Phase Coherence upon Heating in Diblock Copolymer Films J. Cho,* ,† K. Shin,* ,‡ K. S. Cho, § Y.-S. Seo, | S. K. Satija, ⊥ D. Y. Ryu, X and J. K. Kim O Department of Polymer Science and Engineering, Dankook UniVersity and Hyperstructured Organic Materials Research Center, San 44-1, Jukjeon-dong, Suji-gu, Yongin-si, Gyeonggi-do 448-701, Korea, Department of Chemistry and Program of Integrated Biotechnology, Sogang UniVersity, Sinsu-dong, Mapo-gu, Seoul 121-742, Korea, Department of Polymer Science and Engineering, Kyungpook National UniVersity, 1370, Sangyuk-dong, Bukgu, Daeku 702-701, Korea, Department of Nano Science and Technology, Sejong UniVersity, Gunja-dong, Gwangjin-gu, Seoul 143-747, Korea, National Institute of Standards and Technology, 100 Bureau DriVe, Stop 1070, Gaithersburg, Maryland 20899-1070, Department of Chemical Engineering, Yonsei UniVersity, 134 Sinchon-dong, Seodaemun-gu, Seoul 120-749, Korea, and National CreatiVe Research InitiatiVe for Block Copolymer Self Assembly, Department of Chemical Engineering and Polymer Research Institute, Pohang UniVersity of Science and Technology, Kyungpuk, 790-784, Korea ReceiVed July 18, 2007; ReVised Manuscript ReceiVed October 31, 2007 ABSTRACT: Phase coherence behavior in thin films of a diblock copolymer that exhibits microphase separation upon heating in the bulk has been analyzed through a proper mean-field free energy functional based on a compressible random-phase approximation theory. Phase coherent profiles at equilibrium and their decay lengths were obtained analytically for those copolymer films. Taking deuterated polystyrene-b-poly(n-propyl methacrylate) as a model system, molecular parameters characterizing the copolymer were shown to yield the growing tendency of surface segregated or phase coherent profiles upon heating. Neutron reflectivity measurements were performed for the copolymer films to be compared with theory. Phase coherence prior to bulk ordering temperatures and subsequent decay lengths observed for the given system were shown to be in agreement with theory. Introduction Phase separation behaviors of melts and thin films of block copolymers have drawn tremendous interest in the polymer community. Block copolymers exhibit nanoscale self-assembly behavior to form microscopically ordered structures called microphases. Most block copolymers have been known to exhibit a microphase separation from a disordered state to an ordered state upon cooling, which is referred to as the upper order-disorder transition (UODT). The unfavorable interactions between dissimilar monomers comprising a given block co- polymer are considered to be the cause for such behavior. 1-3 There have been in recent decades extensive theoretical developments including Leibler’s Landau approach 4 to analyze the microphase separation behavior and transitions between equilibrium microstructures for molten block copolymers or systems containing block copolymers in the weak to strong segregation regime. 1,4,5 There have been also numerous publica- tions regarding the phase behavior of block copolymer films. 6 Among them, surface ordering or phase coherence phenomena 7,8 were investigated first by Fredrickson 9 and later by Tang and Freed 10 in the weak segregation regime. More thorough self- consistent field calculations, particle-based and field-theoretic simulation studies have appeared in the polymer literature to understand complicated nanopatterns of the copolymer melts and films. 1,6,11,12 Very recently, Angerman et al. developed an analytical Landau free energy density for thin block copolymer films that is amenable to capture a global overview of nano- patterned films in various ways. 13 It is a central concept in all of the works that a composite parameter N F , where N and  F are the copolymer chain size and Flory’s interaction parameter, respectively, forms a relevant parameter to describe the phase behavior of block copolymer systems. The theories mentioned above are based on the common assumption of system incompressibility. However, there have been numerous recent findings that strongly address a clear need for finite compressibility to interpret the compressible nature and the pressure effects of block copolymers. The relevant findings include ordering upon heating, which is referred to as lower disorder-order transition (LDOT) phenomena, in styrenic block copolymer melts and films, 14-17 baroplastic copolymers to utilize pressure-induced flow, 18-23 and loop-forming block copolymers. 20,23-26 Prior to the discovery of loop forming block copolymers, the LDOT and baroplastic character of styrenic block copolymers have been attributed to the difference in monomer structures by Freed and co-workers in their lattice cluster model 27 or to the difference in pure component properties by Ruzette and Mayes in a simple phenomelogical model. 28,29 However, a unified view of the LDOT, loop, and baroplasticity in those styrenic block copolymers has been provided in a recent series of works by one of the present authors on a compressible random-phase approximation (RPA) theory. 30-34 Finite com- pressibility was incorporated into the theory through effective RPA interactions, which is obtained from a molecular equation- of-state model by Cho and Sanchez (C-S). 35,36 The  F was reinterpreted as  F )  app + comp , where  app is the density dependent dimensionless exchange energy and  comp represents compressibility difference between constituent blocks. LDOT or baroplastic block copolymers can offer new types of sensor materials with high-temperature or pressure sensitivity. * To whom correspondence should be addressed. E-mail: jhcho@dku.edu (J.C.), kwshin@sogang.ac.kr (K.S.). † Dankook University, and Hyperstructured Organic Materials Research Center. ‡ Sogang University. § Kyungpook National University. | Sejong University. ⊥ National Institute of Standards and Technology. X Yonsei University. O Pohang University of Science and Technology. 955 Macromolecules 2008, 41, 955-962 10.1021/ma071604r CCC: $40.75 © 2008 American Chemical Society Published on Web 01/16/2008