Response to Mechanical Stress:

The response of most materials to stress is characterized by a Hookean response, that is strain or deformation is proportional to the force or stress applied to the material.  The structural basis for this response has to do with deformation of metallic, ionic or covalent bonds in the crystallographic structure.  A polymer chain is at thermal equilibrium with a variety of configurational states, that is a distribution of these states is possible with some maximum probability for the most likely configurational state in terms of, for instance, the chain's end-to-end-distance.  We can think that thermal energy is distributed in different types of structural vibrations in the polymer chain, modes, and that the sum of the energy in these modes is the total kT energy available to the chain.  Different modes of vibration are defined by different frequencies just as the modes of vibration on a guitar string have different tones, various overtones and the main tone of a string.  Deformation of the chain by an external force leads to a redistribution of energy and a shifting of the probability of configurational states just as stretching a guitar string or shortening of the length changes the tones and over tones.  For a polymer chain, most of the energy is held in the lowest order, lowest frequency mode which is called the Rouse Mode. 

The response of an isolated chain is therefore time dependent with a continuous spectrum of response associated with the configurational states of the chain at dynamic thermal equilibrium.  This time dependence is true of both the amorphous solid state, semi-crystalline state and liquid state (polymers do not display a gas state).  For instance, the viscosity of a polymer, ratio of stress and rate of strain, generally displays a power-law dependence (strong dependence) on the rate of strain (shear rate).  The higher the shear rate, the lower the viscosity.  This shear thinning behavior is advantageous to polymer processing under high strain rates such as in an extruder die or in an injection molding operation.  If not for shear thinning behavior it would be difficult to process polymers into commercial devices. 

The time dependence of mechanical response in polymers means that the very definition of solid/liquid states depends not only on temperature but also on the frequency of mechanical deformation.  For the liquid state, the frequency of deformation is the strain rate, with units of inverse time.  For the solid state, polymers require a new testing device called the dynamic mechanical analyzer or dynamic mechanical thermal analyzer (DMTA) if temperature is scanned.  The DMTA describes the mechanical response at different frequencies in terms of a Hookean modulus and a loss modulus associated with Newtonian flow.  Then we can speak of visco-elastic response as a mechanical response including both static and dynamic components and associated with the temperature and frequency of the measurement.  The visco-elastic response of polymers means that high-frequency or high speed deformations at a temperature where the polymer is elastic or liquid can lead to solid or glassy state response.  This is of vital importance to understanding the proper application of polymers in the manufacturing setting.

In dealing with chains in a dense media it is necessary to use an empirical constitutive approach where the rich modal response of an isolated polymer chain is replace by a series of time constants associated with exponential relaxations in the bulk polymer.  This is an inherent point of disconnection between structural understanding of molecules and chemistry and application of polymers and plastics.  This is another point of difference between metals and ceramics, that is, polymers can be better described as a class of materials with universal types of response while metals and ceramics are generally described in terms of local, atomic features.  The disconnection between local structure and bulk response leads to the use of statistical measures of properties in polymers versus local, non-statistical descriptions in metals and ceramics.