Copolymerization Near a Patterned Surface

Another motivation for this work is the development of copolymers that are tuned to a certain surface, that is, copolymers that have a memory  

To analyze the correlations in the copolymer sequences, one can use the so-called two-point chemical correlators [53]  

The distribution of B blocks, which are included mostly in nonadsorbed chain sections, decays exponentially and thus should obey Bernoullian statistics that correspond to a zeroth-order Markov process [10]. The average length of such blocks is close to 2, that is, the same as that of a random copolymer. In the case of A blocks, the distribution function/a (f) also decays exponentially in the initial region, which corresponds to short blocks included in the random chain sections. For longer A blocks, however, the distribution becomes significantly broader and has a local maximum at i 10 [95]. Hence, one can conclude that the distribution of A blocks strongly deviates from that known for random sequences. 

By varying the distance between nearest adsorption sites, rs, one can control the composition variation period of the synthesized copolymer. From the chemical correlators defined by Eq. 16, it is easy to find the average number of segments in the repeating chain sections, N, for different rs values. It is instructive to analyze the relation between N and rs. As expected, a power law N oc is observed. It is clear that exponent //. in this dependence should be between //, = 1 (for a completely stretched chain) and //. = v 1 with v 0.6 (for a random coil with excluded volume [75]). The calculation [95] yields yu 1.33 for N 15. This supports the aforementioned assumption that the repeating chain sections are strongly stretched between the adsorption sites. The same conclusion can be drawn from the visual analysis of typical snapshots similar to that presented in Fig. 22. 

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