Narrow interphase approximation

Helfand E, Wasserman ZR (1976) Block copolymer theory. 4. Narrow interphase approximation. Macromolecules 9 879-888... 

Theories of block copolymers are usually complex, involving computation of the domain size, the interphase thickness between the blocks, the stmc-ture, and the order-disorder transitions. Helfand and Wasserman [1976, 1978, 1980] using the narrow interphase approximation, showed that Eq 4.4 is valid in the limit of infinitely immiscible blocks having (i.e., the strong segrega-... 

Narrow interphase approximation Order-disorder transition Order-order transition Wave vector... 

In principle, Qc appearing in (9) must be obtained from the solution of (8). Owing to the practical difficulty Helfand and Wasserman [8] had in calculating Qc rigorously from (9), they applied the Narrow Interphase Approximation (NLA) method to calculate Qc. Note that the NLA method is only valid for the situations where the interfacial thickness Aj between block A and block B is very small compared to the domain spacing D, i.e., Xi/D -C 1. Specifically, in place of (9), based on the NIA method Helfand and Wasserman employed the following expression to calculate Qc. ... 

Fig. 5 Free energy per molecule as a function of periodicity distance D for an AB-type diblock copolymer having a of 37. On the abscissa D denotes the periodicity distance, b denotes the Kuhn length, and N denotes the degree of polymerization of the block copolymer. The components of the free energy labeled surface, joint, and domain are, respectively, the first three terms on the right-hand side of (19). The dotted curve is the prediction without making narrow interphase approximation. (Reprinted from Helfand and Wassermann [8]. Cop5rright 1976, with permission from the American Chemical Society)...

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