Lamellar periodicity

Unlike the bulk morphology, block copolymer thin films are often characterized by thickness-dependent highly oriented domains, as a result of surface and interfacial energy minimization [115,116]. For example, in the simplest composition-symmetric (ID lamellae) coil-coil thin films, the overall trend when t>Lo is for the lamellae to be oriented parallel to the plane of the film [115]. Under symmetric boundary conditions, frustration cannot be avoided if t is not commensurate with L0 in a confined film and the lamellar period deviates from the bulk value by compressing the chain conformation [117]. Under asymmetric boundary conditions, an incomplete top layer composed of islands and holes of height Lo forms as in the incommensurate case [118]. However, it has also been observed that microdomains can reorient such that they are perpendicular to the surface [ 119], or they can take mixed orientations to relieve the constraint [66]. 

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-... 

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). 

DOTAP ratios. SAXS data of complexes with 4>DOPE=0.26 and 0.70 clearly show the presence of two different structures. At DOpE=0.26 SAXS of the lamellar complex shows sharp peaks at f/um =0.099 A 1 and oo2=0198 A-1 resulting from the lamellar periodic structure (d =2%lqom=63A1 A), with DNA intercalated between cationic lipid analogous to the structure in DOPC/DOTAP-DNA complexes (Figure 10.1, left). 

Fig. 21. Ziggurat-like structure obtained by SFM after annealing at 170 °C for one day a thin film of symmetric P(S-fo-MMA) diblock copolymer (Mw=57,000 g/mol). A step height of 29 1 nm corresponds to the lamellar periodicity. Reproduced from [261]...

The length of the circular lamellar period is L. A variable d is set to denote the thickness of the barrel structure, d = mL, m is the number of periods. From Figure 30, the interfacial Helmholtz energy of a barrel... 

Figure 30 Symmetrical concentric-ring barrel structure (left) confined in the ringlike surface and a unit cell with one lamellar period L (right).

In this work, we have focused on strong surface preference with only mutual transition between the symmetrical and asymmetrical layer-type structures. SSL theory and MC simulation are further applied to investigate the self-assembled morphology of diblock copolymers confined in the nanopore. MC simulation shows that the Niayer of the concentric cylinder barrel changes with respect to the extent of frustration between the exterior radius Rex and the bulk lamellar period L0. Simultaneously, the predictions of SSL theory also show that both... 

Fig. 15. Reduced lamellar period X =X/Xh as a function of reduced distance between the symmetric walls, d=D/Xb, for 5=(yBW—yAW)/ Yab=0-15- Wherever the vertical arrangement (Fig. 3b) is favored, the bulk equilibrium lamellar period occurs, and hence x =1 From Walton et al. [36]...

Fig. 17. Phase diagram for intermediately segregated (%N=20) symmetric diblock (f=0.5) films confined between identical walls calculated from self-consistent field theory. The film thickness D is normalized by the bulk lamellar period Xb, and the ordinate AN is a measure of the surface field (which has the functional form H(z)=Aj (+cos(ti z/ )) bVN /e for 0

Fig. 57 Generation of large lamellar periodicities via supramolecular ordering of DBSA/ P4VP-PS composites. Reprinted with permission from [209]...

Fig. 31 Variation of the size of the elementary dendrimer cylinder as a function of generation number (G ). is the diameter and h the height of the cylinder (i.e. lamellar periodicity)...

Another series of complexes derived from a dihydroxysilylphthalocyanine (Figure 65, M = trans-Si(OH)2), showed hexagonal mesophases from —7 up to 300°C [137]. If such complexes were held at around 180°C for several hours, a polycondensation reaction occurred which eliminated water to form polymeric materials with a polysiloxane spine (Figure 72). These polymers displayed a lamellar periodicity of 31 A from room temperature up to 60°C, where clearing occurred. X-ray diffraction studies in the lamellar phase, showed that the rings were separated by... 

It has been indicated by experiments that there is another way to achieve perpendicular order even for films containing lamellar mesophases. The use of substrate coatings made of random copolymers allows us to neutralize the interactions of the two blocks with the substrate [16,23,25]. This leads to perpendicular orientation of the lamellae in the vicinity of the so-prepared substrate. It is worth noting that this effect is not simply related to some in-commensurabihty between the lamellar period and the film thickness as has been discussed by several authors, see [52], Remarkably, perpendicular orientation at neutral surfaces can persist against other orientations (e.g. induced by the opposite surface) as has been suggested also by experiments [25]. Furthermore, there are indications from computer simifiations (presented below)... 

Annealed samples show clear lamellar periodicity, with lamellae approximately at 45° to the stretch direction. After high enough annealing temperatures all orientation in the inter-lamellar regions is lost. 

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