Spectral representation of sequence-defined polymers

The sequences of copolymers impact their microphase separation and lead to a variety of self-assembled structures. Manipulation of classical sequence descriptors such as Flory-Huggin interaction parameters or block fractions are known to open and close different regions of phase space. However, these descriptors are statistical; as polymer chemistry moves towards fully sequence-defined polymers, a complete description of sequence becomes defined at the limit of N degrees of freedom, where N is the number of monomers. This precludes efficient exploration of sequence space to target specific structures. In this talk, we show how a spectral representation of sequences presents a representation more amenable to uncovering fundamental links between sequence and structure. The degrees of freedom in a spectral representation describe the sequence on a global level; since structure is a global property, manipulation of spectral degrees of freedom might offer a more systematic way of conducting investigation into sequence space. We explore how attenuation of high frequency Fourier modes of a sequence through signal filters leads to similar phase behavior as the unmodified sequence. This congruence of behavior despite large changes in the sequence highlights how correlated changes in sequence may be necessary for preserving or changing ordered structure.