Inter-aggregates distances

Estimating inter-aggregates distances through a face-centered cubic lattice model. 

Estimating Inter-Aggregates Distances with a Face-Centered Cubic Lattice Model... 

This simple exercise demonstrates that in most well dispersed CB filled rubber compounds, average inter-aggregates distances are close to the average quadratic diameter of the polymer random coil, of the order of 50 nm for diene elastomers with molecular weight of around 400,000 g/mole. In other terms, in most rubber compounds, certain chains of elastomer are in contact with at least two aggregates, whilst others are not. 

In order for aerosol aggregation processes to be much affected by turbulent shear and inertial effects, the particles or droplets need to be of sufficiently high concentration for the inter-particle distances to be less than This applies to clouds, fogs and some industrial aerosols, but not to typical uncontaminated atmospheric aerosols. 

Inter-atomic distances whieh ate established as a result of covalent bond of two atoms are eonstant measures and independently form the aggregation state of the relative substance. 

The chains contained from 3 to 20 NPs (Figure 7(d)). The low fraction of branched chains and the absence of 3D aggregates were indicative of selective functionalization of the NPs at the opposite poles or at least, a much higher reaction rate between the ligands localized at the poles than at the deferts in the ligand shell in other locations. In the chains, the inter-partide distance (defined as the two nearest points between adjacent NPs) correlated with the length of molecular linkers. 

The inter-particle force F can be computed as / = A]idol l2Hl), where Ah is the Hamaker parameter for the liquid-particle system and is the distance between two primary particles. The coordination number is based on experimental observation and can be calculated as kc 150p, where 0p is the volume fraction of solid within the aggregates. In the case of compact (or solid) particles 0p is close to unity, whereas in the case of fractal aggregates 0p can be determined once the fractal dimension T)f of the aggregates is known 0p = (0.414T)f - 0.21 l)(r/p/(io) , where dp is the size of the particle and do is the size of the primary particle (Vanni, 2000b). 

Weingarth et al. have presented a new spectroscopic fingerprint of inter-molecular contacts in halogen bond-driven self-assembling aggregates and a precise determination of intermolecular N- T distances in microcrystalline samples. ... 

---