Distance/interaction profile

The GRID MIFs can also be transformed to alignment independent descriptor (GRIND) aimed to give a distance/interaction profile which has proven to be useful in the description of GYP inhibition, metabolic stability and in the active transporter and recognition area. 

When the Bom, double-layer, and van der Waals forces act over distances that are short compared to the diffusion boundary-layer thickness, and when the e forces form an energy hairier, the adsorption and desorption rates may be calculated by lumping the effect of the interactions into a boundary condition on the usual ccm-vective-diffusion equation. This condition takes the form of a first-order, reversible reaction on the collector s surface. The apparent rate constants and equilibrium collector capacity are explicitly related to the interaction profile and are shown to have the Arrhenius form. They do not depend on the collector geometry or flow pattern. 

Figure B3.6.3. Sketch of the coarse-grained description of a binary blend in contact with a wall, (a) Composition profile at the wall, (b) Effective interaction g(l) between the interface and the wall. The different potentials correspond to complete wettmg, a first-order wetting transition and the non-wet state (from above to below). In case of a second-order transition there is no double-well structure close to the transition, but g(l) exhibits a single minimum which moves to larger distances as the wetting transition temperature is approached from below, (c) Temperature dependence of the thickness / of the enriclnnent layer at the wall. The jump of the layer thickness indicates a first-order wetting transition. In the case of a conthuious transition the layer thickness would diverge continuously upon approaching from below.

Figure 8.3. Wave interactions in planar tensile fracture experiment, (a) Shows the distance-time plot of interacting compression C , rarefaction R , and tension T , waves (b) Shows the corresponding particle-velocity profiles including the initial compressive shock wave (tj, tj), the pull-back signal (tj, tj), and subsequent reflection >h).

The Schlichting finite-boundaries profile is another one that is ftequently used.- Utilization of this profile is specifically fruitful fot describing velocity distribution in complex flows, e.g., a jet in a cross-flow " and jet interaction under the right angle.In such cases, distance from the jet axis, r to the point with an air velocity V, is replaced by the parameter r, = where S, is... 

FIGURE 1.13 The van der Waals interaction energy profile as a fnnction of the distance, r, between the centers of two atoms. The energy was calcnlated nsing the empirical equation U= B/r — A/r. (Values for the parameters B = 11.5 X 10 kJnm /mol and A = 5.96 X 10 kJnmVtiiol for the interaction between two carbon atoms are from Levitt, M., Journal of Molecular Biology... 

Fig. 3 —Schematic energy versus distance profiles of DLVO interaction.

The ionic profile of the metal was modeled as a step function, since it was anticipated that it would be much narrower than the electronic profile, and the distance dx from this step to the beginning of the water monolayer, which reflects the interaction of metal ions and solvent molecules, was taken as the crystallographic radius of the metal ions, Rc. Inside the metal, and out to dl9 the relative dielectric constant was taken as unity. (It may be noted that these calculations, and subsequent ones83 which couple this model for the metal with a model for the interface, take the position of the outer layer of metal ion cores to be on the jellium edge, which is at variance with the usual interpretation in terms of Wigner-Seitz... 

Figure 4.13 shows the free energy profile as a function of the helix-helix distance. Equation (4.47) allows the computation of the contributions to the profile by the different intermolecular potentials. The helix-helix and helix-solvent interactions were considered. The helix-helix van der Waals potential shows a significant minimum... 

The force-distance profiles Al, A2 appear to show the relaxed, or quasi-equilibrium limit for the interaction between the mica plates bearing the PEO in the good solvent conditions of the present study. The adsorbed layer thicknesses 6 are then about half the value of D at which onset of repulsion (A curves) is first noted. 6 thus corresponds to some 3Rg for both polymers in the present investigation, a value comparable to that obtained for hydrodynamic layer thickness of PEO absorbed on latex particles in water, for similar molecular weights, from light scattering studies. 

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