Profiles Across Interfaces

In this paragraph we focus on the properties of interfaces between coexisting phases, i.e., planar interfaces between macroscopic domains. Let S. denote the area of the (planar) interface, so we calculate the free energy that an interface costs per unit area, the interfacial tension y, via  

The results of our calculations at temperature = 0.75 are displayed in Fig. 10 (a). Upon increasing pressure the interfacial tension decreases. At the triple pressure ksT = 0.193174 there is a small jump, because for lower pressure 

The density profiles across the interface are depicted in Fig. 10(b). At low pressure the coexisting phases differ in the density of polymers. The density of the volatile solvent is almost equal in both phases, and very low. At the center of the interface there is a small excess of solvent. Upon increasing pressure, the density of solvent increases both in the vapor and in the liquid. The density of the polymer in the liquid decreases in turn. The interfacial excess of solvent increases and the profile becomes asymmetric most of the excess is found on the vapor side of the interface. The interfacial excess per unit area can be defined by 

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Fig. 8. Microhardness profile across interfaces of two types of explosion clads that show widely divergent response resulting from the inherent cold-work hardening characteristics where Q represents the 3.2-mm type 304L stainless/28.6-mm, A 516-70 control (before cladding) ( ) = clad + flat ...

Fig. 9. Microhardness profiles across interface of explosion-clad age-hardenable aluminum alloy 2014-T3 where the initial hardness is shown as Q (a) low,...

Thirdly, we note that the diffusion coefficient has a composition dependence, which has practical implications when we predict composition profiles across interfaces we now need to use the non-linear version of Pick s second law to predict the shape of interfaces ... 

Diffusion profiles across interfaces can also be extracted from EELS data provided that the effects of the probe size and shape are properly taken into account. An interesting comparison of the near-edge fine structure in EELS spectra from four Si-containing materials is shown in Figure 4. The differences in the shapes of these spectra, which can be replicated theoretically, are due to differences in composition as well as changes in the local chemical bonding (i.e., the local atomic environment). 

By virtue of their simple stnicture, some properties of continuum models can be solved analytically in a mean field approxunation. The phase behaviour interfacial properties and the wetting properties have been explored. The effect of fluctuations is hrvestigated in Monte Carlo simulations as well as non-equilibrium phenomena (e.g., phase separation kinetics). Extensions of this one-order-parameter model are described in the review by Gompper and Schick [76]. A very interesting feature of tiiese models is that effective quantities of the interface—like the interfacial tension and the bending moduli—can be expressed as a fiinctional of the order parameter profiles across an interface [78]. These quantities can then be used as input for an even more coarse-grained description. 

Fig. 6 The electrical potential, ij/, profile across a lipid bilayer. The transmembrane potential, Aij/, is due to the difference in anion and cation concentrations between the two bulk aqueous phases. The surface potential, ij/s, arises from charged residues at the membrane-solution interface. The dipole potential, J/d, results from the alignment of dipolar residues of the lipids and associated water molecules within the membrane...

Fig. 6-20. Charge distribution profile across an interface between metal and vacuum (MAO (a) ionic pseudo-potential in metal, (b) diffuse electron tailing away from the jellium metal edge, (c) excess charge profile. n(x) s electron density at distance x = electron density in metal x, = effective image plane On = differential excess charge On = 0 corresponds to the zero charge interface.

Fig. 6-21. Charge distribution profile across a metal/aqueous solution interface (M/S) (a) the hard sphere model of aqueous solution and the jellium model of metal (the jellium-sphere model), (b) the effective image plane (IMP) and the effective excess charge plane x, (c) reduction in distance /lxd,p to the closest approach of water molecules due to electrostatic pressure, o, = differential excess charge on the solution side og = total excess charge on the solution side Oy = total excess charge on the metal side.

Fig. 5-30. Potential profile across a compact layer estimated by calculations at various electrode potentials for a mercury electrode in a 03 M sodium chloride solution electrode potential changes fivm No. 1 (a cathodic potential) to No. 6 (an anodic potential), and contact adsorption of chloride ions takes place at anodic potentials. E = electrode potential = zero charge potential x = distance fix>m the interface. [From (3raham, 1947.]...

We shall now consider what happens when the film thickness is of the order of the Debye length. In such a situation, no analytical expressions can be derived and numerical calculations should be used [125]. The real situation could be even more complicated, since an ill-defined film thickness can exist, like the example in Figure 2.6. We can use the molecular theory to obtain a self-consistently determined electrostatic potential profile across the interface as was shown in Figure 2.7 (see... 

Figure 12-3 Concentration profiles across a gas-liquid interface in equilibrium and with mass flow from left to right. There is a discontinuity in Ca between the gas-liquid and liquid-liquid phases because of differences in equilibrium...

Figure 5-25 (a) Diffusion profile across a diffusion couple for a given cooling history. This profile is an error function even if temperature is variable as long as D is not composition dependent, (b) Diffusion profile across a miscibility gap for a given cooling history. Because the interface concentration changes with time, each half of the profile is not necessarily an error function. 

However, a direct interface subjects the exit of the column to vacuum conditions. Tire vacuum may lower the inlet pressure required to obtain the desired mass-flow rate of the carrier gas and also changes its linear-velocity profile across the column. These conditions can cause poor retention-time and peak-area precision and can even make the inlet system stop delivering carrier gas to the column. Thus, analysts should use direct interfaces only with long, narrow-bore columns... 

Figure 19.10 Schematic view of concentration profile across a wall boundary between different media with a boundary layer of thickness 8 on the B-side of the interface. Diffusivities are DB —> in the...

Budkowski et al. and Bruder et al. [70] have tried to estimate the bulk phase diagram of polymer mixtures, using a geometry where for Tphase separation with an interface running parallel to the substrate occurs (Fig. Id). They obtained order parameter profiles across the film and associate the order parameter close to both walls with the order parameters ( ) es, ( ) es of the two coexisting phases in the bulk. As shown by the model calculations of Ref. [62], such a procedure also leads to systematic errors due to the finite film thickness D, in particular for T near Tc where qb is large. However, the accuracy with which Budkowski et al. and Bruder et al. [70] estimated (]> es, (]> ,s was rather limited, and... 

Figure 7.9. Interface between a solidified non-reactive Fe-Si alloy and monocrystalline a-SiC (for this alloyd 40°(Kalogeropoulouetal. 1995)). Top high resolution transmission electron Micrograph showing that the interface is sharp at the atomic scale. Bottom Fe concentration profile across the interface. The thickness of the chemical interface is the 1.5 nm resolution of the technique (electron energy-loss spectroscopy). Reprinted from (Lamy, private communication) with kind permission.

Figure 21. Electric field profile across multiple interfaces a) across an air gap the potential gradient is uniform b) with a molecule in the gap, there will be a potential drop which can be different at each interface (note that the potential gradient along the length of the molecule is. not necessarily uniform, as illustrated in case 2) c) with a multilayer of molecules, there is an extra interface between each layer.

Ellipsometry Spectroscopic ellipsometry Imaging ellipsometry Adsorbed amounts/coverages phase transitions thickness and refractive indices. Identification of interfacial molecules. Domain formation eind shape (coexisting phases) internal structure of condensed phases resolution O (1 gm). For interpretation in terms of molecular structure model profiles across the Interface are needed. Problems mono-layer anisotropy, and different profiles may match the experimental data additional (independent) information required. 

Figure 1. Concentration profile across a gas-liquid interface. Component A diffuses from the gas into the liquid. Na = o(Pa Pm) = - cj.

Figure 2. Concentration profile across a gas-liquid interface with very rapid reaction (Regime I). Reactants A and B diffuse into a narrow reaction zone in the liquid film. [J + D CBt/CnD c jj].

Figure 4. Concentration profile across a gas-liquid interface with slow chemical reaction (Regime III), Reactant A diffuses across the liquid film without appreciable chemical reaction. Virtually all chemical reaction takes place in bulk of liquid.

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