Fluctuating dipole forces

Schmitz et al (31) have proposed that the discrepancy between QLS and tracer diffusion measurements can be reconciled by considering the effects of small ions on the dynamics and scattering power of the polyelectrolyte. In this model, the slow mode arises from the formation of "temporal aggregates . These arise as the result of a balance between attractive fluctuating dipole forces coming from the sharing of small ions by several polyions, and repulsive electrostatic and Brownian diffusion forces. This concept is attractive, but needs to be formulated quantitatively before it can be adequately tested. 

At low temperatures they solidify. The solid noble gases have the cubic face-centered crystal lattice. The molecules of solid noble gases are glued by very weak fluctuating dipole forces. The atoms are distorted from the stable configuration and this creates a potential that holds atoms of solid together. This attractive potential depends on the interatomic distance r as the inverse sixth power. The repulsive force depends inversely on the distance to the twelfth power. An empirical formula for potential is known as Leimard-Jones potential (11.26). It is appropriate to use this equation in the dimensionaUy-handy form... 

There are two general cases of dipole-dipole forces those between molecules in which the distribution of electronic charge is centrosymmetric and those in which it is not. In the first case, there are no permanent electrical dipoles, whereas there is a permanent dipole if the charge distribution is non-centro-symmetric. When permanent dipoles are not present, there are nevertheless fluctuating dipoles as a result of atomic vibrations. These are always present because of zero-point motion. At temperatures greater than 0°K, thermal energy further excites the molecular vibrational modes which create fluctuating electric dipoles. 

The term molecular crystal refers to crystals consisting of neutral atomic particles. Thus they include the rare gases He, Ne, Ar, Kr, Xe, and Rn. However, most of them consist of molecules with up to about 100 atoms bound internally by covalent bonds. The dipole interactions that bond them is discussed briefly in Chapter 3, and at length in books such as Parsegian (2006). This book also discusses the Lifshitz-Casimir effect which causes macroscopic solids to attract one another weakly as a result of fluctuating atomic dipoles. Since dipole-dipole forces are almost always positive (unlike monopole forces) they add up to create measurable attractions between macroscopic bodies. However, they decrease rapidly as any two molecules are separated. A detailed history of intermolecular forces is given by Rowlinson (2002). 

The existence of an attractive force between non-polar molecules was first recognized by van der Waals, who published his classic work in 1873. The origin of these forces was not understood until 1930 when Fritz London (1900-1954) published his quantum-mechanical discussion of the interaction between fluctuating dipoles. He showed how these temporary dipoles arose from the motions of the outer electrons on the two molecules. 

It is well known that neutral molecules such as alkanes attract one another, mainly through van der Waals forces. Van der Waals forces arise from the rapidly fluctuating dipoles moment (1015 S-1) of a neutral atom, which leads to polarization and consequently to attraction. This is also called the London potential between two atoms in a vacuum, and is given as... 

Dispersion Interactions. Last but not least in the range of solute-solvent electrostatic interactions come the dispersion forces which depend on the polarizabilities of the molecules. Any atom or molecule—non-polar or polar—has a small fluctuating dipole moment as the electrons move around the nuclei. These instantaneous dipoles induce dipole moments in all other polarizable molecules, so that the interaction energy is proportional to the product of the average polarizabilities aM and as of the solute and solvent molecules... 

VAN DER WAALS FORCES. Interatomic or intermolecular forces of attraction due to the interaction between fluctuating dipole moments associated with molecules not possessing permanent dipole moments. These dipoles result from momentary dissymmetry in the positive and negative charges of the atom or molecule, and on neighboring atoms or molecules. These dipoles tend to align in antiparallel direction and thus result in a net attractive force. This force varies inversely as the seventh power of the distance between ions. 

Van der Waals postulated that neutral molecules exert forces of attraction on each other which are caused by electrical interactions between dipoles. The attraction results from the orientation of dipoles due to any of (1) Keesom forces between permanent dipoles, (2) Debye induction forces between dipoles and induced dipoles, or (3) London-van der Waals dispersion forces between fluctuating dipoles and induced dipoles. (The term dispersion forces arose because they are largely determined by outer electrons, which are also responsible for the dispersion of light [272].) Except for quite polar materials the London-van der Waals dispersion forces are the more significant of the three. For molecules the force varies inversely with the sixth power of the intermolecular distance. 

Let us, then, begin with the simplest possible problem, the interaction of two atoms. Unless they overlap, the only force between them will be the Van der Waals attraction, coming from the polarization of each atom by the fluctuating dipole moment of the other. This type of interaction persists even when the valence electrons of the atoms do overlap. 

A particularly important variant of the optical force, interparticle forces, turns out to be crucial for SERS. This effect is similar to the attractive van der Waals force between small particles, which is due to interactions between spontaneously fluctuating dipoles, but the optical interaction is due to coupling between the actual particle dipoles induced by the trapping laser. Due to the interparticle optical forces, metal nanoparticles aggregate in an optical tweezers and produce hotspots, i.e., particle junctions with intense local fields for SERS. Raman probes can be excited either by the trapping laser or, preferably, by a separate low power beam that does not disturb the trapping. 

Physical adsorption is a universal phenomena, producing some, if not the major, contribution to almost every adhesive contact. It is dependent for its strength upon the van der Waals attraction between individual molecules of the adhesive and those of the substrate. Van der Waals attraction quantitatively expresses the London dispersion force between molecules that is brought about by the rapidly fluctuating dipole moment within an individual molecule polarizing, and thus attracting, other molecules. Grimley (1973) has treated the current quantum mechanical theories involved in simplified mathematical terms as they apply to adhesive interactions. 

Even molecules such as alkanes (which are short oligomeric versions of polyethylenes see Fig. 2-7) that possess no permanent dipole have fluctuating dipoles because of the motion of the electronic cloud around each molecule. Because the dipoles communicate with each other through their electric fields, they are able to correlate their fluctuating magnitudes and orientations to produce a net attractive force, called the London force. Thus, the electric field E produced by one temporary dipole can induce a dipole moment Uind in another molecule, where Ui d = aoE and ao is the molecule s polarizability. Since these fluctuating... 

In nonpolar media due to the low ionization of the solute species, electrostatic attractive or repulsive forces can be ruled out as a major mechanism for adsorption. However, polar interactions have to be considered especially when polar surfaces such as oxides are involved. Recent work has shown acid-base interactions between the surface species and the solute molecules to be responsible for adsorption in nonaqueous media. Fowkes has suggested that the interaction between a solid surface and an uncharged adsorbate can be divided into two parts, dispersive interactions and polar interactions. The dispersive interactions are due to the fluctuating dipole moments created by the movement of electrons in any atom or molecule and thus occur between all atoms and molecules. Polar interactions refer to specific interactions between hydrophilic surface groups and functional groups in the adsorbate molecules. 

Polar molecules have forces between permanent dipoles. With nonpolar molecules London dispersion (or van der Waals ) forces arise between fluctuating dipoles their magnitude is related to molecular polarizability, which generally increases with size. Molecules may also have more specific donor-acceptor interactions including hydrogen bonding. 

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