Effective interface

Continuum models go one step frirtlier and drop the notion of particles altogether. Two classes of models shall be discussed field theoretical models that describe the equilibrium properties in temis of spatially varying fields of mesoscopic quantities (e.g., density or composition of a mixture) and effective interface models that describe the state of the system only in temis of the position of mterfaces. Sometimes these models can be derived from a mesoscopic model (e.g., the Edwards Hamiltonian for polymeric systems) but often the Hamiltonians are based on general symmetry considerations (e.g., Landau-Ginzburg models). These models are well suited to examine the generic universal features of mesoscopic behaviour. 

If one is only interested in the properties of the interface on scales much larger than the width of the intrinsic profiles, the interface can be approximated by an infinitely thin sheet and the properties of the intrinsic profiles can be cast into a few effective parameters. Using only the local position of the interface, effective interface Hamiltonians describe the statistical mechanics of fluctuating interfaces and membranes. 

On short length scales the coarse-grained description breaks down, because the fluctuations which build up the (smooth) intrinsic profile and the fluctuations of the local interface position are strongly coupled and camiot be distinguished. The effective interface Flamiltonian can describe the properties only on length scales large compared with the width w of the intrinsic profile. The absolute value of the cut-off is difficult... 

One can regard the Hamiltonian (B3.6.26) above as a phenomenological expansion in temis of the two invariants Aiand//of the surface. To establish the coimection to the effective interface Hamiltonian (b3.6.16) it is instnictive to consider the limit of an almost flat interface. Then, the local interface position u can be expressed as a single-valued fiinction of the two lateral parameters n(r ). In this Monge representation the interface Hamiltonian can be written as... 

LC operates in the liquid phase, while MS is a gas-phase method, so it is not a simple matter to connect the two. An interface is needed to pass separated components of a mixture from the LC to the MS. With an effective interface, LC/MS becomes a very powerful analytical technique. 

The combined effect of van der Waals and electrostatic forces acting together was considered by Derjaguin and Landau (5) and independently by Vervey and Overbeek (6), and is therefore called DLVO theory. It predicts that the total interaction energy per unit area, also known as the effective interface potential, is given by V(f) = ( ) + dl ( )- absence of externally imposed forces, the equiHbrium thickness of the Hquid film... 

Fig. 2. Effective interface potential (left) and corresponding disjoining pressure (right) vs film thickness as predicted by DLVO theory for an aqueous soap film containing 1 mM of 1 1 electrolyte. The local minimum in H(f), marked by °, gives the equiHbrium film thickness in the absence of appHed pressure as 130 nm the disjoining pressure 11 = —(dV/di vanishes at this minimum. The minimum is extremely shallow compared with the stabilizing energy barrier.

Disjoining Pressure. A static pressure difference can be imposed between the interior and exterior of a soap film by several means including, for example, gravity. In such cases the equiHbrium film thickness depends on the imposed pressure difference as weU as on the effective interface potential. When the film thickness does not minimize lV(f), there arises a disjoining pressure II = —dV/(U which drives the system towards mechanical equiHbrium. 

The other class of phenomenological approaches subsumes the random surface theories (Sec. B). These reduce the system to a set of internal surfaces, supposedly filled with amphiphiles, which can be described by an effective interface Hamiltonian. The internal surfaces represent either bilayers or monolayers—bilayers in binary amphiphile—water mixtures, and monolayers in ternary mixtures, where the monolayers are assumed to separate oil domains from water domains. Random surface theories have been formulated on lattices and in the continuum. In the latter case, they are an interesting application of the membrane theories which are studied in many areas of physics, from general statistical field theory to elementary particle physics [26]. Random surface theories for amphiphilic systems have been used to calculate shapes and distributions of vesicles, and phase transitions [27-31]. 

One important area of technology development is the world-to-chip interface. The requirements for an effective interface are ease of fabrication, low dead volume, ease of automation, no sample biasing from the reagent source, and compatibility with existing sample storage formats. One such interface for high... 

The stability of excipients is almost always taken for granted. Obviously, there is the potential for a phase change with certain lower melting excipients, e.g., semisolid materials, however, this is not a chemical phenomenon although it may enhance the potential for interaction by increasing the effective interface available at which the interaction can take place. However, some materials are not stable under conditions encountered in excipient compatibility screening or accelerated stability testing. A notable example is dibasic calcium phosphate dihydrate. At temperatures as low as 37°C, under certain conditions, the dihydrate can dehydrate to form the anhydrous material with the concomitant loss of water of crystallization (25), and at 25°C, it is a stable solid with a shelf life, when stored correctly, of more than two years. 

Buildup of an emulsion layer at the interface in the treating vessel may be detrimental to treating. In gun barrels with sufficient residence time, it probably won t hurt if its stalilizes at a resonable thickness. In vertical or horizontal treaters il is usually undesirable. Particularly in horizontal treaters, effective interface control is a necessity. The interface must be free of any type of material that may have a tendency to build... 

Although this compound is not a traditional coupling agent, it does provide for a biologically effective interface between microbes and a variety of surfaces, and... 

The major feature of the reactor shown in Fig. 7.9 is its simple structure with few internal parts. This not only reduces the walls on which the solid particles may cake, but also favors increasing the time-averaged effective interface area for transfer because the droplets can essentially keep their fine-dispersed condition during the whole period of contact with the gas flow. For flue gas containing ashes it has the additional function of wet dust-removal. 

Dietrich, S., (1991), Fluid interfaces - wetting, critical adsorption, van der Waals tails, and the concept of the effective interface potential , in Taub, H., Torzo, G., Lauter, HJ. and Fain, S.C., (eds), Phase. Transitions in Surface Films 2, NATO Advanced Science Series, Physics, Vol. 267, 391-423. 

Fig. 6. A rough surface of die wall, where the stagnant (thin) chains allow the unbound chains (the middle thick chain without dot) to entangle and adsorb at the effective interface (dashed line). Adsorbed chains (thick chains with dots) are also present. Such an interface can also produce a stick-slip transition upon a coil-stretch transition involving the thick chains. See Ref. [27]. For clarity, we only draw three tethered chains (two adsorbed and one entangled) besides the stagnant chains in one valley. The chains not drawn here, of course, fill up all the space away from the rough wall...

Once management has made a commitment to the program and goals have been set, a program task force is established. The selection of a team leader will be dependent upon many factors including the ability to effectively interface with both the assessment team and management staff. 

Mass spectrum interpretation is essential to solve one or more of the following problems establishment of molecular weight and of empirical formula detection of functional groups and other substituents determination of overall structural skeleton elucidation of precise structure and possibly of certain stereochemical features. As detailed in the previous sections, ESI and APCI are two of the most effective interfaces for LC/MS that have been developed. Thus, the focus of the discussion will be on interpretation of mass spectra obtained by ESI or APCI. 

The most useful and effective interfaces between HS devices and megabore columns are probably the low-dead volume (LDV) interface and the PT-LDV injector. The former... 

With these relations, the combined films and interface is regarded as an effective interface . There is no need to assume phase equilibrium between liquid and vapour. The entropy production rate can alternatively be expressed by the measurable heat flux in the vapour and fluxes of mass. - This set of flux equations was used to explain the entropy production in tray distillation columns. However, it has not yet been used for predictive purposes. Much work remains to be done to include these equations in a software that is useful for industrial purposes. 

Abbreviations used p, density 0/Si, atomic ratio R, resistivity RF, refractive index BF, breakdown field DI, dielectric constant Ncd.n , effective interface charge density at flatband potential N, interface surface states density mobile ionic charge density r, ratio... 

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