Fluids with competing interactions. I. Decoding the structure factor to detect and characterize self-limited clustering

We use liquid state theory and computer simulations to gain insights into the shape of the structure factor for fluids of particles interacting via a combination of short-range attractions and long-range repulsions. Such systems can reversibly morph between homogeneous phases and states comprising compact self-limiting clusters. We first highlight trends with respect to the presence and location of the intermediate-range order (IRO) pre-peak in the structure factor, which is commonly associated with clustering, for wide ranges of the tunable parameters that control interparticle interactions (e.g., Debye screening length). Next, for approximately 100 different cluster phases at various conditions (where aggregates range in size from six to sixty monomers), we quantitatively relate the shape of the structure factor to physical characteristics including intercluster distance and cluster size. We also test two previously postulated criteria for identifying the emergence of clustered phases that are based on IRO peak-height and-width, respectively. We find that the criterion based on peak-width, which encodes the IRO thermal correlation length, is more robust across a wide range of conditions and interaction strengths but nonetheless approximate. Ultimately, we recommend a hybrid heuristic drawing on both pre-peak height and width for positively identifying the emergence of clustered states.