Non-reactive Mode Research Articles

Wear Resistant Amorphous PVD B-N-C Films for Tribological Applications

AbstractAmorphous B-N-C films with a variety of properties were deposited by PVD-magnetronsputter-ion-plating. Compared to nonconductive reactive r.f. BN-targets the semiconductive behaviour of specially produced B4C-targets permitted a d.c. reactive or non-reactive mode of deposition. These films are characterized by high hardness with decreased coefficient of friction. A tribological evaluation by modified pin-on-disk outline the wear protection effects in tribosystems with metal counter part. This work was partially financed by the Commission of the European Community under Brite/EuRam contract BRE2-CT93-0451.

A two-dimensional model for a light particle tunneling system

We present a model calculation for barrier crossing rates of a light particle such as hydrogen, lithium, or a light interstitial in a symmetric double-well potential. At higher temperatures migration takes place through thermally activated processes, while the dynamics are dominated by tunneling at lower temperatures. We construct a model two-dimensional system that consists of a symmetric double-well potential for the high frequency, light particle mode and a harmonic oscillator for the lower frequency mode coupled closely to the reactive mode. This model system is, in turn, immersed in a classical bath. The reaction rate is calculated without assuming thermal equilibrium either for the light particle mode or for the nonreactive mode. Two distinct symmetries of coupling are considered for tunneling. The energy relaxation rate within each well is shown to have a significant effect on the rate in the high temperature limit. The temperature dependence of low temperature tunneling-dominated rates is determined by the type of coupling and by a parameter that describes the displacement of the nonreactive mode.

Energy diffusion in many-dimensional Markovian systems: The consequences of competition between inter- and intramolecular vibrational energy transfer

We examine the dynamics of barrier crossing using a two-dimensional Langevin equation in the low friction regime. We find that as the friction on the nonreactive mode is increased there is a transition from two-dimensional Markovian dynamics to one-dimensional non-Markovian dynamics resulting in a qualitative change in the behavior of the rate constant as a function of friction. This result supports the conclusion that existing theories which predict rates for energy activation in Markovian and non-Markovian systems have limited ranges of validity and are not as general as had previously been supposed. A method is proposed which analyzes the eigenvalues of the full system and provides a criterion for the validity of the various theories. These ideas are then used to interpret the results of a recent experimental study. In the Appendix we discuss, in some detail, the role of a random force in aiding intramolecular energy transfer.

Classical dynamics of a coupled double-well oscillator in condensed media. III. The constraint of detailed balance and its effects on chemical reaction process

The reacting system is assumed to interact both with an ideal thermal source at the temperature T1 and a (fast) nonreactive oscillator coupled to an ideal thermal source at temperature T2. Special attention is devoted to the case T1=T2 which is characterized by equilibrium distributions of canonical kind. We use the same adiabatic elimination procedure (AEP) as applied in our earlier works [J. Chem. Phys. 79, 3320 (1983); 80, 1826 (1984)] with a projection operator that allows the canonical property to be recovered in the reduced equation of motion. It is shown that in the underdamped regime the chemical reaction rate increases with increasing strength of the coupling between reactive and nonreactive mode. In the high-friction regime the chemical reaction rate decreases with increasing reactive–nonreactive mode coupling. Arguments are also provided for a more complete picture covering the whole friction region. It is also shown that the projection operator used in the two preceding papers implies that T2≫T1.

Theory of activated reaction processes: Non-linear coupling between reactive and non-reactive modes

Deviations from the Kramers predictions resulting from the coupling between a reactive and a non-reactive mode are studied in both the low- and high-friction limits. It is also argued how this simple picture may provide a breakdown of the upper limit imposed on the relaxation rate by transition state theory.

Classical dynamics of a coupled double well oscillator in condensed media. II

The influence exerted on reaction processes by the coupling between the reaction coordinate x and transverse nonreactive modes is discussed. Attention is mainly focused on the synergism of inertia and multiplicative fluctuation, which enhances the reaction rate throughout a wide domain, ranging from the high to the low-friction region. The high-friction region is explored by applying the adiabatic elimination procedure (AEP) described in the first paper of this series: When the relaxation time of x is larger than that of the nonreactive mode, a new term occurs. This term is shown to be responsible for making the ‘‘noise-induced phase transition effects’’ discussed in the first paper more pronounced. The low-friction region is explored with a first-passage time procedure by using energy as the slow variable. The synergism of inertia and multiplicative noise is then shown to produce finite reaction rates even in conditions where Kramers theory predicts them to be vanishingly small.

Classical dynamics of a coupled double well oscillator in condensed mediaa)

The influence of a deterministic coupling between the reaction coordinate and a transverse normal mode on the reaction rate is considered within the context of classical (stochastic) dynamics. Our theoretical approach is based on a scheme of elimination of rapidly relaxing (irrelevant) variables. This procedure, perturbational in nature, makes it possible to get corrections of increasing accuracy to the results of the ‘‘standard adiabatic method’’ as perturbation terms of higher and higher order are taken into account. In the large friction case, the very first significant correction to the standard adiabatic scheme is shown to picture the reaction coordinate as being driven by a diffusionlike equation exhibiting instability phenomena. Thus, our approach makes an intriguing link between the activation of a reaction process via excitation of a nonreactive normal mode and noise-induced phase transition phenomena. When the frequency of the nonreactive mode varies slowly with the reaction coordinate, the reaction threshold can be expressed by a simple analytical formula. Results of computer calculations, which allow the exploration of a still wider range of physical conditions, are also discussed.