Relaxation thermodynamics

Frenkel and Eliashevich (1971, 1975), Frenkel (1974) have put forward an idea to construct a theory of relaxational thermodynamics (thermokinetics). Its basic principle is... 

Relaxation thermodynamics (thermokinetics) includes an explicit dependence of the thermodynamic potentials on the rate of motion of the coiifigiirativc point. 

The situation is more complex for rigid media (solids and glasses) and more complex fluids that is, for most materials. These materials have finite yield strengths, support shears and may be anisotropic. As samples, they usually do not relax to hydrostatic equilibrium during an experiment, even when surrounded by a hydrostatic pressure medium. For these materials, P should be replaced by a stress tensor, <3-j, and the appropriate thermodynamic equations are more complex. 

We assume that the unbinding reaction takes place on a time scale long ( ompared to the relaxation times of all other degrees of freedom of the system, so that the friction coefficient can be considered independent of time. This condition is difficult to satisfy on the time scales achievable in MD simulations. It is, however, the most favorable case for the reconstruction of energy landscapes without the assumption of thermodynamic reversibility, which is central in the majority of established methods for calculating free energies from simulations (McCammon and Harvey, 1987 Elber, 1996) (for applications and discussion of free energy calculation methods see also the chapters by Helms and McCammon, Hermans et al., and Mark et al. in this volume). 

A large programme utilizing temperature-jump relaxation methods for the study of tautomerism in aqueous solution has led the Dubois group to determine the kinetic and thermodynamic parameters of the equilibrium (130a) (130b) (78T2259). The tautomeric... 

The premise of the above analysis is the fact that it has treated the interfacial and bulk viscoelasticity equally (linearly viscoelastic experiencing similar time scales of relaxation). Falsafi et al. make an assumption that the adhesion energy G is constant in the course of loading experiments and its value corresponds to the thermodynamic work of adhesion W. By incorporating the time-dependent part of K t) into the left-hand side (LHS) of Eq. 61 and convoluting it with the evolution of the cube of the contact radius in the entire course of the contact, one can generate a set of [LHS(t), P(0J data. By applying the same procedure described for the elastic case, now the set of [LHS(t), / (Ol points can be fitted to the Eq. 61 for the best values of A"(I) and W. 

A. Milchev, Y. Rouault. A Monte Carlo study of thermodynamic relaxation in living polymers. J Physique II 5 343-347, 1995. 

C. M. Marques, M. E. Cates. Nonlinear thermodynamic relaxation in living polymer systems. J Phys II (France) 7 489-492, 1991. 

The relaxation of a thermodynamic system to an equilibrium configuration can be conveniently described by a master equation [47]. The probability of finding a system in a specific state increases by the incoming jump from adjacent states, and decreases by the outgoing jump from this state to the others. From now on we shall be specific for the lattice-gas model of crystal growth, described in the previous section. At the time t the system will be found in the state. S/ with a probability density t), and its evolution... 

Shown in Fig. 4a is the temperature dependence of the relaxation time obtained from the isothermal electrical resistivity measurement for Ni Pt performed by Dahmani et al [31. A prominent feature is the appearance of slowing down phenomenon near transition temperature. As is shown in Fig. 4b [32], our PPM calculation is able to reproduce similar phenomenon, although the present study is attempted to LIq ordered phase for which the transition temperature, T]., is 1.89. One can confirm that the relaxation time, r, increases as approaching to l/T). 0.52. This has been explained as the insufficiency of the thermodynamic driving force near the transition temperature in the following manner. 

Since we are interested in this chapter in analyzing the T- and P-dependences of polymer viscoelasticity, our emphasis is on dielectric relaxation results. We focus on the means to extrapolate data measured at low strain rates and ambient pressures to higher rates and pressures. The usual practice is to invoke the time-temperature superposition principle with a similar approach for extrapolation to elevated pressures [22]. The limitations of conventional t-T superpositioning will be discussed. A newly developed thermodynamic scaling procedure, based on consideration of the intermolecular repulsive potential, is presented. Applications and limitations of this scaling procedure are described. 

T, 0.1 MPa) condition to be calculated, t is then known for any P and T corresponding to an ambient pressure value of TV. This method is quite powerful because it allows determination of relaxation times for any thermodynamic condition T, P, or V) provided only that the same value of T had been measured at ambient pressure. 

The use of computer simulations to study internal motions and thermodynamic properties is receiving increased attention. One important use of the method is to provide a more fundamental understanding of the molecular information contained in various kinds of experiments on these complex systems. In the first part of this paper we review recent work in our laboratory concerned with the use of computer simulations for the interpretation of experimental probes of molecular structure and dynamics of proteins and nucleic acids. The interplay between computer simulations and three experimental techniques is emphasized (1) nuclear magnetic resonance relaxation spectroscopy, (2) refinement of macro-molecular x-ray structures, and (3) vibrational spectroscopy. The treatment of solvent effects in biopolymer simulations is a difficult problem. It is not possible to study systematically the effect of solvent conditions, e.g. added salt concentration, on biopolymer properties by means of simulations alone. In the last part of the paper we review a more analytical approach we have developed to study polyelectrolyte properties of solvated biopolymers. The results are compared with computer simulations. 

One would prefer to be able to calculate aU of them by molecular dynamics simulations, exclusively. This is unfortunately not possible at present. In fact, some indices p, v of Eq. (6) refer to electronically excited molecules, which decay through population relaxation on the pico- and nanosecond time scales. The other indices p, v denote molecules that remain in their electronic ground state, and hydrodynamic time scales beyond microseconds intervene. The presence of these long times precludes the exclusive use of molecular dynamics, and a recourse to hydrodynamics of continuous media is inevitable. This concession has a high price. Macroscopic hydrodynamics assume a local thermodynamic equilibrium, which does not exist at times prior to 100 ps. These times are thus excluded from these studies. 

Dangles, O and Brouillard, R., Polyphenol interactions. The copigmentation case — thermodynamic data from temperature-variation and relaxation kinetics. Medium effect. Can. J. Chem.-Rev. Can. Chim., 70, 2174, 1992. 

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