Chemical length

The comparison between the two techniques has shown that DPL is more flexible than FDI (any kind of pattern can be transferred on the surface) and less time consuming. On the other hand, very high and large border walls are produced in DPL. The analysis of the properties of these border walls reveals that DPL causes changes in the physical (density) and chemical (length of the chains) properties of the polymer. 

Fig. 1.3. A portion of the node-link-blob superlattice model for p > Pc-The distance between two nodes of the lattice (say A and B) is while the chemical length of the tortuous bond of the superlattice is Lc.

As discussed in Section 1.2.1, for such systems near the percolation threshold Pc the nearest-neighbour occupied bonds (or sites) form a statistically defined super-lattice , made of tortuous link-bonds (of chemical length Lc) crossing at nodes separated by an average distance the percolation correlation length (see Fig. 1.3 of Chapter 1). The external stress... 

In the node-link model of the Swiss-cheese system (see Section 1.2.1 (g)), each link has a distribution P 8) of channel width 6 and hence of local strength, as indicated in Fig. 1.5 of Chapter 1. One expects here the minimum value of = min to be of the order of L , where (Ap) e " is the chemical length of the singly connected link of the percolating network, and P 6) to be finite for 6 —> min-... 

The burner flame lengfh is usually considered as a "chemical" length and is determined based on the measurement along the flame until combustion is completed (for example, C02/C02max = 0.95 or 02mm/02 = 0.95). However, in some cases (open fire), fhe visible flame length measurement is acceptable. The flame fempera-ture is measured by a water-cooled suction pyrometer or available optical means. Heat transfer from the... 

Thus, a changeover to the more rapid OH branching reaction may take place at H2 - 13% and give rise to a more rapid increase in the flame speed. The chemical length scale is also significantly reduced when the kinetic mechanism changes to rapid OH branching. 

Limit criteria for other tube geometries and for unconfined conditions have yet to be established. However, there is no doubt that the limit conditions should be correlated to the fundamental chemical length scale of the mixture (i.e., cell size). 

This gives the chemical length of the reaction vector R, so it represents the number of "electron pushing arrows in the synthesis L,R) of Z thus, it represents the "complexity of chemical operations."... 

Further, the mean squared chemical length of species i is given by (X (t j)). The chemical time scale r h is determined by the characteristic lifetime of the activator, namely tch = The mean squared displacement (MSD) for subdiffusing particles is given by (2.60) ... 

We obtain for the ratio of the mean squared chemical lengths of the inhibitor and the activator... 

This gives a sharp departure from the original disengagement calculation. A smoother form can be obtained with the same threshold value for the chemical length, by replacing Eq. (7.24) by a crossover expression of the end to end pulled chain type (see below) ... 

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