Application of the extended RSA models in studies of particle deposition at partially covered surfaces

This paper reviews the application of the extended random sequential adsorption (RSA) approaches to the modeling of colloid-particle deposition (irreversible adsorption) on surfaces precovered with smaller particles. Hard (noninteracting) particle systems are discussed first. We report on the numerical simulations we performed to determine the available surface function, jamming coverage, and pair-correlation function of the larger particles. We demonstrate the effect of the particle size ratio and the small particle surface coverage. We found that the numerical results were in reasonable agreement with the formula stemming from the scaled-particle theory in 2D with a modification for the sphere geometry. Next, we discuss three approximate models of adsorption allowing electrostatic interaction of colloid particles at a charged interface, employing a many-body superposition approximation. We describe two approaches of the effective hard-particle approximation next. We demonstrate the application of the effective hard-particle concept to the bimodal systems and present the effect of electrolyte concentration on the effective particle size ratio. We present the numerical results obtained from the theoretical models of soft-particle adsorption at precovered surfaces. We used the effective hard-particle approximation to determine the corresponding simpler systems of particles, namely the system of hard spheres and the system of hard discs at equilibrium. We performed numerical computations to determine the effective minimum particle surface-to-surface distance, available surface function, jamming coverage, and pair-correlation function of the larger particles at various electrolyte ionic strengths and particle size ratios. The numerical results obtained in the low-surface coverage limit were in good agreement with the formula stemming from the scaled-particle theory with a modification for the sphere geometry and electrostatic interaction. We compared the results of numerical computations of the effective minimum particle surface-to-surface distance obtained using the 2D, 3D, and curvilinear trajectory model. The results obtained with the 3D and curvilinear trajectory models indicate that large-particle/substrate attractive interaction significantly reduces the kinetic barrier to large, charged-particle adsorption at a surface precovered with small, like-charged particles. The available surface function and jamming-coverage values predicted using the simplified 3D and the more sophisticated curvilinear trajectory models are similar, while the results obtained with the 2D model differ significantly. The pair-correlation function suggests different structures of monolayers obtained with the three models. Unlike the three models of the electrostatic interaction, both effective hard-particle approximations give almost identical results. Results of this research clearly suggest that the extended RSA approaches can fruitfully be exploited for numerical simulations of colloid-particle adsorption at precovered surfaces, allowing the investigation of both hard and soft-particle systems.     

Complexes of Mn(II), Co(II), Ni(II), Cu(II) and Zn(II) with 4-chloro-2-methoxybenzoic acid anion

The complexes of 4-chloro-2-methoxybenzoic acid anion with Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺ and Zn²⁺ were obtained as polycrystalline solids with general formula M(C₈H₆ClO₃)₂·nH₂O and colours typical for M(II) ions (Mn – slightly pink, Co – pink, Ni – slightly green, Cu – turquoise and Zn – white). The results of elemental, thermal and spectral analyses suggest that compounds of Mn(II), Cu(II) and Zn(II) are tetrahydrates whereas those of Co(II) and Ni(II) are pentahydrates. The carboxylate groups in these complexes are monodentate. The hydrates of 4-chloro-2-methoxybenzoates of Mn(II), Co(II), Ni(II), Cu(II) and Zn(II) heated in air to 1273 K are dehydrated in one step in the range of 323–411 K and form anhydrous salts which next in the range of 433–1212 K are decomposed to the following oxides: Mn₃O₄, CoO, NiO and ZnO. The final products of decomposition of Cu(II) complex are CuO and Cu. The solubility value in water at 293 K for all complexes is in the order of 10^–3 mol dm^–3. The plots of χ_M vs. temperature of 4-chloro-2-methoxybenzoates of Mn(II), Co(II), Ni(II) and Cu(II) follow the Curie–Weiss law. The magnetic moment values of Mn²⁺, Co²⁺, Ni²⁺ and Cu²⁺ ions in these complexes were determined in the range of 76−303 K and they change from: 5.88–6.04 μ_B for Mn(C₈H₆ClO₃)₂·4H₂O, 3.96–4.75 μ_B for Co(C₈H₆ClO₃)₂·5H₂O, 2.32–3.02 μ_B for Ni(C₈H₆ClO₃)₂·5H₂O and 1.77–1.94 μ_B for Cu(C₈H₆ClO₃)₂·4H₂O.     

Interaction potentials of the RG-I anions, neutrals, and cations (RG = He, Ne, Ar)

Interaction potentials of the iodine atom, atomic cation, and anion with light rare-gas atoms from He to Ar are calculated within the unified ab initio approach using the unrestricted coupled-cluster with singles and doubles and perturbative treatment of triples correlation treatment, relativistic small-core pseudopotential, and an extended basis set. Ab initio points are fit to a flexible analytical function. The calculated potentials are compared with available literature data, assessed in the I(-)-and I+-ion mobility calculations and the Ar-I(-)-anion zero electron kinetic-energy spectra simulations, and analyzed using the correlation rules. The results indicate a high precision of the reported potentials.     

Construction of a thermoanalyzer for DTA-TD-TMAG-T measurements on metals up to 1100 °C

A thermoanalyzer is described for the simultaneous testing of metals and alloys by three methods: differential thermal analysis (DTA), thermal dilatometry (TD) and thermomagnetometry (TMAG). One reference specimen is used as a standard for each of the above kinds of analysis. Measurements can be performed in vacuum or in a static or dynamic atmosphere of gases at any pressure between normal and 5× 10^–5 Torr. The temperature of the sample can be changed linearly in the range 20–1100 °C. DTA and TD are performed classically, whereas TMAG is based on the temperature and magnetic field-dependences of the reversible magnetic susceptibility of the sample. Some analysis results are presented.

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Zusammenfassung Es wird ein Thermoanalysator zur simultanen Untersuchung von Metallen und Legierungen durch drei Methoden beschrieben: Differentialthermoanalyse (DTA), Thermodilatometrie (TD) und Thermomagnetometrie (TMAG). Für alle drei Verfahren wurde die gleiche Referenzsubstanz als Standard benutzt. Messungen können im Vakuum oder is statischer bzw. bewegter Atmosphäre von Gasen beliebigen Druckes zwischen Normaldruck und 5·10^–5 Torr durchgeführt werden. Die Temperatur der Probe kann zwischen 20 und 1100 °C linear variiert werden. Während DTA und TG die herkömmlichen Verfahren zu Grunde liegen, basiert TMAG auf der Temperatur- und Magnetfeldabhängigkeit der reversiblen magnetischen Suszeptibilität der Probe. Einige Analysenergebnisse wurden dargestellt.

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: (), () (). . , 5·10^–5 . 20–1100°. , . .

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Presented at the 4th European Symposium on Thermal Analysis and Calorimetry, Jena, GDR, August 1987.     

Correlation in calculations of density of states in thin films

The density of electronic states and its spatial distribution in thin films are considered including the electron correlations in the coherent phase approximation applied to the intra-atomic interaction. This new approach allows us to derive the line shape for electronic levels which is important from the point of view of the convergency for the density function in the case of systems with restricted dimensions. Detailed calculations are performed for 4s copper film functions with the fcc lattice and various crystallographic orientations of the surfaces.The authors are very grateful to Professor L. Valenta (Prague) for his kind interest in this paper and to Dr. J. Mizia (Cracow) for helpful discussions. We would like to express our gratitude to Professor M. Wonicki and Mrs M. Firszt (Toru) for their help in obtaining the computer program procedure for two-particle interaction integrals calculations.The paper has been done in the framework of the Problem M.R I-11.     

Thermal investigation of active carbons in presence of air

Thermal analysis data on the oxidation reaction between air and active carbons obtained during activation by carbon dioxide are presented. The correlation between the modified DTA curves and the TG curves leads to the conclusion that the oxidation of active carbons in the temperature range from 20 to 1000° is a two-step process. It is pointed out that the oxidation reactions in the low-temperature region (450–550°) are governed by the oxygen content of the samples, whereas the reactions in the higher temperature region (550–850°) are controlled by the diffusion process.

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Zusammenfassung Die thermoanalytischen Ergebnisse über die während der Aktivierung durch Kohlendioxid stattfindende Oxidationsreaktion zwischen Luft und Aktivkohlen werden vorgestellt. Die Korrelation zwischen den modifizierten DTA-Kurven und den TG-Kurven führte zur Schlußfolgerung, daß die Oxidation der Aktivkohlen im Temperaturbereich von 20 bis 1000° ein Zweistufen-Vorgang ist. Es wird betont, daß die Oxidationsreaktion im niedrigen Temperaturbereich (450 bis 550°) durch den Sauerstoffgehalt der Proben gesteuert wird, während er im Bereich der höheren Temperaturen (550 bis 850°) durch Diffusionsvorgänge geregelt wird.

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Résumé On présente les résultats de l'étude par analyse thermique de la réaction d'oxydation des charbons actifs par l'air qui a lieu lors de l'activation par l'anhydride carbonique. La corrélation entre les courbes ATD modifiées et les courbes TG conduit à la conclusion que l'oxydation des charbons actifs s'effectue entre 20 et 1000°, suivant un processus en deux étapes. Dans l'intervalle des températures faibles (450 à 550°) les réactions d'oxydation sont gouvernées par la teneur en oxygène des échantillons tandis qu aux températures plus élevées (550 à 850°) elles le sont par le processus de diffusion.

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, . , 20 1000° . , (450–550°) , (550–850°) .

     

One-dimensional model with rotational and liquid-crystalline phase transitions

A one-dimensional system of hard-rod particles with rotational-like internal degrees of freedom is considered. Particles interact with each other through the infinite-range, infinitely weak attractive Kac potential, and through a nearest-neighbor short-range potential. The latter depends also on the internal states of the interacting particles. Exact results for thermodynamic properties and for some correlation functions are obtained. It is found that the considered system exhibits several first-order transitions between phases with different rotational structure, i.e., with different ordering with respect to the internal degrees of freedom. The calculated equation of state seems to suggest that in the solutions of liquid-crystalline substances in neutral solvents there may exist regions in which the coefficient of thermal expansion is negative—an effect similar to that well known in liquid water.     

Partial transposition and nonextendible maps

The wide class of nonextendible positive maps inC ^*-algebras [1, 3] is studied. An example is given showing that the set of nonextendible positive maps betweenC ^*-algebras and is not closed inL( ) in the weak topology.     

Laser-Rf double-resonance studies of the hyperfine structure of metastable atomic states of55Mn

The hyperfine structure (hfs) of the metastable atomic states 3d⁶4s⁶ D _{1/2, 3/2, 5/2, 7/2, 9/2} of⁵⁵Mn was measured using theABMR- LIRF method (atomicbeammagneticresonance, detected bylaserinducedresonancefluorescence). The hfs constantsA andB, corrected for second order hfs perturbations, could be derived from these measurements. The theoretical interpretation of these correctedA- andB-factors was performed in the intermediate coupling scheme taking into account the configurations 3d ⁵4s ², 3d ⁶4s and 3d ⁷. Examining the influence of the composition of the eigenvectors on the hfs parameters \(\left\langle {r^{ - 3} } \right\rangle ^{k_s k_l } \) it was found, that for the configuration 3d ⁶4s the two-body magnetic interaction should be considered in the calculation of the eigenvectors. Investigating second order electrostatic configuration interactions and relativistic effects and using calculated relativistic correction factors we obtained for the nuclear quadrupole moment of the nucleus⁵⁵Mn a value ofQ=0.33(1) barn, which is not perturbed by a shielding or antishielding Sternheimer factor. The following hfs constants have been obtained: $$\begin{gathered} A\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 882.056\left( {12} \right)MHz \hfill \\ A\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 469.391\left( 7 \right)MHzB\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 65.091\left( {50} \right)MHz \hfill \\ A\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 436.715\left( 3 \right)MHzB\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 46.769\left( {30} \right)MHz \hfill \\ A\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 458.930\left( 3 \right)MHzB\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 21.701\left( {40} \right)MHz \hfill \\ A\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 510.308\left( 8 \right)MHzB\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 132.200\left( {120} \right)MHz \hfill \\ \end{gathered} $$      

An initial value problem for a singular parabolic equation of even order

At first Cauchy-problem for the equation: \(L[u(X,t)] \equiv \sum\limits_{i = 1}^n {\frac{{\partial ^2 u}}{{\partial x_1^2 }} + \frac{{2v}}{{\left| X \right|^2 }}} \sum\limits_{i = 1}^n {x_i \frac{{\partial u}}{{\partial x_i }} - \frac{{\partial u}}{{\partial t}} = 0} \) wheren≥1,v—an arbitrary constant,t>0,X=(x ₁, …, x_n)∈E ⁿ/{0}, |X|= =(x ₁ ² +…+x _n ² )^1/2, with 0 being a centre of coordinate system, is studied. Basing on the above, the solution of Cauchy-Nicolescu problem is given which consist in finding a solution of the equationL ^p [u (X, t)]=0, withp∈N subject the initial conditions \(\mathop {\lim }\limits_{t \to \infty } L^k [u(X,t)] = \varphi _k (X)\) ,k=0, 1,…,p?1 and ?_k(X) are given functions.