Molecular networks, threshold

Threshold Tear Strength of Some Molecular Networks... 

The threshold tear strength of elastomeric molecular networks does not appear to depend strongly, if at all, upon the uniformify of network strand lengths. It is found to be proportional to Mc where Mc is the mean molecular weight of the strands, in accordance with the theory of Lake and Thomas (3). However, it is considerably smaller for Si-0 networks than for C-C networks at equal Mc values. This is attributed to differences in strand length and extensibility. 

In some colloidal dispersions, the shear rate (flow) remains at zero until a threshold shear stress is reached, termed the yield stress (ry), and then Newtonian or pseudoplastic flow begins. A common cause of such behaviour is the existence of an inter-particle or inter-molecular network, which initially acts like a solid and offers resistance to any positional changes of the volume elements. In this case, flow only occurs when the applied stress exceeds the strength of the network and what was a solid becomes a fluid. Examples include oil well drilling muds, greases, lipstick, toothpaste and natural rubber polymers. An illustration is provided in Figure 6.13. Here, the flocculated structures are responsible for the existence of a yield stress. Once disrupted, the nature of the floe break-up process determines the extent of shear-thinning behaviour as shear rate increases. 

Figure 3. Threshold tear energy T . Key O, A, , PDMS networks , A. PB networks , PI networks versus molecular weight Mc between cross-links calculated from Ct. O, , , random cross-linking A, A. trifunctional end-linking , tetrafunctional end-linking.

Values of Mc calculated from the small-strain tensile modulus, i.e., using C- + C2 in equation 2 in place of Cj, were, of course, smaller than those obtained from Ci values. However, the general form of the dependence of threshold tear strength upon Mc and the relative values obtained for different polymers at the same Mc were not significantly affected by this alternate procedure for calculating the mean molecular weight of network strands. 

Proton conductivities of 0.1 S cm at high excess water contents in current PEMs stem from the concerted effect of a high concentration of free protons, high liquid-like proton mobility, and a well-connected cluster network of hydrated pathways. i i i i Correspondingly, the detrimental effects of membrane dehydration are multifold. It triggers morphological transitions that have been studied recently in experiment and theory.2 .i29.i ,i62 water contents below the percolation threshold, the well-hydrated pathways cease to span the complete sample, and poorly hydrated channels control the overall transports ll Moreover, the structure of water and the molecular mechanisms of proton transport change at low water contents. 

Loveless DM, Jeon SL, Craig SL. Chemoresponsive viscosity switching of a metaUo-supra-molecular polymer network near the percolation threshold. J Mater Chem 2007 17 56-61. 

Clearly, the constant can be included into threshold value B, so that the function /o(C) = 1 is not necessary. We must stress that in such form the probabilistic approach has no tuned parameters at all. Some tuning of naive Bayes classifier can be performed by selection of the molecular structure descriptors [or /(C)] set. This is a wonderful feature in contrast to QSAR methods, especially to Artificial Neural Networks. 

On the basis of random walk arguments, Koplik et al. (1988) show the relations K Pn, K Pn In Pn, and K Pi for (i) a bundle of uniform stream tubes that meet at perfect mixing chambers separated by a characteristic length /, (ii) nonuniform bond transit times, and (iii) the presence of dead-end pores, respectively. The relationship K oc pi is also obtained for percolation networks near the percolation threshold when the characteristic length is the percolation correlation length and the molecular diffusion coefficient is adjusted for the presence of the percolation network. 

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