Adsorption kinetics measurements of some nonionic surfactants

Dynamic surface tension values of aqueous surfactant solutions were measured by using the ring and plate method. The mean diffusion coefficients calculated on the basis of the purely diffusion controlled adsorption model vary between 2 · 10^–6 to 7 · 10^–6 cm²/s for all surfactants studied:n-alkanols,n-alkanoic acids, dimethyl and diethyln-alkyl phosphine oxides. That means the surfactants investigated adsorb with a purely diffusion controlled adsorption mechanism and no barriers excist to hinder sorption processes.Nomenclature c ₀ surfactant bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - ¯ (t)/ ₀ reduced surface concentration - maximum surface concentration - K ₀/c₀ - surface tension - t time - Dt/K ² reduced time - a _L coefficient of the Langmuir isotherm     

Adsorption kinetics of nonionic surfactants using the drop volume method

The kinetic results obtained for the nonionic surfactantsn-octyl,n-decyl, andn-dodecyl dimethyl andn-octyl, andn-decyl diethyl phosphine oxide show purely diffusion controlled adsorption. The drop volume technique applied in a static and dynamic version proves to be useful to measure the adsorption kinetics in the form of surface tensions in function of time. Comparisons of the results obtained from both the static and the dynamic measuring procedure confirm the validity of a theory applied to interpret the kinetic data.Nomenclature a Langmuir parameter - c ₀ surfactant bulk concentration - D diffusion coefficient - surface concentration - ₀ equilibrium surface concentration - ¯ (t)/ ₀ reduced surface concentration - maximum value of - R gas law constant - surface tension - ₀ surface tension of pure water - t time - T absolute temperature     

On the theory of adsorption kinetics of ionic surfactants at fluid interfaces

The kinetic equation to describe the adsorption process of ionic surfactants (derived in part 1) will be solved numerically. The results show the effect of parameters such as ion valencyz, thickness of theDL x ^–1, and surfactant parameters_eq,K, andK _ads on the adsorption process. The results can be used to decide whether the model can explain experimental data on charged surfactant molecules or not.Nomenclature c concentration - c_e bulk concentration in equilibrium - C =c/c _e dimensionless concentration - D diffusion coefficient - e proton charge - F Faraday's constant - f ₀ =e/kTdimensionless potential - k Bolzmann's constant - K _ads rate constant of adsorption - K _des rate constant of desorption - K(f ₀) coefficient of electrostatic deceleration - K = _eq /c _e Henry's constant - R gas law constant - t time - T absolute temperature - z electrovalence - ₀ adsorption of ions - _eq equilibrium value of _o - = ₀/ _eq dimensionless adsorption - , constants - dielectric constants - x Debye-Hückel reciprocal distance - =Dt/K ² dimensionless time - electric potential     

Adsorption Isotherm Accounting for the Electrode Elasticity: Special Solutions

The single-phase adsorption on a solid electrode out of a dilute solution is investigated. As a continuation of the previous paper, on the basis of the complete electrocapillarity equation, an adsorption isotherm equation is derived and supplemented by equations of compatibility of the physical quantities. The equations contain a new parameter, , which is a derivative of the dimensionless surface adsorbate concentration by the relative variation of the electrode surface area. Their solution is obtained in relation to the dimensionless charge density of the electrode surface q for the case of = (). As a result of employing a linear model for q by , the problem of determination of the unknown model functions is reduced to common differential equations that use the capacitance or estance curves as the boundary conditions. In the first case, we suggest to calculate the unknown integration parameter by the method of mathematical optimization, employing coulometric data.     

Phase-fixed double-group 3-Γ symbols. IV. Real 3-Γ symbols and coupling coefficients for the group hierarchies T* ⊃ C 3 * and T* ⊃ C 2 *

We present sets of real 3- symbols which correspond to explicitly given irreducible matrix representations for the two double group hierarchies T* C ₃ ^* and T* C ₂ ^* . They fit into the formalism exposed in a previous paper [1] on the general theory of 3- symbols and coupling coefficients and illustrate much of the discussion in a subsequent one [2] treating the particular properties of the double groups.     

Embedding frequencies of trees

A graph is said to be embedded in a graph if is isomorphic to a subgraph of . The embedding frequency for in ,N( , ), is the number of different subgraphs of to which is isomorphic. We use a computer program to calculate the embedding frequencies of subtrees within trees. We computeN(, ) for trees through 10 vertices and present the results in tabular form. When trees are partially ordered by valence class, their subtrees lie in corresponding order; we give a formal proof of this subtree embedding property. The structure of the embedding relation is exhibited in a topological picture of the zeta function showing the non-zero values ofN(, ).     

Dynamic light scattering of CTAB:NaSal threadlike micelles in the semidilute regime. II. effect of surfactant concentration

Dynamic light scattering measurements are made on networks formed by elongated threadlike micelles of cetyltrimethylammonium bromide (CTAB) in aqueous sodium salicylate (NaSal) solutions at 25°C. The surfactant concentrationC _D of the samples is varied from 0.006 to 0.3 M and the ratio of the salt concentrationC _s toC _D is fixed at unity. The time correlation functionA _q (t) of light intensity scattered from the solutions exhibits transition from the unimodal to the bimodal distribution of the decay rate at aroundC _D=0.05 M. The dependence of the first cumulant _e on the scattering vectorq for the samples withC _D0.03 M is described by the dynamic scaling law. The cooperative diffusion coefficientD _c is obtained from extrapolation of _e/q² for the samples withC _D0.03 M and of _f/q² forC _D0.05 M where _f is the first cumulant from the fast mode. TheD _c is found in proportion toC _D ^0.45, being in agreement with the theoretical prediction for a rigid rod in the semidilute regime by the scaling law. The decay rate _s characteristic of the slow mode is independent ofq, and _s ^–1 roughly agrees with the mechanical relaxation time estimated from a fit of the dynamic viscoelastic data of the same samples by a Maxwell type of model with the single relaxation time .     

Adsorption isotherm for a solid electrode: The link between the differential surface tension and capacitance curves

Investigation of thermodynamically equilibrium single-component adsorption from a liquid solution on a solid electrode with allowance made for elastic deformation of its surface is continued. A full electrocapillarity equation is derived from thermodynamics equations for an interphase layer in the absence of irreversible processes. Thermodynamic aspects of the Shuttleworth equation are discussed and the equation is compared with two-dimensional Murnaghan formulas for elastic isotropic media. An adsorption isotherm equation and compatibility equations that had been derived previously are examined in a special case where the derivative of a surface concentration with respect to depends solely on (=()) and a rigorous solution of these is obtained for a deformed electrode ( 0). The effect of and dimensionless electrode potential on the extreme (at an infinitely high adsorbate concentration) value of is studied. The model of two parallel capacitors is considered in detail for a general case. Owing to the use of capacitance curves for an elastically stretched electrode, a formula that expresses the differential surface tension of a nondeformed electrode through such curves is derived for the first time ever.To the memory of my motherTranslated from Elektrokhimiya, Vol. 41, No. 1, 2005, pp. 20–34.Original Russian Text Copyright © 2005 by Podgaetskii.     

Zur gruppentheoretischen Bestimmung der Atomzustände in Ligandenfeldern

Zusammenfassung Es wird vorgeschlagen, die Bezeichnungen weak-field-Methode bzw. strong-field-Methode durch (L)-Methode bzw. ()-Methode zu ersetzen.Nach einer kurzen Einführung in die ()-Methode wird mit den Mitteln der Gruppen-und Darstellungstheorie eine Formel abgeleitet, mit deren Hilfe man schnell Rasse und Multiplizität der Terme eines Komplexions in der ()-Methode angeben kann. Einige Spezialfälle dieser Formel und die systematische Bestimmung der ()-Funktionen werden erörtert.

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It is suggested that the misleading designations weak field method and strong field method be replaced by (L) method and () method, respectively.Following a brief introduction to the () method an equation is derived by group theoretical means which leads to rapid classification of the () terms. Several special cases and short cuts are discussed as well as the systematic determination of the () functions.

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Résumé Le remplacement des termes «méthode du champ faible» et «méthode du champ fort» par «méthode (L)» et «méthode ()» est proposé.Après une introduction dans la méthode () une formule est dérivée à l'aide de la théorie des groupes et des représentations, qui donne la représentation irréductible et la multiplicité des termes d'un ion complexe dans le cadre de la méthode (). Quelques cas spéciaux de cette formule et la détermination systématique des fonctions (/gG) sont discutés.

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Ich danke Herrn Professor Dr. H. Hartmann für den Hinweis auf das vorliegende Problem und der Deutsehen Forschungsgemeinschaft für ein Stipendium.     

Phase-fixed double-group 3-Γ symbols. II. General features of double groups and their 3-Γ symbols

Following a general exposition of the theory of 3- symbols [1], we now focus on the particular features encountered when dealing with double groups of (proper as well as improper) point groups.The paper starts with a brief outline of the definition of double groups adopted in the present work. After this, some properties of double group 3- symbols are discussed which are independent of the way the 3- symbols have been constructed. The main part of the paper then deals with the actual generation of 3- symbols for the non-commutative double groups.In the approach described, the 3- symbols become determined in part by adaption of the standard matrix irreps to subgroup hierarchies and then completely, phases included, by the specification of standard basis functions (or, equivalently, standard subduction coefficients).     

Phase-fixed double-group 3-Γ symbols. V. 3-Γ symbols and coupling coefficients for all the octahedral double group-subgroup hierarchies

For all the subgroup hierarchies descending from the octahedral double group O ^*, we have obtained sets of 3- symbols and discuss here their properties. We have entirely real sets of 3- symbols for the tetrahedral and tetragonal hierarchies as well as for O ^* C ₃ ^* . For the latter hierarchy and the tetragonal ones, formalisms almost as powerful as the classical one for the rotation group may be established. We also discuss results obtained for cases with strict adaption to D ₃ ^* where it is now known that non-real 3- symbols are unavoidable.The 3- symbols are phase-fixed by the specification of basis functions (or, equivalently, subduction coefficients) generating them.The significance of the concept of associated representations of O* is discussed. The problems raised by the two multiplicity triples UT₁U and UT₂U in O* are given particular attention.     

Photorefractive Composites Based on Nanocrystalline Carbocyanine Dye J-Aggregates with a Fast Response Time

The use of carbocyanine dye J-aggregates as sensitizers of photoelectric sensitivity and chromophores with the third-order nonlinear optical polarizability made it possible, by the action of two intersecting He–Ne laser (633 nm) beams and an applied electric field, to obtain photorefractive spatial modulation of the refractive index in a nonplasticized polymer layer having the glass transition temperature of about 230°C with a short (20 ms) time of response to this action. A fairly high two-beam-coupling gain coefficient was obtained, which reached a value of = 218 cm^–1 at an applied field of E ₀ = 50 V/m. The net internal gain (difference between the beam-coupling gain coefficient and the absorption coefficient ) was – = 143 cm^–1 under these conditions.     

Evaluation of Incomplete Gamma Functions Using Downward Recursion and Analytical Relations

New downward recursion and analytical approaches are presented for the calculation of incomplete gamma functions (,x) and (,x). The efficiency of calculation with an adequate interval of these expressions is compared with those of other methods and great numerical stability and good rate of convergence is obtained for wide range of integral parameters. It is shown that the downward recursive relations are stable for all values of and x of (,x).     

On the solution of diffusion controlled adsorption kinetics for any adsorption isotherms

Summary The problem of diffusion controlled adsorption kinetics is solved by application of an implicite difference method. Thereby all forms of adsorption isotherms can be used in the calculations. Computation examples are given concerning Langmuir, Freundlich, Volmer, Frumkin, and van der Waals isotherms.

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Zusammenfassung Es wird das Problem der diffusions-kontrollierten Adsorptionskinetik durch Anwendung eines impliziten Differenzenverfahrens gelöst. Dabei können bei der Berechnung alle Formen von Adsorptionsisothermen zugrunde gelegt werden. Rechenbeispiele für die Langmuir-, Freundlich-, Volmer-, Frumkin- und van-der-Waals-Isotherme werden angegeben.

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Nomenclature c concentration - c _o bulk concentration - D diffusion coefficient - x distance from the surface - t time - surface concentration - ₀ equilibrium surface concentration - saturation surface concentration - k _o/c _o - K ₁,K ₂ parameters of Henry and Freundlich isotherm with the dimension of a length - n parameter of Freundlich isotherm - a ₁,a ₂ interaction parameters - B ₁,B ₂,B ₃,B ₄ parameters of different isotherms with the dimension of a concentration - R gas law constant - T absolute temperature dimensionless parameters C c/c _o - / _o - X x/k - X step size ofX - Dt/k ² - step size of - _e time at - 0.95 Zentralinstitut für Organische Chemie,Bereich Grenzflhenaktive Stoffe, der Akademie der Wissenschaften der DDR, Berlin-AdlershofWith 6 figures and 1 table     

Thermal decomposition of octahedral Ni(II) complexes with 1-Naphthylacetic acid hydrazide

The thermal decompositions of the octahedral complexes of Ni(II) with 1-naphthylacetic acid hydrazide (L), of the type NiL_nX₂·mH₂O, wheren=2 and 3,m=2 and 4, andX=Cl, Br, I, NCS, OAc and 1/2 SO₄, were studied in both air and nitrogen atmospheres at temperatures up to 1000 C. The most probable mechanism of the process was proposed.

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Zusammenfassung In dieser Arbeit wurde die thermische Zersetzung oktaedrischer Ni(II)-Komplexe mit Hydraziden der 1-Naphthylessigsäure (L) des Types NiL_n X ₂·mH₂O untersucht, wobein=2 bzw. 3,m=2 bzw. 4 undX=Cl, Br, I, NCS, OAc bzw. 1/2 SO₄ ist. Die thermische Zersetzung wurde in Luftbzw. Stickstoffatmosphäre bis zu Temperaturen von 1000 C durchgefürt und der wahrscheinlichste Mechanismus des Prozesses gegeben.

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1- (L) NiL_n X ₂·mH₂O, n=2 3,m=2 4, X=Cl, Br, I, NCS, OAc 1/2SO₄. 1000. .

     

The height of DSC phase transition peaks application to liquid crystals

A new method for differentiating first- and second-order transition in liquid crystalline systems is proposed. It is based on the use of the ratioN=h/h ₀, whereh ₀ is the height of the transition peak recorded by DSC at a heating rateT _p with a massm, andh is the height of the corresponding peak when the heating rate or the mass is doubled. The application of this new concept to phase transitions in octylcyanobiphenyl (8CB) is mentioned.

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Zusammenfassung Eine neue Methode zur Unterscheidung von Umwandlungen erster und zweiter Art in flüssigen Kristallen wird vorgeschlagen, die auf Anwendung des VerhältnissesN=h/h₀ basiert, wobeih ₀ die Höhe des durch DSC bei einer AufheizgeschwindigkeitT _p und für die Massem registrierten Umwandlungspeaks undh die Höhe des entsprechenden Peaks bei Verdoppelung der Aufheizgeschwindigkeit oder der Masse bedeuten. Auf die Anwendung dieses neuen Konzepts auf Phasenübergänge in Octylcyanobiphenyl (8CB) wird eingegangen.

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. N=h/h ₀, h ₀- , T _p m, h- . -.

     

Reduced-density-matrix theory: The electron-pair approximation

The form of the K-space representation, , of the 2-matrix for electronic wave functions, which depends strongly on the form of the wave function, is discussed. For Hartree-Fock functions is diagonal, for antisymmetrized products of strongly orthogonal geminal (APSG) functions has N/2 idempotent blocks plus diagonal terms, and for configuration interactions functions is generally non-diagonal. A new proof of the special properties of for APSG functions is given. The 2-matrix of the truncated natural orbital expansion of the Boys ¹ S Be function is presented and discussed in view of the electron-pair approximation. The natural 3-state functions needed in the 1–3 natural expansion of Be are also presented.

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Zusammenfassung Die Form der K-Raum-Darstellung, , der Zweiermatrix für Elektronenwellenfunktionen, die stark von der Form der Wellenfunktion abhängt, wird diskutiert. Für Hartree-Fock-Funktionen ist diagonal, für antisymmetriesierte Produkte von streng orthogonalen Geminalen (APSG) besteht aus N/2 idempotenten Blöcken plus Diagonaltermen, und für Konfigurationswechselwirkungsfunktionen ist allgemein nicht-diagonal. Für die speziellen Eigenschaften von für APSG's wird ein neuer Beweis gegeben. Die Zweiermatrix der abgebrochenen Entwicklung natürlicher Orbitale der Boys'schen ¹ S-Be-Funktionen wird angegeben und im Hinblick auf die Elektronenpaarapproximation diskutiert. Die in der natürlichen 1–3-Entwicklung von Be benötigten 3-Elektronen-Funktionen werden gleichfalls angegeben.

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Résumé On discute la forme de la représentation dans l'espace K, de la matricedensité du second ordre pour des fonctions d'onde électroniques; elle dépend fortement de la forme de la fonction d'onde. Pour des fonctions de Hartree-Fook est diagonal, pour des produits antisymétrisés de fonctions géminales fortement orthogonales (APSG) a N/2 blocs idempotents et des termes diagonaux, pour des fonctions d'interaction de configuration est généralement non-diagonal. Une nouvelle preuve des propriétés spéciales de pour les fonctions APSG est donnée. La matrice du second-ordre du développement tronqué de Boys en orbitales naturelles pour ¹ S Be est présentée et discutée du point de vue de l'approximation par paires. Les fonctions naturelles a 3 états nécessaires au développement naturel 1–3 de Be sont aussi données.

     

The relationship between the structures of Cu(II) complexes and their chemical transformations

The paper presents the results of a study of M ₂ ^I M ^II(SO₄)₂ compounds withM ^I= K, Rb, Cs or Tl, andM ^II=Cu or Ni, in the interval from room temperature to the melting temperature. All the compounds studied show endo- or exothermic excursions in their DTA curves, corresponding to phase transitions connected with colour changes of the compounds. For M ₂ ^I Cu(SO₄)₂, whereM ^I is K or Tl, several modifications could be prepared at laboratory temperature, probably distortion isomers. No modifications of this type could be prepared, however, for M ₂ ^I Ni(SO₄)₂ compounds.

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Zusammenfassung Die Ergebnisse einer Untersuchung von M ₂ ^I M ^II(SO₄)₂-Verbindungen Cs, Tl;M ^II=Cu, Ni) im Temperaturbereich von Raum- bis Schmelztemperatur werden beschrieben. Alle untersuchten Verbindungen zeigen in ihren DTA-Kurven mit Farbänderungen einhergehende, durch Phasenumwandlungen bedingte endo- und exotherme Peaks. Bei Laboratoriumstemperatur konnten verschiedene Modifikationen von M ₂ ^I Cu(SO₄)₂ (mitM ^I gleich K oder Tl) hergestellt werden, wobei es sich wahrscheinlich um Distorsionsisomere handelt. Keine Modifikationen dieses Typs konnten jedoch für M ₂ ^I Ni(SO₄)₂ erhalten werden.

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M ₂ ^I M ^II(SO₄)₂, ¹-, Rb, Cs Tl, aM ¹¹-Cu Ni, . - -, , . M ₂ ^I Cu(SO₄)₂, ¹- l, , , , . , M _i ² Ni(SO₄)₂ .

     

Thermal decomposition of Cu(I) phosphine complexes

The thermal decomposition of Cu(I) phosphine complexes of the general types (CuXPPh₃)₄, [CuX(PPh₃)₂] and [CuX(PPh₃)₃] was investigated.The thermal decomposition of (CuXPPh₃)₄, where X denotes Cl^–, Br^–, I^–, NO ₃ ^– and PPh₃=P(C₆H₅)₃, occurs with formation of a phosphine oxide intermediate. For the remaining complexes this intermediate was not proved in the thermal decomposition.

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Zusammenfassung Die thermische Zersetzung der Cu(I)-Phosphinkomplexe vom allgemeinen Typ (CuXPPh₃)₄ und [CuX(PPh₃)₂], wie auch [CuX(PPh₃)₃] wurde untersucht. Die thermische Zersetzung von (CuXPPh₃)₄, wobei X=Cl^–, Br^–, I^– und NO ₃ ^– bedeutet und PPh₃=P(C₆H₅)₃, verläuft unter Bildung eines Phosphinoxid Zwischenproduktes, bei den übrigen Komplexen konnte dieses im Laufe der thermischen Zersetzung nicht nachgewiesen werden.

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Résumé On a étudié la décomposition thermique des complexes phosphine-Cu(I) de formule générale (CuXPPh₃)₄, [CuX(PPh₃)₂], [CuX(PPh₃)₃]. La décomposition thermique de (CuXPPh₃)₄, où X désigne Cl^–, Br^–, I^– et NO ₃ ^– , et PPh₃=P(C₆H₅)₃, s'effectue avec formation d'un oxyde de phosphine intermédiaire; avec les autres complexes, cet intermédiaire n'a pas été mis en évidence au cours de la décomposition thermique.

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(CuXPPb₃)₄ [CuX(PPh₃)₂] [CuX(PPh₃)₃]. (CuXPPh₃)₄, X=Cl^–, Br^–, I^–, NO ₃ ^– , PPh₃=(₆₅)₃ . .

     

Thermal properties of the clathrate compounds of binary cyanides

The stoichiometry of thermal decomposition of a particular group of clathrate compounds, of the type Cd(en)Pd(CN)₄·2G, with the same coordination component but different clathrate-enclosed components, was investigated. Irrespective of the experimental conditions, the liberation of the enclosed component G always proceeded in one step. Thermal investigation of the decomposition stoichiometry under identical experimental conditions showed that the temperature intervals in which the enclosed components are given off shift to lower temperatures in the order C₆H₅OH=> C₆H₆ > > C₄H₅N > C₄H₄S. Diffraction measurements indicated a considerable change in the structures of the original clathrate compounds after thermal release of the enclosed componentG.

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Zusammenfassung Die Stöchiometrie der thermischen Zersetzung einer bestimmten Gruppe von Klathratverbindungen vom Typ Cd(en)Pd(CN)₄·2G mit der gleichen Koordinationskomponente und verschiedenen Klathrat-Einschlußkomponenten wurde in dieser Studie untersucht. Ungeachtet der Versuchsbedingungen vollzieht sich die Freisetzung der eingeschlossenen KomponenteG stets in einer Stufe. Die unter gleichen Versuchsbedingungen durchgeführte thermische Untersuchung der Zersetzungsstöchiometrie zeigte, daß die Temperaturbereiche, in denen die eingeschlossenen Komponenten freigesetzt werden in der Reihenfolge C₆H₅OH > C₆H₆ > C₄H₅N > C₄H₄S in Richtung der niedrigeren Temperaturwerte verschoben werden. Die Diffraktionsmessungen weisen darauf hin, daß eine beträchtliche Änderung der Struktur der ursprünglichen Klathratverbindung nach thermischer Freisetzung der eingeschlossenen KomponenteG sichtbar wird.

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Résumé Dans cette étude on a établi la stoechiométrie de la décomposition thermique d'un groupe particulier de clathrates du type Cd(en)Pd(CN)₄·2G, avec le même composant de coordination et différents composants occlus. Indépendamment des conditions d'expériences, la libération du composant occlusG s'effectue toujours en une étape. L'étude thermique de la stoechiométrie de la décomposition effectuée dans les mêmes conditions d'expériences, a montré que les intervalles des températures dans lesquels les composants occlus sont libérés, se déplacent vers les températures plus faibles dans l'ordre suivant: C₆H₅OH > C₆H₆ > > C₄H₅N > C₄H₄S. Les mesures de diffraction indiquent qu'après la libération thermique du composant occlusG, une variation considérable de la structure initiale des clathrates originaux apparaît.

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Cd(en)Pd(CN)₄. 2G . , G . , , , ] ₆₅>₆₆>C₄H₆N>C₄H₄S. - , G.