Crystallization under applied force

The discussion of crystallization kinetics, and the mechanisms involved, has so far been limited to quiescent crystallization. In essence, except for polymer structure and composition, the only variable considered was temperature. This has given a limited perspective to the overall subject, since polymers crystallize when subject to applied forces such as hydrostatic pressure, tensile, biaxial and shear deformation among others. Different morphologies and structures result from these types of crystallization. As a result, properties can be drastically altered. The analysis of the crystallization kinetics of polymeric systems when subject to such external forces is the subject of the present chapter. Although this an important area, the literature is not as rich as in some of the other areas that have been discussed. However, the results that have been obtained are interesting and hopefully will stimulate further inquiry. 

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Crystalline phase volume by itself is generally not sufficient to determine material properties some measure of the dispersion of that crystalline material is also needed. A product that contained all the mass in a few large crystals would have completely different material properties than the same product containing a dispersion of numerous small crystals. Hardness is related to the size of crystals in a system, with more numerous small crystals typically giving a harder product. The product with numerous small crystals has many more interparticle contacts under applied force than a product with the same crystalline phase volume but fewer larger crystals. 

Figure 8. Idealized fat crystal network under extension. Particles (a) are packed in a fractal fashion within floes ( ). A force (F) acting on the network causes the links between floes to yield, and the original length of the system in the direction of the applied force (L) to increase (A/.). Thus, the inter-floc separation distance (I), also increases.

Mechanical strength is studied under the heading of elasticity. This is the science of the response of a solid sample to applied forces. The forces are described by tensors, called stresses, which give the direction of the force and the crystal face to which it is applied. The responses, called strains, are also given by tensors which give the relative changes in dimensions or shape. The ratio of a stress to its corresponding strain is called an elastic modulus. 

By measuring velocity of a spherical particle sinking in a liquid under gravity force the viscosity of the liquid can be found (the buoyancy effect should be taken into account). Note that in Section 7.3.3, using an electric field as an action force, the same Stokes law has been applied (with some precautions) to evaluation of velocity and mobility of spherical ions in isotropic liquids or nematic liquid crystals For large Reynolds numbers, Re = pv//ri>l the flow in no longer laminar and even becomes turbulent. Then, the convective term (vV)v should be added to the left part of the Navier-Stokes equation... 

Piezoelectric crystals can be used as the basis for force measurement. An equivalent circuit is shown in Figure 27.9, which captures the electrical characteristics of this material under an applied force. 

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