Amorphous correlation length

Our third applications example highlights the work of Nakano et al. in modeling structural correlations in porous silica. MD simulations of porous silica in the density range 2.2—0.1 g/cm were carried out on a 41,472-particle system using an iPSC/860. Internal surface area, ratio of pore surface to volume, pore size distribution, fractal dimension, correlation length, and mean particle size were determined as a function of the density, with the structural transition between a condensed amorphous phase and a low density porous phase characterized by these quantities. Various dissimilar porous structures with different fractal dimensions were obtained by controlling the preparation schedule and the temperature. 

Fig. 3.19. Molecular dynamic simulation results for the fracture propagation in amorphous structures (with Lennard-Jones potential) show that the average fracture velocity crosses over to a higher value (ufinai from Uinitiaij indicated by the dotted lines) at the late stages of growth, as the crack size exceeds the typical size (correlation length) of the voids in the network. The inset shows that a corresponding crossover in the fractured surface roughness exponent also occurs along with the crossover in the fracture velocity (from Nakano et al 1995).

Figure 1.13. State dicigram of a binary system with liquid-liquid amorphous separation a presents the bin-odal (solid curve) and spinodal (da.shed curve). The temperature dependences of the correlation length of the concentration fluctuation (at T > 1 ) and of the order parameter Aa 2 (at 7 < Tc) are described by power functions b shows the average molar Gibbs potential at T = 7) [bi,. sp are points on the binodal and spinodal, respectively)...

Walrafen GE, Hokmabadi MS, Yang WH, Piermarini GJ (1988) High-temperature high-pressure Raman spectra from liquid water. J Phys Chem 92 4540-4542 Walrrfen GE, Chu YC (1995) Linearity between structural correlation length and correlated-proton Raman intensity from amorphous ice and supercooled water up to dense supercritical steam. J Phys Chem 99 11225-11229... 

A (bulk) deformation model is able to explain the emission characteristics, if we consider the correlation of the emission processes with molecular fracture. The HDPE is biaxially preoriented, due to the manufacturing process. Defining the correlation length I as the distance in which the mechanical force Y acting on a point is reduced to a portion a, we may characterize the lamellae and the amorphous regions by their correlation length distributions. 

The correlation length gradient at the boundary lamellae/amorphous phase renders it possible to transfer a force T on single tie-molecules that enables a combined mechanical/thermofluctuation activation of bond cleavages (Zhurkov mechanism). 

There is an empirical relation between the correlation length, r, in real space and the peak position, Q, in the intensity profile, i.e., Qr=2.5 in molten transition metal and metalloid alloys (Waseda 1980). It is plausible that this relation is also valid in the amorphous state. Thus, the correlation length causing the prepeak at 13 ran is estimated to be 0.60 nm, which agrees well with the distance between neighboring Y atoms bonded through an A1 atom. Consequently, these experimental results prove the presence of Y atoms surrounded by A1 atoms in the binary AI90Y10 alloy. 

The effects of boundary conditions in this kind of model have yet to be fully evaluated but we can expect that one important condition might be the size of the unit cell in relation to the correlation length along the chain. For small N there is no doubt that the model gives a poor representation of bulk behavior, particularly for less flexible polymer chains, but as N becomes larger we expect it to be an increasingly better approximation to a dense amorphous system. 

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