Diffusion microstructure based modeling

There is a correlation between the mechanical and chemical data of figures 7-10. It is clear from the multilayer or lamellar structure of these in vitro lesions that they are formed by a complex demineralization process that cannot be explained by simple, diffusion-based models. The surface layer, which is extremely weak, has lost almost all of its Ca and P, except for a very small amount close to the surface. This region close to the surface is stronger than the body of the lesion, but still very weak when compared to the underlying enamel. The body of the lesion is extremely compliant and mechanically very weak. The weak interior and surface layers of the lesion make it particularly prone to damage when the surface is mechanically loaded. Collectively, the mechanical, chemical and structural data indicate that even the less demineralized surface zone (A on fig. 7, 8) does not have the same microstructure or mechanical strength as sound enamel. 

In the model calculations [13], the effective diffusion coefficients in the two-phase zone were used. It was established that diffusion coefficients were constant along the conode in case of a phase diagram with parallel conodes. Experimentally obtained zigzag diffusion paths in the two-phase zone of an Al-Cr-Ni system were also presented. The most detailed development of the theoretical approach [12, 13] for the investigation of diffusion interaction between the a phase of the solid solution and the a — f two-phase alloy was performed in [48]. The authors have obtained the dependencies of the contact zone microstructure on the initial conditions of diffusion annealing. The model is based on the following assumptions ... 

To conclude this section, it may be interesting to mention what was concluded recently in (17) on the future of the free-volume diffusion models . .. However, phenomenological transport models based on free-volume concepts are likely to become obsolete during the coming decade, due to the development of computational techniques of simulating polymer microstructures . The development of such techniques and their results are discussed in Section 5.2. 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

Recent experiments by Dr. Bar-Cohen el al. ha e shown that ultrasonic oblique insonification can be used to characterize thermal damage to composites [156]. Using an inversion technique based on a micromechanical model, the reflected ultrasonic signals arc analyzed to determine the overall laminate stiffness constant before and after loading. Another technique developed by the NASA to encompass the limitation of pulse-echo ultrasonic and photomicroscopic methods is diffuse-field acoustoultrasonic coupled vibration damping [157]. Both NASA techniques are complementary and arc used to assess microstructural damage accumulation in ceramic matrix composites. 

The effect of flux is the key model in this correlation equation. This is considered in the Q factor, which is a kind of flux adjustment. The Q facture is a ratio of vacancy concentration to the vacancy concentration at a reference condition. This is based on the idea that the formation of microstructures in low-Cu materials is strongly affected by the diffusion of solute atoms that are considered in the Fc factor.The vacancy concentration can be calculated by solving the equations of balance on the generation and consumption of point defects shown as follows ... 

The nucleation rate, growth rate, and transformation rate equations that we developed in the preceding sections are sufficient to provide a general, semiquantitative understanding of nucleation- and growth-based phase transformations. However, it is important to understand that the kinetic models developed in this introductory text are generally not sufficient to provide a microstructurally predictive description of phase transformation for a specific materials system. It is also important to understand that real phase transformation processes often do not reach completion or do not attain complete equilibrium. In fact, extended defects such as grain boundaries or pores should not exist in a true equilibrium solid, so nearly all materials exist in some sort of metastable condition. Many phase transformation processes produce microstructures that depart wildly from our equilibrium expectation. The limited atomic mobilities associated with solid-state diffusion can frequently cause (and preserve) such nonequilibrium structures. In this section, we will focus more deeply on solidification (a liquid-solid phase transformation) as a way to discuss some of these issues. In particular, we will examine a few kinetic concepts/models... 

The focus of this chapter is on analyzing and modeling the microstructure of gas diffusion layers (GDLs) in polymer electrolyte membrane fuel cells (PEMFCs). GDLs are fiber-based materials and one of their main tasks is the transportation of hydrogen and oxygen towards the electrodes where the electrochemical reaction takes place, that is, electricity is generated and the transport of the byproduct water from the electrode towards the channel is accomplished [1]. 

In order to monitor the mechanical properties in relation to the microstructure, the knowledge of the precipitation state at the end of a thermo-mechanical treatment is of prime importance. In this purpose, Arcelor develops models that allow for the prediction of the influence of the process parameters on the state of precipitation. The model Multipreci, developed at IRSID is one of them. It (Hedicts the precipitation kinetics of mono- and di-atomic particles in ferrite and austenite as a function of the time-temperature history. It is based on the classical theories for diffusive phase transformation and treats simultaneously the nucleation, growth and ripening phenomena. The state of precipitation that is predicted includes the particle size distribution, their number and volume fraction. From these values, the effect of the precipitates on the mechanical properties can be calculated. 

The problem of non-steady state flow-which is characteristic of absorbency in polymers-is analogous to the non-steady state diffusion of solutes in a porous material [2]. Therefore, much of this chapter focuses on the solution of the equations for non-steady state diffusion In a porous medium. The most challenging aspect of the general problem of transport in porous polymers is relating the microscopic characteristics of the pore space (porosity, tortuosity, connectivity) to the macroscopic property of interest (permeability or diffusion coefficient). This chapter describes some of the methods that can be used to relate microstructure to transport. While most of the models presented are based on the general problem of diffusion in porous polymers, they can be adapted to explore the mathematically equivalent problem of absorbency in polymers. 

The diffusion-collision model proposed by Karplus and Weaver (1976) as well as the approaches mentioned previously assumes a folding by steps, based on the formation of several microdomains which associate to form larger structures which on turn associate and so on. The formation of such microstructures would permit one to understand how nature had worked during the early stages of evolution for building a protein from elementary pieces with a given function and also what kind of assembly of these building blocks were necessary to differentiate. 

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