Van der Waals interaction between

The interest in vesicles as models for cell biomembranes has led to much work on the interactions within and between lipid layers. The primary contributions to vesicle stability and curvature include those familiar to us already, the electrostatic interactions between charged head groups (Chapter V) and the van der Waals interaction between layers (Chapter VI). An additional force due to thermal fluctuations in membranes produces a steric repulsion between membranes known as the Helfrich or undulation interaction. This force has been quantified by Sackmann and co-workers using reflection interference contrast microscopy to monitor vesicles weakly adhering to a solid substrate [78]. Membrane fluctuation forces may influence the interactions between proteins embedded in them [79]. Finally, in balance with these forces, bending elasticity helps determine shape transitions [80], interactions between inclusions [81], aggregation of membrane junctions [82], and unbinding of pinched membranes [83]. Specific interactions between membrane embedded receptors add an additional complication to biomembrane behavior. These have been stud-... 

In order to probe the importance of van der Waals interactions between reactants and solvent, experiments in the gas-liqnid transition range appear to be mandatory. Time-resolved studies of the density dependence of the cage and clnster dynamics in halogen photodissociation are needed to extend earlier quantum yield studies which clearly demonstrated the importance of van der Waals clnstering at moderate gas densities [37, 111]... 

Flartmann U 1991 van der Waals interactions between sharp probes and flat sample surfaces Phys. Rev. B 43 2404... 

At large separation r, equation (C2.6.3) decays as oc r just as the van der Waals interactions between... 

The biasing function is applied to spread the range of configurations sampled such that the trajectory contains configurations appropriate to both the initial and final states. For the creation or deletion of atoms a softcore interaction function may be used. The standard Lennard-Jones (LJ) function used to model van der Waals interactions between atoms is strongly repulsive at short distances and contains a singularity at r = 0. This precludes two atoms from occupying the same position. A so-called softcore potential in contrast approaches a finite value at short distances. This removes the sin-... 

Rotation about the 1,1 -bond is resisted by van der Waals interactions between the hydrogens shown in the structures. These hydrogens crowd each other when the two naphthyl groups are coplanar, and the racemization process requires tjie hydrogens to move past each other. The existence of enantiomeric substituted biphenyls also depends on steric interactions between substituents. The relationship between the rate of racemization and... 

The case of a, -unsaturated caAonyl compounds is analogous to that of 1,3-dienes, in that stereoelectronic factors favor coplanaiity of the C=C—C=0 system. The rotamers that are important are the s-trans and s-cis conformations. Microwave data indicate that the s-trans form is the only conformation present in detectable amounts in acrolein (2-propenal). The equilibrium distribution of s-trans and s-cis conformations of a,fi-unsatuiated ketones depends on the extent of van der Waals interaction between substituents. Methyl vinyl ketone has minimal unfavorable van der Waals repulsions between substituents and exists predominantly as the s-trans conformer ... 

There are three types of interactions that contribute to van der Waals forces. These are interactions between freely rotating permanent dipoles (Keesom interactions), dipole-induced dipole interaction (Debye interactions), and instantaneous dip le-induced dipole (London dispersion interactions), with the total van der Waals force arising from the sum. The total van der Waals interaction between materials arise from the sum of all three of these contributions. 

In the second type of interaction contributing to van der Waals forces, a molecule with a permanent dipole moment polarizes a neighboring non-polar molecule. The two molecules then align with each other. To calculate the van der Waals interaction between the two molecules, let us first assume that the first molecule has a permanent dipole with a moment u and is separated from a polarizable molecule (dielectric constant ) by a distance r and oriented at some angle 0 to the axis of separation. The dipole is also oriented at some angle from the axis defining the separation between the two molecules. Overall, the picture would be very similar to Fig. 6 used for dipole-dipole interaction except that the interaction is induced as opposed to permanent. 

The remarkable stability of onion-like particles[15] suggests that single-shell graphitic molecules (giant fullerenes) containing thousands of atoms are unstable and would collapse to form multi-layer particles in this way the system is stabilized by the energy gain from the van der Waals interaction between shells [15,26,27],... 

Both attractive forces and repulsive forces are included in van der Waals interactions. The attractive forces are due primarily to instantaneous dipole-induced dipole interactions that arise because of fluctuations in the electron charge distributions of adjacent nonbonded atoms. Individual van der Waals interactions are weak ones (with stabilization energies of 4.0 to 1.2 kj/mol), but many such interactions occur in a typical protein, and, by sheer force of numbers, they can represent a significant contribution to the stability of a protein. Peter Privalov and George Makhatadze have shown that, for pancreatic ribonuclease A, hen egg white lysozyme, horse heart cytochrome c, and sperm whale myoglobin, van der Waals interactions between tightly packed groups in the interior of the protein are a major contribution to protein stability. 

Probably the most familiar of all clathrates are those formed by Ar, Kr and Xe with quinol, l,4-C6H4(OH)2, and with water. The former are obtained by crystallizing quinol from aqueous or other convenient solution in the presence of the noble gas at a pressure of 10-40 atm. The quinol crystallizes in the less-common -form, the lattice of which is held together by hydrogen bonds in such a way as to produce cavities in the ratio 1 cavity 3 molecules of quinol. Molecules of gas (G) are physically trapped in these cavities, there being only weak van der Waals interactions between... 

Matsui441 has computed energies (Evdw) due to the van der Waals interaction between a-cyclodextrin and some guest molecules by the use of Hill s potential equation 451 ... 

The fracture behavior can be attributed to strain softening [91] in the deformation zone [92, 93] or to stress-activated devitrification [89, 96]. The strands are comparatively free to move in the strain softened regions of the deformation zone. The van der Waals interaction between adjacent strands is greatly reduced and the clearence between molecular segments is enlarged. 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

FlC. 20.—Parallel packing arrangement of 6-fold, curdlan I (17) helices, (a) Stereo view of two unit cells approximately normal to the 6c-plane. The helix is stabilized by intrachain 4-0H---0-5 hydrogen bonds. There are only van der Waals interactions between the helices. 

The DNA double heUx illustrates the contribution of multiple forces to the structure of biomolecules. While each individual DNA strand is held together by covalent bonds, the two strands of the helix are held together exclusively by noncovalent interactions. These noncovalent interactions include hydrogen bonds between nucleotide bases (Watson-Crick base pairing) and van der Waals interactions between the stacked purine and pyrimidine bases. The hehx presents the charged phosphate groups and polar ribose sugars of... 

Physisorption, originating from Van der Waals interaction between reactant and surface. This weakly exothermic process is reversible and does not result in any new chemical bonds being formed. In general physisorption does not lead to catalytic activity but may be a precursor to chemisorption. 

Physisorption is very similar to the molecular van der Waals interaction, which makes gases condense in multilayers. The Van der Waals interaction between molecules is often described by the Lennard-Jones potential, which has the form... 

Under 50 mbar of H2 and 50 °C, SnBu4 reacts selectively on the Pt surface to form surface complexes of average formula Pts[SnBux] /. The empirical formula (values of x and y) depend on the reaction time and on the Snint/Pts ratio (Fig. 6). Note that under these conditions SnBu4 does not chemically react with the silica surface, but it is fully physisorbed on the support [114]. In fact, when silica is contacted with SnBu4, IR spectroscopy shows a shift of the v(0 - H) band of silica to lower wave numbers, i.e. from 3747 cm to ca. 3700 cm which results from van der Waals interactions between the hydroxyl groups of the support and the butyl chains of adsorbed SnBu4 (Scheme 32). 

---