Interdiffusion processes

Diffusion theory involves the interdiffusion of macromolecules between the adhesive and the substrate across the interface. The original interface becomes an interphase composed of mixtures of the two polymer materials. The chemical composition of the interphase becomes complex due to the development of concentration gradients. Such a macromolecular interdiffusion process is only... 

As an illustration, consider the isothermal, isobaric diffusional mixing of two elemental crystals, A and B, by a vacancy mechanism. Initially, A and B possess different vacancy concentrations Cy(A) and Cy(B). During interdiffusion, these concentrations have to change locally towards the new equilibrium values Cy(A,B), which depend on the local (A, B) composition. Vacancy relaxation will be slow if the external surfaces of the crystal, which act as the only sinks and sources, are far away. This is true for large samples. Although linear transport theory may apply for all structure elements, the (local) vacancy equilibrium is not fully established during the interdiffusion process. Consequently, the (local) transport coefficients (DA,DB), which are proportional to the vacancy concentration, are no longer functions of state (Le., dependent on composition only) but explicitly dependent on the diffusion time and the space coordinate. Non-linear transport equations are the result. 

It is a straightforward but rather lengthy exercise to write down and evaluate the flux equations jA, jA, jB, jB under the assumption of local (vacancy) equilibrium (A v = 0). We find that five independent L-ti are needed to fully describe the transport in such a system. However, only four experimental parameters DA, DB, DA, and Db are available from flux measurements. Since DA = DB, jA jB in the solid solution crystal. Lattice site conservation requires that the sum of the fluxes /a + 7b + 7v = 0, that is,, /v = 0, despite X = 0. The external observer of the A-B interdiffusion process therefore sees the fluxes... 

The vacancy flux and the corresponding lattice shift vanish if bA = bB. In agreement with the irreversible thermodynamics of binary systems i.e., if local equilibrium prevails), there is only one single independent kinetic coefficient, D, necessary for a unique description of the chemical interdiffusion process. Information about individual mobilities and diffusivities can be obtained only from additional knowledge about vL, which must include concepts of the crystal lattice and point defects. 

Figure 5-11 illustrates the results of an oxide interdiffusion experiment. Clearly, the transport coefficients are not single valued functions of composition. From the data, one concludes that for a given composition, the chemical diffusion coefficients depend both on time and location in the sample [G. Kutsche, H. Schmalzried (1990)]. Let us analyze this interdiffusion process in the ternary solid solution Co. O-Nq. O, which contains all the elements necessary for a phenomenological treatment of chemical transport in crystals. The large oxygen ions are almost immobile and so interdiffusion occurs only in the cation sublattice of the fee crystal. When we consider the following set ( ) of structure elements... 

The intrinsic diffusion coefficients, Dk and DB, of a binary alloy A-B express the diffusion of the components A and B relative to the lattice planes [7], Therefore, during interdiffusion, a net flux of atoms across any lattice plane is present, where, normally, the diffusion rates of the diffusing particles A and B are different. Subsequently, this interdiffusion process provokes the shift of lattice planes with respect to a fixed axis of the sample, result which is named the Kirkendall effect [9],... 

Not all the terms in these equations have the same importance in determining the flow solution in chemical reactors. The only body force considered in most reactor models, gj (per unit mass), is gravitation which is the same for all chemical species, g. The model equations for momentum and energy can then be simplified. In the momentum equation Pc c = f cS = PS-In the energy equation Xlc=i(jc Sc) = Sc=i jc S = 0- Furthermore, in most multicomponent flows, the energy or heat flux contributions from the interdiffusion processes are in general believed to be small and omitted in most applications, ft-cV jc 0 (e.g., [148], p. 816 [89], p. 198 [11], p. 566). 

He considers that mixing occurs by two independent processes which produce distinguishable results (1) the breaking-up process which reduces sizes of clumps and (2) the interdiffusion process which obliterates differences of concentration between neighboring regions of... 

Several techniques have been reported and, at the present time, the vapor phase deposition processes operating at temperatures around 300 °C are the most used. Thus II-VI compounds films like CdS, CdSe, CdTe, ZnS, ZnSe, and ZnTe have been grown epitaxially on Si, InP, GaAs, GaP, by molecular beam epitaxy (MBE) [204-207], by metal organic chemical vapor deposition (MOCVD) [208-210], or by pulsed laser deposition [211, 212]. Epitaxial deposition from aqueous solutions at low temperatures (< 100 °C) represents another approach. Specific beneficial effects may be also expected due to the simplicity of the process involving low cost investments. On the other hand the low temperature has for consequence the absence of interdiffusion processes around interfaces and the interfacial properties of the solids in contacts with solutions implicate excellent coverage properties at low thicknesses. Different... 

Another class of adherends is that of thermoplastic polymers. In contrast to metal adherends, thermoplastics are not impenetrable and thus absorption effects can be expected in addition to adsorption phenomena. Hence, given sufficient conditions for preferential absorption, a considerable mass uptake by the thermoplastic can occur, potentially resulting in significant stoichiometric imbalances on the epoxy side. Apart from the driving force for absorption of molecules from the liquid epoxy formulation, it is the diffusivity of these molecules within the thermoplastic which plays a major role in the interdiffusion process. In particular, the diffusivity is affected by the mobility of the host molecules. Thus enhancement of diffusivity occurs in the glass transition region and at higher temperatures when intermolecular cooperative motion is activated. 

It should be noted that the assumption of local defect equilibrium may not hold in the very early stages of the interdiffusion process when steep concentration gradients occur, especially if only the outer crystal surface acts as source or sink for point defects. One would expect then time dependent j6(c)-values and nonplanar equiconcentration surfaces. 

Mixtures of deuterated and protonated polystyrene latexes have also been studied by SANS (78,79). The main advantage is the relatively large surface area presented for interdiffusion, since the latex particles are relatively small. Figure 5.12 (79) illustrates the time dependence of the interdiffusion process. The data follow the non-Fickian relationship up to a diffusion distance of about 0.4i g. For diffusion from one side only. Wool (80) derived the break point as 0.8i g. However, equal diffusion from both sides, the present case, yields half that value as intuitively expected, noting that the diffusion distance is measured from the original interface plane rather than the true diffusion distance. 

Figure 11.28 The interdiffusion process at a polymer-polymer interface (57) (a) appearance of the minor chains and (b) the minor chain spherical envelopes.

Yet, we start from Chapter 2. We had two reasons for this. The first reason is the magic word nano in its title. The second reason is that this chapter gives a good example of how academic issues discussed by pure theoreticians can become very fresh and practically important, due to progress in technology and experimental possibilities. From a theoretical viewpoint, this chapter suppHes one with a trace of the long activity (published mainly in Russian), related to the role of nonequilibrium vacancies in interdiffusion processes. 

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