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  • 1
    Digitale Medien
    Digitale Medien
    A simplified stochastic description for the A+B2 surface reaction including A diffusion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 8522-8525 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: We introduce a simplified stochastic model for the A+B2 surface reaction with diffusion of the monomer particle. We use a stochastic description which consists only of an autonomous differential equation system with four variables (the coverage of A and B and the corresponding pairs). The solution of this system is a straightforward process. We compare the values of the phase transition points with a much more complex stochastic ansatz which has been introduced earlier [Mai, Kuzovkov, and von Niessen, J. Chem. Phys. 100, 6073 (1994)]. We find good agreement in the prediction of the first-order phase transition with the complete treatment. The ansatz also gives the second-order transition, but the results are not quantitative in the neighborhood of the second-order phase transition.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.466751
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  • 2
    Digitale Medien
    Digitale Medien
    A stochastic model and a Monte Carlo simulation for the description of CO oxidation on Pt/Sn alloys (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 5037-5044 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: In this paper we study CO oxidation on a catalyst consisting of a Pt/Sn alloy. On this catalyst the reaction can take place at room temperature. We use for the description two basically different methods: Monte Carlo simulations and a theoretical stochastic ansatz. The stochastic ansatz introduced recently [Mai, Kuzovkov, and von Niessen, Physica A 203, 298 (1994)] is a general method for the description of surface reaction systems including mono- and bimolecular steps. Using the Markovian behavior of these systems we formulate this ansatz in terms of master equations. It turns out that the stochastic ansatz can be used as an interesting and advantageous alternative to the standard Monte Carlo simulations. The particles involved in the reaction system have different tendencies toward building structures on the surface. The coverages show a strong dependency, not only on the composition of the gas phase but also on the initial concentration of the reaction promotor OH and the concentration of Pt sites in the catalyst material. The reaction probability does not influence the qualitative trends of the coverages versus the gas phase concentration of CO. © 1995 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.469553
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  • 3
    Digitale Medien
    Digitale Medien
    Stochastic model for the A+B2 surface reaction: Island formation and complete segregation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 100 (1994), S. 6073-6081 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: In this paper we introduce a stochastic model for the A+1/2B2→0 reaction on a square lattice. Reaction between an A and a B particle occurs if they are nearest neighbors on the lattice. To this system which includes adsorption and reaction steps we add the effect of A-diffusion and A-desorption. We describe the model in terms of master equations using the Markovian behavior of the system. The equations are truncated at a certain level via a modified Kirkwood approximation. The reaction is in this paper introduced between particles which are nearest neighbors on the lattice. This approach which is different from a previous article [J. Mai et al., J. Chem. Phys. 98, 10017 (1993)] requires a special treatment of the stochastic equations and the correlation functions. In particular the Kirkwood superposition approximation, which is used to truncate the hierarchy of equations, has to be modified. The resulting system of lattice equations is solved in a small region around a reference point. The solution is connected to continuous functions which describe the system behavior for larger distances. This system shows kinetic phase transitions which separate the reactive regime from two nonreactive states where the lattice is completely covered by A or B. We study the location and the character of the phase transitions in detail. With the help of correlation functions we identify the different phases of particles on the lattice. Island formation and segregation of the particles on the lattice are found to be dominant processes. It is established that finite lattices which have to be used in simulations can be seriously inadequate and miss physical processes. This problem does not appear in the ansatz presented here.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.467118
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  • 4
    Digitale Medien
    Digitale Medien
    The kinetics of the bimolecular A+B→0 reaction in condensed matter: Effects of non-equilibrium charge screening (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 9486-9492 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The kinetics of the bimolecular A+B→0 reaction between charged reactants is studied in two dimensions, i.e., on a surface. The theory is based on the Kirkwood superposition approximation for three-particle densities and the self-consistent treatment of the electrostatic interactions defined by the non-uniform spatial distribution of similar and dissimilar reactants. Special attention is paid to pattern formation and many-particle effects arising from reaction-induced formation of loose domains containing similar reactants only. It is shown that the critical exponent α characterizing the algebraic concentration decay law, n(t)∝t−α, differs strongly between symmetric (DA=DB) and asymmetric (DA=0) reactant mobilities. This effect is abnormal from the point of view of standard chemical kinetics. It arises directly from the specific spatial distribution in the system as in "raisins A in a dough B.'' At long reaction times the asymptotics of the interaction potentials is of non-equilibrium type at large relative distances. The accumulation kinetics in the presence of a permanent source is studied. Results of the microscopic formalism are compared with a previous mesoscopic theory. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.472782
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  • 5
    Digitale Medien
    Digitale Medien
    A theoretical stochastic model for the A+1/2B2→0 reaction (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 10017-10025 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A surface reaction model for the A+1/2B2→0 reaction is studied by a theoretical approach. To this end, we introduce a stochastical ansatz which describes the system behavior by master equations. These equations are solved numerically in the superposition approximation. The results of the theoretical description are in good agreement with the corresponding computer simulations of the system. We focus our interest on the study of oscillations. The correlation functions and the parameter ranges in which oscillations are possible are studied in detail. This model as well as the computer simulations describe some aspects of the heterogeneously catalyzed oxidation of CO on a Pt surface.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.464434
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  • 6
    Digitale Medien
    Digitale Medien
    Kinetic oscillations in the catalytic CO oxidation on Pt single crystal surfaces: Theory and simulation (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 5571-5580 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A simple lattice gas model is studied for the description of the kinetic oscillations in the CO oxidation on the Pt(100) and Pt(110) surfaces. It takes CO diffusion and surface reconstruction into account and exhibits very interesting phenomena such as synchronized oscillations and mesoscopic pattern formation. The model uses only few parameters, the CO gas phase concentration y, the CO diffusion constant D, the surface phase propagation velocity V, and the ratio of the O2 sticking coefficients on the two surface phases. This enables the study of the whole parameter regime and the theoretical stability analysis for the kinetic oscillations. It can be shown that it is only the ratio of the O2 sticking coefficients on the reconstructed and non–reconstructed surfaces which determines the type of oscillations and the parameter range where these oscillations exist. © 1998 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.475341
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  • 7
    Digitale Medien
    Digitale Medien
    The phase diagram of the multi-dimensional Anderson localization via analytic determination of Lyapunov exponents (2004)
    Springer
    The European physical journal 42 (2004), S. 529-542 
    Details
    ISSN: 1434-6036
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract. The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J. Phys.: Condens. Matter 14, 13777 (2002)] is generalized for higher spatial dimensions D. In this way the generalized Lyapunov exponents for diagonal correlators of the wave function, 〈 ψ2n,m 〉, can be calculated analytically and exactly. This permits to determine the phase diagram of the system. For all dimensions D 〉 2 one finds intervals in the energy and the disorder where extended and localized states coexist: the metal-insulator transition should thus be interpreted as a first-order transition. The qualitative differences permit to group the systems into two classes: low-dimensional systems (2≤D ≤3), where localized states are always exponentially localized and high-dimensional systems (D≥ Dc=4), where states with non-exponential localization are also formed. The value of the upper critical dimension is found to be D0=6 for the Anderson localization problem; this value is also characteristic of a related problem – percolation.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1140/epjb/e2005-00011-1
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  • 8
    Digitale Medien
    Digitale Medien
    Theory of diffusion-controlled reactions on a surface (1984)
    Springer
    Theoretical and experimental chemistry 19 (1984), S. 489-493 
    Details
    ISSN: 1573-935X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00526018
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  • 9
    Digitale Medien
    Digitale Medien
    Diffusion chaos in the Lotke-Volterra stochastic model (1988)
    Springer
    Theoretical and experimental chemistry 24 (1988), S. 1-7 
    Details
    ISSN: 1573-935X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract It is shown that a chaotic state exists in the Lotke-Volterra model because of diffusion control in a bimolecular reaction chain; this stochastic model is used to show that irregularities occur only when there are two intermediate reaction products and are related to deviation from the mass-action law.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01392182
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  • 10
    Digitale Medien
    Digitale Medien
    Multiparticle effects in the kinetics of diffusion-controlled reactions (1985)
    Springer
    Theoretical and experimental chemistry 21 (1985), S. 31-35 
    Details
    ISSN: 1573-935X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract We present the equations for the kinetics of the bimolecular reaction A + B → AB, taking into account both the competition of adjacent reagents and strong interaction with the environment. For the electrostatic forces we give a modification of the equations with self-consistent determination of the effective potential. We have shown that multiparticle effects are apparent in the time dependence of the reaction rate constant and the deviation from the formal kinetics laws.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00524307
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