Diffusion interface structure

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

Recently an alternative approach for the description of the structure in systems with self-assembling molecules has been proposed in Ref. 68. In this approach no particular assumption about the nature of the internal interfaces or their bicontinuity is necessary. Therefore, within the same formahsm, localized, well-defined thin films and diffuse interfaces can be described both in the ordered phases and in the microemulsion. This method is based on the vector field describing the orientational ordering of surfactant, u, or rather on its curlless part s defined in Eq. (55). 

In order to find the effect of broadening of the surface on the structure parameters H and K, we first study the ordered phases with the diffusive interfaces. The ordered phases can be described by the periodic surfaces (0(r)) = 0 and we can compare and with H and K. The numerators in the definitions (76) and (77) in the Fourier representation assume the forms [68]... 

Having determined the effect of the diffusive interfaces on the structure parameters, we now turn to the calculation of H and K in microemulsions. In the case of oil-water symmetry three-point correlation functions vanish and = 0. In order to calculate K from (77) and (83) we need the exphcit expressions for the four-point correlation functions. In the Gaussian approximation... 

When speculating about the hypothetical structure of interfaces with minimal free energy, the diffuse interfaces formed by the properly grafted water-soluble... 

Kossel [8] and Stranski [9] were the first to focus attention on the interface structure, after considering the experimental results obtained by Volmer [10], who demonstrated the existence of surface diffusion. It thus became possible to discuss the mechanism of crystal growth at an atomic level, starting from these analyses. 

Among the most common surface X-ray scattering techniques used to probe mineral-fluid interface structure is the measurement of crystal truncation rods (CTRs). CTRs are diffuse streaks of intensity connecting bulk reciprocal lattice (Bragg) points in the direction perpendicular to a surface, and arise as a natural... 

Because experimental study of the structure of crystal/liquid interfaces has been difficult due to the buried nature of the interface and rapid structural fluctuations in the liquid, it has been investigated by computer simulation and theory. Figure B.3 provides several views of crystal/liquid (or amorphous phase) interfaces, which must be classified as diffuse interfaces because the phases adjoining the interface are perturbed significantly over distances of several atomic layers. 

Figure 18.7 Interfaces resulting from two types of continuous transformation, (a) Initial structure consisting of randomly mixed alloy, (b) After spinodal decomposition. Regions of B-rich and B-lean phases separated by diffuse interfaces formed as a result of long-range diffusion, (c) After an ordering transformation. Equivalent ordering variants (domains) separated by two antiphase boundaries (APBs). The APBs result from A and B atomic rearrangement onto different sublattices in each domain.

On the other hand, a diffuse interface possesses a significantly wider core that extends over a number of atomic distances. A diffuse crystalline/amorphous phase interface is shown in Fig. B.3. Similar structures exist in crystal/liquid interfaces [5]. 

Studies of the electrical characteristics of Au contacts on InP(llO) (45), GaAs(llO) (45), CdS(1010) (46), and CdSe(lOlO) (46) confirm the expectations based on the insight gleaned from our examination of replacement reactions on GaAs(llO). The presence of a few monolayers of reactive metal (e.g., A1 or Ni) prior to deposition of the Au suppresses the diffusion of the semiconductor species through the Au overlayer and reduces the asymmetry of the I-V characteristic of the Schottky barrier, making it more "ohmic". Indeed, a few monolayers of A1 on CdSe(lOlO) renders the resulting Au/Al/CdSe composite contact completely ohmic (46). Thus, studies of semiconductor-metal interface structure in this case led to a new technique for... 

Assuming thin layer thicknesses and large Hn, it is still necessary that the hard layer resists reversal. From the discussion of propagation in Section 4.3.1., the question arises whether juoHp 1 T may be attained. The best properties will require sharp interface. When a close relationship exists between hard phase and soft phase crystal structures, it may be anticipated that the formation of diffuse interfaces will be favoured. This is expected to favour propagation and thus be detrimental to coercivity. In other systems,... 

Although simple impedance measurement can tell the existence of an anodic film, electrochemical impedance spectroscopy (EIS) can obtain more information about the electrochemical processes. In general, the anode/electrolyte interface consists of an anodic film (under mass transport limited conditions) and a diffuse mobile layer (anion concentrated), as illustrated in Fig. 10.13a. The anodic film can be a salt film or a cation (e.g., Cu ) concentrated layer. The two layers double layer) behave like a capacitor under AC electric field. The diffuse mobile layer can move toward or away from anode depending on the characteristics of the anode potential. The electrical behavior of the anode/electrolyte interface structure can be characterized by an equivalent circuit as shown in Fig. 10.13. Impedance of the circuit may be expressed as... 

The same approach can be used to find the interface structure for different kinds of time-dependent strain. For example, both the shear or the vortex flows described in Sect. 2.7.1 lead to interfaces described by (5.11) with /(2r1/2) — x/4Dt/3 at long times. In these cases the interface region, aligned with the shear flow, widens diffusively in time. We have Ct VDt and the production per unit length p = Crit) + A(t)Cr(t) (D/t)1/2 decreases in time. At any fixed time both the interface width and the production behave as Pe-1/2, as in the pure strain case. 

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