4.2 Accessible Pore Sizes
The range of feature sizes accessible using porous block copoylmer templates is largely determined by the degree of polymerization (N) of the copolymer, scaling as N2/3 in the strong segregation regime (see Section 2.2). A lower limit is set by the thermodynamics of microphase separation requiring that the degree of segregation (χN) is around 10.5 or greater (smaller than this and the copolymer will form a single homogeneous phase). On the other hand, good vertical ordering of the microphase becomes progressively more difficult with increased N. While the driving force for local phase separation is stronger, this requires only short-range rearrangements of the chains. Alignment of the domains, however, requires coordinated motions of many chains — a diffusive process that becomes prohibitively slow with increasing N. High-molecularweight copolymer films are trapped in a nonequilibrium state reflected in poor ordering. In practice, Xu et al. found that standing cylindrical pores between 14 and 50 nm in diameter with center-to-center distances of 24 to 89 nm could be acheived in PS-b-PMMA templates by varying the molecular weight between 42 and 295 Kg mol−1 (Fig. 2.9).