A lattice model for dense polymer solutions and polymer mixtures in three dimensions is presented, aiming to develop a model suitable for efficient computer simulation on vector processors, with a qualitatively realistic local dynamics. It is shown that the bond fluctuation algorithm for a suitable set of allowed bond vectors has the property that due to the excluded volume constraint no crossing of bonds by local motions can occur, and entanglement restrictions thus are fully taken into account. For athermal binary (AB) symmetrical polymer mixtures, the dependence of both self‐diffusion coefficient and interdiffusion coefficient on polymer density is obtained, simulating a thin film geometry where a film of polymer A is coated with a film of polymer B. For one density, the dependence of the interdiffusion coefficient on an attractive energy between unlike monomers is also studied. For weak attraction an enhancement of interdiffusion proportional to this energy occurs. For strong attraction, however, a rather immobile tightly bound AB layer forms in the interface which hampers further unmixing.

Interdiffusion and self‐diffusion in polymer mixtures: A Monte Carlo study

Ten measurements of the isotope effict for diffusion of Fe/sup 55/ and Fe/sup 59/ in pure single cryatals of silver and copper were made over approximately a 300 deg C temperature interval below the melting point. The measured isotope effect was found to be about 2/3, significantly less than the value of unity expected from conventional reaction rate theory. It is shown from Vineyard's extension of reaction rate theory that the measured isotope effect is to a good approximation a product of the Bardeen-Herring correlation factor and the fraction of the total translational kinetic energy associated with the diffusing tracer in a tracervacancy exchange. It is shown that the ring, interstitialcy, crowdion, and relaxion mechanisms are not responsible for diffusion in the systems studied. The three-frequency theory of correlation for vacancy diffusion in fcc lattices is extended to show that the relative frequency factors are vacancy exchange. It is shown that the ring, interstitialcy, crowdion, and relaxion mechanisms are not responsible for diffusion in the systems studied. The three-frequency completely specified by a knowledge of the correlation factor and the diffusion coefficients. An expression for the difference in the Arrhenius Q and the activation energy due to the temperature dependencemore » of the correlation factor is derived. This theory is shown to be inconsistent with the observed isotope effect if many-body effects are neglected. It is shown that a "long-range" repulsive interaction between the vacancy and impurity would be necessary if the measured isotope effect is to be explained purely in terms of correlation. (auth)« less

Isotope Effect in Intermetallic Diffusion.

This review considers the calculation of point defect parameters in ionic solids by atomistic simulation. Both static and dynamic methods are discussed. After a brief overview of the field, the author considers how to obtain a reliable model of the crystal potential. This matter is fundamental to any adequate simulation. The author then turns to consider the calculation of defect energies and entropies. The following section discusses how the results of such simulations are to be interpreted. This requires a discussion of the reaction rate theory for defect motion, in particular recent work on what the theory means and how its shortcomings can be corrected. The author then turns to the interaction of point defects with interfaces and to their interaction with dislocations. The effects of the long-range electrical terms are shown to be particularly important in these circumstances. Finally, the author summarizes the review and discuss future directions in the field.

https://iopscience.iop.org/article/10.1088/0034-4885/53/11/002/pdf

Computer simulation of defects in ionic solids

Kinetics of non-equilibrium grain-boundary segregation

Chapter 7 – diffusion in metals and alloys

This review is concerned with the fundamentals of the theory of the transport of atoms through crystalline solids, such as may result from the existence of gradients of chemical and isotopic composition, electrical potential, stress, temperature, etc. The main emphasis is on the statistical description of these processes via the theory of mobile lattice imperfections-vacancies and interstitial atoms. Only processes taking place in the bulk of the solid are considered, i.e. enhanced diffusion and migration in the vicinity of dislocations, grain boundaries and other interfaces are not discussed. The various statistical theories available at the present time are reviewed against the phenomenological framework provided by nonequilibrium thermodynamics. One object of this work is to demonstrate the interrelations among the different theories and to disclose where they are equivalent. Another is to show that the means are now available to calculate all the phenomenological transport coefficients which arise in the nonequilibrium thermodynamics of these processes in terms of the assumed properties of the defects, their interactions with solute atoms, etc. Although this review is thus primarily concerned with the theory of atomic transport at an abstract level, the physical aspects of the subject are referred to throughout. Explicit solutions of the transport equations, however, are not considered.

http://iopscience.iop.org/article/10.1088/0034-4885/50/4/001/pdf

A B Lidiard

Papers

Statistical theories of atomic transport in crystalline solids