Equilibrium distribution, polymer crystal

At this point a third intermediate approach deserves mentioning. It is due to Allegra [43] who proposed that polymer crystallization is controlled by a metastable equilibrium distribution of intramolecular clusters, the so-called bundles , forming in the liquid phase. These subsequently aggregate to the side surfaces of the crystals, driven by van der Waals interactions. The lamellar thickness is determined by the average contour length of the loops within the bundles. Although the model can... 

Flory considers two distribution functions needed to characterize the system. The first is the initial distribution, the distribution of crystallizable sequences in the uncrystallized polymer. For stereoregular polymers, as discussed above, this is described by Equation 2. The second distribution function, which is a function of temperature, is the equilibrium distribution which follows from the condition that all sequences of length greater than be in equilibrium with crystallites of each length . Crystallization can occur only at values of for which the initial distribution exceeds the equilibrium distribution. The extent of crystallization depends on the difference between the initial and equilibrium distributions. At any temperature there will exist... 

In previous sections we have shown that the redistribution of additives at the spherulite boundaries during polymer crystallization leads to the additives uneven distribution, whose form is determined by the kinetics of the growth rejection process. In time, this initial dynamic distribution should relax to an equilibrium form in which the noncrystalline polymer is uniformly permeated by the additive, whose distribution reflects that of the noncrystalline polymer. The relevanoe of these observations to oxidative degradation processes in semi-crystalline polyolefins is discussed in this section. 

Now we compare the isotropic-liquid crystal phase boundary concentrations for various polymer solution systems with the scaled particle theory for the wormlike spherocylinder. If the equilibrium orientational distribution function f(a) in the coexisting liquid crystal phase is approximated by the Onsager trial... 

The PDLC system performance depends strongly on the final morphology of the liquid crystal domains dispersed inside the polymer matrix. The size, shape and distribution of liquid crystal domains are generally dictated not only by thermodynamic phase equilibrium, but also by the type of material used and by interfacial interactions [58-62]. 

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