Interaction concave-convex

For clarity and because of space limitations, we will consider only examples of complexes in which the guest interacts with the host from above (or/and below) the cavity, and the structure has been confirmed by X-ray analysis. These complexes serve as models for the interaction of neutral molecules which are nearly concave/ convex complementary in their. spatial interaction. Although complementary in shape, some guest molecules simply fill spatial voids in the host lattice. These clathrate-like structures will not be considered. 

The wafer contour determines the area of contact between the wafer and the pad along with the abrasives. Thus, the amount of surface asperity interaction and the particle-wafer interaction also depends on the wafer contour. The fluid film that is in contact with the wafer surface is also dependent on the wafer contour. Thus, the pressure experienced by the wafer at different applied pressures and velocities changes with the shape of the surface. Scarfo et al. [20] conducted polishing tests on wafer samples with concave, convex, and intermediate surface contours and noted that the shape of the wafer affects the coefficient of friction. 

A classification of solubilization isotherms for small polar molecules into nonaqueous solvents by surfactants, based on the strength of interaction between solubilizate and surfactant, has been proposed by Kon-no and Kitahara (Kon-no, 1972a). When the moles of material solubilized per mole of surfactant are plotted against the relative vapor pressure, p/p°, of the system at constant temperature (where p is the vapor pressure of the water in the system and p" is the vapor pressure of pure water), isotherms are obtained whose shapes reflect the strength of the solubilizate-surfactant interaction. Systems having strong surfactant-solubilizate interaction are concave to the plp° axis, whereas those showing weak interaction are convex to that axis. Systems with very weak solubilizate-surfactant interaction show almost linear isotherms. 

There is a dependency between the shape of the chromatographic peak and the profile of the adsorption isotherm on the stationary phase. Symmetric peaks for which retention time does not depend on the volume of probe injected onto the column, which imply a linear adsorption (partition) isotherm, are usually obtained in the case of non-specific (dispersive) adsorbate—adsorbate and adsorbate-adsorbent interactions. The convex isotherm is usually obtained when the diffusive parts of the dependent peaks overlap and the adsorbate-adsorbent interactions are relatively stronger in comparison with the adsorbate-adsorbate interactions. The concave isotherm is usually obtained when the self-sharpening parts of the dependent peaks superimpose and the adsorbate-adsorbate interactions are relatively stronger in comparison with the adsorbate-adsorbent interactions. 

Kawase T, Kurata H (2006) Ball-, bowl-, and belt-shaped conjugated systems and their complexing abilities exploration of the concave-convex jc-jc interaction. Chem Rev 106... 

In retrospect, donor-acceptor interactions between the n-electron rich aromatic rings and the r-electron deficient domains of Ceo, together with van der Waals forces, provide the major stabilization for the solution complexes. While the complementary of the curvature of the interacting species maximizes the number of intermolecular contact, formation of these concave - convex composites are entropically disfavored due to a more ordered state. The above outlined examples manifest... 

Zhao, Y., 8c Truhlar, D. G. (2008). Computational characterization and modeling of buckyball tweezers Density functional study of concave convex interactions. Physical Chemistry Chemical Physics, 10, 2813-2818. 

According to their syntheses, four kinds of Cgo supramolecular polymers can be formed (Figure 1.10) (Chapter 9) (a) systems obtained by interactions between funchonalized polymers and C o derivatives or fullerene itself (b) assembly of self-complementary C o derivahves (c) multisubstituted fullerene derivatives and complementary polymeric backbones and (d) assemblies between ditopic concave guests and C o by means of concave-convex complementary interactions. 

As stated, this has been the last family to appear since the first example was reported in 1999 by the group of Dai, regarding the significant enhancement in the conduction experienced by polyanilines when mixed with polysulfonated fullerene [54]. Recently, other interesting examples of supramolecular helical polymers have been reported (Chapter 6) [55] as well as head-to-tail donor-acceptor supramolecular polymers based in concave-convex interactions [56]. 

I (curve D). Thus the micropores had been able to enhance the adsorbent-adsorbate interaction sufficiently to replace monolayer-multilayer formation by micropore filling and thereby change the isotherm from being convex to being concave to the pressure axis. 

An anticooperative mode of interactions was assumed in case of concave-shaped Scatchard plots, as alrea% proposed by other authors (Mattai Kwak, 1986 Gamier et al, 1994). A convexe curvature of the plots indicated a cooperative binding process (figure 4). 

In order to improve such a work-up, two concave pyridines 3 have been attached to a polymeric back-bone in order to recover the concave base by simple filtration. A spacer has been attached to the convex outside of the pyridine 3, i.e. in 4-position of the pyridine ring. As spacer, an ethyleneglycol unit was chosen because the spacer should not be too long to avoid a folding of the hollow cave of the concave pyridine onto the polymeric backbone. On the other hand, a spacer reduces interactions between the backbone and the concave pyridine and enhances partial solvation. 

By my remarks I wanted to emphasize the importance of concavity of enzymes as a feature that determines the specificity and stereospecificity. I didn t want to say that it is a feature that is necessary for all enzymes. However, starting with a globular convex substrate, a concave active site allows a strategic distribution of a number of small and large interactions that make the enzyme specific and stereospecific. 

The successful use of - interactions to anchor an electron-donating extTTF to the surface of SWNT was recently demonstrated (Scheme 9.23).73 Interaction between the concave hydrocarbon skeleton of exTTF and the convex surface of SWNT adds further strength and stability to the SWNT/pyrene-exTTF nanohybrid. Because of the close proximity of the exTTF to the electron acceptor SWNT, a very rapid intrahybrid electron transfer affords a photogenerated radical ion pair, whose lifetime is only a few nanoseconds. The present method for the preparation of SWNT/ exTTF nanohybrids nicely complements the covalent approach and bears a strong... 

Discrete and continuum models of transfer of molecules over various sorption sites of a microheterogeneous membrane were considered for systems with weak intermolecular interactions and membranes with constant composition and structure. An equation for estimating size effects on permeability coefficient II of microheterogeneous membranes was derived [188], and the possibility of applying the continuum model to calculate the n value in thin films of thickness L is numerically analyzed. The effect of the composition and structure of a uniformly microheterogeneous membrane on the permeability coefficients II was studied. The dependence of n on the composition is a convex function if the migration between different sorption sites proceeds more quickly than between identical sites and a concave one in the opposite case [189],... 

In most interactions between two reactants, local shape complementarity of functional groups is of importance. A local shape complementarity of molecular electron densities represented by FIDCOs implies complementary curvatures for complementary values of the charge density threshold parameters a. For various curvature domains of a FIDCO, we shall use the notations originally proposed for complete molecues [2], For example, the symbol D2(b),i(a, Fj) stands for the i-th locally convex domain of a FIDCO G(a) of functional group Fj, where local convexity, denoted by subscript 2(b), is interpreted relative to a reference curvature b. For locally saddle type and locally concave domains relative to curvature b, the analogous subscripts 1(b) and 0(b) are used, respectively. 

For these isotherms, different geometries may be possible for one equation. If the lateral interactions are weak, the isotherm is convex. On the other hand, if these interactions are very strong, the function f(v) is not monotonic and the function v = g(u) is multi-valued. The case we study here is an intermediate between these two extremes. We assume that the function f(v) is monotonic but has an inflection point (u, g(u)). The function g(u) is thus defined, perhaps, implicitly. We assume that g(u) is concave for u < u and convex for u < u and also that v = 1 is an asymptote. 

Figure 2. The exchange repulsion contours for several molecules, obtained for interactions with rare-gas atoms, and defined by two polar coordinates measured from the center of mass (Energy, 0) [31,32], The contours are the images of molecules shapes, probed by structureless atoms. In contrast to plots that show isoeneigetic regions, these contours reveal an enhanced anisotropy. Convex and concave regions indicate, respectively, the areas of increased and reduced exchange repulsion.

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