Characteristic interaction distance

Numerical calculations can be carried out on the basis of Eqs. (70)-(74), and to show the influence of the image forces on the disjoining pressure between two plates, we will compare these results with the frequently used expression in Eq. (75). We have still to adhere to the approximations accepted in the text, and, first of all, the bulk electrolyte concentration c0 = 1 mmol/L will be chosen. For this concentration the Bierrum (or plasma) parameter is n — ky q = 0.04, and, as a consequence, for characteristic interparticle distances of a colloid domain the relationship a = Kr /x is much smaller than one. This allows to simplify our equations sufficiently leading to the final expression for the disjoining pressure, where the dominant role plays the self-image interaction... 

In the case of using a substrate with surface-relief nanostructures, overall trends would agree with what is mentioned in (Sect. 2.1.2), i.e., momentum-matching would occur at higher plasmon momentum. Since gold nanoparticles act as a target of supermolecules, plasmon momentum would be shifted further, which may induce nonlinear plasmon characteristics. Here, the effects of particle parameters, such as particle size, concentration, shape, and interaction distance between metal surface and nanoparticles, are discussed briefly based on experimental data of the interaction between particle plasmons and conventional SPs. 

In an aqueous medium, the hydrophobic interaction plays a very important role. It is the major driving force for hydrophobic molecules to aggregate in an aqueous medium, as seen in the formation of a cell membrane from lipid-based components. The hydrophobic interaction is not, as its name may suggest, an interaction between hydrophobic molecules. This interaction is related to the hydration structure present around hydrophobic molecules. Water molecules form structured hydration layers that are not entropically advantageous. It is believed that hydrophobic substances aggregate to minimize the number water molecules involved in hydration layers. However, the mechanism and nature of the hydrophobic interaction is not that clear. Unusual characteristics, such as incredible interaction distances, have been reported for the hydrophobic interaction, and the fundamentals of hydrophobic interaction are still under debate even today. 

A unique feature of H20 is the formation and sharing of hydrogen bonds with other molecules. Such bonds play a major role in determining the structure of both liquid and solid phases of H20. It is believed that for intermolecular spacings of less than 2 A, the two water molecules exert strong repulsive forces on each other. As such, there exists a hard sphere radius of little interpenetration of the molecules. Usually, the repulsive part of Lennard-Jones 6—12 potential can be considered appropriate to describe these repulsive characteristics. At distances of separation greater than 5 A, dipole-dipole interaction plays a dominant role. This is reasonable, because each H20 molecule has a large dipole moment, p = 1.84 D. 

For normal liquids the characteristic structural distance is of order 1 A. A probe of liquid structure should therefore have a characteristic wavelength Z in this range. This calls for using X-rays or light atomic particles as probes. In liquids we are interested in the short-range stmcture, on the scale of intermolecular distances. This implies the need to apply short range interactions and therefore the use of particles should be limited to neutral ones, such as neutrons. 

Tij — interaction parameter for characteristic molecular distance parameter, a between substance i and / = mixture reference system molecular distance parameter... 

To adjust for errors introduced by modeling these highly complex interactions with simple geometries, we consider the characteristic interaction-separation distances in expressions derived for the models to be adjustable parameters. The DLVO-Lifshitz potentials are evaluated for characteristic distances found to fit data for Si02, where AGads and U determinations are most accurate. These distances are then used for all other solids. Since the assumptions used in the double-layer and van der Waals models (described in following sections) are quite... 

The characteristic model distance des is taken to be zero at coincidence of the Stern surfaces, implying that the actual virus-to-solid separation distance would be approximately I nm on the basis of Smith s work (29). This is quite reasonable, and all solid-virus interaction potentials and free energy differences are matched with a single model distance. 

The integral equation (14) can be converted to a much simpler differential equation assuming that density is changing only slightly over distances comparable with the characteristic interaction length. Then one can expand... 

Thus, the difference in the hydration characteristics of silica OX-50 in the aqueous suspension and hydrated powder in different media depends on the particle-particle interactions (distances between particles) and the textural porosity in the powders. Nonpolar (methane) or weakly polar (chloroform) coadsorbates can reduce interaction of water with the silica surface because water-water and water-silica interactions are much stronger than that of water-organics. Therefore, rearrangement of the system organization leads to an increase in the size of water domains with parallel diminution of the contact area between water-organics and water-silica but with increasing silica-organics contact area. 

For molecules with a regular secondary structure, like RNA duplexes, there are numerous characteristic interproton distances below 5 A between adjacent nucleotides [41, 42] which give rise to typical cross peak patterns in the NOESY spectra. For a regular A-RNA, the distance between the aromatic proton (C6H or C8H) of a given nucleotide and the 2 -ri-bose proton of the 3 -neighboured nucleotide, as well as the one between the aromatic proton and the 3 -ribose proton of the same residue is particularly small (ca. 2.0-2.5 A). The cross peaks in the NOESY spectrum caused by the interaction between the corresponding protons are therefore especially strong. 

The characteristic adhesion distance In Eqs.( 1) and ( 4) lies in a molecular scale a = 3 =0 0.3 - 0.4 rum. It depends mainly on the properties of liquid-equivalent packed adsorbed layers and is to be estimated for a molecular interaction potential minimum. Provided that these molecular contacts are stiff enough compared with the soft particle contact behaviour influenced by mobile adsorption layers due to molecular rearrangement, this separation ap-o is assumed to be constant during loading and unloading in the interesting macroscopic pressure range of o = 0.1 - 100 kPa. The Hamaker constant solid-liquid-solid Ch,jIs acc. to Lifschitz theory is related to continuous media dependent on their permittivities (dielectric constants) and refractive indices, see Israelachvili [23]. 

Hard-sphere models lack a characteristic energy scale and, hence, only entropic packing effects can be investigated. A more realistic modelling has to take hard-core-like repulsion at small distances and an attractive interaction at intennediate distances into account. In non-polar liquids the attraction is of the van der Waals type and decays with the sixth power of the interparticle distance r. It can be modelled in the fonn of a Leimard-Jones potential Fj j(r) between segments... 

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