Static Displacements of Chains Against Crystal Lattices

Static Displacements of Chains Against Crystal Lattices 

The first investigations of the loading of chains displaced with respect to their equilibrium positions within a crystal lattice have been carried out by Chevychelov [20]. He used a continuum approach, i.e. replaced the string of discrete chain atoms by a continuous mass distribution. Each mass point experiences a periodic repulsive crystal potential if displaced from its equilibrium position. Later Kausch and Langbein [21] and Kausch and Becht [22] extended these calculations to treat the static and dynamic interaction of chains of discrete atoms with arbitrary periodic potentials. 

A tie molecule thus embedded in two different crystalline layers is streched if the crystal lamellae are separated by macroscopic stresses. Because of the large elastic modulus of the chain molecule very high axial stresses are exerted onto the chain if it experiences the same strain as its amorphous vicinity. This high axial stress tends to pull the tie molecule against the intracrystalline potential and out of the crystal lamella. 

Each point along a tie chain is characterized by its distance z from the crystal boundary, where z refers to the unstressed situation. The displacement of the molecular point z under stress is denoted by u = u (z) and the crystal potential per unit 

This relation implies no assumptions with respect to the form of V(u) or the response s(u) of the chain. 

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B. Static Displacements of Chains Against Crystal Lattices.99... 

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