London forces adhesion

As previously mentioned, electrodynamic interactions, such as those arising from London forces, can also contribute to the adhesion of particles. These forces are dominated by dipole interactions and are broadly lumped into the classification known as van der Waals interactions. A more detailed description of van der Waals interactions than can be presented in this article is given in books by Israelachvili [95] and by Rimai and Quesnel [96]. 

The radial hydrodynamic component (y component) of the force is denoted by fj, and represents the net externally applied hydrodynamic force on the particle resulting from the particle being driven toward (or away from) the collector by the external flow (undisturbed or disturbed) plus any negative resistive lubrication force arising from a close approach of the particle to the collector. The attractive molecular London force acting along the line of centers is denoted by (Ad denotes adhesion). Because of the linearity of the Stokes-Oseen equation, the velocity fields and associated forces may be superposed. 

The conclusion from this brief discussion is that molecular adhesion is caused by electromagnetic forces, but not the simple forces that operate in electric motors or between magnets. Those Coulombic forces can be either attractions or repulsions and obey Newton s inverse square law. By contrast, molecular adhesion is caused by London forces which are always attractive and which fall off extremely rapidly with separation. 

Bradley had read Tomlinson s paper and developed an improved method of measuring the adhesion, together with a better theory based on London s wave mechanics theory of the forces between molecules. By adding up the London forces for all the molecules in two rigid sphaes, Bradley came to the conclusion that the adhesive force required to separate them should be proportional to the sphere diameter, as shown in Fig. 4.11. He also showed that the force should be proportional to the work of adhesion W of the spheres, that is the energy required to separate one square meter of intaface reversibly. Thus he produced his famous equation for adhesion of spheres shown in Fig. 4.11. 

Molecular adhesion was first noted by van der Waals as a force which fouled up the perfect gas laws, but it was only when quantum theory was developed in the 1930s that the electronic nature of the molecular forces could be understood. The London force is perhaps the best understood of these molecular forces an... 

The first criterion for good adhesion is intimate contact, that is good wetting of the surface. Wetting is a necessary, but not sufficient, condition for good adhesion [109]. In addition, one should seek to maximise the work of adhesion. The simplest case is to consider the work of adhesion to be attributable solely to non polar (London) forces between the materials. This is indeed the case when at least the adhesive (polymer melt) or adherand (filler surface) is non-polar. So, for thermoplastics such as PE, PP and polytetrafluoroethylene (PTFE) this simple case should apply. 

If we set out to unravel surface chemical functionalities with high spatial resolution down to atomic detail, we also encounter various practical (technical) problems. It is fair to say that the technique development for direct space analysis (again, we exclude Fourier space methods) is still lagging much behind. Chemical force microscopy can be considered as a first step in the direction of a true description of surface chemical functionalities with high spatial resolution in polymers, primarily based on the chemically sensitive analysis of AFM data via adhesion mapping. At this point the detailed theory for force spectroscopy is not developed beyond the description of London forces. The consideration of the effect of polar functional groups in force spectroscopy (similar to difficulties with solubihty parameter and surface tension approaches for polar forces, as well as specific interactions) is still in its infancy. Instead, one must still rely on continuiun contact mechanics to couple measured forces and surface free energies. 

By far the most important of the adhesive bonds are the secondary or Van der Waals" bonds that give rise to attraction between molecules. Most significant of these are the London or dispersion forces. They are responsible for virtually all the molar cohesion of nonpolar polymers such as polyethylene, natural rubber, SBR, and butyl rubber. These forces act at a distance of approximately 4 A, and fall off rapidly, as the sixth power of the distance between atoms. Consequently, molecules must be in close proximity for London forces to be effective. This helps to explain why a very flexible molecule such as natural rubber is a better adhesive than a moderately flexible molecule such as polystyrene. Low modulus, indicating free-... 

If only Londons forces are present across the interface, the work of adhesion is fiiUy determined because the nondispersive part is equal to zero. Indeed and can be easily determined by wettability experiments (Wu 1982). The only existence of London interactions at the interface between to adherends leads to ... 

Among all the low energy interactions, London dispersion forces are considered as the main contributors to the physical adsorption mechanism. They are ubiquitous and their range of interaction is in the order 2 molecular diameters. For this reason, this mechanism is always operative and effective only in the topmost surface layers of a material. It is this low level of adhesion energy combined with the viscoelastic properties of the silicone matrix that has been exploited in silicone release coatings and in silicone molds used to release 3-dimensional objects. However, most adhesive applications require much higher energies of adhesion and other mechanisms need to be involved. 

Adhesion of particles Small particles experience adhesion forces, allowing them to attach to surfaces. These forces may be made up from surface tension of liquid films, or London (Van der Waals) forces. 

Fowkes and co-workers also clearly demonstrated that the physical Interaction of polymers with neighboring molecules was determined by only two kinds of interactions London dispersion forces and Lewis acid-base interactions (21) Calculations based on this concept were shown to correct many of the problems inherent in the solubility approach. They were also able to use the concept to study the distribution of molar heats of absorption of various polymers onto ferric oxides, and thereby more accurately described the requirements for adequate adhesion to steel substrates (21) In the symposium on which this book is based, Fowkes summarized work showing that the polar Interactions between polymers and metal surfaces that are... 

The London dispersion forces are present and important in most adsorption processes and in adhesive interactions between dissimilar materials. The free energy of interaction per unit area between materials 1 and 2 in contact is where W 2 -s... 

D. Gingell and J. A. Pomes, "Demonstration of intermolecular forces in cell adhesion using a new electrochemical technique," Nature (London), 256, 210-11 (1975) D. Gingell and I. Todd, "Red blood cell adhesion. II. Interferometric examination of the Interaction with hydrocarbon oil and glass," J. Cell Sci., 41, 135-49 (1980). 

The combined effect of attraction and repulsion forces has been treated by many investigators in terms borrowed from theories of colloidal stability (Weiss, 1972). These theories treat the adhesion of colloidal particles by taking into account three types of forces (a) electrostatic repulsion force (Hogg, Healy Fuerstenau, 1966) (b) London-Van der Waals molecular attraction force (Hamaker, 1937) (c) gravity force. The electrostatic repulsion force is due to the negative charges that exist on the cell membrane and on the deposition surface because of the development of electrostatic double layers when they are in contact with a solution. The London attraction force is due to the time distribution of the movement of electrons in each molecule and, therefore, it exists between each pair of molecules and consequently between each pair of particles. For example, this force is responsible, among other phenomena, for the condensation of vapors to liquids. 

Other forces existing between particles often operate against hydrodynamic drag that produces fluidization. Thus, when particles touch one another, there exists a London-van der Waals force of a molecular nature at the point of contact. This force looms in proportion when gravity and drag forces diminish as a particle becomes smaller. For a small particle, the surface force of adhesion may often be thousands of times greater than its weight. 

The adhesion of a coating to plastic is related to the substrate wettability and also to physical-chemical forces. Both covalent (bond formation) and dispersive (London or van der Waals) forces are responsible for the adhesion of the coating due to physical-chemical forces. 

Again in the lubrication of moving metal parts oriented layers are produced, solidly anchored to the metal by carboxyl groups etc. Only the London interaction between the hydrocarbon tails then still acts between the two metal parts each with their layer of lubricating oil. A pure hydrocarbon (kerosene or paraffin oil) lubricates badly since this is forced away through inadequate adhesion to the metal. This is not only a consequence of too small a viscosity since a soap solution (potassium oleate etc.) is serviceable (drilling oil). 

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. 

Of the different types of forces responsible for intermolecular attraction, the foremost are the London or dispersion forces that act between all atoms and account for virtually all of the molecular attraction or cohesion in all molecules except the very polar molecules (described later). Dispersion forces are short-range interactions, effective at about 4 A, and rapidly decrease with the sixth power of the distance between molecules. Therefore, the adhesive polymer molecule must be flexible enough to come within this range of interaction with the rigid adherent surface under the conditions of bond formation. 

In the case of physical bonds (London dispersion, Keesom orientation, and Debye induction forces), the energy of interaction or reversible energy of adhesion can be directly calculated from the surface free energies of the solids in contact. 

A more vital application is to discern how reinforcement surface treatments improve adhesion to thermoplastic matrices. Since the nonreactive nature of thermoplastics normally precludes interfacial covalent bond formation, secondary bonding forces, such as London dispersion interactions and Lewis add/base interactions, may play a major role in these drcumstances. These secondary binding forces are subject to surface energetics analysis. 

Depending on the geometrical model (Figure 17) used and on the theoretical approach taken, different relationships exist for the approximation of adhesion by van der Waals forces. The best known equations are those developed by Hamaker based on the microscopic theory of London-Heitler. For the model sphere/plane. Figure 17(a), a distance a< 100 nm, and the particle diameter x, the adhesion force A, i is... 

H. Rumpf and H. Schubert, Adhesion forces in agglomeration processes, in Ceramic Processing before Firing (eds. G. Onoda, Jr and L. Hench), John Wiley and Sons, London, UK, 1978, pp. 357-76. 

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