  Small-angle scattering is a commonly used tool to analyze the dispersion of
nanoparticles in all kinds of matrices. Besides some obvious cases, the
associated structure factor is often complex and cannot be reduced to a simple
interparticle interaction, like excluded volume only. In recent experiments, we
have encountered a surprising absence of structure factors (S(q) = 1) in
scattering from rather concentrated polymer nanocomposites [A.-C. Genix et al,
ACS Appl. Mater. Interfaces 11 (2019) 17863]. In this case, quite pure form
factor scattering is observed. This somewhat ``ideal'' structure is further
investigated here making use of reverse Monte Carlo simulations in order to
shed light on the corresponding nanoparticle structure in space. By fixing the
target ``experimental'' apparent structure factor to one over a given q-range
in these simulations, we show that it is possible to find dispersions with this
property. The influence of nanoparticle volume fraction and polydispersity has
been investigated, and it was found that for high concentrations only a high
polydispersity allows reaching a state of S = 1. The underlying structure in
real space is discussed in terms of the pair-correlation function, which
evidences the importance of attractive interactions between polydisperse
nanoparticles. The calculation of partial structure factors shows that there is
no specific ordering of large or small particles, but that the presence of
attractive interactions together with polydispersity allows reaching an almost
``structureless'' state.
