Mean interparticle distance

Table 12 Peak positions from structure factor maxima, ds, and mean interparticle distances,...

The samples with the lower rhodium loadings appear to be relatively more capable of exchanging oxygen of the support. This could be indicative of marked heterogeneity, as the number of particles increases. The mean interparticle distances are 57, 29, 15, 13 and 11 nm in samples 1-5, respectively rhodium particles act as individual sources interfering much more rapidly in highly loaded catalysts, particularly if the rhodium particles are not homogeneously distributed at the alumina surface. 

The kinetic factor D(q) characterizes the average particle flux, and S(q), the interparticle structure factor, is equivalent to the integrated scattered light intensity. When the range of interparticle interactions a is comparable with d, the mean interparticle distance, then D(q) may exhibit angle-dependent behavior. In the limits q- 0, co, D(q) reduces to the translational diffusion constant Dt (93), The data of Berne and... 

Based on this observation a preliminary answer can be given to the second question wake effects should be taken into account when the particle concentration corresponds to a mean interparticle distance D of only a few particle diameters d. The critical concentrations C and distances D may therefore be related by... 

For the example of a dilute mixture of in Ng gas at 1 atm and 300 K considered in Section 2.2, we find that the mean relative speed is 516 m sec . Assuming, as before, that Jab 0-4 nm, we obtain a collision frequency 6.4 X 10 sec and a mean free path Slnm. It is worth noting that Asig is much larger than the mean interparticle distance, which is only 3.4 nm at this density. 

For polyelectrolyte solutions the relation between the mean interparticle distance d and the concentration is of great interest. Assuming that polyions fill the space homogeneously due to their strong mutual repulsion, the ple relation... 

Liu Z H, Li Y and Kowk K W (2001) Mean interparticle distances between hard particles in one to three dinieiisions. Polymer 42 2701-2706. 

Note that when the particle concentration increases in a dispersion then the important mean interparticle distance decreases. It is, however, rather difficult to estimate the three-dimensional mean interparticle distance in a dispersion containing polydisperse... 

The first example involves a two-dimensional model system with dipole-dipole (r ) interactions. This model corresponds, as far as the interactions are concerned, to the qnasi-two-dimensional system of paramagnetic colloidal particles studied by Zahn et al. [57], defined by the pair potential 3M(r) = r(l/ry, with I being the mean interparticle distance / = n and T being the ratio of the potential at mean distance in nnits of k T. The specific conditions considered below refer to a highly interacting (T = 4.4) and very dilute ( = n[Pg.14]

U(r) = 0 from the effective mean interaction potential shown in Figure 4.7. (b) Effective mean interaction potential at the mean interparticle distance as a function of ( ). Dashed line indicates U r )lk T = 1. 

Note, however, that we expect the position of the repulsive barrier to continuously decrease with increasing ( ) for equivalent purely repulsive systems. This is shown in Figure 4.9a, where we display the Yukawa potentials calculated for systems with volume fractions as the one investigated and for which we impose that the peak heights in S(q) correspond to the one of our experimental S(q)s. The position of the repulsive barrier decreases here proportionally to over the entire volume fraction range investigated. This is shown in Figure 4.9b, where we report r, determined at U(r)lk T = 1 as a function of < ) as the mean interparticle distance, the position of the repulsive barrier exhibits the... 

FIGURE 4.14 (a) Result of the scaling procedure described in the text, (b) Volume fraction dependence of the localization length in units of mean interparticle distances. Dashed horizontal line corresponds to the Lindemann criterion, = 0.1. 

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