Static interfaces

We can see that two SE s on each side of the interface are involved in the transfer. Matter transport across the interfaces and, in particular, the dynamic equilibrium exchange fluxes j therefore concern the building elements or components k. At equilibrium, 

The principle of microscopic reversibility across a boundary is thus applicable to building elements. Since boundary crossing by particles is a thermally activated process, the net flux of building element A across the interface exposed to an external field can be formulated as 

One notes that RA is inversely proportional to the exchange flux (/a) °f the dynamic equilibrium interface. 

If we denote the point defect injected by the applied field into the wrong sublattice of AX by i (e.g A ), and the conjugate defect that carries the flux in AX by j (e.g., V ), then the steady state condition for both fluxes (i, j) in the defect recombination zone r is 

The second condition for bulk transport in AX is A A in accordance with our assumptions. The point defects relax by a bimolecular reaction mode (see Section 5.3.3). In order to simplify the formal treatment, we linearize the recombination rate 

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Figure 10-1. Field-driven cation flux and its effect on the boundary motion DA,DB>Dx,DY). a) Static interface, b) moving (without reaction), c) moving (with reaction, />., AY formation).

Depending on the type of boundary and field, a force may act on the static interface. This can be seen from Figure 10-8. For the analysis, let us place the crystal between asymmetric capacitor plates. Without the field, the boundary (b) is surrounded by a symmetric (AX/AX) or an asymmetric (AX/AY) space charge. Thus, an inhomogeneous electric field exerts a force on the (dipolar) interface. The boundary... 

Figure 10-9. a) The elementary transfer steps of a static interface AY/AX under load (Da> Dx,Dy). b) Static interface AY/AX under load. Concentrations of irregular SE s (A, V ) in the relaxation zone ( R) are indicated. 

The first of these two shortcomings has been addressed using the free-energy functional approach by assuming a physical picture where a static interface of smoothly varying dielectric properties is considered (effectively, a mixed... 

As indicated above, the Young-Laplace equation (Equation 1.22) is one fundamental result obtained from the theory of interfaces. Because this equation relates interfadal tension to the pressure difference between fluids at each point along an interface, it can be used with the equations of hydrostatics to calculate the shape of a static interface. Or, if interfadal shape can be determined... 

Static Spectroscopic Cells. ESR and NMR tubes can be sealed for gas-liquid reactions, and high pressure tubes have been constructed. However, ESR and NMR tubes represent extremely poor contacting patterns. Gas-liquid mass transfer will be controlled by diffusion across the more-or-less static interface and hence very low mass-transfer rates will occur. 

The quantum atomistic static interface (QuASI) methodology of Tavazza et is inspired by the flexible boundary condition idea (e.g., the... 

The above result was confirmed by Yethiraj et al [56, 66] using an optical technique that quantified intensity fluctuations in the liquid crystal. Since the intensity fluctuations in the nematic phase are caused by nematic director fluctuations, which in turn are suppressed in the smectic-A phase, this is a very sensitive probe of the phase transition. In addition, the temperature dependence of the phase transition was obtained optically by placing the sample in a well-calibrated temperature gradient. Indeed the existence of a sharp static interface is itself a qualitative indicator of first-order character. Not only was the transition in the 8CB-10CB system always first order, the strength of the discontinuity was larger not smaller than the HLM prediction. This result is consistent with a subsequent calculation by Herbut et al which takes into account tp fluctuations. 

In prefilled syringes, silicone oil is available in two forms with which a protein can interact surface bound and free. Surface bound silicone oil provides a static interface with water in a device. Free sificone oil is present because of the application of excess sificone oil, poor coating process, or product mishandling [102], which may leach into the bulk. The leached sificone oil results in an increase in the interfacial area available for protein adsorption and it also presents a problem from a regulatory perspective because of enhanced particulate load in the drug solution. 

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