Force van der Waals interactions

In 1991, lijima [2] found, by electron diffraction, that the interlayer spacing within multi-walled nanotubes (d(oo2) = 3.4 A) was slightly greater than that of graphite (d(oo2) = 3.35 A). This fact was ascribed to a combination of tubule curvature and van der Waals force interactions between successive graphene layers. The X-ray diffraction pattern is consistent with this spacing and provides information about crystallinity and structural dimensions in the bulk phase. 

The morphology, including features of adsorbates, can be determined with a small tip that scans the electrode surface mechanically using a very low contact pressure. This method is termed atomic force microscopy (AFM) [67] because van der Waals force interactions are probed. The first applications in metal deposition studies have been reported [68-71],... 

Taking cognizance of the considerations discussed under Lifshitz-van der Waals forces, the van der Waals force component to surface energy has often been written in recent literature as Y f where LW stands for Lifshitz-van der Waals. y represents ail the van der Waals force interactions, that is, in the earlier terminology, dispersion plus polar. Its contribution to the lowering of interfacial tension can be represented by a geometric mean relationship, see Eqn. 4,... 

The second general cause of a variable heat of adsorption is that of adsorbate-adsorbate interaction. In physical adsorption, the effect usually appears as a lateral attraction, ascribable to van der Waals forces acting between adsorbate molecules. A simple treatment led to Eq. XVII-53. 

Adsorbates can physisorb onto a surface into a shallow potential well, typically 0.25 eV or less [25]. In physisorption, or physical adsorption, the electronic structure of the system is barely perturbed by the interaction, and the physisorbed species are held onto a surface by weak van der Waals forces. This attractive force is due to charge fiuctuations in the surface and adsorbed molecules, such as mutually induced dipole moments. Because of the weak nature of this interaction, the equilibrium distance at which physisorbed molecules reside above a surface is relatively large, of the order of 3 A or so. Physisorbed species can be induced to remain adsorbed for a long period of time if the sample temperature is held sufficiently low. Thus, most studies of physisorption are carried out with the sample cooled by liquid nitrogen or helium. 

Note that the van der Waals forces tliat hold a physisorbed molecule to a surface exist for all atoms and molecules interacting with a surface. The physisorption energy is usually insignificant if the particle is attached to the surface by a much stronger chemisorption bond, as discussed below. Often, however, just before a molecule fonus a strong chemical bond to a surface, it exists in a physisorbed precursor state for a short period of time, as discussed below in section AL7.3.3. 

As the tip is brought towards the surface, there are several forces acting on it. Firstly, there is the spring force due to die cantilever, F, which is given by = -Icz. Secondly, there are the sample forces, which, in the case of AFM, may comprise any number of interactions including (generally attractive) van der Waals forces, chemical bonding interactions, meniscus forces or Bom ( hard-sphere ) repulsion forces. The total force... 

The measurement of surface forces out-of-plane (nonual to the surfaces) represents a central field of use of the SFA teclmique. Besides the ubiquitous van der Waals dispersion interaction between two (mica) surfaces... 

Similarly, van der Waals forces operate between any two colloidal particles in suspension. In the 1930s, predictions for these interactions were obtained from the pairwise addition of molecular interactions between two particles [38]. The interaction between two identical spheres is given by... 

The Hamaker constant can be evaluated accurately using tire continuum tlieory, developed by Lifshitz and coworkers [40]. A key property in tliis tlieory is tire frequency dependence of tire dielectric pennittivity, (cij). If tills spectmm were tlie same for particles and solvent, then A = 0. Since tlie refractive index n is also related to f (to), tlie van der Waals forces tend to be very weak when tlie particles and solvent have similar refractive indices. A few examples of values for A for interactions across vacuum and across water, obtained using tlie continuum tlieory, are given in table C2.6.3. 

Halgren T A 1992. Representation of van der Waals (vdW) Interactions in Molecular Mechanics Force Fields Potential Form, Combination Rules, and vdW Parameters. Journal of the American Chemical Society 114 7827-7843. 

In molecular mechanics, van der Waals forces are thought to inlliieiiee atoms that are wnthiii the same molecule but are not connected by chemical bonds. They are sometimes called 1-4 interactions, implying that a chemical bond does not exist between atoms 1 and 4 but one does exist between atoms 2 and 3... 

Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled. 

Nonbonded interactions are the forces be tween atoms that aren t bonded to one another they may be either attractive or repulsive It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep arated from each other by many bonds Induced dipole/induced dipole interactions make van der Waals forces in alkanes weakly attractive at most distances but when two atoms are closer to each other than the sum of their van der Waals radii nuclear-nuclear and electron-electron repulsive forces between them dominate the fvan derwaais term The resulting destabilization is called van der Waals strain... 

Polymer alloys are physical mixtures of structurally different homopolymers or copolymers. The mixture is held together by secondary intermolecular forces such as dipole interaction, hydrogen bonding, or van der Waals forces. 

Adsorption on a nonpolar surface such as pure siUca or an unoxidized carbon is dominated by van der Waals forces. The affinity sequence on such a surface generally follows the sequence of molecular weights since the polarizabiUty, which is the main factor governing the magnitude of the van der Waals interaction energy, is itself roughly proportional to the molecular weight. 

Absorption, metaboHsm, and biological activities of organic compounds are influenced by molecular interactions with asymmetric biomolecules. These interactions, which involve hydrophobic, electrostatic, inductive, dipole—dipole, hydrogen bonding, van der Waals forces, steric hindrance, and inclusion complex formation give rise to enantioselective differentiation (1,2). Within a series of similar stmctures, substantial differences in biological effects, molecular mechanism of action, distribution, or metaboHc events may be observed. Eor example, (R)-carvone [6485-40-1] (1) has the odor of spearrnint whereas (5)-carvone [2244-16-8] (2) has the odor of caraway (3,4). 

Sorption of nonionic, nonpolar hydrophobic compounds occurs by weak attractive interactions such as van der Waals forces. Net attraction is the result of dispersion forces the strength of these weak forces is about 4 to 8 kj/mol ( 1 2 kcal/mol). Electrostatic interactions can also be important, especially when a molecule is polar in nature. Attraction potential can develop between polar molecules and the heterogeneous sod surface that has ionic and polar sites, resulting in stronger sorption. 

Although most nonionic organic chemicals are subject to low energy bonding mechanisms, sorption of phenyl- and other substituted-urea pesticides such as diuron to sod or sod components has been attributed to a variety of mechanisms, depending on the sorbent. The mechanisms include hydrophobic interactions, cation bridging, van der Waals forces, and charge-transfer complexes. 

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