Van-der-Waals Attraction

polymeric interaction This results in a total interaction Gibbs free energy 

The attractive van der Waals interaction is always present and can be modelled. The electrostatic force and the polymeric force, primarily the most important forces in suspension formulation, can be controlled in order to give the suspension the required properties they can also be modelled. 

Three cases for the total Gibbs free energy will now be decdt with. 

This case has been evaluated in the well known DLVO theory named after the Russians Derjaguin and Landau and the Dutch Verwey and Overbeek. 

Solvation forces from the solvent structure near the particle surface can be attractive (hydrophobic attraction) or repulsive (hydration repulsion). Treatises on these forces can be found in Refs. [26,27] and [22]. Hydrogen bonding may be important but its effect is not yet well-known. For the time being the effect is not taken into account. 

As is well known, atoms or molecules always attract each other at short separations. The attractive forces are of three different types Dipole-dipole interaction 

At small distances of separation r in vacuum, the attractive energy between two atoms or molecules is given by 

For colloidal particles made of atom or molecular assemblies, the attractive energies may be added, resulting in the following expression for two spheres (at small h), 

All is the Hamaker constant between particles in a vacuum and A22 Hamaker constant for equivalent volumes of the medium. 

Total Enei of Interaction Deryaguin-Landau-Verwey-Overbeek (DLVO) Theory 

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Often the van der Waals attraction is balanced by electric double-layer repulsion. An important example occurs in the flocculation of aqueous colloids. A suspension of charged particles experiences both the double-layer repulsion and dispersion attraction, and the balance between these determines the ease and hence the rate with which particles aggregate. Verwey and Overbeek [44, 45] considered the case of two colloidal spheres and calculated the net potential energy versus distance curves of the type illustrated in Fig. VI-5 for the case of 0 = 25.6 mV (i.e., 0 = k.T/e at 25°C). At low ionic strength, as measured by K (see Section V-2), the double-layer repulsion is overwhelming except at very small separations, but as k is increased, a net attraction at all distances... 

The quantity zoi will depend very much on whether adsorption sites are close enough for neighboring adsorbate molecules to develop their normal van der Waals attraction if, for example, zu is taken to be about one-fourth of the energy of vaporization [16], would be 2.5 for a liquid obeying Trouton s rule and at its normal boiling point. The critical pressure P, that is, the pressure corresponding to 0 = 0.5 with 0 = 4, will depend on both Q and T. A way of expressing this follows, with the use of the definitions of Eqs. XVII-42 and XVII-43 [17] ... 

As with any collision process, to understand the dynamics of collisions we need an appreciation of the relevant forces and masses. Far from the surface, the incoming atom or molecule will experience tire van der Waals attraction of the fonn... 

The van der Waals attraction arises from tlie interaction between instantaneous charge fluctuations m the molecule and surface. The molecule interacts with the surface as a whole. In contrast the repulsive forces are more short-range, localized to just a few surface atoms. The repulsion is, therefore, not homogeneous but depends on the point of impact in the surface plane, that is, the surface is corrugated. 

Theta conditions in dilute polymer solutions are similar to tire state of van der Waals gases near tire Boyle temperature. At this temperature, excluded-volume effects and van der Waals attraction compensate each other, so tliat tire second virial coefficient of tire expansion of tire pressure as a function of tire concentration vanishes. On dealing witli solutions, tire quantity of interest becomes tire osmotic pressure IT ratlier tlian tire pressure. Its virial expansion may be written as... 

Hamaker H C 1937 London-van der Waals attraction between spherical particles Physica 4 1058-72... 

Boiling Point When describing the effect of alkane structure on boiling point m Sec tion 2 17 we pointed out that van der Waals attractive forces between neutral molecules are of three types The first two involve induced dipoles and are often referred to as dis persion forces or London forces... 

In general arenes resemble other hydrocarbons in their physical properties They are nonpolar insoluble in water and less dense than water In the absence of polar sub stituents mtermolecular forces are weak and limited to van der Waals attractions of the induced dipole/mduced dipole type... 

The ion that has the greater polarizability (which determines the Van der Waals attraction). 

TT-stacking and charge-transfer interaction between aromatic residues in the receptor and delocalized regions of the substrate van der Waals attraction between hydrophobic regions on the two components... 

The chemical, stmctural, and electronic characteristics of surfaces and interfaces are usually different from those of the bulkphase(s). Thus, methods to be used for the analysis of surfaces must be selective in response to the surface or interfacial region relative to the bulk. Surfaces and interfaces are most commonly explored using techniques based on the interaction of photons, electrons, or ions with the surface or using a force such as electric field or van der Waals attraction. These excitations generate a response involving the production of photons, electrons, ions or the alteration of a force that is then sensed in the analysis. 

V n der W ls Interactions. Van der Waals iateractions result from the asymmetric distribution of electronic charge surrounding an atom, which induces a complementary dipole in a neighboring atom, resulting in an attractive force. In general, the attractive force of van der Waals interactions is very weak (<4.2 kJ/mol (1 kcal/mol)) but may become significant if steric complementarity creates an opportunity to form a large number of van der Waals attractions. 

The well-known DLVO theory of coUoid stabiUty (10) attributes the state of flocculation to the balance between the van der Waals attractive forces and the repulsive electric double-layer forces at the Hquid—soHd interface. The potential at the double layer, called the zeta potential, is measured indirectly by electrophoretic mobiUty or streaming potential. The bridging flocculation by which polymer molecules are adsorbed on more than one particle results from charge effects, van der Waals forces, or hydrogen bonding (see Colloids). 

The size of particles removed by such filters is less than the size of the passages. The mechanism of removal includes adsorption (qv) of the impurities at the interface between the media and the water either by specific chemical or van der Waals attractions or by electrostatic interaction when the medium particles have surface charges opposite to those on the impurities to be removed. 

Attractive and Repulsive Forces. The force that causes small particles to stick together after colliding is van der Waals attraction. There are three van der Waals forces (/) Keesom-van der Waals, due to dipole—dipole interactions that have higher probabiUty of attractive orientations than nonattractive (2) Debye-van der Waals, due to dipole-induced dipole interactions (ie, uneven charge distribution is induced in a nonpolar material) and (J) London dispersion forces, which occur between two nonpolar substances. 

DLVO Theory. The overall stabiUty of a particle dispersion depends on the sum of the attractive and repulsive forces as a function of the distance separating the particles. DLVO theory, named for Derjaguin and Landau (11) and Verwey and Overbeek (12), encompasses van der Waals attraction and electrostatic repulsion between particles, but does not consider steric stabilization. The net energy, AGp between two particles at a given distance is the sum of the repulsive and attractive forces ... 

AGrjp = (electrostatic repulsive forces ) — (van der Waals attractive forces)... 

The electrostatic repulsive forces are a function of particle kinetic energy (/ T), ionic strength, zeta potential, and separation distance. The van der Waals attractive forces are a function of the Hamaker constant and separation distance. 

The wettiag eaergies give repulsive forces exceeding that of the van der Waals attractive force under certain conditions. The combiaed van der Waals and wettiag force is givea by equatioa 7 ia which h is the distance perpendicular to the iaterface that the particle has moved from its equiHbrium positioa. 

Let us now calculate the three components of the van der Waals attraction by first calculating these interactions between two molecules. Subsequently, the total van der Waals potential between bodies will be determined by assuming that the molecules belong to two different materials and integrating the molecular interactions over the volumes of the materials. 

Micro-mechanical processes that control the adhesion and fracture of elastomeric polymers occur at two different size scales. On the size scale of the chain the failure is by breakage of Van der Waals attraction, chain pull-out or by chain scission. The viscoelastic deformation in which most of the energy is dissipated occurs at a larger size scale but is controlled by the processes that occur on the scale of a chain. The situation is, in principle, very similar to that of glassy polymers except that crack growth rate and temperature dependence of the micromechanical processes are very important. 

These equations show that hydrophobic and steric (van der Waals) interactions are of prime importance in the inclusion processes of cyclodextrin-alcohol systems. The coefficient of Es was positive in sign for an a-cyclodextrin system and negative for a P-cyclodextrin system. These clear-cut differences in sign reflect the fact that a bulky alcohol is subject to van der Waals repulsion by the a-cyclodextrin cavity and to van der Waals attraction by the p-cyclodextrin cavity. 

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