Equilibrium dynamic properties

By virtue of the slithering-snake algorithm it is (hitherto) possible to remove all non-equilibrium effects up to T 0.16 so that one can study the equilibrium dynamic properties of the model in the supercooled state. During supercooling the structural relaxation time increases over several orders of magnitude, and dynamic... 

On the other hand, we have, for non-equilibrium dynamic property, the time correlation function TCF, which is dynamic counterpart to g(r). One can define various TCP s for each purpose. However, at the present stage, no extensive theoretical relation has been derived between TCF and ([(r). Therefore, direct determination of self-diffusion coefficient, viscosity coefficient by the molecular simulation gives significant contribution in dynamics studies. 

It is difficult to summarize all the phenomena discussed in this volume. However, major topics include ultralow interfacial tension, phase behavior, microstructure of surfactant systems, optimal salinity concept, middle-phase microemuIsions, interfacial rheology, flow of emulsions in porous media, wettability of rocks, rock-fluid interactions, surfactant loss mechanisms, precipitation and redissolution of surfactants, coalescence of drops in emulsions and in porous media, surfactant mass transfer across interfaces, equilibrium dynamic properties of surfactant/oil/brine systems, mechanisms of oil displacement in porous media, ion-... 

The formal similarity between statistical mechanics and real-time dynamics is extremely handy in the computation of mixed equilibrium/dynamic properties. For example, the equilibrium correlation function... 

Cao, J., Voth, G.A. The formulation of quantum statistical mechanics based on the Feynman path centroid density. I. Equilibrium properties. J. Chem. Phys. 100 (1994) 5093-5105 II Dynamical properties. J. Chem. Phys. 100 (1994) 5106-5117 III. Phase space formalism and nalysis of centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6157-6167 IV. Algorithms for centroid molecular dynamics. J. Chem. Phys. 101 (1994) 6168-6183 V. Quantum instantaneous normal mode theory of liquids. J. Chem. Phys. 101 (1994) 6184 6192. 

D. R. Cmise, Theoretical Computation of Equilibrium Composition, Thermal Dynamic Properties, and Peformance Characteristics of Propellants Systems, NWC... 

Generally, the models used for simulation of living polymers can be divided roughly into two classes, focused on static or dynamic properties of the LP or GM. The static models are mainly designed to study equilibrium conformational properties of the polymer chains, critical behavior at the polymerization transition, and molecular weight distribution... 

V. SIMULATIONAL RESULTS—DYNAMIC PROPERTIES A. Kinetics of Relaxation to Equilibrium... 

Up to now we have considered non-dynamical equilibrium properties, namely time-independent properties but the richness of a liquid is related to its flow, gradients, and dynamics. We will briefly consider a few dynamical properties of liquid water here and refer the interested readers to Refs. 31, 46, and 47 for details and others. 

This report has been written in order to demonstrate the nature of spin-state transitions and to review the studies of dynamical properties of spin transition compounds, both in solution and in the solid state. Spin-state transitions are usually rapid and thus relaxation methods for the microsecond and nanosecond range have been applied. The first application of relaxation techniques to the spin equilibrium of an iron(II) complex involved Raman laser temperature-jump measurements in 1973 [28]. The more accurate ultrasonic relaxation method was first applied in 1978 [29]. These studies dealt exclusively with the spin-state dynamics in solution and were recently reviewed by Beattie [30]. A recent addition to the study of spin-state transitions both in solution and the... 

Assuming an infinite number of realizations of the process, equilibrium properties can be obtained from the non-equilibrium dynamics by the Jarzynski equality,... 

Jacucci G, McDonald IR, Rahman A (1976) Effects of polarization on equilibrium and dynamic properties of ionic systems. Phys Rev A 13(4) 1581—1592... 

Besides the static scaling relations, scaling of dynamic properties such as viscosity rj and equilibrium modulus Ge [16,34], see Eqs. 1-7 and 1-8, is also predicted. The equilibrium modulus can be extrapolated from dynamic experiments, but it actually is a static property [38]. 

In addition to the described above methods, there are computational QM-MM (quantum mechanics-classic mechanics) methods in progress of development. They allow prediction and understanding of solvatochromism and fluorescence characteristics of dyes that are situated in various molecular structures changing electrical properties on nanoscale. Their electronic transitions and according microscopic structures are calculated using QM coupled to the point charges with Coulombic potentials. It is very important that in typical QM-MM simulations, no dielectric constant is involved Orientational dielectric effects come naturally from reorientation and translation of the elements of the system on the pathway of attaining the equilibrium. Dynamics of such complex systems as proteins embedded in natural environment may be revealed with femtosecond time resolution. In more detail, this topic is analyzed in this volume [76]. 

The Boltzmann constant is represented by kB. It is more difficult to use Monte Carlo methods to investigate dynamic events as there is no intrinsic concept of time but an ensemble average over the generated states of the system should give the same equilibrium thermodynamic properties as the MD methods. A good review of both MD and the Monte Carlo methods can be found in the book by Frenkel and Smit [40]. 

Calvo, F. Neirotti, J.P. Freeman, D.L. Doll, J.D., Phase changes in 38-atom Lennard-Jones clusters. II. A parallel tempering study of equilibrium and dynamic properties in the molecular dynamics and microcanonical ensembles, J. Chem. Phys. 2000, 112, 10350-10357... 

Lobaugh, J. Voth, G. A., A quantum model for water equilibrium and dynamical properties, J. Chem. Phys. 1997,106, 2400-2410... 

Film balance techniques 49 Equilibrium thermodynamic properties 51 n/A curves and phase transitions 54 Dynamic methods 57... 

Taken together, the equilibrium spreading pressures of films spread from the bulk surfactant, the dynamic properties of the films spread from solution, the shape of the Ylj A isotherms, the monolayer stability limits, and the dependence of all these properties on temperature indicate that the primary mechanism for enantiomeric discrimination in monolayers of SSME is the onset of a highly condensed phase during compression of the films. This condensed phase transition occurs at lower surface pressures for the R( —)- or S( + )-films than for their racemic mixture. 

Continuum models remove the difficulties associated with the statistical sampling of phase space, but they do so at the cost of losing molecular-level detail. In most continuum models, dynamical properties associated with the solvent and with solute-solvent interactions are replaced by equilibrium averages. Furthermore, the choice of where the primary subsystem ends and the dielectric continuum begins , i.e., the boundary and the shape of the cavity containing the primary subsystem, is ambiguous (since such a boundary is intrinsically nonphysical). Typically this boundary is placed on some sort of van der Waals envelope of either the solute or the solute plus a few key solvent molecules. 

Comparison of Equilibrium and Dynamic Properties of Polymethylene Melts of n-C44Hso Chains from Simulations and Experiments. 

Different equilibrium, hydrodynamic, and dynamic properties are subsequently obtained. Thus, the time-correlation function of the stress tensor (corresponding to any crossed-coordinates component of the stress tensor) is obtained as a sum over all the exponential decays of the Rouse modes. Similarly, M[rj] is shown to be proportional to the sum of all the Rouse relaxation times. In the ZK formulation [83], the connectivity matrix A is built to describe a uniform star chain. An (f-l)-fold degeneration is found in this case for the f-inde-pendent odd modes. Viscosity results from the ZK method have been described already in the present text. 

When very high pressures (> 1 GPa) are applied to liquid phases, glasses, or molecular crystals, mobility is reduced and steric effects become more important both in equilibrium and in kinetic aspects. Equations (9) and (14) are still valid, but equilibria and kinetics of chemical reactions must take into account the energetic, structural, and dynamic properties of the environment as well. 

---