unter Verwendung der Theorien der Lichtstreuung von Gans, Vrklajan, Katalinic und Debye abgeleitet. Die Stärke des Abbaues, dem die Kautschukmoleküle bei der Chlorierung unterworfen sind, wurde abgeschätzt.

     

Röntgenuntersuchungen zur Kristallstruktur von Polybutylenterephthalat (PBT)

Zusammenfassung Polybutylenterephthalat (PBT) gewinnt als Spritzgußmaterial und als Faserrohstoff zunehmend an Bedeutung. Die thermischen und mechanischen Eigenschaften des PBT sind von denen des Polyäthylenterephthalates (PET) erheblich abweichend. Die vorliegende Arbeit soll einen Beitrag liefern, die abweichenden Ergebnisse deuten zu können.Deswegen wurden die Gitterzelle und die Kettenanordnung im Kristallverband des PBT untersucht. Aus Röntgenmessungen ergaben sich die folgenden Gitterzellenparameter:a=4,83 Å,b=6,05 Å,c=11,45 Å,=100,5°,=117°,=110,8°.Damit ergibt sich eine Kristalldichte von=1,433 g/cm³ im Vergleich zu=1,515 g/cm³ beim PET.Mit der Annahme einer abgewinkelten Kettenkonformation kann in befriedigender Weise die verkürzte Faseridentitätsperiode und die gegenüber dem PET verlängerte Zellenkante a des PBT erklärt werden.

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Summary Polybutylenterephthalate (PBT) is a new molding and fibre spinning material for industrial applications. The thermal and mechanical properties of PBT are quite different from those of polyethyleneterephthalate (PET).The unit cell of PBT was found by X-ray diffraction studies to be triclinic, similar to that of PET, but having the parameters:a=4.83 A,b=6.05 Å,c=11.45 Å,a=100.5°=117°,=110.8°. This gives a crystalline density of=1,433 g/cm³ compared with=1.515 g/cm³ for PET.Since a completely extended PBT chain would theoretical have a repeat length of 13.25 Å the above unit cell requires a kinked chain conformation. The increaseda axis dimension, in comparison to PET would be in agreement with this conclusion.

     

The molecular complex of dibenz[a,c]anthracene and trinitrobenzene

The crystal structure of the complex between the polycyclic aromatic hydrocarbon di-benz[a,c]anthracene and 1,3,5-trinitrobenzene is reported. The crystals are triclinic, space group P¯1 with unit cell dimensionsa=7.277(2) å,b=11.237(6) å, andc=13.902(5) å,= 104.13(4),=96.04(3), and =95.15(2). Diffraction data were measured at 121(2) K. The structure was determined and refined toR ₁=0.046. The structure consists of layers containing both dibenz[a,c]anthracene and 1,3,5-trinitrobenzene molecules, interconnected within a layer by C-H O interactions. Layers stack on one another so that dibenz[a,c]anthracene molecules are sandwiched between 1,3,5-trinitrobenzene molecules and vice versa. The average distance between molecules in these sandwiches is 3.23 å.     

Acid — Base properties of 3(5)-azido-1,2,4-triazoles

The pK_a and values of a series of 3(5)-azido-1,2,4-triazoles are correlated with the _I and _C constants according to the equation pK =_II + _CC + pK_o. The high _I values in both cases are due to the closeness of the substituent to the reaction center. The _C/_I ratio attests to different contributions of the inductive and mesomeric effects of a substituent during transmission of its effect from the 5-position to the N₁ and N₄ heteroatoms.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1288–1291, September, 1974.     

1A1⇔5T2 Spin Transition in Heterometallic Solid Phases FexNi1-x(Htrz)3(NO3)2 · H2O (Htrz = 1,2,4‐Triazole)

Solid phases Fe_xNi_1-x(Htrz)₃(NO₃)₂ · H₂O (0.4 x 0.8$) and Ni(Htrz)₃(NO₃)₂ · H₂O were synthesized and studied. The phases were studied by means of magnetochemistry, powder Xray difraction analysis, and electronic and IR spectroscopy. The heterometallic phases are described by the stoichiographic method of differentiating dissolution (DD). The values of x were determined by two methods — atomic absorption and DD. Magnetochemical data showed that the solid phases exhibit a hightemperature ¹A₁ ⁵T₂ 0.5 x 0.8 and disappears at x = 0.4. The spin transition is accompanied by thermochromism (color changed from pink to white at 0.6 x 1 and from pink to light lilac at x = 0.5). A decrease in x leads to a decrease in the temperature of the forward (under heating T_c ) and reverse (under cooling T_c ) transitions, a decrease in hysteresis value ( T_c), and a smearing of the spin transition.     

Structure of casein micelles I. Small angle neutron scattering and light scattering fromβ- andχ-casein

Casein is the main protein component of milk and is of remarkable colloidal stability. Under the influence of milk clotting enzymes casein shows the striking behaviour of coagulation. This clotting process has already been studied by other groups, neglecting the fact that casein is not a homogeneous protein. The purpose of the present study is focused, in this first stage, on the determination of the structure of the various casein components. In cooperation with other laboratories we have been able to obtain the well separated individual proteins. Studies have been performed so far with- and-casein. For detailed structural information we carried out small angle neutron scattering and combined static and dynamic light scattering measurements and determined the molecular weight,M _w, the radius of gyration, S ² the hydrodynamic radius,R _H, the-value and the particle scattering factor, P_z(q). The two caseins show a strikingly different behaviour. For the-casein we found a star-like structure, i. e. an aggregation pattern that is expected for a common micelle. The micelle consists of about 38 monomer chains. The aggregates of-casein appear to be composed of star-like submicelles, where each submicelle contains nine-casein chains and the total degree of aggregation is about 140.     

Zr<Subscript>5</Subscript>Ir<Subscript>2</Subscript>In<Subscript>4</Subscript> – A Superstructure of the Lu<Subscript>5</Subscript>Ni<Subscript>2</Subscript>In<Subscript>4</Subscript> Type

Summary. Zr₅Ir₂In₄ was synthesized by reaction of the elements in a glassy carbon crucible in a water-cooled sample chamber of an induction furnace. The sample was characterized by X-ray diffraction on both powder and single crystals. Zr₅Ir₂In₄ crystallizes with a pronounced Lu₅Ni₂In₄ type subcell, space group Pbam, a=1739.5(6), b=766.3(2), c=338.9(2) pm. Weak additional reflections force a doubling of the subcell c axis. The superstructure of Zr₅Ir₂In₄ is of a new type: Pnma, a=1739.5(6), b=677.8(2), c=766.3(2) pm, wR2=0.0529, 1592 F² values, and 60 variable parameters. The group-subgroup scheme for the klassengleiche symmetry reduction is presented. The formation of the superstructure is most likely due to a puckering effect (size of the iridium atoms). The crystal chemistry of Zr₅Ir₂In₄ is briefly discussed.