Force chain

Adhesion in which interfaces between phases or components are maintained by intermolecular forces, chain entanglements, or both, across the interfaces. 

In addition to the contribution of intermolecular forces, chain entanglement is also an important contributory factor to the physical properties of polymers. While paraffin wax and HDPE are homologs with relatively high molecular weights, the chain length of paraffin is too short to permit chain entanglement, and hence lacks the strength and other characteristic properties of HDPE. 

Thermoplastics consist of long chains of molecules, in the case of PE these are unbranched. Many of these chains together form a tangle which is more difficult to unravel the more branched the chains are. The branches are like hooks which cause the molecules to catch. Under the influence of relatively small external forces chains and parts of chains can slide across each other. PE is for instance used to make containers, chemical tubing and blow-moulded bottles. Some other thermoplastics are polypropylene (crates), polyvinyl chloride PVC (pipes) and polystyrene (foam). 

The kinetic flexibility of a macromolecule is directly related to the ease with which conformational changes between trans and gauche states can take place. The lower the energy barrier AE in Fig. 4-2, the greater the ease of rotation about main chain bonds. Polymers with low chain stiffnesses will have low Tg s in the absence of complications from interchain forces. Chain backbones with... 

The correlation for Tg was developed by analyzing the dataset for relationships between the polymeric structure and the two important physical factors summarized in Section 6. A, namely chain stiffness and cohesive forces. Chain stiffness is, admittedly, a somewhat nebulous concept, which has been quantified in different ways by different authors. It is hoped that the reader will agree that the manner in which this key physical factor will be incorporated into our correlation for Tg makes sense at an intuitive level. 

Interfacial adhesion is the adhesion in which interfaces between phases or components are maintained by intermolecular forces, chain entanglements, or both, across the interfaces. Interfacial adhesion between rubber and PMMA must be sufficient to permit the effective transfer of stress to the rubber particles and also to provide multiple sites for crazing and localized shear yielding for effective impact energy dissipation. 

This stage is a stage of the forced chain branching (i.e. it leads to appearance on the new OH radical), which is an initiator of the chain process of carbohydrate oxidation. The macro-radical RO is usually less active and could cause the chain to break according to the reaction (6.12) with formation of the peroxide linkage ... 

Figure 4. Rearrangement to Non-Propagating Living End Forces Chain Transfer to Monomer.

The disks are between crossed linear polarizers, and stress-induced birefringence results in the picture shown the white streaks are force chains. 

E.T. Owens and K.E. Daniels. Sound propagation and force chains in granular materials. EPL (Europhysics Letters), 94(5) 54005, 2011. 

Equations 4.48 through 4.50 specify the volume fraction and the stress ratio as functions of the inertial parameter, the coefficient of restitution, and the parameter c. These relations are equivalent to those proposed hy GDR Midi (2004) over the range of volume fractions and coefficients of restitution for which exchanges of momentum in collisions dominate the momentum transfer and before force chains span the system. That is, as v increases for a given e, the chain length I given hy (4.46) will approach the system size. When it does, there is an additional mechanism for the transfer of momentum in the flow that we do not consider (e.g., Hatano et al. 2007)—ephemeral chains of particles that transfer force across the flow and are responsible for the development of a yield stress. The model of GDR Midi continues to apply above this volume fraction and includes the rate-independent mechanism of momentum transfer, but the model described here does not. 

M. E. Cates, J. P. Wittmer, J. P. Bouchaud, and P. Claudin. Jamming, force chains, and fragile matter. Physical Review Letters, 81 1841-1844, 1998. 

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