DOI 10.1140/epje/i2008-10402-8 Eur. Phys. J. E 27, 407–411 (2008) T HE EUROPEAN P HYSICAL JOURNAL E Kinetics of layer hopping in a diblock copolymer lamellar phase A.B. Croll 1 , M.W. Matsen 2 , A.-C. Shi 1 , and K. Dalnoki-Veress 1, a 1 Department of Physics & Astronomy and the Brockhouse Institute for Materials Research, McMaster University, Hamilton, ON, Canada 2 Department of Mathematics, University of Reading, Whiteknights, Reading, UK Received 3 November 2008 Published online: 9 December 2008 – c  EDP Sciences / Societ`a Italiana di Fisica / Springer-Verlag 2008 Abstract. In the ordered state, symmetric diblock copolymers self-assemble into an anisotropic lamellar morphology. The equilibrium thickness of the lamellae is the result of a delicate balance between enthalpic and entropic energies, which can be tuned by controlling the temperature. Here we devise a simple yet powerful method of detecting tiny changes in the lamellar thickness using optical microscopy. From such measurements we characterize the enthalpic interaction as well as the kinetics of molecules as they hop from one layer to the next in order to adjust the lamellar thickness in response to a temperature jump. The resolution of the measurements facilitate a direct comparison to predictions from self-consistent field theory. PACS. 83.80.Uv Block copolymers – 68.47.Mn Polymer surfaces – 82.35.Jk Copolymers, phase transitions, structure – 68.55.J- Morphology of films Often the most fascinating features of nature are rooted in the complexity and order found in self-assem- bling patterns. The innate interest in self-assembly, cou- pled with the technological need for simple cost-effective templates results in a significant research effort to under- stand pattern formation [1]. Of the many self-assembling nanoscale polymeric structures, some of the most remark- able are formed by block copolymers [2,3]. Block copoly- mers are long chain molecules made up of segments of different chemical constituents joined together by a cova- lent bond. In the simplest case, a block of fN segments is attached to another block of (1 − f )N segments to form a diblock copolymer. Because of the general incom- patibility of the chemically distinct blocks, the molecules exhibit amphiphilic properties: that is, the blocks tend to segregate into structures that minimize contact be- tween unlike segments. These molecules will typically self- assemble into long-range periodically ordered morpholo- gies composed of nanosized domains, when cooled below an order-disorder transition (ODT). The composition of the molecule, f , sets the preferred curvature of the internal interfaces which, in turn, controls the geometry of the re- sulting morphology; symmetric diblocks (f ∼ 1/2) prefer zero curvature resulting in a simple lamellar phase, where the incompatible domains form flat alternating layers. The repeat period, L, is on the order of the relaxed molecular size (i.e., the polymer radius of gyration, R g ∼ 10 nm), but a e-mail: dalnoki@mcmaster.ca the precise value of L is controlled by the product, χN , where the Flory-Huggins parameter, χ, is a temperature- dependent quantity that specifies the incompatibility of the unlike segments. Here we examine thin films of a symmetric diblock copolymer, which form a stack of lamellae oriented paral- lel to the substrate. Using a simple optical measurement, we are able to monitor changes in the domain size, L, in situ with an unprecedented sensitivity. By comparing the measured L with predictions from self-consistent field the- ory (SCFT), we extract the temperature dependence of χ and verify the technique. With the methodology estab- lished, we measure the equilibration of L as the lamellae respond to a sudden temperature jump. The resolution of the experiments facilitates a direct comparison of the data with SCFT, which provides a quantitative, parameter-free measure of the kinetic energy barrier, Δ, for an individual molecule to hop between adjacent layers. The kinetics of molecular motion in structured mor- phologies is of wide interest [4–7]. It is relevant to virtu- ally all complex liquids and biological systems; such as the exchange of molecules between layers in smetic liquid crys- tals and between the inner and outer layers of lipid mem- branes. In the model system of block copolymer melts, Lodge and co-workers have tried to differentiate between lateral diffusion where the molecules move with their junc- tion point on the same interface, and perpendicular diffu- sion where the junction point jumps between neighboring interfaces [8]. In our experiment, the rate of change in the