Packing Effect

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... 

The principal effect of the presence of a smooth wall, compared to a free surface, is the occurrence of a maximum in the density near the interface due to packing effects. The height of the first maximum in the density profile and the existence of additional maxima depend on the strength of the surface-water interactions. The thermodynamic state of the liquid in a slit pore, which has usually not been controlled in the simulations, also plays a role. If the two surfaces are too close to each other, the liquid responds by producing pronounced density oscillations. 

Luminescence from the solid slate is strongly subject to packing effects. Some arc related to molecular conformation, some result from electronic interactions be-... 

The Rh-Rh distance is 3.12 A, long compared with Rh-Rh single bonds (2.624A in Rh2(MeCN) J([, 2.73 A in Rh4(CO)12) there is a weaker (3.31 A) intermolecular attraction. Dipole moment and IR studies indicate that the structure is retained in solution and is, therefore, a consequence of electronic rather than solid-state packing effects. Furthermore, it is found for some other (but not all) [RhCl(alkene)2]2 and [RhCl(CO)(PR3)]2 systems. SCF MO calculations indicate that bending favours a Rh-Cl bonding interaction which also includes a contribution from Rh—Rh bonding [56b]. 

The purpose of this article is to discuss conformational shift variations in some selected solid state spectra on the basis of discrete rotational isomeric states and to compare them with molecular packing effects. 

Equations 22.3-22.14 represent the simplest formulation of filled phantom polymer networks. Clearly, specific features of the fractal filler structures of carbon black, etc., are totally neglected. However, the model uses chain variables R(i) directly. It assumes the chains are Gaussian the cross-links and filler particles are placed in position randomly and instantaneously and are thereafter permanent. Additionally, constraints arising from entanglements and packing effects can be introduced using the mean field approach of harmonic tube constraints [15]. 

The presented scheme offers several extensions. For example, the model gives a clear route for an additional inclusion of entanglement constraints and packing effects [15]. Again, this can be realized with the successful mean field models based on the conformational tube picture [7,9] where the chains do not have free access to the total space between the cross-links but are trapped in a cage due to the additional topological restrictions, as visualized in the cartoon. 

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