Proximity force

The Derjaguin idea, a mainstay in colloid science since its 1934 publication, was rediscovered by nuclear physicists in the 1970s. In the physics literature one speaks of "proximity forces," surface forces that fit the criteria already given. The "Derjaguin transformation" or "Derjaguin approximation" of colloid science, to convert parallel-surface interaction into that between oppositely curved surfaces, becomes the physicists "proximity force theorem" used in nuclear physics and in the transformation of Casimir forces.23... 

For two surfaces in proximity, force balance is obtained if the attractive electrostatic force is opposed by the repulsive osmotic pressure [23]... 

Derjaguin used this approach to calculate the interaction between two ellipsoids [84]. The same approximation was also introduced in 1977 by Blodd et al. [85] for calculating interaction forces between nuclei of atoms. They coined the term proximity forces in their publication. While the term Derjaguin approximation is stUl the standard term in surface science, the term proximity force approximation has become popular among physicists in the field of nuclear physics and the Casimir force (see Section 2.6). 

Casimir Force for Nontriviai Geometries As in the case of the normal van der Waals forces, the Derjaguin approximation can be used to calculate the Casimir force for geometries other than that of parallel plates. Note that in many papers on the Casimir force, this approach is called "proximity force approximation due to historic reasons (see Section 2.3). It was shown that the error introduced by this approximation should be smaller than 0.4 D/R for D < 300 nm [129]. Full calculations without approximation have been done for some configurations, for example, sphere/plate [130], but these are usually cumbersome. An alternative approach for approximate calculations was introduced by Jaffe and Scardicchio [131]. It is based... 

The Derjaguin approximation (also called proximity force approximation) allows the calculation of the van der Waals interaction between macroscopic bodies with complex geometries from the knowledge of the interaction potential between planar surfaces, as long as the radii of curvature of the objects are large compared to the separation between them. 

In addition to specific surface area and the fractal nature of carbon black as discussed above, it may be expected that rubber-filler interactions, which are the roots of reinforcement, somewhat depend upon the surface activity of the particles. The so-called surface activity is not however a clearly defined concept as many phenomena might be involved, from Van der Waals proximity forces (around 4 kj/mole) to specific chemical interactions (e.g., hydrogen bonding, 20 kj/mole ionic bonds, 30 kj/mole). Despite the considerable literature on the subject, there is so far no standard method to measure siuface activity. 

In this section we consider electromagnetic dispersion forces between macroscopic objects. There are two approaches to this problem in the first, microscopic model, one assumes pairwise additivity of the dispersion attraction between molecules from Eq. VI-15. This is best for surfaces that are near one another. The macroscopic approach considers the objects as continuous media having a dielectric response to electromagnetic radiation that can be measured through spectroscopic evaluation of the material. In this analysis, the retardation of the electromagnetic response from surfaces that are not in close proximity can be addressed. A more detailed derivation of these expressions is given in references such as the treatise by Russel et al. [3] here we limit ourselves to a brief physical description of the phenomenon. 

Appreciable interaction between chromophores does not occur unless they are linked directly to each other, or forced into close proximity as a result of molecular stereochemical configuration. Interposition of a single methylene group, or meta orientation about an aromatic ring, is sufficient to insulate chromophores almost completely from each other. Certain combinations of functional groups afford chromophoric systems which give rise to characteristic absorption bands. 

European siting considerations are somewhat different than those in the United States. Germany, the Netherlands, France, and Italy were traditionally the favored locations for European CPI industry plants because of their proximity to the markets, cheap energy, and presence of a skilled labor force. 

The behavior of colloidal suspensions is controlled by iaterparticle forces, the range of which rarely extends more than a particle diameter (see Colloids). Consequentiy suspensions tend to behave like viscous Hquids except at very high particle concentrations when the particles are forced iato close proximity. Because many coating solutions consist of complex mixtures of polymer and coUoidal material, a thorough characterization of the bulk rheology requires a number of different measurements. 

It eliminates the proximity effect (extra forces and heating) by providing a magnetic shielding to the supporting and metallic structures in the vicinity. 

The three phases are now completely isolated and adequately spaced. They are thus hardly under any influence of proximity. The forces are now greater between... 

RBS is based on collisions between atomic nuclei and derives its name from Lord Ernest Rutherford who first presented the concept of atoms having nuclei. When a sample is bombarded with a beam of high-energy particles, the vast majority of particles are implanted into the material and do not escape. This is because the diameter of an atomic nucleus is on the order of 10 A while the spacing between nuclei is on the order of 1 A. A small fraction of the incident particles do undergo a direct collision with a nucleus of one of the atoms in the upper few pm of the sample. This collision actually is due to the Coulombic force present between two nuclei in close proximity to each other, but can be modeled as an elastic collision using classical physics. 

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