Halperin theory, block copolymers

It is worth emphasizing that all scaling theories (due to de Gennes, Daoud and Cotton, Zhulina and Birshtein, and Halperin) for block copolymer micelles with a small core and large corona predict that the association number and core radius are independent of the coronal chain length. 

Halperin and Alexander extended the theory of the Aniansson and Wall approach to calculate the detailed rate constants and the associated activation energies for polymeric materials, i.e., block copolymer micelles. We briefly review the central results in the following section. 

Exchange Kinetics in Block Copolymer Micelles Halperin and Alexander Theory... 

The last reported diblock copolymer family that formed tubular aggregates in block-selective solvents was poly(phenylquinoline)-fc/ock-polystyrene or PPQ-PS, where PPQ was a rigid-rod block [47]. Such tubes are not discussed further for the following reasons First, the tubes had diameters of several micrometers and were not nanotubes. Second, the formation mechanism and chain packing in such tubes were not well understood at all. While Halperin [48] has developed a scaling theory for micelle formation from rod-coil diblock copolymers with the rod block forming the core, the theory did not apply to the PPQ-PS system as the block-selective solvents used were good for the rod PPQ block rather than the coil PS blocL... 

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