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  • 1
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 93 (1989), S. 3605-3612 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 93 (1989), S. 3613-3624 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 470-481 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider the kinetics of the reversible aggregation of monomers to form roughly spherical clusters where the effect of excluded volume is taken into account by using Lebowitz's exact solution of the Percus–Yevick equation for a mixture of hard spheres, assuming rapid spatial equilibration relative to the rate of aggregation. Using the radial distribution function evaluated at the contact distance between two spheres, we obtain a differential equation for the aggregation process that is a sum over cubic terms in the appropriate cluster densities. The differential equation is converted into a recursion relation for the coefficients in a series in powers of the time. The series can then be used to estimate the asymptotic relaxation time for the aggregation process.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 91 (1989), S. 1885-1896 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A simple matrix method is given that generates the probability distribution for the coordinates of the end of a polymer chain (modeled as a random walk on a regular lattice with a finite range of intrachain correlation). From this information the exact end-to-end distance distribution can be constructed. The method can be applied to specific sequence copolymers and to the distance distribution for arbitrary points within a polymer chain.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 95 (1991), S. 7984-7997 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In a previous work we showed that the kinetics of a mass-action mechanism in the neighborhood of a steady state arbitrarily far from equilibrium could be expressed in terms of a sum of matrices, one of which we could identify as the source of all potential instabilities. In the present work we examine various truncated versions of the full linearized kinetic equation, including the maximum truncation that contains only the single interesting matrix, for several classic models exhibiting instabilities far from equilibrium in order to see at what level of truncation the true nature of the instability emerges. We utilize dimensionless ratios of steady-state concentrations and currents, which can be displayed in appropriate graphs, as variables in order to minimize the number of kinetic parameters in the analysis. In general, we find that the interesting matrix by itself usually correctly signals potential instabilities. Since this single matrix is often much simpler than the total kinetic matrix, its use simplifies the task of locating interesting regions (i.e., instabilities) in parameter space.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 4427-4439 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We consider the stability of chemical systems whose evolution is governed by mass action reactions. We show, with no reference to the second law of thermodynamics, that the stability of equilibrium in a closed system follows from the fact that one can express the kinetic matrix for the linearized equations near equilibrium in the form of a matrix times its transpose. This is a necessary and sufficient condition that the matrix be positive indefinite (some of the eigenvalues are necessarily zero due to the existence of conservation relations in a closed system). We then extend this approach to open systems where one finds that a component of the kinetic matrix cannot be expressed as the product of a matrix times its transpose. It is this matrix, having a simple expression in terms of stoichiometric matrices, thus expressing the basic mechanisms of the chemistry, that is potentially responsible for instabilities, oscillations, and chaos far from equilibrium. Examination of this matrix leads naturally to autocatalytic reactions as candidates for interesting behavior far from equilibrium. We conclude that all of the interesting features of mass action kinetics can be determined directly from the kinetic equations and the principle of detailed balance with no additional constraints coming uniquely from thermodynamics.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 4862-4877 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Cooperative interactions between reacting species (nonideal effects) enhance the nonlinear character of chemical reactions kinetics. In the limit that the equilibration between the solvent and the reactants and products is rapid compared to the rate of conversion of reactants to products (and vice versa), one can use grand partition function techniques to calculate the probabilities of the appropriate reactant and product complexes with solvent. This leads in turn to the rate equation in terms of the activities of the particles; relations from equilibrium statistical mechanics allow one to convert back and forth between concentrations and activities. For the example of chemistry occurring in a one-dimensional lattice gas, a grand partition function-like quantity is used to generate the rate equation (a sum over all solvent cages weighted with the appropriate rate constants). A general form is given for the linearized rate equation in nonideal systems arbitrarily far from equilibrium. As expected, it is found that nonideality as well as distance from equilibrium can lead to instabilities and oscillations. As an example, we treat a simple association reaction (2x↔y), where the only nonideal effect is excluded volume. If we make the system open by allowing x to enter the system with a rate proportional to the number of vacant lattice sites (and y to leave the system with first order kinetics), then far from equilibrium this reaction shows oscillations (stable spirals) with and without the effect of excluded volume. We discuss the use of the angle between the eigenvectors (in the appropriate coordinate system) as a measure of the distance to the onset of oscillation.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    Langmuir 7 (1991), S. 514-519 
    ISSN: 1520-5827
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 2604-2613 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The maximum-entropy method is used to construct the end-to-end distribution function for lattice polymers when a large number of moments are known exactly. We use two-dimensional lattice polymers with a finite range of intrachain interaction as examples since, for these systems, the end-to-end distribution function and any number of moments can be calculated exactly using Toeplitz matrices. For chains with strong intrachain interactions the distributions are very non-Gaussian requiring up to six moments to reproduce the main features of the functions. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 69 (1965), S. 2431-2442 
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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