Figure 4. Predictions of an energy model for ordering of a BCP blend on a chemical line pattern.

(a) Predicted relative energy between competing formation of line patterns and dot patterns, as a function of the pitch and the normalized oxide linewidth of the underlying chemical pattern. Purple indicates that line patterns are lower energy, while green indicates dot patterns are lower energy. White indicates that the two pattern types are energetically degenerate; one would thus expect to see coexistence of patterns. (b) Fraction of line patterns (f_l) as a function of pitch, for three different doses used to generate the chemical pattern. A constant dose corresponds to a curve through the energy landscape, shown by the corresponding dashed lines in a. Depending on the pitch or dose, either line patterns or dot patterns will be favoured. Predictions are consistent with the experimental results of Fig. 3f. (c) Microscopic origin of the relative energies. When the template pitch deviates from the equilibrium spacing of the BCP pattern, the polymer chain must distort (compress or stretch) to accommodate. For line patterns, variation of pitch causes all the polymer chains to compress (or stretch). By comparison, the hexagonal-dot pattern, when distorted, involves a combination of chain stretching and compression (with some chains relatively unperturbed). Thus, dot patterns are more ‘tolerant' of distortion. (Refer to Supplementary Information for details).