Theoretical Studies of Interphase

For analytical purposes, the fiber composites are conveniently modeled using axisymmetric three-phase (i.e. fiber-interlayer-matrix), four-phase (i.e. fiber-interlayer-matrix-composite medium) cylindrical composites, or in rare cases multi-layer composites (Zhang, 1993). These models are schematically presented in Fig. 7.9. The three-phase uniform interphase model is typified by the work of Nairn (1985) and Beneveniste et al. (1989), while Mitaka and Taya (1985a, b, 1986) were the pioneers in developing four-phase models with interlayer/interphase of varying stiffness and CTE values to characterize the stress fields due to thermo-mechanical loading. The four phase composite models contain another cylinder at the outermost surface as an equivalent composite (Christensen, 1979 Theocaris and Demakos, 1992 Lhotellier and Brinson, 1988). 

Normalized Rarfial Distance from Rber Center 

Normalized Radial Distance from Fiber Center 

In summary, based on the previous studies as reviewed above, the variables which affect most the mechanical performance of composites have been identified  

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Schrage, R. W., A Theoretical Study of Interphase Mass Transfer. Columbia Univ. Press, New York, 1953. 

Theoretical studies of interphase and three engineered interphase concepts... 

Schrage RW (1953) A theoretical study of interphase mass transfer. Columbia University Press, New York... 

In a sense, all the present papers treat problems in interphase contacting. On the theoretical and observational sides, respectively, Davies and Kintner explore the properties of two-phase systems undergoing mass transfer. In a third study, both the descriptive and the theoretical properties of cocurrent two-phase flow systems are presented by Scott. Longitudinal dispersion (or axial mixing), which has only recently been identified and analyzed as a substantial factor in equipment performance, is reviewed by Levenspiel and Bischoff. 

Preliminary studies of the interphase between respective domains by Van Bogart et al. (53) indicate the thickness of this region, assuming a linear density gradient, is on the order of 10-20 A for polyester and polyether urethanes (MDI-BD based). Theoretically, the interfacial thickness is inversely related to the square root of the hard segment-soft segment interaction parameter (54). 

The performance of trickle-bed reactors may be affected by many factors, such as interphase mass transfer, intraparticle diffusion, axial dispersion and incomplete catalyst wetting. Therefore, knowledge about these influenced factors is important for their mathematical description by an unsteady-state reactor model. Until now, the literature analysis shows the experimental and theoretical understanding of trickle-bed reactors under unsteady-state-operation conditions has improved, but not considerably. The following studies are focused on the trickling regime under unsteady-state-operation conditions. 

Earlier we considered the regularities of the effect of simfactants on the oligomer surface tension. The properties of adhesive-bonded joints are also determined by the character and the magnitude of the interaction at the adhesive-substrate interface, which to a greater extent is characterized by the magnitude of the interphase tension [82]. Study of the interphase tension is of great theoretical and practical interest, but at present there are no direct methods for its determination. 

McAdams, E.T., Jossinet, J., 1994. The detection of the onset of electrode-electrolyte interphase impedance nonlinearity a theoretical study. IEEE Trans. Biomed. Eng. 41 (5), 498—500. 

In the Cora code, the corrosion product layers outside the reactor core are rather arbitrarily subdivided into two layers, a transient one and a permanently deposited one. Supply to the transient layer occurs via deposition of suspended particles from the coolant, release from it includes erosion of particles back to the coolant as well as transport into the permanently deposited layer and partial conversion into dissolved species. In a comparable manner, the supply of nuclides to the permanent layer is assumed to result from transfer from the transient layer and the exchange equilibrium with the dissolved species present in the coolant. The deposition coefficients of suspended solids can be calculated on the basis of particle size and flow characteristics. The coefficients of relevance for the permanently deposited layer, including ionic transfer mechanisms between liquid and solid phases, can be derived from theoretical considerations as well as from laboratory studies of corrosion product solubilities. Finally, diffusion rates of nuclides at the interphase layers are needed, from the oxide layer to the coolant as well as in the reverse direction. These data can be obtained in part by theoretical considerations and by measurements at the plants. 

The principles of modelling of viscoelastic roperties which account for the interphase participation were developed. Also, the dependence of viscoelastic properties on thickness of the interphase was theoretically studied using a mechanical model. ... 

A piece of ordinary solid metal is not a single crystal of metal. One always finds the grain boundaries where the forces, even inside the metal, are not spherically symmetrical. In addition, one always finds various kinds of imperfections inside a crystal where the forces are, again, assymetric. These faults are transferred from the bulk to the surface making the surface far from ideally smooth. Moreover, the surface of a solid can never be accurately represented by a continuous plane of atoms, the way it is often done. All these deviations from ideality give rise to various effects which do not represent the major phenomenon, but must be considered in the theoretical interpretation of experiments. These side effects are often so large as to mask the major phenomenon itself. A liquid metal is, of course, free from those side effects it is smooth and not as structured as a solid one. Therefore it is more suitable for the study of the interphase itself without the side effects. Since kinetics of electrode reactions depend also on the state of the surface, liquid electrodes are also very suitable for kinetic studies. Thus one would use the liquid electrode (mercury) as often as possible in electrodics. Indeed, mercury occupies a unique position in electrodics because of the above reasons, as well as others which will become apparent later. 

It is evident that the study of crystalline copolymers presents some very difficult as well as intriguing problems. The theoretical development of equilibrium relations and phase diagrams can be accomplished in principle when it is recognized that one must be concerned with the sequence propagation probability and not the composition. One major difficulty is that although the liquidus of the phase diagram can be determined quite easily, the solidus is extremely difficult to establish in most cases. In addition, it is virtually impossible to establish equilibrium on an experimental basis. As we have enumerated above there is a large number of important contributions to the deviations from equilibrium. The major ones are the finite crystallite size (relative to the equilibrium requirement), possible defected structures within the lattice and most importantly the structure of the interphase. 

Monotectic reactions in which a liquid phase decomposes to form a solid and another liquid phase (Fig. 5.15) have also received little attention. The experimental work of Delves and the theoretical treatment of Chadwick showed that either regular rod-like structures or macroscopic phase separation should occur, depending on the various interphase surface energies. Subsequently Livingston and Cline,working with copper-lead alloys, established that the growth conditions also had a marked influence on the nature of the transformation structure. Their results are summarised in Fig. 5.16. It would be valuable if these studies could be extended to other suitable systems. 

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