Number-average cluster size

It should be noted that the predictions for the number average cluster size and polydispersity agree with analytical results for K(x, y) = 1, x + y, and xy. Furthermore, the short-time form of number average size in Eq. (81) matches the form of s(t) predicted by the scaling ansatz. Computational simulations (Hansen and Ottino, 1996b) also verify these predictions (Fig. 38). 

The number average cluster size takes a finite value at the percolation threshold, and hence... 

Run this example using the following parameter setup. Record the average cluster size and the percent of percolations over a number of runs. The number of iterations will be zero and only the initial grid configuration will be used. A suggested number of runs is 1000. 

As previously discussed, we expect the scaling to hold if the polydisper-sity, P, remains constant with respect to time. For the well-mixed system the polydispersity reaches about 2 when the average cluster size is approximately 10 particles, and statistically fluctuates about 2 until the mean field approximation and the scaling break down, when the number of clusters remaining in the system is about 100 or so. The polydispersity of the size distribution in the poorly mixed system never reaches a steady value. The ratio which is constant if the scaling holds and mass is conserved,... 

Numbers on Figure indicate average cluster size (after Baetzold103)... 

It seems significant that the average cluster size for HVL-P and SP-300 are identical (vide infra). This would seem to indicate that although SP-300 has considerably more linking units intact, as evidenced by the number of clusters per molecule (//cl), the actual clusters have essentially the same size (R ///cl). This reinforces the notion that the aromatic clusters are stable even under the relatively drastic conditions by which HVL-P was produced. 

We calculate the polydispersity of a system consisting of one cluster of arbitrary size and a swarm of primary particles as a function of the average cluster size and the number of particles ... 

As expected, the length of the tube grows linearly with the polymer molecular weight (the number N of reptons in a cluster). Notice that the entropic tension and the average cluster size increase with the coordination number 2. 

Thus, the parameter value of u can be determined by the observed binding isotherm onto polymers. In addition, the number of bound surfactant ion clusters (Z) is given by d In Aj/d In Hence, the average cluster size of bound surfactant ions (m) and unoccupied binding sites (p) can be derived... 

Figure 117 Water mobility on the surface of a flexible lysozyme. Left panel normalized inverse time r(200)/r(Ww) corresponding to the two total MSB (r ) =0.1 nm and (r ) = 1.0 nm as function of the normalized average cluster size S. Linear dependences are shown by dashed lines. Right panel inverse time corresponding to the total MSB (r ) = 0.1 nm as a function of the average number h of H-bonded neighbors. Linear fit is shown by dashed line (data from [630]).

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