Homopolymers, length polydispersity

We now illustrate how the moment method is applied and demonstrate its usefulness for several examples. The first two (Flory-Huggins theory for length-polydisperse homopolymers and dense chemically polydisperse copolymers, respectively) contain only a single moment density in the excess free energy and are therefore particularly simple to analyze and visualize. In the third example (chemically polydisperse copolymers in a polymeric solvent), the excess free energy depends on two moment densities, and this will give us the opportunity to discuss the appearance of more complex phenomena such as tricritical points. 

LCs were the earliest studied structures, in which polypeptide homopolymer rods pack in an ordered manner to form smectic, nematic, and cholesteric phases. The smectic LCs are mainly formed by polypeptide homopolymers with identical polymer length. The cholesteric phase can be prepared by synthetic polypeptides with polydisperse chain length. The nematic phase can be regarded as a special example of the cholesteric phase with an infinite cholesteric pitch. The cholesteric pitch and chirahty in the polypeptide LCs are dependent on many factors, such as temperature, polymer concentration, solvent nature, and polypeptide cOTiformation. Deep understanding of such phenomena is necessary for preparation of ordered polypeptide assembles with delicate stmctures. The addition of denaturing solvent to polypeptide solution can lead to an anisotropic-isotropic reentrant transition at low temperatures where the intramolecular helix-coil transformation occurs. However, the helical structure is more stable in LC phase than in dilute solution due to the conformational ordering effect. 

Recently, microemulsion route [193,243,431-433] has been developed to enable strict control over molecular parameters (e.g., molecular weights of the homopolymers A and B, and the molecular weight and composition of the A-B-type linear DBG) that can lead to a stable co-continuous microemulsion (Figure 1.25a), indeed a nanoblend However, the major drawback of the co-continuous microemulsions is that they require polymers with similar lengths and sizes (low polydispersity) that are expensive... 

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