Stress-Strain Curve of a Single Chain

Static Displacements of Chains Against Crystal Lattices.99 

Thermally Activated Displacements of Chains Against Crystal Lattices. . . . 105 

Chain Displacements Against Randomly Distributed Forces.107 

A chain molecule as part of a thermoplastic body is in thermal contact with other chains and — at room temperature — constantly in motion. The atoms vibrate and take part in the more or less hindered rotations of groups and even of chain segments. With no external forces acting all molecular entities try to approach — and fluctuate around — the most stable positions attainable to them. The action of external forces causes — or maintains — displacements of the chain from those positions and evokes retractive forces. Let us consider a chain or a bundle of chains in thermal contact with the surrounding and at constant volume. The condition of thermodynamic stabihty of such a system is that the free energy 

An increase of U can be effected by heat dQ flowing into the system from the outside or by mechanical work dW done onto the system. The change of entropy may be split up into a portion —d S which is equal to dQ/T and into the internal entropy production d S caused by irreversible processes as for instance by stress relaxation or generation of heat through friction  

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To give an example of what can be achieved in such simulations we discuss below the stress-strain behavior as observed in simulations of the model PE I of polyethylene at a range of temperatures in the glass and melt. The sample size was 1000 monomers formed into a single linear chain as described in Section 5.4. The coohng curve for these samples is shown in... 

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