Lamellar wavelength

The length scale A is the wavelength of the lamellar structure. Minimization of Eq. (100) with respect to A gives... 

Fig. 8 Various structure parameters appearing in the crystallization process of PET at 80 °C A, characteristic wavelength of SD D, dense domain size L, long period /p, persistence length Dc, lamellar stem length [19]...

Fig. 4a—d. Lamellar structures in thin films that are not considered further in detail in the present article a Thin film confined between inequivalent walls, where the lower one favors the B-rich domains and the upper one the A-rich domains. Then an arrangement where the interfaces run parallel to the walls requires that thickness D and wavelength X are related as D=(n+1/2)A, n=0,l, 2... b Thin film on a substrate that favors B-rich domains undergo at the order-disorder transition (ODT) of the block copolymer melt a phase separation into a fraction x of thickness nXh and a fraction 1-x of thickness (n+1) Xh, such that D=[xn+(l-x) (n+l)] K if the air also favors B-rich domains, c If the air favors A-rich domains instead, the phase separation happens in a fraction x of thickness (n-l/2)A and a fraction 1-x of thickness (n+ 1/2)X with n= 1,2,3... d If the block copolymer film undergoes dewetting at the substrate, droplets form with a step-pyramide like structure ( Tower of Babel [30]). 

For this problem already the simple mean field approximation becomes rather involved [197,213]. Therefore, we describe here only an approach, which is even more simplified, appropriate for wavenumbers q near the characteristic wavenumber q, but strictly correct neither for q—>0 nor for large q the spirit of our approach is similar to the long wavelength approximation encountered in the mean field theory of blends, Eq. (7). That is, we write the effective free energy functional as an expansion in powers of t t and include terms (Vv /)2 as well as (V2 /)2, as in the related problem of lamellar phases of microemulsions [232,233],namely [234]... 

An intriguing point also is that for block copolymers with lamellar ordering parallel to the walls in general there will be a misfit between the wavelength that the system likes to form in the bulk (A.0) and the film thickness D (i.e., D n ). 

Fig. 28 Growth and short-term stability of the normalized photoinduced birfringence relating to the azobenzene content in PMMA-based block copolymer films with a lamellar (azobenzene content 31.6 wt%), cylindrical (23 wt%), and spherical (7.9 wt%) morphology. Writing time 3,600 s, writing wavelength 532 nm, reading wavelength 630 nm...

The same fact is true for surface effects on the dynamics of spinodal decomposition in polymer blends [374,375], dynamics of surface enrichment in blends [367, 375, 376], and, last but not least, for surface effects on block copolymers there one may have surface - induced ordering [377, 379] and interesting competition effects between the lamellar ordering (of wavelength X) and film thickness D in thin block copolymer films [380—388]. These phenomena are outside of our consideration here. 

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