Ionic liquids have been shown to form extended ordered structures near surfaces and in bulk. Identifying fundamental driving force(s) for this organization has been elusive. In this paper, we test a hypothesis that the ionic liquid asymmetry, inherent in many of the IL formulations to frustrate crystallization, is a significant contributor to the observed ordering. We have carried out measurements to track the ordering of ionic liquids composed of "spherical" cations, namely, tetraoctylphosphonium ([P8888]) and tetra(propoxymethyl)phosphonium [P(3O1)4] paired with tetracyanoborate anion [B(CN)4]. Analysis of the infrared signatures for films of these ionic liquids shows very little evidence of ordered structures. These liquids instead remain in a more isotropic environment even when confined to volumes of few micrometer dimensions.