Crystallization from dilute solution flexible chains

3 Crystallization from dilute solution flexible chains 

The melting, or dissolution, of long chain molecules at high dilution is a natural consequence of phase equilibrium. The dissolution process results in the separation of the solute molecules and is usually accompanied by a change in the molecular conformation of the chain from an ordered structure to a statistical coil. However, it is also possible for the individual polymer molecules to maintain the conformation in solution that is typical of the crystalline state. This is particularly true if the steric requirements that favor the perpetuation of a preferred bond orientation or the ordered crystalline structure can be maintained by intramolecular bonding, such as hydrogen bonds. Further alterations in the thermodynamic environment can cause a structural transformation in the individual molecules. Each molecule is then 

In order to develop a theory for crystallization from dilute solution it is necessary to express the chemical potential of the polymer species in the disordered state. In the general theory of dilute solutions the chemical potential of the solvent species can be expressed in virial form. Consequently, the chemical potential of the solvent species can be given quite generally as(l) 

Here v is the partial specific volume of the polymer. In the development that follows, we utilize the theory of Rory and Krigbaum.(42) The second virial coefficient can then be expressed as 

The value of the integration constant is obtained from the lattice theory as V2 0. After dividing by the number of units per molecule, xVi/Vu, Eq. (3.20) can be recast as 

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The manner in which individual molecules crystallize depends on the conformation of the chains. Flexible chain polymers, as shown schematically in Figure 5.18, fold to form microlamellar plates. Rigid chain polymers form bundles of rod-like structures. The bulk structure or macrostmc-ture of the polymer depends on whether crystallization occurs from dilute solution or from the melt state. When crystallization occurs under quiescent conditions in a dilute solution, then single crystals consisting of folded chains arise. When crystallization from the melt occurs under quiescent... 

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