The total PDF, G(r), is an average over every interatomic pair in the whole measured sample. We are interested in searching for DIPA-water interactions and higher order MCSs in the DIPA-water mixed phase of the sample, as exemplified in Figure , and mapping these as a function of composition and temperature. To access these signals from the total PDF signal, we have used a double-difference approach, described in detail in the Experimental Section. Briefly, in this approach, we measure the total PDFs of DIPA-water mixtures (Figure , red and yellow) and subtract a linear combination of the pure water and pure DIPA PDFs (Figure , gray and green, respectively). This treatment eliminates the contributions of water molecules coordinating with each other, and likewise DIPA-DIPA correlations. The signal resulting from this approach, the double-differential pair distribution function, which we refer to as ddG, is shown in Figure The ddG signal is very small compared to the total PDF (the plots have been rescaled for clarity). However, as demonstrated below, the signals are from the MCSs and are not the result of experimental or data processing errors. We briefly discuss the features in a qualitative way to build understanding. In the total PDFs of the DIPA-water mixture samples (Figure1A, red and yellow), the sharp peaks at 1.5 and 2.5 Å come from covalently-bonded carbon and nitrogen atoms in the DIPA backbone. These appear only vestigially in the ddG (as sharp valleys followed by sharp peaks) because they are removed during the subtraction process. Imperfect subtraction of these features is due to a very slight shift in the length of the covalent bonds in the mixture. On the other hand, broad features in the region above 3 Å in the ddG (Figure ) originate from inter-molecular packing correlations that are present in the mixture but not in the pure liquids. Inter-molecular packing that is disordered and averaged over many different conformations and molecular orientations will result in no signal in the PDF (i.e., a flat line with G = 0 for all r). On the other hand, signals that survive in the ddG originate from specific, preferred molecular packings (i.e., molecular cluster structures) that are not dynamically-or ensemble-averaged away. The main features in the ddG are strong, broad peaks centered at 3.7, 7.5, and 12 Å. The peaks and valleys are damped with increasing r, monotonically decreasing in amplitude with r. The signal finally disappears at around 20 Å (Figure ).