SAXS anti-peaks reveal the length-scales of dual positive-negative and polar-apolar ordering in room-temperature ionic liquids

Structural patterns that have the same spatial periodicity but a phase offset give rise to peaks and anti-peaks (negative-going peaks) at the same q value in the SAXS structure function S(q). As an example, in ionic liquids we often find charge alternation, and at the distance where one finds a density enhancement of charges of the same type one also finds a depletion of charges of opposite sign. Another such situation arises with polar-apolar densities. At distances where there is enhancement of same-type (polar-polar or apolar-apolar) densities there is also a depletion of opposite-type (polar-apolar) density. This gives rise to prepeaks and what we call same spatial periodicity anti-prepeaks.