Lamellae film thickness

Figure 6-14. Average domain size vs. inverse deposition temperature Tor different film thicknesses. Error bars represent the mean absolute error and straight lines the best lit for each film thickness. Doited line is the locus of the transition from grains to lamellae. Data for 50-nm films are estimated from the correlation length of the topography fluctuations. Adapted from Ref. [501.

To explain the role of the medium capillary pressure upon foam coalescence, consider a flat, cylindrical, stationary foam lamella of thickness, 2h, circa 1000 A, and radius, R (i.e., 50 to 100 /xm), subject to a capillary pressure, P, at the film meniscus or Plateau border, as shown in Figure 3. The liquid pressure at the film meniscus is (P - P ), where P is the gas pressure. g c g... 

In the case of t < Lo, it has been suggested that perpendicular lamellae are favored in the boundary-symmetric confined film because they avoid the entropic penalty associated with the compressed chain conformations in parallel-oriented microdomains [109]. In boundary-asymmetric substrate-supported films, various kinds of morphologies, including hybrid morphologies that combine surface-parallel and surface-perpendicular components, are predicted, as well as observed, depending on the film thickness difference and surface/interface energies [14,41,120]. 

Fig. 5 Schematic cross-sections of thin film morphologies of the topographic pattern grown by a graphoepitaxy method. A micropattern with different lamellar domain orientation is shown, a Surface-parallel lamellae, typical of film thickness t greater than the natural equilibrium period Lq. b Surface-perpendicular lamellae, typical of film thickness t less than L0. (adapted from [41])...

The morphology of spin-cast film, thickness of 180 nm, from polycaprolactone shows many spherulitic structures with fibrillar nanostructures formed of lamellae lying edge on (about 10 nm thick) and areas with lamellar sheets lying flat on. Different crystalline structures are found when the sample is melted and crystallized as a function of temperature. These two studies reinforce the complex inner relationship between physical treatment and nanostructure. 

The effect of constraints introduced by confining diblock copolymers between two solid surfaces was examined by Lambooy et al. (1994) and Russell et al. (1995). They studied a symmetric PS-PMMA diblock sandwiched between a silicon substrate, and silicon oxide evaporated onto the top (homopolymer PMMA) surface. Neutron reflectivity showed that lamellae formed parallel to the solid interfaces with PMMA at both surfaces. The period of the confined multilayers deviated from the bulk period in a cyclic manner as a function of the confined film thickness, as illustrated in Fig. 2.60. First-order transitions were observed at t d0 = (n + j)d0, where t is the film thickness and d0 is the bulk lamellar period, between expanded states with n layers and states with (n + 1) layers where d was contracted. Finally, the deviation from the bulk lamellar spacing was found to decrease with increasing film thickness (Lambooy et al. 1994 Russell et al. 1995). These experimental results are complemented by the phenomenologi-... 

Fig. 2.60 The period, d, of lamellae formed in symmetric

Lattice Model Carlo simulations of a block copolymer confined between parallel hard walls by Kikuchi and Binder (1993,1994) revealed a complex interplay between film thickness and lamellar period. In the case of commensurate length-scales (f an integral multiple of d), parallel ordering of lamellae was observed. On the other hand, tilted or deformed lamellar structures, or even coexistence of lamellae in different orientations, were found in the case of large incommensurability. Even at temperatures above the bulk ODT, weak order was observed parallel to the surface and the transition from surface-induced order to bulk ordering was found to be gradual. The latter observations are in agreement with the experimental work of Russell and co-workers (Anastasiadis et al. 1989 Menelle et al. 1992) and Foster et al. (1992). 

Preferential attraction of one of the blocks to the surface brakes the symmetry of the structure and results in layering of microdomains parallel to the surface plane through the entire film thickness. The energetically favored film thicknesses are then quantinized with the characteristic structure period in the bulk through the formation of surface relief structures, also called terrace formation. These structures were established initially for lamella systems [37-39] and later for cylinder- [40-43] and sphere-forming block copolymers. 

For a strong surface field and symmetric wetting conditions, a perforated lamella (PL) phase typically develops in up to four layers of structures, with an exception for the first layer of structures at the favored film thickness. For one layer and all transition regions between terraces a Cy phase was found. 

In contrast to swollen homopolymer films, only a limited number of studies on thin films of block copolymers have been reported in which the degree of the film swelling has been directly accessed. In situ SE has been used to evaluate the polymer-solvent interaction parameters [144], to construct phase diagrams of surface structures [49, 51], and to control the mechanism of lamella reorientation in thick swollen films [118, 163, 164], Spectroscopic reflectometry combined with real-time GISAXS has been used to follow structural instabilities in swollen lamella films [165], Recently, it was demonstrated that swelling of diblock copolymer films in organic selective and non-selective solvents follows the same physical behavior as in thin films of homopolymers [119]. 

Figure S.6 The total interaction energy, VT, between the surfaces of a thin liquid film or foam lamella, as a function ofthe film thickness, t.

As a result, the wavelength X in units of X0 exhibits a sawtooth -profile as function of the film thickness (Figs. 15,32) for a parallel arrangement of the lamellae between symmetric walls (Fig. 3a, Fig. 26b,d, Fig. 27b,d) the domains are compressed or expanded to enforce the condition D=nIUn the whole range from... 

An explanation based on simple thermodynamics of the preferred orientation of edge-on and flat-on lamellae on thick and thin films, respectively, was given by Wang et al. [80]. As shown in Fig. 10, a primary rectangular nucleus of size a x a x l can assume either edge-on or flat-on orientation on a sub-... 

However, in thin films, the growth of the edge-on lamellae is limited by the film thickness (h). The formation of many edge-on lamellae on a thin film cre-... 

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