Amorphous packing fraction

Inspection of Eq. 7 reveals that the molecular interference function, s(x), can be derived from the ratio of the total cross-section to the fitted IAM function, when the first square bracketed factor has been accounted for. A widely used model of the liquid state assumes that the molecules in liquids and amorphous materials may be described by a hard-sphere (HS) radial distribution function (RDF). This correctly predicts the exclusion property of the intermolecular force at intermolecular separations below some critical dimension, identified with the sphere diameter in the HS model. The packing fraction, 17, is proportional for a monatomic species to the bulk density, p. The variation of r(x) on 17 is reproduced in Fig. 14, taken from the work of Pavlyukhin [29],... 

The fusion of amorphous polymer particles above their Tg is a slow coalescence process most likely driven by surface energy, which reduces the free volume and the total surface area (Rosenzweig and Narkis 1983 Palzer 2011). Since amorphous dispersions often have a polymeric component, the sintering of amorphous polymer colloids occurs at/or above the Tg which is dependent on the particle size and packing fraction within the polymer as determined by the melt viscosity (Mazur et al. 1997). 

To a stirred solution of ethyl l-(NG-nitro-L-arginyl)-4-methyl-2-piperidinecarboxylate hydrochloride in 200 ml of chloroform were added in turn 18.5 g of triethylamine, and 14.7 g of 3-methyl-8-quinolinesulfonyl chloride at 5°C, and stirring was continued for 3 hours at room temperature. At the end of this period, the solution was washed twice with 50 ml of water. The chloroform solution was dried over anhydrous sodium sulfate. Upon evaporation of the solvent, the residue was chromatographed on 50 g of silica gel packed in chloroform, washed with chloroform and eluted with 3% methanol-chloroform. The fraction eluted from 3% methanol-chloroform was evaporated to give 32.1 g (91%) of ethyl l-[NG-nitro-N2-(3-methyl-8-quinolinesulfonyl)-L-arginyl]-4-methyl-2-piperidinecarboxylate in the form of an amorphous solid. 

Floes pack in a space-filling, Euclidean fashion hence, at the floe level of structure, the material can be considered as an orthodox amorphous substance. Within the floes, however, particles pack in a non-Euclidean, fractal fashion. For such a structural arrangement, the volume fraction of particles in a floe (O ) is equivalent to the volume fraction of particles in the entire system (O), namely = O. This well-known relation of polymer physics (11) has been experimentally shown to also apply to colloidal aggregates above their gelation threshold (12). 

---