Computer Simulation of Confined Block Copolymers

This subsection has to be very brief, since only rather preliminary qualitative studies are available [34,35]. The model used are self-avoiding walks with N=16 

Squared interfacial width w2 vs film thickness D, for the model of Fig. 24. The straight line is the corresponding theoretical prediction (cf. text). All lengths are measured in units of the lattice spacing. From Werner et al. [266] 

As observed for block copolymers in the bulk [190-193], there is a detailed interplay between the order in the system and the chain linear dimension chains like to stretch out somewhat in the direction perpendicular to the lamellae. If one studies the mean square gyration radius component RgZ in the z-direction perpendicular to the walls, one hence observes an oscillatory dependence on thickness D for 1/T 0.5,since only for n ib=D (n=l,2,3.) the parallel morphology fits nicely into the film, cf. Sect. 2.3, and the dumbbell -like block copoly- 

While in the bulk the phases of the growing concentration waves are random, and also the directions of the wavevectors q are controlled by random fluctuations in the inital states, a surface creates a boundary condition, and working out adynamic extension [45,129,132,133,144,156] of the model in Sect. 2.1 Eqs. (7)-(10) one finds that under typical conditions wavevectors oriented perpendicular to the walls occur, with phases such that the maxima of the waves occur at the walls (Fig. 28). In terms of a normalized order parameter i /(Z, R, x) where x is a scaled time and Z, R, are scaled coordinates perpendicular and parallel to the walls, Z=z/2 b, R=q/2 b, V /=(( )-( )crit)/(( )coex-( )crit), this dynamic extension is the Cahn-Hilliard equation [291-294] 

As discussed already in the introduction, there is a huge and diverse literature on thin films of polymer blends and block copolymers. The field is rapidly developing, and many phenomena are as yet not fully understood. In this section, we hence cannot attempt to give a fair evaluation of this rich literature, but focus 

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