DENSITY FUNCTIONAL THEORY OF LAMELLAR ORDERING IN DIBLOCK COPOLYMERS

Density functional theory has been used to describe the ordering phenomena of amorphous A-B diblock copolymers. The resulting formalism was then used to study the ordering of asymmetric diblock copolymer to the lamellar morphology for values of chi-N above the microphase separation transition value. The number of statistical segments per diblock copolymer chain is denoted by N and chi is the Flory interaction parameter. We have identified three distinct regimes for the N dependence of the domain spacing D. For 10.495 less-than-or-equal-to chi-N less-than-or-equal-to 12.5, the weak segregation limit of Leibler is realized where the domain spacing D is proportional to N0.5. For chi-N > 100, the strong segregation limit is achieved where D is proportional to N0.67. In the newly discovered intermediate regime (15 less-than-or-equal-to chi-N less-than-or-equal-to 95), D is proportional to N0.72 and the domain boundaries support substantial fluctuations. The distinct features of the microscopic density profiles in the various regimes are discussed. In addition, the present theoretical results are compared with the most recent experimental investigations reported in the literature.