Particle interaction screened

Despite the fact that formalism of the standard chemical kinetics (Chapter 2) was widely and successfully used in interpreting actual experimental data [70], it is not well justified theoretically in fact, in its derivation the solution of a pair problem with non-screened potential U (r) = — e2/(er) is used. However, in the statistical physics of a system of charged particles the so-called Coulomb catastrophes [75] have been known for a long time and they have arisen just because of the neglect of the essentially many-particle charge screening effects. An attempt [76] to use the screened Coulomb interaction characterized by the phenomenological parameter - the Debye radius Rd [75] does not solve the problem since K(oo) has been still traditionally calculated in the same pair approximation. 

Experiments due to neutron scattering by the labelled macromolecules allow one to estimate the effective size of macromolecular coils in very concentrated solutions and melts of polymers (Graessley 1974 Maconachie and Richards 1978 Higgins and Benoit 1994) and confirm that the dimensions of macromolecular coils in the very concentrated system are the same as the dimensions of ideal coils. It means, indeed, that the effective interaction between particles of the chain in very concentrated solutions and melts of polymers appears changes due to the presence of other chains in correspondence with the excluded-volume-interaction screening effect. The recent discussion of the problem was given by Wittmer et al. (2007). 

Fuzzy spheres. Radially varying dielectric response, 79 "Point-particle" interactions, 79 Point-particle substrate interactions, 85 Particles in a dilute gas, 86 Screening of "zero-frequency" fluctuations in ionic solutions, 89 Forces created by fluctuations in local concentrations of ions, 90 Small-sphere ionic-fluctuation forces, 91... 

Screening factor for point-particle interaction + I rn) energy. 

Table S.8. Point-particle interaction in vapor, like particles without retardation screening...

In the limit r = 0, at which there are no retardation effects because of the finite velocity of light, the screening factor Raj) rn) goes to 1 and the small-particle interaction becomes... 

The particle interactions based on van der Waals forces between hydrophilic particles covered by a resin layer are almost completely screened. This implies that, for a discussion of the rheologically relevant interaction forces, non-DLVO effects such as polymer bridging have also to be taken into account as discussed above. For a theoretical treatment of these effects, approximations given by Napper and Vincent, respectively, can be applied [11,14]. 

The electrostatic screening realized in an electrolyte can be used to control the particle-particle interactions. This interaction potential, R(r), is characterized by the Debye length which in the simplest mean field models describes the electrostatic screening of ionic particles interacting via Coulomb forces in a dielectric continuum, viz V(r) oc exp(— r). It is convenient to... 

Recent studies on the energy loss of atomic particles interacting with solid surfaces are reviewed. Different approximations for the treatment of the screening and scattering are presented and their validity in the different couphng regimes is discussed. Illustrative comparisons with available experiments are provided. 

As mentioned above, measurements at finite concentrations lead to a non-vanishing influence of the structure factor S(q). For the overwhelming majority of the latex systems studied by SAS-experiments so far, colloid stability has been achieved by a screened Coulomb interaction [5,62,63]. The structure factor of such a system of particles interacting through a Yukawa-potential has been extensively studied theoretically by Klein and coworkers (see Ref. [63] and further citations given there) who extended the treatment to polydisperse systems. 

Figure 6 shows the structure factor S(q) calculated for electrostatic repulsion (dotted line dashed line) and for hard core repulsion (solid line) for a system of spheres having a diameter of 80 nm and a volume fraction of 20% [46]. Again the abscissa has been scaled by the number-average diameter Dj. At low ionic strength there is a strong electrostatic repulsion between the spheres leading to a pronounced maximum in the structure factor (Fig. 6 dotted line). If the ionic strength in increased, however, the repulsive electrostatic interaction is screened and the variation of S(q) is much weaker (dashed line in Fig. 6). At high ionic strength the electrostatic repulsion of the latex particles is screened considerably and in first approximation the structure factor may be calculated in terms of effective hard sphere interaction (cf. Refs. [64] and [65]).

Free ions are usually not included explicitly in the simulations, but their overall effects on monomer-monomer and monomer-particle interactions are described via the dependence of the inverse Debye screening length (m" ) on the electrolyte concentration according to... 

Neglect of Hydrodynamic Interactions.—The coupling of hydrodynamic flow exerts a major influence on the dynamics of colloidal dispersions.In certain special cases, however, it has proved reasonable or expedient to neglect the hydrodynamic interactions. One such instance is the very dilute, electrostatically-stabilized dispersion in which particles interact via a screened Coulomb potential, that is, equation (2) with ku 1. 

The influence of different screening parameters on the stripe formation can be seen in Fig. 6. The comparison between the ImM NaCl series and the series with lOmM NaCl shows that the stripe distance increases with decreasing particle interaction. As can be seen from Figs. 5 and 6 there is a relationship between pulling speed and stripe for-... 

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