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  • 1
    Digitale Medien
    Digitale Medien
    Limit cycles and discontinuous entropy production changes in the reversible Oregonator (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 7929-7935 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: We show that the chemical entropy production in the reversible Oregonator changes discontinuously at critical values of the concentration parameter at which points a limit cycle bifurcates out of an unstable steady state. The discontinuities in the entropy production are reminiscent of the behavior of the entropy change accompanying a first order phase transition in thermodynamics. They appear to be an example of dynamic phase transitions. For this model, by using Poore's algorithm, we show that in the case of f=1 the limit cycle is orbitally asymptotically unstable and the bifurcation is subcritical, but in the case of f=0.5 the limit cycle bifurcation at the higher critical concentration of P is subcritical whereas the one at the lower critical concentration of P is supercritical. Therefore, a discontinuous change in chemical entropy production accompanies subcritical Hopf bifurcations and possibly a supercritical Hopf bifurcation. It is conjectured that if a bifurcation is subcritical, attractors of different topological dimensions have different characteristic entropy productions in the same manner as two different states of aggregation of matter have different entropies associated with them.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.459322
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  • 2
    Digitale Medien
    Digitale Medien
    Direct observation of a nonequilibrium velocity distribution function in a system with a thermally activated chemical reaction (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 6695-6699 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The velocity distribution functions for the reactant and product of a thermally activated reaction A+A→B+B are calculated from molecular dynamics simulations. The results are compared with a simple phenomenological theory, which assumes that the temperature of the reactant A may be different from the temperature of the system as a whole. Good agreement between the two methods is observed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.463675
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  • 3
    Digitale Medien
    Digitale Medien
    Some identities and relations for transport coefficients of dense fluids (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 485-493 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The transport coefficients appearing in the dense fluid kinetic theory by the author are cast in the forms of time correlation functions suitable for numerical simulation methods. The Einstein relation for the diffusion coefficient and friction constant is found to follow exactly from the collision integral for the diffusion coefficient in the dense fluid kinetic theory. By assuming that the momentum and the force (or configuration) relax at different rates in the dilute and dense regimes of density, it is shown that the self-diffusion coefficient and the viscosity have two different relations, i.e., the one predicted by the mean free path theory and the Stokes–Einstein-type relation. The intrinsic viscosity of a polymer solution is shown to scale like mν/2a, where ν is an index and ma is the molecular weight, if the momentum relaxation time of the polymer scales like (∼(l−2a))ν/2 with ∼(l−2a) denoting the mean square end-to-end distance. If ν=1, the scaling follows Flory's prediction for instrinsic viscosity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.455490
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  • 4
    Digitale Medien
    Digitale Medien
    Modified Padé approximants and equation of state (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 5334-5339 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A modified Padé approximant is proposed for a resummation of the virial expansion. It includes the Carnahan–Starling equation of state as a special case. The second Padé approximant is comparable in accuracy to the Carnahan–Starling formula, the Ree–Hoover [3,3] Padé approximant, and the computer simulation results. A generalized Carnahan–Starling formula is then obtained for the equation of state for the Lennard-Jones fluid by using the modified Padé approximant summing the virial expansion. The generalized Carnahan–Starling formula is comparable with computer simulation results and the Song–Mason equation of state down to the critical temperature, but its accuracy deteriorates below the critical temperature.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.462718
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  • 5
    Digitale Medien
    Digitale Medien
    Ornstein–Zernike derivative relations and thermodynamic functions (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 558-564 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The consequences of the derivatives of the Ornstein–Zernike relation with respect to the density (ρ) and temperature (T) are examined. An approximate closure for the Ornstein–Zernike relation is used to evaluate the derivatives of the pair-correlation function to all orders without knowing explicitly the correlation functions higher in order than the pair-correlation function. The first- and second-order thermodynamic (ρ or T) derivatives of the pair-correlation function are calculated and compared with the experiments of Egelstaff et al. In addition, the thermodynamic functions involving these derivatives are evaluated to demonstrate the utility and accuracy of the method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.462494
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  • 6
    Digitale Medien
    Digitale Medien
    The Debye–Waller factor and the phonon frequency spectrum in molecule–surface scattering (1988)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 89 (1988), S. 3389-3390 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.454953
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  • 7
    Digitale Medien
    Digitale Medien
    Integral equations of the correlation functions for polymeric liquids (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 4084-4102 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The integral equations for intramolecular and intermolecular correlation functions are derived for nonrigid polymeric (polyatomic) liquids by the device of the Kirkwood charging parameters. These integral equations are cast into mean-field-type equations by using the potential elimination method, reported previously for dense simple fluids. Based on the mean-field integral equations, we examine the superposition approximations for various levels of correlation. The present theory provides a means to make systematic corrections for superposition approximations for correlation functions of various orders. Upon using the superposition approximations for the triplet correlation functions in the Kirkwood hierarchy and an assumption or another concerning the charging parameter dependence of the cavity functions, we derive a set of generalized Percus–Yevick and hypernetted chain integral equations for the intramolecular and intermolecular pair correlation functions for beads (sites) of polymeric (polyatomic) liquids. This set of integral equations allows the intramolecular and intermolecular correlation functions to be determined self-consistently. The connection of this set of integral equations to the bead–bead (molecular) Ornstein–Zernike relation is pointed out. The integral equations for the intramolecular correlation functions will be numerically solved for some properties of a single polymer chain in the infinite dilution limit in the sequel to this paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.466105
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  • 8
    Digitale Medien
    Digitale Medien
    Application of the integral equation theory of polymers: Distribution function, chemical potential, and mean expansion coefficient (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 4103-4111 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A recursive integral equation for the intramolecular correlation function of an isolated linear polymer of N bonds is derived from the integral equations presented in the preceding paper. The derivation basically involves limiting the density of the polymer to zero so that polymers do not interact with each other, and thus taking into account the intramolecular part only. The integral equation still has the form of a generalized Percus–Yevick integral equation. The intramolecular correlation function of a polymer of N bonds is recursively generated by means of it from those of polymers of 2, 3,..., (N−1) bonds. The end-to-end distance distribution functions are computed by using the integral equation for various chain lengths, temperatures, and bond lengths in the case of a repulsive soft-sphere potential. Numerical solutions of the recursive integral equation yield universal exponents for the mean square end-to-end distance in two and three dimensions with values which are close to the Flory results: 0.77 and 0.64 vs Flory's values 0.75 and 0.6 for two and three dimensions, respectively. The intramolecular correlation functions computed can be fitted with displaced Gaussian forms. The N dependence of the internal chemical potential is found to saturate after some value of N depending on the ratio of the bond length to the bead radius.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.466106
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  • 9
    Digitale Medien
    Digitale Medien
    Self-consistent integral-equation theory of chain-molecular liquids. II. Improved intermolecular equations (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 4323-4341 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: Improved self-consistent intermolecular integral equations for a chain-molecular liquid are derived from the polymer Kirkwood hierarchy. The present work is a continuation of our recent work reported in a previous paper [J. Chem. Phys. 103, 2140 (1995)]. It is shown that the reference interaction site model (RISM) equation and extensions thereof can be obtained from the new intermolecular equations. The solutions of the new self-consistent set of intra- and intermolecular equations are compared with computer simulation data for chains with repulsive interaction potentials whose lengths N vary from 4 to 100 sites. The intermolecular correlation functions obtained from simulations are accurately reproduced. Comparisons with simulation data for the pressure equation of state and excess chemical potential show that the predictions of the self-consistent theory are accurate for packing fractions up to 0.4. These thermodynamic functions are found to scale as N for N(approximately-greater-than)16, implying that results obtained for short chains can be extrapolated to much longer chains. © 1996 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.472249
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  • 10
    Digitale Medien
    Digitale Medien
    On the integrability of differential forms related to nonequilibrium entropy and irreversible thermodynamics (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 3012-3029 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: The Boltzmann equation has been used in the literature to show that the entropy differential consists of a Pfaffian form in the space of conserved and nonconserved variables (moments) and a term related to the energy dissipation due to the irreversible processes in the system. The said Pfaffian form is called the compensation differential. In this paper, the integrability of the compensation differential is examined by means of the theory of differential forms. The integrability conditions turn out to be generalized forms of the Maxwell relations in equilibrium thermodynamics. It is also shown that the generalized form of the Gibbs–Duhem relation can be seen as an equivalent of the integrability conditions. This conclusion is drawn by using the notion of homotopy operator. The Caratheodory principle is also applied to make the connection with the second law of thermodynamics more intimate than the direct but mathematically more abstract approach using the integrability conditions. The meaning of the integrating factor is clarified by using the notion of contact temperature since the integrating factor, a mathematical function, is endowed with a thermodynamically operational meaning when it is identified with the inverse local absolute temperature through the notion of contact temperature, and the compensation differential is thereby made a thermodynamically meaningful equation governing nonequilibrium processes. Through this study it is shown that in irreversible thermodynamics the compensation differential can play the role parallel to the equilibrium Gibbs relation for the entropy in equilibrium thermodynamics and thus can serve as the foundation on which to formulate a theory of irreversible processes.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.530060
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